Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.4% → 82.3%

Time: 27.8s

Alternatives: 26

Speedup: 0.5×

• 57.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot c - y \cdot i\\ \mathbf{if}\;j \cdot t_2 + t_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t_2, t_1\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_2 (- (* a c) (* y i))))
   (if (<= (+ (* j t_2) t_1) INFINITY)
     (fma j t_2 t_1)
     (+ (* i (- (* t b) (* y j))) (* z (- (* x y) (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if (((j * t_2) + t_1) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(j * t_2) + t_1) <= Inf)
		tmp = fma(j, t_2, t_1);
	else
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(j * t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 90.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 90.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 90.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 90.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 90.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 5.7%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in a around 0 39.6%

      \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)\right) - c \cdot \left(z \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 39.6%

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + y \cdot \left(z \cdot x\right)\right)} - c \cdot \left(z \cdot b\right) \]

      2. associate--l+ 39.6%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right)} \]

      3. *-commutative 39.6%

         \[\leadsto \left(\color{blue}{\left(t \cdot b\right) \cdot i} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      4. *-commutative 39.6%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \left(y \cdot \color{blue}{\left(j \cdot i\right)}\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      5. associate-*r* 37.7%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \color{blue}{\left(\left(y \cdot j\right) \cdot i\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      6. associate-*l* 37.7%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right) \cdot i}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      7. distribute-rgt-in 52.8%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      8. mul-1-neg 52.8%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      9. unsub-neg 52.8%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      10. *-commutative 52.8%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      11. associate-*r* 51.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - \color{blue}{\left(c \cdot b\right) \cdot z}\right) \]

      12. cancel-sign-sub-inv 51.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(-c \cdot b\right) \cdot z\right)} \]

      13. *-commutative 51.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \color{blue}{\left(x \cdot z\right)} + \left(-c \cdot b\right) \cdot z\right) \]

      14. associate-*r* 49.2%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\color{blue}{\left(y \cdot x\right) \cdot z} + \left(-c \cdot b\right) \cdot z\right) \]

      15. mul-1-neg 49.2%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\left(y \cdot x\right) \cdot z + \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z\right) \]

      16. distribute-rgt-in 54.9%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{z \cdot \left(y \cdot x + -1 \cdot \left(c \cdot b\right)\right)} \]

   7. Simplified 54.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - c \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 2: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (* j (- (* a c) (* y i)))
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))))
   (if (<= t_1 INFINITY)
     t_1
     (+ (* i (- (* t b) (* y j))) (* z (- (* x y) (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 90.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 5.7%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in a around 0 39.6%

      \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)\right) - c \cdot \left(z \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 39.6%

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + y \cdot \left(z \cdot x\right)\right)} - c \cdot \left(z \cdot b\right) \]

      2. associate--l+ 39.6%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right)} \]

      3. *-commutative 39.6%

         \[\leadsto \left(\color{blue}{\left(t \cdot b\right) \cdot i} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      4. *-commutative 39.6%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \left(y \cdot \color{blue}{\left(j \cdot i\right)}\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      5. associate-*r* 37.7%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \color{blue}{\left(\left(y \cdot j\right) \cdot i\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      6. associate-*l* 37.7%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right) \cdot i}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      7. distribute-rgt-in 52.8%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      8. mul-1-neg 52.8%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      9. unsub-neg 52.8%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      10. *-commutative 52.8%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      11. associate-*r* 51.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - \color{blue}{\left(c \cdot b\right) \cdot z}\right) \]

      12. cancel-sign-sub-inv 51.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(-c \cdot b\right) \cdot z\right)} \]

      13. *-commutative 51.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \color{blue}{\left(x \cdot z\right)} + \left(-c \cdot b\right) \cdot z\right) \]

      14. associate-*r* 49.2%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\color{blue}{\left(y \cdot x\right) \cdot z} + \left(-c \cdot b\right) \cdot z\right) \]

      15. mul-1-neg 49.2%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\left(y \cdot x\right) \cdot z + \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z\right) \]

      16. distribute-rgt-in 54.9%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{z \cdot \left(y \cdot x + -1 \cdot \left(c \cdot b\right)\right)} \]

   7. Simplified 54.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - c \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) \leq \infty:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 3: 60.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 53000000000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.55e+184)
     t_1
     (if (<= x -3.5e+144)
       (- (* j (- (* a c) (* y i))) (* c (* z b)))
       (if (<= x -3.8e+70)
         (* y (- (* x z) (* i j)))
         (if (<= x 53000000000000.0)
           (+ (* i (- (* t b) (* y j))) (* z (- (* x y) (* b c))))
           (if (<= x 1.22e+162) (* a (- (* c j) (* x t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.55e+184) {
		tmp = t_1;
	} else if (x <= -3.5e+144) {
		tmp = (j * ((a * c) - (y * i))) - (c * (z * b));
	} else if (x <= -3.8e+70) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 53000000000000.0) {
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	} else if (x <= 1.22e+162) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-1.55d+184)) then
        tmp = t_1
    else if (x <= (-3.5d+144)) then
        tmp = (j * ((a * c) - (y * i))) - (c * (z * b))
    else if (x <= (-3.8d+70)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 53000000000000.0d0) then
        tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)))
    else if (x <= 1.22d+162) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.55e+184) {
		tmp = t_1;
	} else if (x <= -3.5e+144) {
		tmp = (j * ((a * c) - (y * i))) - (c * (z * b));
	} else if (x <= -3.8e+70) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 53000000000000.0) {
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	} else if (x <= 1.22e+162) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.55e+184:
		tmp = t_1
	elif x <= -3.5e+144:
		tmp = (j * ((a * c) - (y * i))) - (c * (z * b))
	elif x <= -3.8e+70:
		tmp = y * ((x * z) - (i * j))
	elif x <= 53000000000000.0:
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)))
	elif x <= 1.22e+162:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.55e+184)
		tmp = t_1;
	elseif (x <= -3.5e+144)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(c * Float64(z * b)));
	elseif (x <= -3.8e+70)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 53000000000000.0)
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (x <= 1.22e+162)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.55e+184)
		tmp = t_1;
	elseif (x <= -3.5e+144)
		tmp = (j * ((a * c) - (y * i))) - (c * (z * b));
	elseif (x <= -3.8e+70)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 53000000000000.0)
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	elseif (x <= 1.22e+162)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+184], t$95$1, If[LessEqual[x, -3.5e+144], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.8e+70], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 53000000000000.0], N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e+162], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.5499999999999999e184 or 1.22e162 < x

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 77.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 74.1%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in x around inf 81.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -1.5499999999999999e184 < x < -3.4999999999999998e144

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 75.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 75.8%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 75.8%

         \[\leadsto \left(-c \cdot \color{blue}{\left(z \cdot b\right)}\right) + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 75.8%

         \[\leadsto \color{blue}{c \cdot \left(-z \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      4. distribute-rgt-neg-in 75.8%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 75.8%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if -3.4999999999999998e144 < x < -3.7999999999999998e70

   1. Initial program 92.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 92.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 92.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 92.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 92.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 92.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 92.3%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in y around inf 69.9%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 69.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 69.9%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 69.9%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   7. Simplified 69.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -3.7999999999999998e70 < x < 5.3e13

   1. Initial program 66.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 66.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 66.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 61.8%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in a around 0 65.9%

      \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)\right) - c \cdot \left(z \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 65.9%

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + y \cdot \left(z \cdot x\right)\right)} - c \cdot \left(z \cdot b\right) \]

      2. associate--l+ 65.9%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right)} \]

      3. *-commutative 65.9%

         \[\leadsto \left(\color{blue}{\left(t \cdot b\right) \cdot i} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      4. *-commutative 65.9%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \left(y \cdot \color{blue}{\left(j \cdot i\right)}\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      5. associate-*r* 63.8%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \color{blue}{\left(\left(y \cdot j\right) \cdot i\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      6. associate-*l* 63.8%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right) \cdot i}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      7. distribute-rgt-in 68.3%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      8. mul-1-neg 68.3%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      9. unsub-neg 68.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      10. *-commutative 68.3%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      11. associate-*r* 71.1%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - \color{blue}{\left(c \cdot b\right) \cdot z}\right) \]

      12. cancel-sign-sub-inv 71.1%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(-c \cdot b\right) \cdot z\right)} \]

      13. *-commutative 71.1%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \color{blue}{\left(x \cdot z\right)} + \left(-c \cdot b\right) \cdot z\right) \]

      14. associate-*r* 71.1%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\color{blue}{\left(y \cdot x\right) \cdot z} + \left(-c \cdot b\right) \cdot z\right) \]

      15. mul-1-neg 71.1%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\left(y \cdot x\right) \cdot z + \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z\right) \]

      16. distribute-rgt-in 71.8%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{z \cdot \left(y \cdot x + -1 \cdot \left(c \cdot b\right)\right)} \]

   7. Simplified 71.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - c \cdot b\right)} \]

   if 5.3e13 < x < 1.22e162

   1. Initial program 70.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 70.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 70.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 70.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 70.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 64.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 64.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 64.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 64.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 64.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 64.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 53000000000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 4: 65.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-15} \lor \neg \left(x \leq 5.2 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -7.8e-15) (not (<= x 5.2e-42)))
   (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
   (+ (* i (- (* t b) (* y j))) (* z (- (* x y) (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -7.8e-15) || !(x <= 5.2e-42)) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-7.8d-15)) .or. (.not. (x <= 5.2d-42))) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else
        tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -7.8e-15) || !(x <= 5.2e-42)) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -7.8e-15) or not (x <= 5.2e-42):
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	else:
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -7.8e-15) || !(x <= 5.2e-42))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -7.8e-15) || ~((x <= 5.2e-42)))
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	else
		tmp = (i * ((t * b) - (y * j))) + (z * ((x * y) - (b * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -7.8e-15], N[Not[LessEqual[x, 5.2e-42]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.80000000000000053e-15 or 5.2e-42 < x

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 68.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   if -7.80000000000000053e-15 < x < 5.2e-42

   1. Initial program 62.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 62.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 62.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 62.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 62.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 62.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 62.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 60.2%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in a around 0 70.4%

      \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)\right) - c \cdot \left(z \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 70.4%

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + y \cdot \left(z \cdot x\right)\right)} - c \cdot \left(z \cdot b\right) \]

      2. associate--l+ 70.4%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right)} \]

      3. *-commutative 70.4%

         \[\leadsto \left(\color{blue}{\left(t \cdot b\right) \cdot i} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      4. *-commutative 70.4%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \left(y \cdot \color{blue}{\left(j \cdot i\right)}\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      5. associate-*r* 67.0%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \color{blue}{\left(\left(y \cdot j\right) \cdot i\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      6. associate-*l* 67.0%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right) \cdot i}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      7. distribute-rgt-in 71.5%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      8. mul-1-neg 71.5%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      9. unsub-neg 71.5%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      10. *-commutative 71.5%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      11. associate-*r* 74.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - \color{blue}{\left(c \cdot b\right) \cdot z}\right) \]

      12. cancel-sign-sub-inv 74.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(-c \cdot b\right) \cdot z\right)} \]

      13. *-commutative 74.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \color{blue}{\left(x \cdot z\right)} + \left(-c \cdot b\right) \cdot z\right) \]

      14. associate-*r* 74.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\color{blue}{\left(y \cdot x\right) \cdot z} + \left(-c \cdot b\right) \cdot z\right) \]

      15. mul-1-neg 74.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\left(y \cdot x\right) \cdot z + \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z\right) \]

      16. distribute-rgt-in 74.9%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{z \cdot \left(y \cdot x + -1 \cdot \left(c \cdot b\right)\right)} \]

   7. Simplified 74.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - c \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-15} \lor \neg \left(x \leq 5.2 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 5: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 205000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -4e+56)
     t_2
     (if (<= z 4.4e-209)
       t_1
       (if (<= z 1.3e-174)
         (* y (- (* x z) (* i j)))
         (if (<= z 4e-148)
           t_1
           (if (<= z 1.02e-85)
             (* b (- (* t i) (* z c)))
             (if (<= z 205000000.0) (* i (- (* t b) (* y j))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4e+56) {
		tmp = t_2;
	} else if (z <= 4.4e-209) {
		tmp = t_1;
	} else if (z <= 1.3e-174) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 4e-148) {
		tmp = t_1;
	} else if (z <= 1.02e-85) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= 205000000.0) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-4d+56)) then
        tmp = t_2
    else if (z <= 4.4d-209) then
        tmp = t_1
    else if (z <= 1.3d-174) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= 4d-148) then
        tmp = t_1
    else if (z <= 1.02d-85) then
        tmp = b * ((t * i) - (z * c))
    else if (z <= 205000000.0d0) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4e+56) {
		tmp = t_2;
	} else if (z <= 4.4e-209) {
		tmp = t_1;
	} else if (z <= 1.3e-174) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 4e-148) {
		tmp = t_1;
	} else if (z <= 1.02e-85) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= 205000000.0) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -4e+56:
		tmp = t_2
	elif z <= 4.4e-209:
		tmp = t_1
	elif z <= 1.3e-174:
		tmp = y * ((x * z) - (i * j))
	elif z <= 4e-148:
		tmp = t_1
	elif z <= 1.02e-85:
		tmp = b * ((t * i) - (z * c))
	elif z <= 205000000.0:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -4e+56)
		tmp = t_2;
	elseif (z <= 4.4e-209)
		tmp = t_1;
	elseif (z <= 1.3e-174)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= 4e-148)
		tmp = t_1;
	elseif (z <= 1.02e-85)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (z <= 205000000.0)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -4e+56)
		tmp = t_2;
	elseif (z <= 4.4e-209)
		tmp = t_1;
	elseif (z <= 1.3e-174)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= 4e-148)
		tmp = t_1;
	elseif (z <= 1.02e-85)
		tmp = b * ((t * i) - (z * c));
	elseif (z <= 205000000.0)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+56], t$95$2, If[LessEqual[z, 4.4e-209], t$95$1, If[LessEqual[z, 1.3e-174], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-148], t$95$1, If[LessEqual[z, 1.02e-85], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 205000000.0], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.00000000000000037e56 or 2.05e8 < z

   1. Initial program 64.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 68.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -4.00000000000000037e56 < z < 4.40000000000000019e-209 or 1.3000000000000001e-174 < z < 3.99999999999999974e-148

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 56.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 56.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 56.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 56.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 56.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 56.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 4.40000000000000019e-209 < z < 1.3000000000000001e-174

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 67.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in y around inf 75.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 75.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 75.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 75.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   7. Simplified 75.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if 3.99999999999999974e-148 < z < 1.02000000000000001e-85

   1. Initial program 78.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 46.3%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   if 1.02000000000000001e-85 < z < 2.05e8

   1. Initial program 83.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 61.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 61.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 61.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 61.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 61.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 61.9%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 61.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 61.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 205000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 6: 51.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 300000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -2.45e+55)
     t_1
     (if (<= z 5.2e-210)
       (* a (- (* c j) (* x t)))
       (if (<= z 1.9e-168)
         (* y (- (* x z) (* i j)))
         (if (<= z 8.5e-149)
           (* x (- (* y z) (* t a)))
           (if (<= z 4e-90)
             (* b (- (* t i) (* z c)))
             (if (<= z 300000000.0) (* i (- (* t b) (* y j))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.45e+55) {
		tmp = t_1;
	} else if (z <= 5.2e-210) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 1.9e-168) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 8.5e-149) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= 4e-90) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= 300000000.0) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-2.45d+55)) then
        tmp = t_1
    else if (z <= 5.2d-210) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= 1.9d-168) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= 8.5d-149) then
        tmp = x * ((y * z) - (t * a))
    else if (z <= 4d-90) then
        tmp = b * ((t * i) - (z * c))
    else if (z <= 300000000.0d0) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.45e+55) {
		tmp = t_1;
	} else if (z <= 5.2e-210) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 1.9e-168) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 8.5e-149) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= 4e-90) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= 300000000.0) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.45e+55:
		tmp = t_1
	elif z <= 5.2e-210:
		tmp = a * ((c * j) - (x * t))
	elif z <= 1.9e-168:
		tmp = y * ((x * z) - (i * j))
	elif z <= 8.5e-149:
		tmp = x * ((y * z) - (t * a))
	elif z <= 4e-90:
		tmp = b * ((t * i) - (z * c))
	elif z <= 300000000.0:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -2.45e+55)
		tmp = t_1;
	elseif (z <= 5.2e-210)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= 1.9e-168)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= 8.5e-149)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (z <= 4e-90)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (z <= 300000000.0)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.45e+55)
		tmp = t_1;
	elseif (z <= 5.2e-210)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= 1.9e-168)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= 8.5e-149)
		tmp = x * ((y * z) - (t * a));
	elseif (z <= 4e-90)
		tmp = b * ((t * i) - (z * c));
	elseif (z <= 300000000.0)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45e+55], t$95$1, If[LessEqual[z, 5.2e-210], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-168], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-149], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-90], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 300000000.0], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.45000000000000007e55 or 3e8 < z

   1. Initial program 64.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 68.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -2.45000000000000007e55 < z < 5.1999999999999997e-210

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 77.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 56.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 56.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 56.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 56.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 56.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 56.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 5.1999999999999997e-210 < z < 1.9e-168

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 67.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in y around inf 75.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 75.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 75.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 75.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   7. Simplified 75.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if 1.9e-168 < z < 8.5000000000000006e-149

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 100.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 100.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 100.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 99.4%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in x around inf 59.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if 8.5000000000000006e-149 < z < 3.99999999999999998e-90

   1. Initial program 78.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 46.3%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   if 3.99999999999999998e-90 < z < 3e8

   1. Initial program 83.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 61.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 61.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 61.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 61.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 61.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 61.9%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 61.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 61.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 300000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 7: 50.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-71}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-107}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.15e+119)
     t_1
     (if (<= x -3.1e-71)
       (* j (- (* a c) (* y i)))
       (if (<= x -1.25e-107)
         (- (* i (* t b)) (* z (- (* b c) (* x y))))
         (if (<= x 1.02e+15)
           (- (* y (* i (- j))) (* z (* b c)))
           (if (<= x 2.05e+162) (* a (- (* c j) (* x t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+119) {
		tmp = t_1;
	} else if (x <= -3.1e-71) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= -1.25e-107) {
		tmp = (i * (t * b)) - (z * ((b * c) - (x * y)));
	} else if (x <= 1.02e+15) {
		tmp = (y * (i * -j)) - (z * (b * c));
	} else if (x <= 2.05e+162) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-1.15d+119)) then
        tmp = t_1
    else if (x <= (-3.1d-71)) then
        tmp = j * ((a * c) - (y * i))
    else if (x <= (-1.25d-107)) then
        tmp = (i * (t * b)) - (z * ((b * c) - (x * y)))
    else if (x <= 1.02d+15) then
        tmp = (y * (i * -j)) - (z * (b * c))
    else if (x <= 2.05d+162) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+119) {
		tmp = t_1;
	} else if (x <= -3.1e-71) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= -1.25e-107) {
		tmp = (i * (t * b)) - (z * ((b * c) - (x * y)));
	} else if (x <= 1.02e+15) {
		tmp = (y * (i * -j)) - (z * (b * c));
	} else if (x <= 2.05e+162) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.15e+119:
		tmp = t_1
	elif x <= -3.1e-71:
		tmp = j * ((a * c) - (y * i))
	elif x <= -1.25e-107:
		tmp = (i * (t * b)) - (z * ((b * c) - (x * y)))
	elif x <= 1.02e+15:
		tmp = (y * (i * -j)) - (z * (b * c))
	elif x <= 2.05e+162:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.15e+119)
		tmp = t_1;
	elseif (x <= -3.1e-71)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (x <= -1.25e-107)
		tmp = Float64(Float64(i * Float64(t * b)) - Float64(z * Float64(Float64(b * c) - Float64(x * y))));
	elseif (x <= 1.02e+15)
		tmp = Float64(Float64(y * Float64(i * Float64(-j))) - Float64(z * Float64(b * c)));
	elseif (x <= 2.05e+162)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.15e+119)
		tmp = t_1;
	elseif (x <= -3.1e-71)
		tmp = j * ((a * c) - (y * i));
	elseif (x <= -1.25e-107)
		tmp = (i * (t * b)) - (z * ((b * c) - (x * y)));
	elseif (x <= 1.02e+15)
		tmp = (y * (i * -j)) - (z * (b * c));
	elseif (x <= 2.05e+162)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+119], t$95$1, If[LessEqual[x, -3.1e-71], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.25e-107], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+15], N[(N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+162], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.15e119 or 2.05e162 < x

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 79.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 75.8%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in x around inf 75.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -1.15e119 < x < -3.10000000000000002e-71

   1. Initial program 71.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 71.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 71.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 71.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 71.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 71.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 55.3%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   if -3.10000000000000002e-71 < x < -1.24999999999999993e-107

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 64.3%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in a around 0 87.8%

      \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)\right) - c \cdot \left(z \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 87.8%

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + y \cdot \left(z \cdot x\right)\right)} - c \cdot \left(z \cdot b\right) \]

      2. associate--l+ 87.8%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right)} \]

      3. *-commutative 87.8%

         \[\leadsto \left(\color{blue}{\left(t \cdot b\right) \cdot i} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      4. *-commutative 87.8%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \left(y \cdot \color{blue}{\left(j \cdot i\right)}\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      5. associate-*r* 87.8%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \color{blue}{\left(\left(y \cdot j\right) \cdot i\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      6. associate-*l* 87.8%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right) \cdot i}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      7. distribute-rgt-in 87.8%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      8. mul-1-neg 87.8%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      9. unsub-neg 87.8%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      10. *-commutative 87.8%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      11. associate-*r* 87.8%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - \color{blue}{\left(c \cdot b\right) \cdot z}\right) \]

      12. cancel-sign-sub-inv 87.8%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(-c \cdot b\right) \cdot z\right)} \]

      13. *-commutative 87.8%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \color{blue}{\left(x \cdot z\right)} + \left(-c \cdot b\right) \cdot z\right) \]

      14. associate-*r* 87.6%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\color{blue}{\left(y \cdot x\right) \cdot z} + \left(-c \cdot b\right) \cdot z\right) \]

      15. mul-1-neg 87.6%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\left(y \cdot x\right) \cdot z + \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z\right) \]

      16. distribute-rgt-in 87.6%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{z \cdot \left(y \cdot x + -1 \cdot \left(c \cdot b\right)\right)} \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - c \cdot b\right)} \]

   8. Taylor expanded in t around inf 87.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} + z \cdot \left(x \cdot y - c \cdot b\right) \]
   9. Step-by-step derivation

      1. *-commutative 87.6%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} + z \cdot \left(x \cdot y - c \cdot b\right) \]

   10. Simplified 87.6%

       \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} + z \cdot \left(x \cdot y - c \cdot b\right) \]

   if -1.24999999999999993e-107 < x < 1.02e15

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 66.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 65.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 65.7%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 65.7%

         \[\leadsto \left(-c \cdot \color{blue}{\left(z \cdot b\right)}\right) + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 65.7%

         \[\leadsto \color{blue}{c \cdot \left(-z \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      4. distribute-rgt-neg-in 65.7%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 65.7%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   7. Taylor expanded in a around 0 59.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out 59.8%

         \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right) + c \cdot \left(z \cdot b\right)\right)} \]

      2. *-commutative 59.8%

         \[\leadsto -1 \cdot \left(y \cdot \left(i \cdot j\right) + c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      3. associate-*r* 60.6%

         \[\leadsto -1 \cdot \left(y \cdot \left(i \cdot j\right) + \color{blue}{\left(c \cdot b\right) \cdot z}\right) \]

   9. Simplified 60.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right) + \left(c \cdot b\right) \cdot z\right)} \]

   if 1.02e15 < x < 2.05e162

   1. Initial program 69.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 69.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 69.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 66.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 66.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-71}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-107}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 8: 54.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2.9e+88)
   (* c (- (* a j) (* z b)))
   (if (<= c -4.2e-80)
     (- (* i (* t b)) (* z (- (* b c) (* x y))))
     (if (<= c 2.2e-129)
       (* y (- (* x z) (* i j)))
       (- (* j (- (* a c) (* y i))) (* b (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.9e+88) {
		tmp = c * ((a * j) - (z * b));
	} else if (c <= -4.2e-80) {
		tmp = (i * (t * b)) - (z * ((b * c) - (x * y)));
	} else if (c <= 2.2e-129) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-2.9d+88)) then
        tmp = c * ((a * j) - (z * b))
    else if (c <= (-4.2d-80)) then
        tmp = (i * (t * b)) - (z * ((b * c) - (x * y)))
    else if (c <= 2.2d-129) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.9e+88) {
		tmp = c * ((a * j) - (z * b));
	} else if (c <= -4.2e-80) {
		tmp = (i * (t * b)) - (z * ((b * c) - (x * y)));
	} else if (c <= 2.2e-129) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2.9e+88:
		tmp = c * ((a * j) - (z * b))
	elif c <= -4.2e-80:
		tmp = (i * (t * b)) - (z * ((b * c) - (x * y)))
	elif c <= 2.2e-129:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2.9e+88)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (c <= -4.2e-80)
		tmp = Float64(Float64(i * Float64(t * b)) - Float64(z * Float64(Float64(b * c) - Float64(x * y))));
	elseif (c <= 2.2e-129)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -2.9e+88)
		tmp = c * ((a * j) - (z * b));
	elseif (c <= -4.2e-80)
		tmp = (i * (t * b)) - (z * ((b * c) - (x * y)));
	elseif (c <= 2.2e-129)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -2.9e+88], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.2e-80], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-129], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.9e88

   1. Initial program 59.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 59.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 59.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 66.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -2.9e88 < c < -4.20000000000000003e-80

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 70.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 70.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 70.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 70.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 70.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 67.6%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in a around 0 63.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)\right) - c \cdot \left(z \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 63.1%

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + y \cdot \left(z \cdot x\right)\right)} - c \cdot \left(z \cdot b\right) \]

      2. associate--l+ 63.1%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot b\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right)} \]

      3. *-commutative 63.1%

         \[\leadsto \left(\color{blue}{\left(t \cdot b\right) \cdot i} + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      4. *-commutative 63.1%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \left(y \cdot \color{blue}{\left(j \cdot i\right)}\right)\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      5. associate-*r* 63.1%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + -1 \cdot \color{blue}{\left(\left(y \cdot j\right) \cdot i\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      6. associate-*l* 63.1%

         \[\leadsto \left(\left(t \cdot b\right) \cdot i + \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right) \cdot i}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      7. distribute-rgt-in 66.0%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      8. mul-1-neg 66.0%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      9. unsub-neg 66.0%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + \left(y \cdot \left(z \cdot x\right) - c \cdot \left(z \cdot b\right)\right) \]

      10. *-commutative 66.0%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      11. associate-*r* 66.1%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \left(z \cdot x\right) - \color{blue}{\left(c \cdot b\right) \cdot z}\right) \]

      12. cancel-sign-sub-inv 66.1%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(-c \cdot b\right) \cdot z\right)} \]

      13. *-commutative 66.1%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot \color{blue}{\left(x \cdot z\right)} + \left(-c \cdot b\right) \cdot z\right) \]

      14. associate-*r* 71.5%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\color{blue}{\left(y \cdot x\right) \cdot z} + \left(-c \cdot b\right) \cdot z\right) \]

      15. mul-1-neg 71.5%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \left(\left(y \cdot x\right) \cdot z + \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z\right) \]

      16. distribute-rgt-in 71.5%

          \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{z \cdot \left(y \cdot x + -1 \cdot \left(c \cdot b\right)\right)} \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - c \cdot b\right)} \]

   8. Taylor expanded in t around inf 62.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} + z \cdot \left(x \cdot y - c \cdot b\right) \]
   9. Step-by-step derivation

      1. *-commutative 62.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} + z \cdot \left(x \cdot y - c \cdot b\right) \]

   10. Simplified 62.9%

       \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} + z \cdot \left(x \cdot y - c \cdot b\right) \]

   if -4.20000000000000003e-80 < c < 2.20000000000000003e-129

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 79.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 79.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 79.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 79.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 79.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in y around inf 60.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 60.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 60.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 60.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if 2.20000000000000003e-129 < c

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 61.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 61.5%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 61.5%

         \[\leadsto \left(-c \cdot \color{blue}{\left(z \cdot b\right)}\right) + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*r* 62.6%

         \[\leadsto \left(-\color{blue}{\left(c \cdot z\right) \cdot b}\right) + j \cdot \left(a \cdot c - y \cdot i\right) \]

      4. *-commutative 62.6%

         \[\leadsto \left(-\color{blue}{\left(z \cdot c\right)} \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 62.6%

      \[\leadsto \color{blue}{\left(-\left(z \cdot c\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 9: 52.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 310000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -1.55e+54)
     t_1
     (if (<= z 6e-209)
       (* a (- (* c j) (* x t)))
       (if (<= z 6e-167)
         (* y (- (* x z) (* i j)))
         (if (<= z 1.16e-92)
           (* t (- (* b i) (* x a)))
           (if (<= z 310000000.0) (* j (- (* a c) (* y i))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.55e+54) {
		tmp = t_1;
	} else if (z <= 6e-209) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 6e-167) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 1.16e-92) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 310000000.0) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-1.55d+54)) then
        tmp = t_1
    else if (z <= 6d-209) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= 6d-167) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= 1.16d-92) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 310000000.0d0) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.55e+54) {
		tmp = t_1;
	} else if (z <= 6e-209) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 6e-167) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 1.16e-92) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 310000000.0) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.55e+54:
		tmp = t_1
	elif z <= 6e-209:
		tmp = a * ((c * j) - (x * t))
	elif z <= 6e-167:
		tmp = y * ((x * z) - (i * j))
	elif z <= 1.16e-92:
		tmp = t * ((b * i) - (x * a))
	elif z <= 310000000.0:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.55e+54)
		tmp = t_1;
	elseif (z <= 6e-209)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= 6e-167)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= 1.16e-92)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 310000000.0)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.55e+54)
		tmp = t_1;
	elseif (z <= 6e-209)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= 6e-167)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= 1.16e-92)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 310000000.0)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+54], t$95$1, If[LessEqual[z, 6e-209], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-167], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e-92], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 310000000.0], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.55e54 or 3.1e8 < z

   1. Initial program 64.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 68.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -1.55e54 < z < 5.9999999999999997e-209

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 77.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 56.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 56.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 56.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 56.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 56.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 56.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 5.9999999999999997e-209 < z < 5.9999999999999996e-167

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 67.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in y around inf 75.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 75.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 75.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 75.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   7. Simplified 75.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if 5.9999999999999996e-167 < z < 1.1599999999999999e-92

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 60.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 60.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \cdot t \]

      2. associate-*r* 60.7%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x - i \cdot b\right) \cdot t\right)} \]

      3. mul-1-neg 60.7%

         \[\leadsto \color{blue}{-\left(a \cdot x - i \cdot b\right) \cdot t} \]

      4. *-commutative 60.7%

         \[\leadsto -\color{blue}{t \cdot \left(a \cdot x - i \cdot b\right)} \]

   6. Simplified 60.7%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - i \cdot b\right)} \]

   if 1.1599999999999999e-92 < z < 3.1e8

   1. Initial program 85.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 85.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 85.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 85.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 85.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 57.9%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 310000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 10: 30.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.6 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-99}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+43} \lor \neg \left(i \leq 2.5 \cdot 10^{+133}\right):\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.6e+114)
   (* y (* i (- j)))
   (if (<= i -7e-308)
     (* a (* x (- t)))
     (if (<= i 2e-99)
       (* c (* a j))
       (if (<= i 1.9e-23)
         (* x (* y z))
         (if (or (<= i 1.65e+43) (not (<= i 2.5e+133)))
           (* j (* i (- y)))
           (* t (* b i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.6e+114) {
		tmp = y * (i * -j);
	} else if (i <= -7e-308) {
		tmp = a * (x * -t);
	} else if (i <= 2e-99) {
		tmp = c * (a * j);
	} else if (i <= 1.9e-23) {
		tmp = x * (y * z);
	} else if ((i <= 1.65e+43) || !(i <= 2.5e+133)) {
		tmp = j * (i * -y);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-3.6d+114)) then
        tmp = y * (i * -j)
    else if (i <= (-7d-308)) then
        tmp = a * (x * -t)
    else if (i <= 2d-99) then
        tmp = c * (a * j)
    else if (i <= 1.9d-23) then
        tmp = x * (y * z)
    else if ((i <= 1.65d+43) .or. (.not. (i <= 2.5d+133))) then
        tmp = j * (i * -y)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.6e+114) {
		tmp = y * (i * -j);
	} else if (i <= -7e-308) {
		tmp = a * (x * -t);
	} else if (i <= 2e-99) {
		tmp = c * (a * j);
	} else if (i <= 1.9e-23) {
		tmp = x * (y * z);
	} else if ((i <= 1.65e+43) || !(i <= 2.5e+133)) {
		tmp = j * (i * -y);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.6e+114:
		tmp = y * (i * -j)
	elif i <= -7e-308:
		tmp = a * (x * -t)
	elif i <= 2e-99:
		tmp = c * (a * j)
	elif i <= 1.9e-23:
		tmp = x * (y * z)
	elif (i <= 1.65e+43) or not (i <= 2.5e+133):
		tmp = j * (i * -y)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.6e+114)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= -7e-308)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 2e-99)
		tmp = Float64(c * Float64(a * j));
	elseif (i <= 1.9e-23)
		tmp = Float64(x * Float64(y * z));
	elseif ((i <= 1.65e+43) || !(i <= 2.5e+133))
		tmp = Float64(j * Float64(i * Float64(-y)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.6e+114)
		tmp = y * (i * -j);
	elseif (i <= -7e-308)
		tmp = a * (x * -t);
	elseif (i <= 2e-99)
		tmp = c * (a * j);
	elseif (i <= 1.9e-23)
		tmp = x * (y * z);
	elseif ((i <= 1.65e+43) || ~((i <= 2.5e+133)))
		tmp = j * (i * -y);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.6e+114], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7e-308], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e-99], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.9e-23], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 1.65e+43], N[Not[LessEqual[i, 2.5e+133]], $MachinePrecision]], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -3.6000000000000001e114

   1. Initial program 63.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 55.1%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around 0 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 54.6%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. *-commutative 54.6%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 54.6%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   7. Simplified 54.6%

      \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   if -3.6000000000000001e114 < i < -7e-308

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 44.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 44.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 44.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 33.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 33.3%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 33.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 33.3%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 33.3%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -7e-308 < i < 2e-99

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 68.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 68.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 68.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 68.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 55.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 55.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 55.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 40.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 40.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if 2e-99 < i < 1.90000000000000006e-23

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 88.2%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in x around -inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(-1 \cdot \left(y \cdot z\right) + a \cdot t\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 49.4%

         \[\leadsto \color{blue}{-\left(-1 \cdot \left(y \cdot z\right) + a \cdot t\right) \cdot x} \]

      2. *-commutative 49.4%

         \[\leadsto -\color{blue}{x \cdot \left(-1 \cdot \left(y \cdot z\right) + a \cdot t\right)} \]

      3. distribute-rgt-neg-in 49.4%

         \[\leadsto \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z\right) + a \cdot t\right)\right)} \]

      4. +-commutative 49.4%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot t + -1 \cdot \left(y \cdot z\right)\right)}\right) \]

      5. mul-1-neg 49.4%

         \[\leadsto x \cdot \left(-\left(a \cdot t + \color{blue}{\left(-y \cdot z\right)}\right)\right) \]

      6. unsub-neg 49.4%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot t - y \cdot z\right)}\right) \]

      7. *-commutative 49.4%

         \[\leadsto x \cdot \left(-\left(\color{blue}{t \cdot a} - y \cdot z\right)\right) \]

   7. Simplified 49.4%

      \[\leadsto \color{blue}{x \cdot \left(-\left(t \cdot a - y \cdot z\right)\right)} \]

   8. Taylor expanded in t around 0 43.5%

      \[\leadsto x \cdot \left(-\color{blue}{-1 \cdot \left(y \cdot z\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 43.5%

         \[\leadsto x \cdot \left(-\color{blue}{\left(-y \cdot z\right)}\right) \]

      2. distribute-rgt-neg-in 43.5%

         \[\leadsto x \cdot \left(-\color{blue}{y \cdot \left(-z\right)}\right) \]

   10. Simplified 43.5%

       \[\leadsto x \cdot \left(-\color{blue}{y \cdot \left(-z\right)}\right) \]

   if 1.90000000000000006e-23 < i < 1.6500000000000001e43 or 2.4999999999999998e133 < i

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 66.0%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around 0 63.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot i\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. neg-mul-1 63.4%

         \[\leadsto \color{blue}{\left(-y \cdot i\right)} \cdot j \]

      2. distribute-rgt-neg-in 63.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(-i\right)\right)} \cdot j \]

   7. Simplified 63.4%

      \[\leadsto \color{blue}{\left(y \cdot \left(-i\right)\right)} \cdot j \]

   if 1.6500000000000001e43 < i < 2.4999999999999998e133

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 39.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 39.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 39.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 39.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 39.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 39.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 39.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 39.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 35.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 43.3%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 43.3%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.6 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-99}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+43} \lor \neg \left(i \leq 2.5 \cdot 10^{+133}\right):\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 11: 30.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;i \leq -2.1 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= i -2.1e+114)
     t_1
     (if (<= i -7e-308)
       (* a (* x (- t)))
       (if (<= i 8e-48)
         (* c (* a j))
         (if (<= i 3.5e+64)
           t_1
           (if (<= i 2.4e+83)
             (* a (* c j))
             (if (<= i 7.2e+137) (* t (* b i)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (i <= -2.1e+114) {
		tmp = t_1;
	} else if (i <= -7e-308) {
		tmp = a * (x * -t);
	} else if (i <= 8e-48) {
		tmp = c * (a * j);
	} else if (i <= 3.5e+64) {
		tmp = t_1;
	} else if (i <= 2.4e+83) {
		tmp = a * (c * j);
	} else if (i <= 7.2e+137) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (i * -j)
    if (i <= (-2.1d+114)) then
        tmp = t_1
    else if (i <= (-7d-308)) then
        tmp = a * (x * -t)
    else if (i <= 8d-48) then
        tmp = c * (a * j)
    else if (i <= 3.5d+64) then
        tmp = t_1
    else if (i <= 2.4d+83) then
        tmp = a * (c * j)
    else if (i <= 7.2d+137) then
        tmp = t * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (i <= -2.1e+114) {
		tmp = t_1;
	} else if (i <= -7e-308) {
		tmp = a * (x * -t);
	} else if (i <= 8e-48) {
		tmp = c * (a * j);
	} else if (i <= 3.5e+64) {
		tmp = t_1;
	} else if (i <= 2.4e+83) {
		tmp = a * (c * j);
	} else if (i <= 7.2e+137) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if i <= -2.1e+114:
		tmp = t_1
	elif i <= -7e-308:
		tmp = a * (x * -t)
	elif i <= 8e-48:
		tmp = c * (a * j)
	elif i <= 3.5e+64:
		tmp = t_1
	elif i <= 2.4e+83:
		tmp = a * (c * j)
	elif i <= 7.2e+137:
		tmp = t * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (i <= -2.1e+114)
		tmp = t_1;
	elseif (i <= -7e-308)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 8e-48)
		tmp = Float64(c * Float64(a * j));
	elseif (i <= 3.5e+64)
		tmp = t_1;
	elseif (i <= 2.4e+83)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 7.2e+137)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	tmp = 0.0;
	if (i <= -2.1e+114)
		tmp = t_1;
	elseif (i <= -7e-308)
		tmp = a * (x * -t);
	elseif (i <= 8e-48)
		tmp = c * (a * j);
	elseif (i <= 3.5e+64)
		tmp = t_1;
	elseif (i <= 2.4e+83)
		tmp = a * (c * j);
	elseif (i <= 7.2e+137)
		tmp = t * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.1e+114], t$95$1, If[LessEqual[i, -7e-308], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8e-48], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.5e+64], t$95$1, If[LessEqual[i, 2.4e+83], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.2e+137], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.1e114 or 7.9999999999999998e-48 < i < 3.4999999999999999e64 or 7.1999999999999999e137 < i

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 68.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 68.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 68.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 68.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 58.4%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around 0 54.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. *-commutative 54.4%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 54.4%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   7. Simplified 54.4%

      \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   if -2.1e114 < i < -7e-308

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 44.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 44.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 44.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 33.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 33.3%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 33.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 33.3%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 33.3%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -7e-308 < i < 7.9999999999999998e-48

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 45.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 45.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 33.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.9%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 33.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if 3.4999999999999999e64 < i < 2.39999999999999991e83

   1. Initial program 82.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 82.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 74.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 74.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 74.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 74.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 74.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 74.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 51.6%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 51.6%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if 2.39999999999999991e83 < i < 7.1999999999999999e137

   1. Initial program 55.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 55.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 55.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 55.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 55.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 55.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 55.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 46.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 46.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 46.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 46.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 46.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 46.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 46.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 55.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 55.4%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 64.3%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 64.3%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.1 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 12: 30.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{if}\;i \leq -2.8 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+82}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* i (- y)))))
   (if (<= i -2.8e+114)
     (* y (* i (- j)))
     (if (<= i -7e-308)
       (* a (* x (- t)))
       (if (<= i 1.08e-48)
         (* c (* a j))
         (if (<= i 2.45e+64)
           t_1
           (if (<= i 3.9e+82)
             (* a (* c j))
             (if (<= i 9e+130) (* t (* b i)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (i * -y);
	double tmp;
	if (i <= -2.8e+114) {
		tmp = y * (i * -j);
	} else if (i <= -7e-308) {
		tmp = a * (x * -t);
	} else if (i <= 1.08e-48) {
		tmp = c * (a * j);
	} else if (i <= 2.45e+64) {
		tmp = t_1;
	} else if (i <= 3.9e+82) {
		tmp = a * (c * j);
	} else if (i <= 9e+130) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (i * -y)
    if (i <= (-2.8d+114)) then
        tmp = y * (i * -j)
    else if (i <= (-7d-308)) then
        tmp = a * (x * -t)
    else if (i <= 1.08d-48) then
        tmp = c * (a * j)
    else if (i <= 2.45d+64) then
        tmp = t_1
    else if (i <= 3.9d+82) then
        tmp = a * (c * j)
    else if (i <= 9d+130) then
        tmp = t * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (i * -y);
	double tmp;
	if (i <= -2.8e+114) {
		tmp = y * (i * -j);
	} else if (i <= -7e-308) {
		tmp = a * (x * -t);
	} else if (i <= 1.08e-48) {
		tmp = c * (a * j);
	} else if (i <= 2.45e+64) {
		tmp = t_1;
	} else if (i <= 3.9e+82) {
		tmp = a * (c * j);
	} else if (i <= 9e+130) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (i * -y)
	tmp = 0
	if i <= -2.8e+114:
		tmp = y * (i * -j)
	elif i <= -7e-308:
		tmp = a * (x * -t)
	elif i <= 1.08e-48:
		tmp = c * (a * j)
	elif i <= 2.45e+64:
		tmp = t_1
	elif i <= 3.9e+82:
		tmp = a * (c * j)
	elif i <= 9e+130:
		tmp = t * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(i * Float64(-y)))
	tmp = 0.0
	if (i <= -2.8e+114)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= -7e-308)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 1.08e-48)
		tmp = Float64(c * Float64(a * j));
	elseif (i <= 2.45e+64)
		tmp = t_1;
	elseif (i <= 3.9e+82)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 9e+130)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (i * -y);
	tmp = 0.0;
	if (i <= -2.8e+114)
		tmp = y * (i * -j);
	elseif (i <= -7e-308)
		tmp = a * (x * -t);
	elseif (i <= 1.08e-48)
		tmp = c * (a * j);
	elseif (i <= 2.45e+64)
		tmp = t_1;
	elseif (i <= 3.9e+82)
		tmp = a * (c * j);
	elseif (i <= 9e+130)
		tmp = t * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.8e+114], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7e-308], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.08e-48], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.45e+64], t$95$1, If[LessEqual[i, 3.9e+82], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e+130], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -2.8e114

   1. Initial program 63.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 55.1%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around 0 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 54.6%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. *-commutative 54.6%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 54.6%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   7. Simplified 54.6%

      \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   if -2.8e114 < i < -7e-308

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 44.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 44.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 44.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 33.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 33.3%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 33.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 33.3%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 33.3%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -7e-308 < i < 1.08e-48

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 45.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 45.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 33.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.9%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 33.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if 1.08e-48 < i < 2.4500000000000001e64 or 9.00000000000000078e130 < i

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 72.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 61.1%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around 0 56.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot i\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. neg-mul-1 56.0%

         \[\leadsto \color{blue}{\left(-y \cdot i\right)} \cdot j \]

      2. distribute-rgt-neg-in 56.0%

         \[\leadsto \color{blue}{\left(y \cdot \left(-i\right)\right)} \cdot j \]

   7. Simplified 56.0%

      \[\leadsto \color{blue}{\left(y \cdot \left(-i\right)\right)} \cdot j \]

   if 2.4500000000000001e64 < i < 3.89999999999999976e82

   1. Initial program 82.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 82.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 82.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 74.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 74.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 74.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 74.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 74.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 74.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 51.6%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 51.6%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if 3.89999999999999976e82 < i < 9.00000000000000078e130

   1. Initial program 55.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 55.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 55.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 55.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 55.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 55.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 55.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 46.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 46.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 46.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 46.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 46.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 46.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 46.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 55.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 55.4%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 64.3%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 64.3%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.8 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{+64}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+82}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 13: 41.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;i \leq -3.3 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.05 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= i -3.3e+156)
     (* y (* i (- j)))
     (if (<= i 4.1e-99)
       t_2
       (if (<= i 3.5e-24)
         t_1
         (if (<= i 3.2e+79)
           t_2
           (if (<= i 2.05e+101)
             t_1
             (if (<= i 1.35e+131) (* t (* b i)) (* j (* i (- y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (i <= -3.3e+156) {
		tmp = y * (i * -j);
	} else if (i <= 4.1e-99) {
		tmp = t_2;
	} else if (i <= 3.5e-24) {
		tmp = t_1;
	} else if (i <= 3.2e+79) {
		tmp = t_2;
	} else if (i <= 2.05e+101) {
		tmp = t_1;
	} else if (i <= 1.35e+131) {
		tmp = t * (b * i);
	} else {
		tmp = j * (i * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = a * ((c * j) - (x * t))
    if (i <= (-3.3d+156)) then
        tmp = y * (i * -j)
    else if (i <= 4.1d-99) then
        tmp = t_2
    else if (i <= 3.5d-24) then
        tmp = t_1
    else if (i <= 3.2d+79) then
        tmp = t_2
    else if (i <= 2.05d+101) then
        tmp = t_1
    else if (i <= 1.35d+131) then
        tmp = t * (b * i)
    else
        tmp = j * (i * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (i <= -3.3e+156) {
		tmp = y * (i * -j);
	} else if (i <= 4.1e-99) {
		tmp = t_2;
	} else if (i <= 3.5e-24) {
		tmp = t_1;
	} else if (i <= 3.2e+79) {
		tmp = t_2;
	} else if (i <= 2.05e+101) {
		tmp = t_1;
	} else if (i <= 1.35e+131) {
		tmp = t * (b * i);
	} else {
		tmp = j * (i * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if i <= -3.3e+156:
		tmp = y * (i * -j)
	elif i <= 4.1e-99:
		tmp = t_2
	elif i <= 3.5e-24:
		tmp = t_1
	elif i <= 3.2e+79:
		tmp = t_2
	elif i <= 2.05e+101:
		tmp = t_1
	elif i <= 1.35e+131:
		tmp = t * (b * i)
	else:
		tmp = j * (i * -y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (i <= -3.3e+156)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= 4.1e-99)
		tmp = t_2;
	elseif (i <= 3.5e-24)
		tmp = t_1;
	elseif (i <= 3.2e+79)
		tmp = t_2;
	elseif (i <= 2.05e+101)
		tmp = t_1;
	elseif (i <= 1.35e+131)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(j * Float64(i * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (i <= -3.3e+156)
		tmp = y * (i * -j);
	elseif (i <= 4.1e-99)
		tmp = t_2;
	elseif (i <= 3.5e-24)
		tmp = t_1;
	elseif (i <= 3.2e+79)
		tmp = t_2;
	elseif (i <= 2.05e+101)
		tmp = t_1;
	elseif (i <= 1.35e+131)
		tmp = t * (b * i);
	else
		tmp = j * (i * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.3e+156], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.1e-99], t$95$2, If[LessEqual[i, 3.5e-24], t$95$1, If[LessEqual[i, 3.2e+79], t$95$2, If[LessEqual[i, 2.05e+101], t$95$1, If[LessEqual[i, 1.35e+131], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.2999999999999999e156

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 58.7%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around 0 58.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 58.1%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. *-commutative 58.1%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 58.1%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   7. Simplified 58.1%

      \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   if -3.2999999999999999e156 < i < 4.10000000000000029e-99 or 3.4999999999999996e-24 < i < 3.20000000000000003e79

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 75.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 46.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 46.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 46.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 46.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 4.10000000000000029e-99 < i < 3.4999999999999996e-24 or 3.20000000000000003e79 < i < 2.05e101

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 77.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 73.0%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in x around -inf 60.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(-1 \cdot \left(y \cdot z\right) + a \cdot t\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 60.8%

         \[\leadsto \color{blue}{-\left(-1 \cdot \left(y \cdot z\right) + a \cdot t\right) \cdot x} \]

      2. *-commutative 60.8%

         \[\leadsto -\color{blue}{x \cdot \left(-1 \cdot \left(y \cdot z\right) + a \cdot t\right)} \]

      3. distribute-rgt-neg-in 60.8%

         \[\leadsto \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z\right) + a \cdot t\right)\right)} \]

      4. +-commutative 60.8%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot t + -1 \cdot \left(y \cdot z\right)\right)}\right) \]

      5. mul-1-neg 60.8%

         \[\leadsto x \cdot \left(-\left(a \cdot t + \color{blue}{\left(-y \cdot z\right)}\right)\right) \]

      6. unsub-neg 60.8%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot t - y \cdot z\right)}\right) \]

      7. *-commutative 60.8%

         \[\leadsto x \cdot \left(-\left(\color{blue}{t \cdot a} - y \cdot z\right)\right) \]

   7. Simplified 60.8%

      \[\leadsto \color{blue}{x \cdot \left(-\left(t \cdot a - y \cdot z\right)\right)} \]

   8. Taylor expanded in t around 0 56.3%

      \[\leadsto x \cdot \left(-\color{blue}{-1 \cdot \left(y \cdot z\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 56.3%

         \[\leadsto x \cdot \left(-\color{blue}{\left(-y \cdot z\right)}\right) \]

      2. distribute-rgt-neg-in 56.3%

         \[\leadsto x \cdot \left(-\color{blue}{y \cdot \left(-z\right)}\right) \]

   10. Simplified 56.3%

       \[\leadsto x \cdot \left(-\color{blue}{y \cdot \left(-z\right)}\right) \]

   if 2.05e101 < i < 1.35000000000000002e131

   1. Initial program 58.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 58.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 58.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 58.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 58.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 58.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 58.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 58.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 58.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 58.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 58.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 58.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 58.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 58.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 57.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 57.7%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 58.0%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 58.0%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 1.35000000000000002e131 < i

   1. Initial program 57.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 57.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 57.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 57.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 57.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 57.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 57.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 72.2%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around 0 68.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot i\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. neg-mul-1 68.6%

         \[\leadsto \color{blue}{\left(-y \cdot i\right)} \cdot j \]

      2. distribute-rgt-neg-in 68.6%

         \[\leadsto \color{blue}{\left(y \cdot \left(-i\right)\right)} \cdot j \]

   7. Simplified 68.6%

      \[\leadsto \color{blue}{\left(y \cdot \left(-i\right)\right)} \cdot j \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.05 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 14: 49.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.6e+199)
     t_1
     (if (<= x -6.4e-92)
       (* y (- (* x z) (* i j)))
       (if (<= x 1.36e+14)
         (- (* y (* i (- j))) (* z (* b c)))
         (if (<= x 1.22e+162) (* a (- (* c j) (* x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.6e+199) {
		tmp = t_1;
	} else if (x <= -6.4e-92) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.36e+14) {
		tmp = (y * (i * -j)) - (z * (b * c));
	} else if (x <= 1.22e+162) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2.6d+199)) then
        tmp = t_1
    else if (x <= (-6.4d-92)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 1.36d+14) then
        tmp = (y * (i * -j)) - (z * (b * c))
    else if (x <= 1.22d+162) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.6e+199) {
		tmp = t_1;
	} else if (x <= -6.4e-92) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.36e+14) {
		tmp = (y * (i * -j)) - (z * (b * c));
	} else if (x <= 1.22e+162) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.6e+199:
		tmp = t_1
	elif x <= -6.4e-92:
		tmp = y * ((x * z) - (i * j))
	elif x <= 1.36e+14:
		tmp = (y * (i * -j)) - (z * (b * c))
	elif x <= 1.22e+162:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.6e+199)
		tmp = t_1;
	elseif (x <= -6.4e-92)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 1.36e+14)
		tmp = Float64(Float64(y * Float64(i * Float64(-j))) - Float64(z * Float64(b * c)));
	elseif (x <= 1.22e+162)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.6e+199)
		tmp = t_1;
	elseif (x <= -6.4e-92)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 1.36e+14)
		tmp = (y * (i * -j)) - (z * (b * c));
	elseif (x <= 1.22e+162)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+199], t$95$1, If[LessEqual[x, -6.4e-92], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.36e+14], N[(N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e+162], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.6000000000000001e199 or 1.22e162 < x

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 74.9%

      \[\leadsto \color{blue}{\left(\left(i \cdot \left(t \cdot b\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in x around inf 81.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -2.6000000000000001e199 < x < -6.3999999999999994e-92

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 74.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 73.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in y around inf 54.5%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 54.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 54.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 54.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   7. Simplified 54.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -6.3999999999999994e-92 < x < 1.36e14

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 67.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 65.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 65.4%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 65.4%

         \[\leadsto \left(-c \cdot \color{blue}{\left(z \cdot b\right)}\right) + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 65.4%

         \[\leadsto \color{blue}{c \cdot \left(-z \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      4. distribute-rgt-neg-in 65.4%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 65.4%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   7. Taylor expanded in a around 0 59.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out 59.6%

         \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right) + c \cdot \left(z \cdot b\right)\right)} \]

      2. *-commutative 59.6%

         \[\leadsto -1 \cdot \left(y \cdot \left(i \cdot j\right) + c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      3. associate-*r* 60.4%

         \[\leadsto -1 \cdot \left(y \cdot \left(i \cdot j\right) + \color{blue}{\left(c \cdot b\right) \cdot z}\right) \]

   9. Simplified 60.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right) + \left(c \cdot b\right) \cdot z\right)} \]

   if 1.36e14 < x < 1.22e162

   1. Initial program 69.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 69.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 69.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 66.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 66.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 15: 51.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -9.8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.62 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -9.8e-8)
     t_1
     (if (<= c 1.25e-120)
       (* i (- (* t b) (* y j)))
       (if (<= c 1.62e+75)
         (* a (- (* c j) (* x t)))
         (if (<= c 3e+103) (* t (* b i)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -9.8e-8) {
		tmp = t_1;
	} else if (c <= 1.25e-120) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 1.62e+75) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= 3e+103) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-9.8d-8)) then
        tmp = t_1
    else if (c <= 1.25d-120) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 1.62d+75) then
        tmp = a * ((c * j) - (x * t))
    else if (c <= 3d+103) then
        tmp = t * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -9.8e-8) {
		tmp = t_1;
	} else if (c <= 1.25e-120) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 1.62e+75) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= 3e+103) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -9.8e-8:
		tmp = t_1
	elif c <= 1.25e-120:
		tmp = i * ((t * b) - (y * j))
	elif c <= 1.62e+75:
		tmp = a * ((c * j) - (x * t))
	elif c <= 3e+103:
		tmp = t * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -9.8e-8)
		tmp = t_1;
	elseif (c <= 1.25e-120)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 1.62e+75)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (c <= 3e+103)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -9.8e-8)
		tmp = t_1;
	elseif (c <= 1.25e-120)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 1.62e+75)
		tmp = a * ((c * j) - (x * t));
	elseif (c <= 3e+103)
		tmp = t * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.8e-8], t$95$1, If[LessEqual[c, 1.25e-120], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.62e+75], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e+103], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.8000000000000004e-8 or 3e103 < c

   1. Initial program 59.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 59.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 59.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 66.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -9.8000000000000004e-8 < c < 1.25000000000000002e-120

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 47.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 47.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 47.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 47.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 47.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 47.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 47.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 47.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if 1.25000000000000002e-120 < c < 1.6200000000000001e75

   1. Initial program 78.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 50.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 1.6200000000000001e75 < c < 3e103

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 69.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 69.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 69.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 69.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 69.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 47.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 47.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 47.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 47.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 47.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 47.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 47.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 47.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.3%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 67.8%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 67.8%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.8 \cdot 10^{-8}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.62 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 16: 28.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-z \cdot b\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+163}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* z b)))) (t_2 (* a (* x (- t)))))
   (if (<= x -5.8e-55)
     t_2
     (if (<= x 9.6e-164)
       t_1
       (if (<= x 1.15e-83)
         (* t (* b i))
         (if (<= x 2.9e-68) t_1 (if (<= x 1.85e+163) (* c (* a j)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * -(z * b);
	double t_2 = a * (x * -t);
	double tmp;
	if (x <= -5.8e-55) {
		tmp = t_2;
	} else if (x <= 9.6e-164) {
		tmp = t_1;
	} else if (x <= 1.15e-83) {
		tmp = t * (b * i);
	} else if (x <= 2.9e-68) {
		tmp = t_1;
	} else if (x <= 1.85e+163) {
		tmp = c * (a * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * -(z * b)
    t_2 = a * (x * -t)
    if (x <= (-5.8d-55)) then
        tmp = t_2
    else if (x <= 9.6d-164) then
        tmp = t_1
    else if (x <= 1.15d-83) then
        tmp = t * (b * i)
    else if (x <= 2.9d-68) then
        tmp = t_1
    else if (x <= 1.85d+163) then
        tmp = c * (a * j)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * -(z * b);
	double t_2 = a * (x * -t);
	double tmp;
	if (x <= -5.8e-55) {
		tmp = t_2;
	} else if (x <= 9.6e-164) {
		tmp = t_1;
	} else if (x <= 1.15e-83) {
		tmp = t * (b * i);
	} else if (x <= 2.9e-68) {
		tmp = t_1;
	} else if (x <= 1.85e+163) {
		tmp = c * (a * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * -(z * b)
	t_2 = a * (x * -t)
	tmp = 0
	if x <= -5.8e-55:
		tmp = t_2
	elif x <= 9.6e-164:
		tmp = t_1
	elif x <= 1.15e-83:
		tmp = t * (b * i)
	elif x <= 2.9e-68:
		tmp = t_1
	elif x <= 1.85e+163:
		tmp = c * (a * j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(-Float64(z * b)))
	t_2 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (x <= -5.8e-55)
		tmp = t_2;
	elseif (x <= 9.6e-164)
		tmp = t_1;
	elseif (x <= 1.15e-83)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= 2.9e-68)
		tmp = t_1;
	elseif (x <= 1.85e+163)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * -(z * b);
	t_2 = a * (x * -t);
	tmp = 0.0;
	if (x <= -5.8e-55)
		tmp = t_2;
	elseif (x <= 9.6e-164)
		tmp = t_1;
	elseif (x <= 1.15e-83)
		tmp = t * (b * i);
	elseif (x <= 2.9e-68)
		tmp = t_1;
	elseif (x <= 1.85e+163)
		tmp = c * (a * j);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e-55], t$95$2, If[LessEqual[x, 9.6e-164], t$95$1, If[LessEqual[x, 1.15e-83], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-68], t$95$1, If[LessEqual[x, 1.85e+163], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.8e-55 or 1.84999999999999996e163 < x

   1. Initial program 78.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 41.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 41.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 41.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 41.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 41.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 41.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 33.8%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 33.8%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 33.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 33.8%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 33.8%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -5.8e-55 < x < 9.59999999999999932e-164 or 1.14999999999999995e-83 < x < 2.9e-68

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 81.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in c around inf 54.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.0%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   7. Simplified 54.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   8. Taylor expanded in j around 0 40.9%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 40.9%

         \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(z \cdot b\right)}\right) \]

      2. neg-mul-1 40.9%

         \[\leadsto c \cdot \color{blue}{\left(-z \cdot b\right)} \]

      3. distribute-rgt-neg-in 40.9%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   10. Simplified 40.9%

       \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if 9.59999999999999932e-164 < x < 1.14999999999999995e-83

   1. Initial program 59.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 59.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 59.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 65.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 65.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 65.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 65.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 65.8%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 65.8%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 65.8%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 65.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 43.0%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 43.0%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 2.9e-68 < x < 1.84999999999999996e163

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 58.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 58.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 58.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 58.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 43.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 43.6%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 43.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-55}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-164}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-68}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+163}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 17: 28.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-z \cdot b\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+162}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* z b)))))
   (if (<= x -1.7e-54)
     (* a (* x (- t)))
     (if (<= x 9e-165)
       t_1
       (if (<= x 2.9e-84)
         (* t (* b i))
         (if (<= x 3.2e-64)
           t_1
           (if (<= x 1.7e+162) (* c (* a j)) (* x (* t (- a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * -(z * b);
	double tmp;
	if (x <= -1.7e-54) {
		tmp = a * (x * -t);
	} else if (x <= 9e-165) {
		tmp = t_1;
	} else if (x <= 2.9e-84) {
		tmp = t * (b * i);
	} else if (x <= 3.2e-64) {
		tmp = t_1;
	} else if (x <= 1.7e+162) {
		tmp = c * (a * j);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * -(z * b)
    if (x <= (-1.7d-54)) then
        tmp = a * (x * -t)
    else if (x <= 9d-165) then
        tmp = t_1
    else if (x <= 2.9d-84) then
        tmp = t * (b * i)
    else if (x <= 3.2d-64) then
        tmp = t_1
    else if (x <= 1.7d+162) then
        tmp = c * (a * j)
    else
        tmp = x * (t * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * -(z * b);
	double tmp;
	if (x <= -1.7e-54) {
		tmp = a * (x * -t);
	} else if (x <= 9e-165) {
		tmp = t_1;
	} else if (x <= 2.9e-84) {
		tmp = t * (b * i);
	} else if (x <= 3.2e-64) {
		tmp = t_1;
	} else if (x <= 1.7e+162) {
		tmp = c * (a * j);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * -(z * b)
	tmp = 0
	if x <= -1.7e-54:
		tmp = a * (x * -t)
	elif x <= 9e-165:
		tmp = t_1
	elif x <= 2.9e-84:
		tmp = t * (b * i)
	elif x <= 3.2e-64:
		tmp = t_1
	elif x <= 1.7e+162:
		tmp = c * (a * j)
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(-Float64(z * b)))
	tmp = 0.0
	if (x <= -1.7e-54)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= 9e-165)
		tmp = t_1;
	elseif (x <= 2.9e-84)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= 3.2e-64)
		tmp = t_1;
	elseif (x <= 1.7e+162)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * -(z * b);
	tmp = 0.0;
	if (x <= -1.7e-54)
		tmp = a * (x * -t);
	elseif (x <= 9e-165)
		tmp = t_1;
	elseif (x <= 2.9e-84)
		tmp = t * (b * i);
	elseif (x <= 3.2e-64)
		tmp = t_1;
	elseif (x <= 1.7e+162)
		tmp = c * (a * j);
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[x, -1.7e-54], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-165], t$95$1, If[LessEqual[x, 2.9e-84], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-64], t$95$1, If[LessEqual[x, 1.7e+162], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.69999999999999994e-54

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 40.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 40.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 40.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 40.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 28.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 28.5%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 28.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 28.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 28.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -1.69999999999999994e-54 < x < 8.99999999999999985e-165 or 2.90000000000000019e-84 < x < 3.19999999999999975e-64

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 81.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in c around inf 54.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.0%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   7. Simplified 54.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   8. Taylor expanded in j around 0 40.9%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 40.9%

         \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(z \cdot b\right)}\right) \]

      2. neg-mul-1 40.9%

         \[\leadsto c \cdot \color{blue}{\left(-z \cdot b\right)} \]

      3. distribute-rgt-neg-in 40.9%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   10. Simplified 40.9%

       \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if 8.99999999999999985e-165 < x < 2.90000000000000019e-84

   1. Initial program 59.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 59.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 59.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 65.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 65.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 65.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 65.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 65.8%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 65.8%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 65.8%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 65.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 43.0%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 43.0%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 3.19999999999999975e-64 < x < 1.70000000000000001e162

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 58.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 58.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 58.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 58.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 43.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 43.6%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 43.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if 1.70000000000000001e162 < x

   1. Initial program 83.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 45.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 45.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 45.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 45.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 45.4%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. distribute-rgt-neg-in 45.4%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      3. *-commutative 45.4%

         \[\leadsto \color{blue}{\left(-t \cdot x\right) \cdot a} \]

      4. distribute-lft-neg-in 45.4%

         \[\leadsto \color{blue}{\left(\left(-t\right) \cdot x\right)} \cdot a \]

      5. *-commutative 45.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(-t\right)\right)} \cdot a \]

      6. associate-*l* 45.6%

         \[\leadsto \color{blue}{x \cdot \left(\left(-t\right) \cdot a\right)} \]

      7. distribute-lft-neg-in 45.6%

         \[\leadsto x \cdot \color{blue}{\left(-t \cdot a\right)} \]

      8. distribute-rgt-neg-in 45.6%

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   9. Simplified 45.6%

      \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-a\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-165}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+162}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 18: 45.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-50} \lor \neg \left(x \leq 8.4 \cdot 10^{+14}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -8.4e-50) (not (<= x 8.4e+14)))
   (* a (- (* c j) (* x t)))
   (* c (- (* a j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -8.4e-50) || !(x <= 8.4e+14)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-8.4d-50)) .or. (.not. (x <= 8.4d+14))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -8.4e-50) || !(x <= 8.4e+14)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -8.4e-50) or not (x <= 8.4e+14):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -8.4e-50) || !(x <= 8.4e+14))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -8.4e-50) || ~((x <= 8.4e+14)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -8.4e-50], N[Not[LessEqual[x, 8.4e+14]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.4000000000000003e-50 or 8.4e14 < x

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 47.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 47.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 47.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -8.4000000000000003e-50 < x < 8.4e14

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 65.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 65.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 65.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 65.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 65.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 65.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 49.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-50} \lor \neg \left(x \leq 8.4 \cdot 10^{+14}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 19: 52.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{-5} \lor \neg \left(c \leq 6.5 \cdot 10^{-72}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.15e-5) (not (<= c 6.5e-72)))
   (* c (- (* a j) (* z b)))
   (* y (- (* x z) (* i j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.15e-5) || !(c <= 6.5e-72)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-2.15d-5)) .or. (.not. (c <= 6.5d-72))) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.15e-5) || !(c <= 6.5e-72)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.15e-5) or not (c <= 6.5e-72):
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.15e-5) || !(c <= 6.5e-72))
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.15e-5) || ~((c <= 6.5e-72)))
		tmp = c * ((a * j) - (z * b));
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.15e-5], N[Not[LessEqual[c, 6.5e-72]], $MachinePrecision]], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.1500000000000001e-5 or 6.4999999999999997e-72 < c

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 62.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -2.1500000000000001e-5 < c < 6.4999999999999997e-72

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 79.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 78.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in y around inf 56.2%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 56.2%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 56.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   7. Simplified 56.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{-5} \lor \neg \left(c \leq 6.5 \cdot 10^{-72}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 20: 28.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+162}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -2.55e-62)
   (* a (* x (- t)))
   (if (<= x 4.4e-67)
     (* z (- (* b c)))
     (if (<= x 1.5e+162) (* c (* a j)) (* x (* t (- a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -2.55e-62) {
		tmp = a * (x * -t);
	} else if (x <= 4.4e-67) {
		tmp = z * -(b * c);
	} else if (x <= 1.5e+162) {
		tmp = c * (a * j);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-2.55d-62)) then
        tmp = a * (x * -t)
    else if (x <= 4.4d-67) then
        tmp = z * -(b * c)
    else if (x <= 1.5d+162) then
        tmp = c * (a * j)
    else
        tmp = x * (t * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -2.55e-62) {
		tmp = a * (x * -t);
	} else if (x <= 4.4e-67) {
		tmp = z * -(b * c);
	} else if (x <= 1.5e+162) {
		tmp = c * (a * j);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -2.55e-62:
		tmp = a * (x * -t)
	elif x <= 4.4e-67:
		tmp = z * -(b * c)
	elif x <= 1.5e+162:
		tmp = c * (a * j)
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -2.55e-62)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= 4.4e-67)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (x <= 1.5e+162)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -2.55e-62)
		tmp = a * (x * -t);
	elseif (x <= 4.4e-67)
		tmp = z * -(b * c);
	elseif (x <= 1.5e+162)
		tmp = c * (a * j);
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -2.55e-62], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-67], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 1.5e+162], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.55e-62

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 40.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 40.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 40.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 40.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 28.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 28.5%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 28.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 28.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 28.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -2.55e-62 < x < 4.4000000000000002e-67

   1. Initial program 63.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around 0 79.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Taylor expanded in c around inf 48.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.7%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   7. Simplified 48.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   8. Taylor expanded in j around 0 36.9%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 36.9%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. *-commutative 36.9%

         \[\leadsto -\color{blue}{\left(z \cdot b\right) \cdot c} \]

      3. associate-*l* 37.7%

         \[\leadsto -\color{blue}{z \cdot \left(b \cdot c\right)} \]

      4. *-commutative 37.7%

         \[\leadsto -z \cdot \color{blue}{\left(c \cdot b\right)} \]

      5. distribute-rgt-neg-in 37.7%

         \[\leadsto \color{blue}{z \cdot \left(-c \cdot b\right)} \]

      6. distribute-rgt-neg-in 37.7%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   10. Simplified 37.7%

       \[\leadsto \color{blue}{z \cdot \left(c \cdot \left(-b\right)\right)} \]

   if 4.4000000000000002e-67 < x < 1.4999999999999999e162

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 58.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 58.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 58.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 58.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 43.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 43.6%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 43.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if 1.4999999999999999e162 < x

   1. Initial program 83.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 45.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 45.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 45.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 45.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 45.4%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. distribute-rgt-neg-in 45.4%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      3. *-commutative 45.4%

         \[\leadsto \color{blue}{\left(-t \cdot x\right) \cdot a} \]

      4. distribute-lft-neg-in 45.4%

         \[\leadsto \color{blue}{\left(\left(-t\right) \cdot x\right)} \cdot a \]

      5. *-commutative 45.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(-t\right)\right)} \cdot a \]

      6. associate-*l* 45.6%

         \[\leadsto \color{blue}{x \cdot \left(\left(-t\right) \cdot a\right)} \]

      7. distribute-lft-neg-in 45.6%

         \[\leadsto x \cdot \color{blue}{\left(-t \cdot a\right)} \]

      8. distribute-rgt-neg-in 45.6%

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   9. Simplified 45.6%

      \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+162}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 21: 29.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{-89}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= i -5e+46)
     t_1
     (if (<= i -2.4e-295)
       (* t (* x (- a)))
       (if (<= i 1.12e-89) (* c (* a j)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -5e+46) {
		tmp = t_1;
	} else if (i <= -2.4e-295) {
		tmp = t * (x * -a);
	} else if (i <= 1.12e-89) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b * i)
    if (i <= (-5d+46)) then
        tmp = t_1
    else if (i <= (-2.4d-295)) then
        tmp = t * (x * -a)
    else if (i <= 1.12d-89) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -5e+46) {
		tmp = t_1;
	} else if (i <= -2.4e-295) {
		tmp = t * (x * -a);
	} else if (i <= 1.12e-89) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (b * i)
	tmp = 0
	if i <= -5e+46:
		tmp = t_1
	elif i <= -2.4e-295:
		tmp = t * (x * -a)
	elif i <= 1.12e-89:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -5e+46)
		tmp = t_1;
	elseif (i <= -2.4e-295)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (i <= 1.12e-89)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (b * i);
	tmp = 0.0;
	if (i <= -5e+46)
		tmp = t_1;
	elseif (i <= -2.4e-295)
		tmp = t * (x * -a);
	elseif (i <= 1.12e-89)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5e+46], t$95$1, If[LessEqual[i, -2.4e-295], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.12e-89], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.0000000000000002e46 or 1.12e-89 < i

   1. Initial program 66.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 66.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 66.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 57.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 57.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 57.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 57.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 57.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 57.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 57.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 57.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 27.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 27.4%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 32.6%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 32.6%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -5.0000000000000002e46 < i < -2.3999999999999998e-295

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 39.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 39.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \cdot t \]

      2. associate-*r* 39.8%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x - i \cdot b\right) \cdot t\right)} \]

      3. mul-1-neg 39.8%

         \[\leadsto \color{blue}{-\left(a \cdot x - i \cdot b\right) \cdot t} \]

      4. *-commutative 39.8%

         \[\leadsto -\color{blue}{t \cdot \left(a \cdot x - i \cdot b\right)} \]

   6. Simplified 39.8%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - i \cdot b\right)} \]

   7. Taylor expanded in a around inf 33.6%

      \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.6%

         \[\leadsto -t \cdot \color{blue}{\left(x \cdot a\right)} \]

   9. Simplified 33.6%

      \[\leadsto -t \cdot \color{blue}{\left(x \cdot a\right)} \]

   if -2.3999999999999998e-295 < i < 1.12e-89

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 51.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 51.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 39.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.3%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 39.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{-89}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 22: 29.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -3.8 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-89}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= i -3.8e+46)
     t_1
     (if (<= i -7.2e-308)
       (* a (* x (- t)))
       (if (<= i 2.7e-89) (* c (* a j)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -3.8e+46) {
		tmp = t_1;
	} else if (i <= -7.2e-308) {
		tmp = a * (x * -t);
	} else if (i <= 2.7e-89) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b * i)
    if (i <= (-3.8d+46)) then
        tmp = t_1
    else if (i <= (-7.2d-308)) then
        tmp = a * (x * -t)
    else if (i <= 2.7d-89) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -3.8e+46) {
		tmp = t_1;
	} else if (i <= -7.2e-308) {
		tmp = a * (x * -t);
	} else if (i <= 2.7e-89) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (b * i)
	tmp = 0
	if i <= -3.8e+46:
		tmp = t_1
	elif i <= -7.2e-308:
		tmp = a * (x * -t)
	elif i <= 2.7e-89:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -3.8e+46)
		tmp = t_1;
	elseif (i <= -7.2e-308)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 2.7e-89)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (b * i);
	tmp = 0.0;
	if (i <= -3.8e+46)
		tmp = t_1;
	elseif (i <= -7.2e-308)
		tmp = a * (x * -t);
	elseif (i <= 2.7e-89)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.8e+46], t$95$1, If[LessEqual[i, -7.2e-308], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.7e-89], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.7999999999999999e46 or 2.69999999999999988e-89 < i

   1. Initial program 66.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 66.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 66.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 57.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 57.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 57.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 57.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 57.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 57.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 57.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 57.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 27.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 27.4%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 32.6%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 32.6%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -3.7999999999999999e46 < i < -7.1999999999999997e-308

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 79.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 45.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 45.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 45.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around 0 34.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 34.6%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 34.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 34.6%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 34.6%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -7.1999999999999997e-308 < i < 2.69999999999999988e-89

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 72.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 52.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 52.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 52.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 52.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 39.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.6%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 39.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.8 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-89}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 23: 28.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+215} \lor \neg \left(a \leq 7.6 \cdot 10^{-37}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -3.2e+215) (not (<= a 7.6e-37))) (* c (* a j)) (* t (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -3.2e+215) || !(a <= 7.6e-37)) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-3.2d+215)) .or. (.not. (a <= 7.6d-37))) then
        tmp = c * (a * j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -3.2e+215) || !(a <= 7.6e-37)) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -3.2e+215) or not (a <= 7.6e-37):
		tmp = c * (a * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -3.2e+215) || !(a <= 7.6e-37))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -3.2e+215) || ~((a <= 7.6e-37)))
		tmp = c * (a * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -3.2e+215], N[Not[LessEqual[a, 7.6e-37]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1999999999999999e215 or 7.6000000000000008e-37 < a

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 69.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 63.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 63.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 63.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 63.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 63.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 63.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 45.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.5%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 45.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if -3.1999999999999999e215 < a < 7.6000000000000008e-37

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 72.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 38.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 38.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 38.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 38.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 38.9%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 38.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 38.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 20.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 20.6%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 24.0%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 24.0%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+215} \lor \neg \left(a \leq 7.6 \cdot 10^{-37}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 24: 28.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+215}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -3.2e+215)
   (* j (* a c))
   (if (<= a 8.2e-43) (* t (* b i)) (* c (* a j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -3.2e+215) {
		tmp = j * (a * c);
	} else if (a <= 8.2e-43) {
		tmp = t * (b * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-3.2d+215)) then
        tmp = j * (a * c)
    else if (a <= 8.2d-43) then
        tmp = t * (b * i)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -3.2e+215) {
		tmp = j * (a * c);
	} else if (a <= 8.2e-43) {
		tmp = t * (b * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -3.2e+215:
		tmp = j * (a * c)
	elif a <= 8.2e-43:
		tmp = t * (b * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -3.2e+215)
		tmp = Float64(j * Float64(a * c));
	elseif (a <= 8.2e-43)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -3.2e+215)
		tmp = j * (a * c);
	elseif (a <= 8.2e-43)
		tmp = t * (b * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -3.2e+215], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e-43], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1999999999999999e215

   1. Initial program 43.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 43.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 43.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 43.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 43.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 43.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 43.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 75.6%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   5. Taylor expanded in c around inf 70.0%

      \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   if -3.1999999999999999e215 < a < 8.1999999999999996e-43

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 72.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 38.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot t\right) \cdot b}\right) \]

      2. neg-mul-1 38.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-t\right)} \cdot b\right) \]

      3. cancel-sign-sub 38.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + t \cdot b\right)} \]

      4. +-commutative 38.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 38.9%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 38.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 38.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around inf 20.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 20.6%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. associate-*l* 24.0%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   9. Simplified 24.0%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 8.1999999999999996e-43 < a

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 75.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 61.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 61.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 61.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 61.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 41.2%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.2%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 41.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+215}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 25: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub 71.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   2. cancel-sign-sub-inv 71.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   3. *-commutative 71.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

   4. remove-double-neg 71.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

   5. *-commutative 71.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

3. Simplified 71.6%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

4. Taylor expanded in a around inf 37.7%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 37.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 37.7%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 37.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 37.7%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

6. Simplified 37.7%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

7. Taylor expanded in j around inf 21.5%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 21.5%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

9. Simplified 21.5%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

10. Final simplification 21.5%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Alternative 26: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(a \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* c (* a j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return c * (a * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = c * (a * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return c * (a * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return c * (a * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(c * Float64(a * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = c * (a * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub 71.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   2. cancel-sign-sub-inv 71.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   3. *-commutative 71.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

   4. remove-double-neg 71.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

   5. *-commutative 71.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

3. Simplified 71.6%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

4. Taylor expanded in a around inf 37.7%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 37.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 37.7%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 37.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 37.7%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

6. Simplified 37.7%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

7. Taylor expanded in j around inf 23.1%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 23.1%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

9. Simplified 23.1%

   \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

10. Final simplification 23.1%

    \[\leadsto c \cdot \left(a \cdot j\right) \]

Developer target: 58.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023181 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))