Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.7% → 81.2%

Time: 23.6s

Alternatives: 23

Speedup: 0.5×

• 58.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 72.7% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 81.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot z - t \cdot a\\ t_3 := t \cdot c - y \cdot i\\ \mathbf{if}\;\left(x \cdot t_2 + t_1\right) + j \cdot t_3 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, t_2, \mathsf{fma}\left(j, t_3, t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (- (* y z) (* t a)))
        (t_3 (- (* t c) (* y i))))
   (if (<= (+ (+ (* x t_2) t_1) (* j t_3)) INFINITY)
     (fma x t_2 (fma j t_3 t_1))
     (* 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 = b * ((a * i) - (z * c));
	double t_2 = (y * z) - (t * a);
	double t_3 = (t * c) - (y * i);
	double tmp;
	if ((((x * t_2) + t_1) + (j * t_3)) <= ((double) INFINITY)) {
		tmp = fma(x, t_2, fma(j, t_3, t_1));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(y * z) - Float64(t * a))
	t_3 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(Float64(x * t_2) + t_1) + Float64(j * t_3)) <= Inf)
		tmp = fma(x, t_2, fma(j, t_3, t_1));
	else
		tmp = 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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision], Infinity], N[(x * t$95$2 + N[(j * t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 93.7%

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

      1. sub-neg 93.7%

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

      2. associate-+l+ 93.7%

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

      3. fma-def 93.7%

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

      4. +-commutative 93.7%

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

      5. fma-def 93.7%

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

      6. *-commutative 93.7%

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

      7. *-commutative 93.7%

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

      8. distribute-rgt-neg-in 93.7%

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

      9. sub-neg 93.7%

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

      10. +-commutative 93.7%

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

      11. distribute-neg-in 93.7%

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

      12. unsub-neg 93.7%

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

      13. remove-double-neg 93.7%

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

      14. *-commutative 93.7%

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

      15. *-commutative 93.7%

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

   3. Simplified 93.7%

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

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

   1. Initial program 0.0%

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

      1. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. remove-double-neg 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 49.8%

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

4. Final simplification 85.6%

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

Alternative 2: 81.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j (- (* t c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* 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 * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = 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 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = 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 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = 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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 93.7%

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

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

   1. Initial program 0.0%

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

      1. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. remove-double-neg 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 49.8%

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

4. Final simplification 85.6%

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

Alternative 3: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -5.4e+91)
     t_3
     (if (<= t -2.4e+41)
       (* i (- (* a b) (* y j)))
       (if (<= t -1.55e-79)
         (* c (- (* t j) (* z b)))
         (if (<= t -4e-153)
           t_2
           (if (<= t -2.05e-296)
             t_1
             (if (<= t 5e-230) t_2 (if (<= t 3.2e+65) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.4e+91) {
		tmp = t_3;
	} else if (t <= -2.4e+41) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= -1.55e-79) {
		tmp = c * ((t * j) - (z * b));
	} else if (t <= -4e-153) {
		tmp = t_2;
	} else if (t <= -2.05e-296) {
		tmp = t_1;
	} else if (t <= 5e-230) {
		tmp = t_2;
	} else if (t <= 3.2e+65) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-5.4d+91)) then
        tmp = t_3
    else if (t <= (-2.4d+41)) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= (-1.55d-79)) then
        tmp = c * ((t * j) - (z * b))
    else if (t <= (-4d-153)) then
        tmp = t_2
    else if (t <= (-2.05d-296)) then
        tmp = t_1
    else if (t <= 5d-230) then
        tmp = t_2
    else if (t <= 3.2d+65) then
        tmp = t_1
    else
        tmp = t_3
    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 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.4e+91) {
		tmp = t_3;
	} else if (t <= -2.4e+41) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= -1.55e-79) {
		tmp = c * ((t * j) - (z * b));
	} else if (t <= -4e-153) {
		tmp = t_2;
	} else if (t <= -2.05e-296) {
		tmp = t_1;
	} else if (t <= 5e-230) {
		tmp = t_2;
	} else if (t <= 3.2e+65) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -5.4e+91:
		tmp = t_3
	elif t <= -2.4e+41:
		tmp = i * ((a * b) - (y * j))
	elif t <= -1.55e-79:
		tmp = c * ((t * j) - (z * b))
	elif t <= -4e-153:
		tmp = t_2
	elif t <= -2.05e-296:
		tmp = t_1
	elif t <= 5e-230:
		tmp = t_2
	elif t <= 3.2e+65:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5.4e+91)
		tmp = t_3;
	elseif (t <= -2.4e+41)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= -1.55e-79)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (t <= -4e-153)
		tmp = t_2;
	elseif (t <= -2.05e-296)
		tmp = t_1;
	elseif (t <= 5e-230)
		tmp = t_2;
	elseif (t <= 3.2e+65)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -5.4e+91)
		tmp = t_3;
	elseif (t <= -2.4e+41)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= -1.55e-79)
		tmp = c * ((t * j) - (z * b));
	elseif (t <= -4e-153)
		tmp = t_2;
	elseif (t <= -2.05e-296)
		tmp = t_1;
	elseif (t <= 5e-230)
		tmp = t_2;
	elseif (t <= 3.2e+65)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+91], t$95$3, If[LessEqual[t, -2.4e+41], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.55e-79], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e-153], t$95$2, If[LessEqual[t, -2.05e-296], t$95$1, If[LessEqual[t, 5e-230], t$95$2, If[LessEqual[t, 3.2e+65], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.4e91 or 3.20000000000000007e65 < t

   1. Initial program 70.2%

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

      1. cancel-sign-sub 70.2%

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

      2. cancel-sign-sub-inv 70.2%

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

      3. *-commutative 70.2%

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

      4. *-commutative 70.2%

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

      5. remove-double-neg 70.2%

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

      6. *-commutative 70.2%

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

      7. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in t around inf 69.5%

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

      1. *-commutative 69.5%

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

      2. mul-1-neg 69.5%

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

      3. unsub-neg 69.5%

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

   6. Simplified 69.5%

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

   if -5.4e91 < t < -2.4000000000000002e41

   1. Initial program 70.5%

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

      1. cancel-sign-sub 70.5%

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

      2. cancel-sign-sub-inv 70.5%

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

      3. *-commutative 70.5%

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

      4. *-commutative 70.5%

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

      5. remove-double-neg 70.5%

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

      6. *-commutative 70.5%

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

      7. *-commutative 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in i around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. sub-neg 70.9%

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

      3. mul-1-neg 70.9%

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

      4. remove-double-neg 70.9%

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

      5. +-commutative 70.9%

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

      6. mul-1-neg 70.9%

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

      7. unsub-neg 70.9%

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

      8. *-commutative 70.9%

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

   6. Simplified 70.9%

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

   if -2.4000000000000002e41 < t < -1.55e-79

   1. Initial program 76.5%

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

      1. cancel-sign-sub 76.5%

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

      2. cancel-sign-sub-inv 76.5%

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

      3. *-commutative 76.5%

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

      4. *-commutative 76.5%

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

      5. remove-double-neg 76.5%

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

      6. *-commutative 76.5%

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

      7. *-commutative 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in c around inf 62.6%

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

   if -1.55e-79 < t < -4.00000000000000016e-153 or -2.04999999999999997e-296 < t < 5.00000000000000035e-230

   1. Initial program 85.9%

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

      1. cancel-sign-sub 85.9%

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

      2. cancel-sign-sub-inv 85.9%

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

      3. *-commutative 85.9%

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

      4. *-commutative 85.9%

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

      5. remove-double-neg 85.9%

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

      6. *-commutative 85.9%

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

      7. *-commutative 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in y around inf 65.4%

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

      1. +-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

   6. Simplified 65.4%

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

   if -4.00000000000000016e-153 < t < -2.04999999999999997e-296 or 5.00000000000000035e-230 < t < 3.20000000000000007e65

   1. Initial program 79.9%

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

      1. cancel-sign-sub 79.9%

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

      2. cancel-sign-sub-inv 79.9%

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

      3. *-commutative 79.9%

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

      4. *-commutative 79.9%

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

      5. remove-double-neg 79.9%

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

      6. *-commutative 79.9%

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

      7. *-commutative 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in b around inf 60.7%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 4: 60.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7.4 \cdot 10^{+158}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -7.4e+158)
   (* i (- (* a b) (* y j)))
   (if (<= j 9e+77)
     (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
     (* c (- (* t 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 (j <= -7.4e+158) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 9e+77) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = c * ((t * 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 (j <= (-7.4d+158)) then
        tmp = i * ((a * b) - (y * j))
    else if (j <= 9d+77) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = c * ((t * 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 (j <= -7.4e+158) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 9e+77) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -7.4e+158:
		tmp = i * ((a * b) - (y * j))
	elif j <= 9e+77:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -7.4e+158)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (j <= 9e+77)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(c * Float64(Float64(t * 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 (j <= -7.4e+158)
		tmp = i * ((a * b) - (y * j));
	elseif (j <= 9e+77)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -7.4e+158], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e+77], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.40000000000000021e158

   1. Initial program 84.0%

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

      1. cancel-sign-sub 84.0%

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

      2. cancel-sign-sub-inv 84.0%

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

      3. *-commutative 84.0%

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

      4. *-commutative 84.0%

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

      5. remove-double-neg 84.0%

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

      6. *-commutative 84.0%

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

      7. *-commutative 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in i around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. sub-neg 65.9%

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

      3. mul-1-neg 65.9%

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

      4. remove-double-neg 65.9%

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

      5. +-commutative 65.9%

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

      6. mul-1-neg 65.9%

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

      7. unsub-neg 65.9%

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

      8. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   if -7.40000000000000021e158 < j < 9.00000000000000049e77

   1. Initial program 77.7%

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

      1. cancel-sign-sub 77.7%

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

      2. cancel-sign-sub-inv 77.7%

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

      3. *-commutative 77.7%

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

      4. *-commutative 77.7%

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

      5. remove-double-neg 77.7%

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

      6. *-commutative 77.7%

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

      7. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in j around 0 71.5%

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

      1. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   if 9.00000000000000049e77 < j

   1. Initial program 68.5%

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

      1. cancel-sign-sub 68.5%

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

      2. cancel-sign-sub-inv 68.5%

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

      3. *-commutative 68.5%

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

      4. *-commutative 68.5%

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

      5. remove-double-neg 68.5%

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

      6. *-commutative 68.5%

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

      7. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in c around inf 60.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.4 \cdot 10^{+158}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 5: 51.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+169} \lor \neg \left(a \leq -1 \cdot 10^{+129}\right) \land \left(a \leq -600000000 \lor \neg \left(a \leq 2.6 \cdot 10^{-23} \lor \neg \left(a \leq 2.3 \cdot 10^{+114}\right) \land a \leq 5.2 \cdot 10^{+142}\right)\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -8.2e+169)
         (and (not (<= a -1e+129))
              (or (<= a -600000000.0)
                  (not
                   (or (<= a 2.6e-23)
                       (and (not (<= a 2.3e+114)) (<= a 5.2e+142)))))))
   (* a (- (* b i) (* x t)))
   (* c (- (* t 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 ((a <= -8.2e+169) || (!(a <= -1e+129) && ((a <= -600000000.0) || !((a <= 2.6e-23) || (!(a <= 2.3e+114) && (a <= 5.2e+142)))))) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = c * ((t * 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 ((a <= (-8.2d+169)) .or. (.not. (a <= (-1d+129))) .and. (a <= (-600000000.0d0)) .or. (.not. (a <= 2.6d-23) .or. (.not. (a <= 2.3d+114)) .and. (a <= 5.2d+142))) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = c * ((t * 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 ((a <= -8.2e+169) || (!(a <= -1e+129) && ((a <= -600000000.0) || !((a <= 2.6e-23) || (!(a <= 2.3e+114) && (a <= 5.2e+142)))))) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -8.2e+169) or (not (a <= -1e+129) and ((a <= -600000000.0) or not ((a <= 2.6e-23) or (not (a <= 2.3e+114) and (a <= 5.2e+142))))):
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -8.2e+169) || (!(a <= -1e+129) && ((a <= -600000000.0) || !((a <= 2.6e-23) || (!(a <= 2.3e+114) && (a <= 5.2e+142))))))
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(c * Float64(Float64(t * 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 ((a <= -8.2e+169) || (~((a <= -1e+129)) && ((a <= -600000000.0) || ~(((a <= 2.6e-23) || (~((a <= 2.3e+114)) && (a <= 5.2e+142)))))))
		tmp = a * ((b * i) - (x * t));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -8.2e+169], And[N[Not[LessEqual[a, -1e+129]], $MachinePrecision], Or[LessEqual[a, -600000000.0], N[Not[Or[LessEqual[a, 2.6e-23], And[N[Not[LessEqual[a, 2.3e+114]], $MachinePrecision], LessEqual[a, 5.2e+142]]]], $MachinePrecision]]]], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.2000000000000006e169 or -1e129 < a < -6e8 or 2.6e-23 < a < 2.3e114 or 5.20000000000000043e142 < a

   1. Initial program 68.4%

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

      1. cancel-sign-sub 68.4%

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

      2. cancel-sign-sub-inv 68.4%

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

      3. *-commutative 68.4%

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

      4. *-commutative 68.4%

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

      5. remove-double-neg 68.4%

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

      6. *-commutative 68.4%

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

      7. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in a around inf 65.9%

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

      1. associate-*r* 65.9%

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

      2. neg-mul-1 65.9%

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

      3. cancel-sign-sub 65.9%

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

      4. +-commutative 65.9%

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

      5. mul-1-neg 65.9%

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

      6. unsub-neg 65.9%

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

      7. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   if -8.2000000000000006e169 < a < -1e129 or -6e8 < a < 2.6e-23 or 2.3e114 < a < 5.20000000000000043e142

   1. Initial program 82.6%

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

      1. cancel-sign-sub 82.6%

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

      2. cancel-sign-sub-inv 82.6%

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

      3. *-commutative 82.6%

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

      4. *-commutative 82.6%

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

      5. remove-double-neg 82.6%

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

      6. *-commutative 82.6%

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

      7. *-commutative 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in c around inf 56.1%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+169} \lor \neg \left(a \leq -1 \cdot 10^{+129}\right) \land \left(a \leq -600000000 \lor \neg \left(a \leq 2.6 \cdot 10^{-23} \lor \neg \left(a \leq 2.3 \cdot 10^{+114}\right) \land a \leq 5.2 \cdot 10^{+142}\right)\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6: 50.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.7 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b))))
        (t_2 (* i (- (* a b) (* y j))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -5.7e+91)
     t_3
     (if (<= t -1.2e+40)
       t_2
       (if (<= t -2.9e-77)
         t_1
         (if (<= t -8.6e-148)
           (* y (- (* x z) (* i j)))
           (if (<= t 1.9e-143) t_2 (if (<= t 1.3e+46) t_1 t_3))))))))

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 * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.7e+91) {
		tmp = t_3;
	} else if (t <= -1.2e+40) {
		tmp = t_2;
	} else if (t <= -2.9e-77) {
		tmp = t_1;
	} else if (t <= -8.6e-148) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 1.9e-143) {
		tmp = t_2;
	} else if (t <= 1.3e+46) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-5.7d+91)) then
        tmp = t_3
    else if (t <= (-1.2d+40)) then
        tmp = t_2
    else if (t <= (-2.9d-77)) then
        tmp = t_1
    else if (t <= (-8.6d-148)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 1.9d-143) then
        tmp = t_2
    else if (t <= 1.3d+46) then
        tmp = t_1
    else
        tmp = t_3
    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 * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.7e+91) {
		tmp = t_3;
	} else if (t <= -1.2e+40) {
		tmp = t_2;
	} else if (t <= -2.9e-77) {
		tmp = t_1;
	} else if (t <= -8.6e-148) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 1.9e-143) {
		tmp = t_2;
	} else if (t <= 1.3e+46) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -5.7e+91:
		tmp = t_3
	elif t <= -1.2e+40:
		tmp = t_2
	elif t <= -2.9e-77:
		tmp = t_1
	elif t <= -8.6e-148:
		tmp = y * ((x * z) - (i * j))
	elif t <= 1.9e-143:
		tmp = t_2
	elif t <= 1.3e+46:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5.7e+91)
		tmp = t_3;
	elseif (t <= -1.2e+40)
		tmp = t_2;
	elseif (t <= -2.9e-77)
		tmp = t_1;
	elseif (t <= -8.6e-148)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 1.9e-143)
		tmp = t_2;
	elseif (t <= 1.3e+46)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -5.7e+91)
		tmp = t_3;
	elseif (t <= -1.2e+40)
		tmp = t_2;
	elseif (t <= -2.9e-77)
		tmp = t_1;
	elseif (t <= -8.6e-148)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 1.9e-143)
		tmp = t_2;
	elseif (t <= 1.3e+46)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.7e+91], t$95$3, If[LessEqual[t, -1.2e+40], t$95$2, If[LessEqual[t, -2.9e-77], t$95$1, If[LessEqual[t, -8.6e-148], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-143], t$95$2, If[LessEqual[t, 1.3e+46], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.69999999999999964e91 or 1.30000000000000007e46 < t

   1. Initial program 69.1%

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

      1. cancel-sign-sub 69.1%

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

      2. cancel-sign-sub-inv 69.1%

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

      3. *-commutative 69.1%

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

      4. *-commutative 69.1%

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

      5. remove-double-neg 69.1%

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

      6. *-commutative 69.1%

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

      7. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in t around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. mul-1-neg 68.5%

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

      3. unsub-neg 68.5%

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

   6. Simplified 68.5%

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

   if -5.69999999999999964e91 < t < -1.2e40 or -8.5999999999999997e-148 < t < 1.89999999999999991e-143

   1. Initial program 80.1%

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

      1. cancel-sign-sub 80.1%

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

      2. cancel-sign-sub-inv 80.1%

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

      3. *-commutative 80.1%

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

      4. *-commutative 80.1%

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

      5. remove-double-neg 80.1%

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

      6. *-commutative 80.1%

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

      7. *-commutative 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in i around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. sub-neg 59.1%

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

      3. mul-1-neg 59.1%

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

      4. remove-double-neg 59.1%

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

      5. +-commutative 59.1%

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

      6. mul-1-neg 59.1%

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

      7. unsub-neg 59.1%

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

      8. *-commutative 59.1%

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

   6. Simplified 59.1%

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

   if -1.2e40 < t < -2.8999999999999999e-77 or 1.89999999999999991e-143 < t < 1.30000000000000007e46

   1. Initial program 80.8%

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

      1. cancel-sign-sub 80.8%

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

      2. cancel-sign-sub-inv 80.8%

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

      3. *-commutative 80.8%

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

      4. *-commutative 80.8%

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

      5. remove-double-neg 80.8%

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

      6. *-commutative 80.8%

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

      7. *-commutative 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in c around inf 57.8%

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

   if -2.8999999999999999e-77 < t < -8.5999999999999997e-148

   1. Initial program 83.8%

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

      1. cancel-sign-sub 83.8%

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

      2. cancel-sign-sub-inv 83.8%

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

      3. *-commutative 83.8%

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

      4. *-commutative 83.8%

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

      5. remove-double-neg 83.8%

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

      6. *-commutative 83.8%

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

      7. *-commutative 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in y around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. mul-1-neg 61.7%

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

      3. unsub-neg 61.7%

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

   6. Simplified 61.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-143}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 7: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.75 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -2.25 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-302}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))) (t_2 (* y (* i (- j)))))
   (if (<= j -1e+158)
     t_2
     (if (<= j -1e+27)
       t_1
       (if (<= j -2.75e-43)
         (* b (* a i))
         (if (<= j -2.25e-231)
           t_1
           (if (<= j 7.8e-302)
             (* a (* t (- x)))
             (if (<= j 3.5e-149)
               t_1
               (if (<= j 1.3e+29) (* a (* b i)) 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 = y * (i * -j);
	double tmp;
	if (j <= -1e+158) {
		tmp = t_2;
	} else if (j <= -1e+27) {
		tmp = t_1;
	} else if (j <= -2.75e-43) {
		tmp = b * (a * i);
	} else if (j <= -2.25e-231) {
		tmp = t_1;
	} else if (j <= 7.8e-302) {
		tmp = a * (t * -x);
	} else if (j <= 3.5e-149) {
		tmp = t_1;
	} else if (j <= 1.3e+29) {
		tmp = a * (b * i);
	} 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 = y * (i * -j)
    if (j <= (-1d+158)) then
        tmp = t_2
    else if (j <= (-1d+27)) then
        tmp = t_1
    else if (j <= (-2.75d-43)) then
        tmp = b * (a * i)
    else if (j <= (-2.25d-231)) then
        tmp = t_1
    else if (j <= 7.8d-302) then
        tmp = a * (t * -x)
    else if (j <= 3.5d-149) then
        tmp = t_1
    else if (j <= 1.3d+29) then
        tmp = a * (b * i)
    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 = y * (i * -j);
	double tmp;
	if (j <= -1e+158) {
		tmp = t_2;
	} else if (j <= -1e+27) {
		tmp = t_1;
	} else if (j <= -2.75e-43) {
		tmp = b * (a * i);
	} else if (j <= -2.25e-231) {
		tmp = t_1;
	} else if (j <= 7.8e-302) {
		tmp = a * (t * -x);
	} else if (j <= 3.5e-149) {
		tmp = t_1;
	} else if (j <= 1.3e+29) {
		tmp = a * (b * i);
	} 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 = y * (i * -j)
	tmp = 0
	if j <= -1e+158:
		tmp = t_2
	elif j <= -1e+27:
		tmp = t_1
	elif j <= -2.75e-43:
		tmp = b * (a * i)
	elif j <= -2.25e-231:
		tmp = t_1
	elif j <= 7.8e-302:
		tmp = a * (t * -x)
	elif j <= 3.5e-149:
		tmp = t_1
	elif j <= 1.3e+29:
		tmp = a * (b * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	t_2 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (j <= -1e+158)
		tmp = t_2;
	elseif (j <= -1e+27)
		tmp = t_1;
	elseif (j <= -2.75e-43)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= -2.25e-231)
		tmp = t_1;
	elseif (j <= 7.8e-302)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (j <= 3.5e-149)
		tmp = t_1;
	elseif (j <= 1.3e+29)
		tmp = Float64(a * Float64(b * i));
	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 = y * (i * -j);
	tmp = 0.0;
	if (j <= -1e+158)
		tmp = t_2;
	elseif (j <= -1e+27)
		tmp = t_1;
	elseif (j <= -2.75e-43)
		tmp = b * (a * i);
	elseif (j <= -2.25e-231)
		tmp = t_1;
	elseif (j <= 7.8e-302)
		tmp = a * (t * -x);
	elseif (j <= 3.5e-149)
		tmp = t_1;
	elseif (j <= 1.3e+29)
		tmp = a * (b * i);
	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[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1e+158], t$95$2, If[LessEqual[j, -1e+27], t$95$1, If[LessEqual[j, -2.75e-43], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.25e-231], t$95$1, If[LessEqual[j, 7.8e-302], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e-149], t$95$1, If[LessEqual[j, 1.3e+29], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -9.99999999999999953e157 or 1.3e29 < j

   1. Initial program 73.9%

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

      1. cancel-sign-sub 73.9%

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

      2. cancel-sign-sub-inv 73.9%

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

      3. *-commutative 73.9%

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

      4. *-commutative 73.9%

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

      5. remove-double-neg 73.9%

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

      6. *-commutative 73.9%

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

      7. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in i around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. sub-neg 47.1%

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

      3. mul-1-neg 47.1%

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

      4. remove-double-neg 47.1%

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

      5. +-commutative 47.1%

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

      6. mul-1-neg 47.1%

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

      7. unsub-neg 47.1%

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

      8. *-commutative 47.1%

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

   6. Simplified 47.1%

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

   7. Taylor expanded in b around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. associate-*r* 41.7%

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

      3. *-commutative 41.7%

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

      4. associate-*r* 44.8%

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

      5. distribute-rgt-neg-in 44.8%

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

      6. distribute-lft-neg-in 44.8%

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

      7. *-commutative 44.8%

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

   9. Simplified 44.8%

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

   if -9.99999999999999953e157 < j < -1e27 or -2.75000000000000006e-43 < j < -2.2499999999999999e-231 or 7.7999999999999998e-302 < j < 3.5e-149

   1. Initial program 76.3%

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

      1. cancel-sign-sub 76.3%

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

      2. cancel-sign-sub-inv 76.3%

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

      3. *-commutative 76.3%

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

      4. *-commutative 76.3%

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

      5. remove-double-neg 76.3%

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

      6. *-commutative 76.3%

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

      7. *-commutative 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in z around inf 57.2%

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

   5. Taylor expanded in y around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. distribute-lft-neg-in 39.4%

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

   7. Simplified 39.4%

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

   if -1e27 < j < -2.75000000000000006e-43

   1. Initial program 92.5%

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

      1. cancel-sign-sub 92.5%

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

      2. cancel-sign-sub-inv 92.5%

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

      3. *-commutative 92.5%

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

      4. *-commutative 92.5%

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

      5. remove-double-neg 92.5%

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

      6. *-commutative 92.5%

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

      7. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around inf 52.0%

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

      1. associate-*r* 52.0%

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

      2. neg-mul-1 52.0%

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

      3. cancel-sign-sub 52.0%

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

      4. +-commutative 52.0%

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

      5. mul-1-neg 52.0%

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

      6. unsub-neg 52.0%

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

      7. *-commutative 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in b around inf 37.4%

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

      1. associate-*r* 44.2%

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

      2. *-commutative 44.2%

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

   9. Simplified 44.2%

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

   if -2.2499999999999999e-231 < j < 7.7999999999999998e-302

   1. Initial program 72.3%

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

      1. cancel-sign-sub 72.3%

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

      2. cancel-sign-sub-inv 72.3%

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

      3. *-commutative 72.3%

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

      4. *-commutative 72.3%

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

      5. remove-double-neg 72.3%

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

      6. *-commutative 72.3%

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

      7. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in a around inf 70.0%

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

      1. associate-*r* 70.0%

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

      2. neg-mul-1 70.0%

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

      3. cancel-sign-sub 70.0%

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

      4. +-commutative 70.0%

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

      5. mul-1-neg 70.0%

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

      6. unsub-neg 70.0%

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

      7. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in b around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. distribute-lft-neg-out 58.5%

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

      3. *-commutative 58.5%

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

   9. Simplified 58.5%

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

   if 3.5e-149 < j < 1.3e29

   1. Initial program 80.5%

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

      1. cancel-sign-sub 80.5%

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

      2. cancel-sign-sub-inv 80.5%

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

      3. *-commutative 80.5%

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

      4. *-commutative 80.5%

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

      5. remove-double-neg 80.5%

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

      6. *-commutative 80.5%

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

      7. *-commutative 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in a around inf 63.7%

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

      1. associate-*r* 63.7%

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

      2. neg-mul-1 63.7%

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

      3. cancel-sign-sub 63.7%

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

      4. +-commutative 63.7%

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

      5. mul-1-neg 63.7%

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

      6. unsub-neg 63.7%

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

      7. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in b around -inf 51.4%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq -2.75 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -2.25 \cdot 10^{-231}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-302}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 8: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -8.2 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-303}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))) (t_2 (* i (* y (- j)))))
   (if (<= j -8.2e+156)
     t_2
     (if (<= j -1.1e+27)
       t_1
       (if (<= j -1.5e-43)
         (* b (* a i))
         (if (<= j -3e-233)
           t_1
           (if (<= j 1.75e-303)
             (* a (* t (- x)))
             (if (<= j 1.3e-149)
               t_1
               (if (<= j 7.2e+29) (* a (* b i)) 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 = i * (y * -j);
	double tmp;
	if (j <= -8.2e+156) {
		tmp = t_2;
	} else if (j <= -1.1e+27) {
		tmp = t_1;
	} else if (j <= -1.5e-43) {
		tmp = b * (a * i);
	} else if (j <= -3e-233) {
		tmp = t_1;
	} else if (j <= 1.75e-303) {
		tmp = a * (t * -x);
	} else if (j <= 1.3e-149) {
		tmp = t_1;
	} else if (j <= 7.2e+29) {
		tmp = a * (b * i);
	} 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 = i * (y * -j)
    if (j <= (-8.2d+156)) then
        tmp = t_2
    else if (j <= (-1.1d+27)) then
        tmp = t_1
    else if (j <= (-1.5d-43)) then
        tmp = b * (a * i)
    else if (j <= (-3d-233)) then
        tmp = t_1
    else if (j <= 1.75d-303) then
        tmp = a * (t * -x)
    else if (j <= 1.3d-149) then
        tmp = t_1
    else if (j <= 7.2d+29) then
        tmp = a * (b * i)
    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 = i * (y * -j);
	double tmp;
	if (j <= -8.2e+156) {
		tmp = t_2;
	} else if (j <= -1.1e+27) {
		tmp = t_1;
	} else if (j <= -1.5e-43) {
		tmp = b * (a * i);
	} else if (j <= -3e-233) {
		tmp = t_1;
	} else if (j <= 1.75e-303) {
		tmp = a * (t * -x);
	} else if (j <= 1.3e-149) {
		tmp = t_1;
	} else if (j <= 7.2e+29) {
		tmp = a * (b * i);
	} 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 = i * (y * -j)
	tmp = 0
	if j <= -8.2e+156:
		tmp = t_2
	elif j <= -1.1e+27:
		tmp = t_1
	elif j <= -1.5e-43:
		tmp = b * (a * i)
	elif j <= -3e-233:
		tmp = t_1
	elif j <= 1.75e-303:
		tmp = a * (t * -x)
	elif j <= 1.3e-149:
		tmp = t_1
	elif j <= 7.2e+29:
		tmp = a * (b * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (j <= -8.2e+156)
		tmp = t_2;
	elseif (j <= -1.1e+27)
		tmp = t_1;
	elseif (j <= -1.5e-43)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= -3e-233)
		tmp = t_1;
	elseif (j <= 1.75e-303)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (j <= 1.3e-149)
		tmp = t_1;
	elseif (j <= 7.2e+29)
		tmp = Float64(a * Float64(b * i));
	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 = i * (y * -j);
	tmp = 0.0;
	if (j <= -8.2e+156)
		tmp = t_2;
	elseif (j <= -1.1e+27)
		tmp = t_1;
	elseif (j <= -1.5e-43)
		tmp = b * (a * i);
	elseif (j <= -3e-233)
		tmp = t_1;
	elseif (j <= 1.75e-303)
		tmp = a * (t * -x);
	elseif (j <= 1.3e-149)
		tmp = t_1;
	elseif (j <= 7.2e+29)
		tmp = a * (b * i);
	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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.2e+156], t$95$2, If[LessEqual[j, -1.1e+27], t$95$1, If[LessEqual[j, -1.5e-43], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3e-233], t$95$1, If[LessEqual[j, 1.75e-303], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.3e-149], t$95$1, If[LessEqual[j, 7.2e+29], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.2000000000000003e156 or 7.19999999999999952e29 < j

   1. Initial program 73.9%

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

      1. cancel-sign-sub 73.9%

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

      2. cancel-sign-sub-inv 73.9%

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

      3. *-commutative 73.9%

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

      4. *-commutative 73.9%

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

      5. remove-double-neg 73.9%

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

      6. *-commutative 73.9%

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

      7. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in i around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. sub-neg 47.1%

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

      3. mul-1-neg 47.1%

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

      4. remove-double-neg 47.1%

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

      5. +-commutative 47.1%

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

      6. mul-1-neg 47.1%

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

      7. unsub-neg 47.1%

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

      8. *-commutative 47.1%

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

   6. Simplified 47.1%

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

   7. Taylor expanded in b around 0 46.9%

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

      1. associate-*r* 46.9%

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

      2. neg-mul-1 46.9%

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

   9. Simplified 46.9%

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

   if -8.2000000000000003e156 < j < -1.0999999999999999e27 or -1.50000000000000002e-43 < j < -2.99999999999999999e-233 or 1.75e-303 < j < 1.29999999999999999e-149

   1. Initial program 76.3%

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

      1. cancel-sign-sub 76.3%

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

      2. cancel-sign-sub-inv 76.3%

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

      3. *-commutative 76.3%

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

      4. *-commutative 76.3%

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

      5. remove-double-neg 76.3%

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

      6. *-commutative 76.3%

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

      7. *-commutative 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in z around inf 57.2%

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

   5. Taylor expanded in y around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. distribute-lft-neg-in 39.4%

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

   7. Simplified 39.4%

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

   if -1.0999999999999999e27 < j < -1.50000000000000002e-43

   1. Initial program 92.5%

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

      1. cancel-sign-sub 92.5%

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

      2. cancel-sign-sub-inv 92.5%

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

      3. *-commutative 92.5%

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

      4. *-commutative 92.5%

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

      5. remove-double-neg 92.5%

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

      6. *-commutative 92.5%

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

      7. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around inf 52.0%

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

      1. associate-*r* 52.0%

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

      2. neg-mul-1 52.0%

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

      3. cancel-sign-sub 52.0%

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

      4. +-commutative 52.0%

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

      5. mul-1-neg 52.0%

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

      6. unsub-neg 52.0%

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

      7. *-commutative 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in b around inf 37.4%

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

      1. associate-*r* 44.2%

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

      2. *-commutative 44.2%

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

   9. Simplified 44.2%

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

   if -2.99999999999999999e-233 < j < 1.75e-303

   1. Initial program 72.3%

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

      1. cancel-sign-sub 72.3%

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

      2. cancel-sign-sub-inv 72.3%

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

      3. *-commutative 72.3%

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

      4. *-commutative 72.3%

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

      5. remove-double-neg 72.3%

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

      6. *-commutative 72.3%

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

      7. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in a around inf 70.0%

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

      1. associate-*r* 70.0%

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

      2. neg-mul-1 70.0%

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

      3. cancel-sign-sub 70.0%

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

      4. +-commutative 70.0%

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

      5. mul-1-neg 70.0%

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

      6. unsub-neg 70.0%

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

      7. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in b around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. distribute-lft-neg-out 58.5%

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

      3. *-commutative 58.5%

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

   9. Simplified 58.5%

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

   if 1.29999999999999999e-149 < j < 7.19999999999999952e29

   1. Initial program 80.5%

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

      1. cancel-sign-sub 80.5%

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

      2. cancel-sign-sub-inv 80.5%

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

      3. *-commutative 80.5%

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

      4. *-commutative 80.5%

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

      5. remove-double-neg 80.5%

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

      6. *-commutative 80.5%

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

      7. *-commutative 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in a around inf 63.7%

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

      1. associate-*r* 63.7%

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

      2. neg-mul-1 63.7%

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

      3. cancel-sign-sub 63.7%

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

      4. +-commutative 63.7%

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

      5. mul-1-neg 63.7%

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

      6. unsub-neg 63.7%

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

      7. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in b around -inf 51.4%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.2 \cdot 10^{+156}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-303}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 9: 50.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b))))
        (t_2 (* i (- (* a b) (* y j))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -4.8e+91)
     t_3
     (if (<= t -1.35e+41)
       t_2
       (if (<= t -1.55e-79)
         t_1
         (if (<= t 2e-147) t_2 (if (<= t 3.2e+45) t_1 t_3)))))))

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 * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.8e+91) {
		tmp = t_3;
	} else if (t <= -1.35e+41) {
		tmp = t_2;
	} else if (t <= -1.55e-79) {
		tmp = t_1;
	} else if (t <= 2e-147) {
		tmp = t_2;
	} else if (t <= 3.2e+45) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-4.8d+91)) then
        tmp = t_3
    else if (t <= (-1.35d+41)) then
        tmp = t_2
    else if (t <= (-1.55d-79)) then
        tmp = t_1
    else if (t <= 2d-147) then
        tmp = t_2
    else if (t <= 3.2d+45) then
        tmp = t_1
    else
        tmp = t_3
    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 * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.8e+91) {
		tmp = t_3;
	} else if (t <= -1.35e+41) {
		tmp = t_2;
	} else if (t <= -1.55e-79) {
		tmp = t_1;
	} else if (t <= 2e-147) {
		tmp = t_2;
	} else if (t <= 3.2e+45) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -4.8e+91:
		tmp = t_3
	elif t <= -1.35e+41:
		tmp = t_2
	elif t <= -1.55e-79:
		tmp = t_1
	elif t <= 2e-147:
		tmp = t_2
	elif t <= 3.2e+45:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4.8e+91)
		tmp = t_3;
	elseif (t <= -1.35e+41)
		tmp = t_2;
	elseif (t <= -1.55e-79)
		tmp = t_1;
	elseif (t <= 2e-147)
		tmp = t_2;
	elseif (t <= 3.2e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -4.8e+91)
		tmp = t_3;
	elseif (t <= -1.35e+41)
		tmp = t_2;
	elseif (t <= -1.55e-79)
		tmp = t_1;
	elseif (t <= 2e-147)
		tmp = t_2;
	elseif (t <= 3.2e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+91], t$95$3, If[LessEqual[t, -1.35e+41], t$95$2, If[LessEqual[t, -1.55e-79], t$95$1, If[LessEqual[t, 2e-147], t$95$2, If[LessEqual[t, 3.2e+45], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999966e91 or 3.2000000000000003e45 < t

   1. Initial program 69.1%

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

      1. cancel-sign-sub 69.1%

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

      2. cancel-sign-sub-inv 69.1%

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

      3. *-commutative 69.1%

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

      4. *-commutative 69.1%

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

      5. remove-double-neg 69.1%

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

      6. *-commutative 69.1%

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

      7. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in t around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. mul-1-neg 68.5%

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

      3. unsub-neg 68.5%

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

   6. Simplified 68.5%

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

   if -4.79999999999999966e91 < t < -1.35e41 or -1.55e-79 < t < 1.9999999999999999e-147

   1. Initial program 80.7%

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

      1. cancel-sign-sub 80.7%

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

      2. cancel-sign-sub-inv 80.7%

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

      3. *-commutative 80.7%

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

      4. *-commutative 80.7%

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

      5. remove-double-neg 80.7%

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

      6. *-commutative 80.7%

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

      7. *-commutative 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in i around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. sub-neg 55.6%

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

      3. mul-1-neg 55.6%

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

      4. remove-double-neg 55.6%

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

      5. +-commutative 55.6%

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

      6. mul-1-neg 55.6%

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

      7. unsub-neg 55.6%

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

      8. *-commutative 55.6%

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

   6. Simplified 55.6%

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

   if -1.35e41 < t < -1.55e-79 or 1.9999999999999999e-147 < t < 3.2000000000000003e45

   1. Initial program 80.8%

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

      1. cancel-sign-sub 80.8%

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

      2. cancel-sign-sub-inv 80.8%

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

      3. *-commutative 80.8%

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

      4. *-commutative 80.8%

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

      5. remove-double-neg 80.8%

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

      6. *-commutative 80.8%

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

      7. *-commutative 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in c around inf 57.8%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+41}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-147}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+45}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 10: 52.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-159}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-107}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 0.0073:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -2.0)
     t_1
     (if (<= z 2.5e-159)
       (* i (- (* a b) (* y j)))
       (if (<= z 9.8e-107)
         (* c (- (* t j) (* z b)))
         (if (<= z 0.0073)
           (* a (- (* b i) (* x t)))
           (if (<= z 1.55e+44) (* t (- (* c j) (* x a))) 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 <= -2.0) {
		tmp = t_1;
	} else if (z <= 2.5e-159) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 9.8e-107) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= 0.0073) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.55e+44) {
		tmp = t * ((c * j) - (x * a));
	} 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 <= (-2.0d0)) then
        tmp = t_1
    else if (z <= 2.5d-159) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 9.8d-107) then
        tmp = c * ((t * j) - (z * b))
    else if (z <= 0.0073d0) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 1.55d+44) then
        tmp = t * ((c * j) - (x * a))
    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 <= -2.0) {
		tmp = t_1;
	} else if (z <= 2.5e-159) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 9.8e-107) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= 0.0073) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.55e+44) {
		tmp = t * ((c * j) - (x * a));
	} 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 <= -2.0:
		tmp = t_1
	elif z <= 2.5e-159:
		tmp = i * ((a * b) - (y * j))
	elif z <= 9.8e-107:
		tmp = c * ((t * j) - (z * b))
	elif z <= 0.0073:
		tmp = a * ((b * i) - (x * t))
	elif z <= 1.55e+44:
		tmp = t * ((c * j) - (x * a))
	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 <= -2.0)
		tmp = t_1;
	elseif (z <= 2.5e-159)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 9.8e-107)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (z <= 0.0073)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 1.55e+44)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	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 <= -2.0)
		tmp = t_1;
	elseif (z <= 2.5e-159)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 9.8e-107)
		tmp = c * ((t * j) - (z * b));
	elseif (z <= 0.0073)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 1.55e+44)
		tmp = t * ((c * j) - (x * a));
	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, -2.0], t$95$1, If[LessEqual[z, 2.5e-159], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e-107], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0073], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+44], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2 or 1.54999999999999998e44 < z

   1. Initial program 67.7%

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

      1. cancel-sign-sub 67.7%

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

      2. cancel-sign-sub-inv 67.7%

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

      3. *-commutative 67.7%

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

      4. *-commutative 67.7%

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

      5. remove-double-neg 67.7%

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

      6. *-commutative 67.7%

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

      7. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in z around inf 65.5%

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

   if -2 < z < 2.50000000000000016e-159

   1. Initial program 85.9%

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

      1. cancel-sign-sub 85.9%

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

      2. cancel-sign-sub-inv 85.9%

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

      3. *-commutative 85.9%

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

      4. *-commutative 85.9%

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

      5. remove-double-neg 85.9%

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

      6. *-commutative 85.9%

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

      7. *-commutative 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in i around inf 55.2%

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

      1. *-commutative 55.2%

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

      2. sub-neg 55.2%

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

      3. mul-1-neg 55.2%

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

      4. remove-double-neg 55.2%

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

      5. +-commutative 55.2%

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

      6. mul-1-neg 55.2%

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

      7. unsub-neg 55.2%

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

      8. *-commutative 55.2%

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

   6. Simplified 55.2%

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

   if 2.50000000000000016e-159 < z < 9.79999999999999959e-107

   1. Initial program 75.0%

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

      1. cancel-sign-sub 75.0%

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

      2. cancel-sign-sub-inv 75.0%

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

      3. *-commutative 75.0%

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

      4. *-commutative 75.0%

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

      5. remove-double-neg 75.0%

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

      6. *-commutative 75.0%

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

      7. *-commutative 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in c around inf 74.9%

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

   if 9.79999999999999959e-107 < z < 0.00730000000000000007

   1. Initial program 88.1%

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

      1. cancel-sign-sub 88.1%

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

      2. cancel-sign-sub-inv 88.1%

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

      3. *-commutative 88.1%

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

      4. *-commutative 88.1%

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

      5. remove-double-neg 88.1%

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

      6. *-commutative 88.1%

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

      7. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in a around inf 65.7%

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

      1. associate-*r* 65.7%

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

      2. neg-mul-1 65.7%

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

      3. cancel-sign-sub 65.7%

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

      4. +-commutative 65.7%

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

      5. mul-1-neg 65.7%

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

      6. unsub-neg 65.7%

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

      7. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   if 0.00730000000000000007 < z < 1.54999999999999998e44

   1. Initial program 66.5%

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

      1. cancel-sign-sub 66.5%

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

      2. cancel-sign-sub-inv 66.5%

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

      3. *-commutative 66.5%

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

      4. *-commutative 66.5%

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

      5. remove-double-neg 66.5%

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

      6. *-commutative 66.5%

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

      7. *-commutative 66.5%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in t around inf 88.8%

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

      1. *-commutative 88.8%

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

      2. mul-1-neg 88.8%

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

      3. unsub-neg 88.8%

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

   6. Simplified 88.8%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-159}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-107}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 0.0073:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 11: 49.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= j -2.4e+158)
     t_1
     (if (<= j 1.75e-146)
       (- (* x (- (* y z) (* t a))) (* c (* z b)))
       (if (<= j 4.2e+79) t_1 (* c (- (* t 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 t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (j <= -2.4e+158) {
		tmp = t_1;
	} else if (j <= 1.75e-146) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else if (j <= 4.2e+79) {
		tmp = t_1;
	} else {
		tmp = c * ((t * 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) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (j <= (-2.4d+158)) then
        tmp = t_1
    else if (j <= 1.75d-146) then
        tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
    else if (j <= 4.2d+79) then
        tmp = t_1
    else
        tmp = c * ((t * 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 t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (j <= -2.4e+158) {
		tmp = t_1;
	} else if (j <= 1.75e-146) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else if (j <= 4.2e+79) {
		tmp = t_1;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if j <= -2.4e+158:
		tmp = t_1
	elif j <= 1.75e-146:
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
	elif j <= 4.2e+79:
		tmp = t_1
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (j <= -2.4e+158)
		tmp = t_1;
	elseif (j <= 1.75e-146)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b)));
	elseif (j <= 4.2e+79)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (j <= -2.4e+158)
		tmp = t_1;
	elseif (j <= 1.75e-146)
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	elseif (j <= 4.2e+79)
		tmp = t_1;
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.4e+158], t$95$1, If[LessEqual[j, 1.75e-146], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.2e+79], t$95$1, N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.40000000000000008e158 or 1.7500000000000001e-146 < j < 4.20000000000000016e79

   1. Initial program 80.6%

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

      1. cancel-sign-sub 80.6%

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

      2. cancel-sign-sub-inv 80.6%

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

      3. *-commutative 80.6%

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

      4. *-commutative 80.6%

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

      5. remove-double-neg 80.6%

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

      6. *-commutative 80.6%

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

      7. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in i around inf 63.2%

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

      1. *-commutative 63.2%

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

      2. sub-neg 63.2%

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

      3. mul-1-neg 63.2%

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

      4. remove-double-neg 63.2%

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

      5. +-commutative 63.2%

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

      6. mul-1-neg 63.2%

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

      7. unsub-neg 63.2%

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

      8. *-commutative 63.2%

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

   6. Simplified 63.2%

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

   if -2.40000000000000008e158 < j < 1.7500000000000001e-146

   1. Initial program 77.8%

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

      1. cancel-sign-sub 77.8%

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

      2. cancel-sign-sub-inv 77.8%

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

      3. *-commutative 77.8%

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

      4. *-commutative 77.8%

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

      5. remove-double-neg 77.8%

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

      6. *-commutative 77.8%

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

      7. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in j around 0 74.0%

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

      1. *-commutative 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in c around inf 64.4%

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

   if 4.20000000000000016e79 < j

   1. Initial program 68.5%

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

      1. cancel-sign-sub 68.5%

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

      2. cancel-sign-sub-inv 68.5%

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

      3. *-commutative 68.5%

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

      4. *-commutative 68.5%

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

      5. remove-double-neg 68.5%

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

      6. *-commutative 68.5%

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

      7. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in c around inf 60.4%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+158}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 12: 39.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-292}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= c -4.8e-12)
     (* z (* b (- c)))
     (if (<= c -8.6e-171)
       t_1
       (if (<= c -5.6e-292)
         (* i (* y (- j)))
         (if (<= c 3e+110) t_1 (* (* z c) (- b))))))))

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 * ((b * i) - (x * t));
	double tmp;
	if (c <= -4.8e-12) {
		tmp = z * (b * -c);
	} else if (c <= -8.6e-171) {
		tmp = t_1;
	} else if (c <= -5.6e-292) {
		tmp = i * (y * -j);
	} else if (c <= 3e+110) {
		tmp = t_1;
	} else {
		tmp = (z * c) * -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) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (c <= (-4.8d-12)) then
        tmp = z * (b * -c)
    else if (c <= (-8.6d-171)) then
        tmp = t_1
    else if (c <= (-5.6d-292)) then
        tmp = i * (y * -j)
    else if (c <= 3d+110) then
        tmp = t_1
    else
        tmp = (z * c) * -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 t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (c <= -4.8e-12) {
		tmp = z * (b * -c);
	} else if (c <= -8.6e-171) {
		tmp = t_1;
	} else if (c <= -5.6e-292) {
		tmp = i * (y * -j);
	} else if (c <= 3e+110) {
		tmp = t_1;
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if c <= -4.8e-12:
		tmp = z * (b * -c)
	elif c <= -8.6e-171:
		tmp = t_1
	elif c <= -5.6e-292:
		tmp = i * (y * -j)
	elif c <= 3e+110:
		tmp = t_1
	else:
		tmp = (z * c) * -b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (c <= -4.8e-12)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (c <= -8.6e-171)
		tmp = t_1;
	elseif (c <= -5.6e-292)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 3e+110)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * c) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (c <= -4.8e-12)
		tmp = z * (b * -c);
	elseif (c <= -8.6e-171)
		tmp = t_1;
	elseif (c <= -5.6e-292)
		tmp = i * (y * -j);
	elseif (c <= 3e+110)
		tmp = t_1;
	else
		tmp = (z * c) * -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.8e-12], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.6e-171], t$95$1, If[LessEqual[c, -5.6e-292], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e+110], t$95$1, N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.79999999999999974e-12

   1. Initial program 68.0%

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

      1. cancel-sign-sub 68.0%

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

      2. cancel-sign-sub-inv 68.0%

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

      3. *-commutative 68.0%

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

      4. *-commutative 68.0%

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

      5. remove-double-neg 68.0%

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

      6. *-commutative 68.0%

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

      7. *-commutative 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in z around inf 56.7%

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

   5. Taylor expanded in y around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-rgt-neg-in 48.1%

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

   7. Simplified 48.1%

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

   if -4.79999999999999974e-12 < c < -8.6000000000000004e-171 or -5.6000000000000003e-292 < c < 3.00000000000000007e110

   1. Initial program 82.0%

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

      1. cancel-sign-sub 82.0%

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

      2. cancel-sign-sub-inv 82.0%

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

      3. *-commutative 82.0%

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

      4. *-commutative 82.0%

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

      5. remove-double-neg 82.0%

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

      6. *-commutative 82.0%

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

      7. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in a around inf 44.2%

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

      1. associate-*r* 44.2%

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

      2. neg-mul-1 44.2%

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

      3. cancel-sign-sub 44.2%

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

      4. +-commutative 44.2%

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

      5. mul-1-neg 44.2%

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

      6. unsub-neg 44.2%

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

      7. *-commutative 44.2%

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

   6. Simplified 44.2%

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

   if -8.6000000000000004e-171 < c < -5.6000000000000003e-292

   1. Initial program 90.9%

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

      1. cancel-sign-sub 90.9%

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

      2. cancel-sign-sub-inv 90.9%

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

      3. *-commutative 90.9%

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

      4. *-commutative 90.9%

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

      5. remove-double-neg 90.9%

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

      6. *-commutative 90.9%

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

      7. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in i around inf 54.2%

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

      1. *-commutative 54.2%

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

      2. sub-neg 54.2%

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

      3. mul-1-neg 54.2%

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

      4. remove-double-neg 54.2%

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

      5. +-commutative 54.2%

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

      6. mul-1-neg 54.2%

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

      7. unsub-neg 54.2%

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

      8. *-commutative 54.2%

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

   6. Simplified 54.2%

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

   7. Taylor expanded in b around 0 48.5%

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

      1. associate-*r* 48.5%

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

      2. neg-mul-1 48.5%

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

   9. Simplified 48.5%

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

   if 3.00000000000000007e110 < c

   1. Initial program 64.2%

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

      1. cancel-sign-sub 64.2%

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

      2. cancel-sign-sub-inv 64.2%

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

      3. *-commutative 64.2%

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

      4. *-commutative 64.2%

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

      5. remove-double-neg 64.2%

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

      6. *-commutative 64.2%

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

      7. *-commutative 64.2%

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

   3. Simplified 64.2%

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

   4. Taylor expanded in b around inf 50.4%

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

   5. Taylor expanded in a around 0 45.8%

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

      1. neg-mul-1 45.8%

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

      2. distribute-lft-neg-in 45.8%

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

      3. *-commutative 45.8%

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

   7. Simplified 45.8%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-171}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-292}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]

Alternative 13: 30.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.1 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* z (* b (- c)))))
   (if (<= c -5e-16)
     t_2
     (if (<= c -3.7e-199)
       t_1
       (if (<= c -6.1e-277)
         (* x (* y z))
         (if (<= c -6.6e-295) t_1 (if (<= c 3.4e+103) (* b (* a i)) 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 = i * (y * -j);
	double t_2 = z * (b * -c);
	double tmp;
	if (c <= -5e-16) {
		tmp = t_2;
	} else if (c <= -3.7e-199) {
		tmp = t_1;
	} else if (c <= -6.1e-277) {
		tmp = x * (y * z);
	} else if (c <= -6.6e-295) {
		tmp = t_1;
	} else if (c <= 3.4e+103) {
		tmp = b * (a * i);
	} 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 = i * (y * -j)
    t_2 = z * (b * -c)
    if (c <= (-5d-16)) then
        tmp = t_2
    else if (c <= (-3.7d-199)) then
        tmp = t_1
    else if (c <= (-6.1d-277)) then
        tmp = x * (y * z)
    else if (c <= (-6.6d-295)) then
        tmp = t_1
    else if (c <= 3.4d+103) then
        tmp = b * (a * i)
    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 = i * (y * -j);
	double t_2 = z * (b * -c);
	double tmp;
	if (c <= -5e-16) {
		tmp = t_2;
	} else if (c <= -3.7e-199) {
		tmp = t_1;
	} else if (c <= -6.1e-277) {
		tmp = x * (y * z);
	} else if (c <= -6.6e-295) {
		tmp = t_1;
	} else if (c <= 3.4e+103) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = z * (b * -c)
	tmp = 0
	if c <= -5e-16:
		tmp = t_2
	elif c <= -3.7e-199:
		tmp = t_1
	elif c <= -6.1e-277:
		tmp = x * (y * z)
	elif c <= -6.6e-295:
		tmp = t_1
	elif c <= 3.4e+103:
		tmp = b * (a * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(z * Float64(b * Float64(-c)))
	tmp = 0.0
	if (c <= -5e-16)
		tmp = t_2;
	elseif (c <= -3.7e-199)
		tmp = t_1;
	elseif (c <= -6.1e-277)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -6.6e-295)
		tmp = t_1;
	elseif (c <= 3.4e+103)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	t_2 = z * (b * -c);
	tmp = 0.0;
	if (c <= -5e-16)
		tmp = t_2;
	elseif (c <= -3.7e-199)
		tmp = t_1;
	elseif (c <= -6.1e-277)
		tmp = x * (y * z);
	elseif (c <= -6.6e-295)
		tmp = t_1;
	elseif (c <= 3.4e+103)
		tmp = b * (a * i);
	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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5e-16], t$95$2, If[LessEqual[c, -3.7e-199], t$95$1, If[LessEqual[c, -6.1e-277], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.6e-295], t$95$1, If[LessEqual[c, 3.4e+103], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.0000000000000004e-16 or 3.3999999999999998e103 < c

   1. Initial program 66.5%

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

      1. cancel-sign-sub 66.5%

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

      2. cancel-sign-sub-inv 66.5%

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

      3. *-commutative 66.5%

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

      4. *-commutative 66.5%

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

      5. remove-double-neg 66.5%

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

      6. *-commutative 66.5%

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

      7. *-commutative 66.5%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in z around inf 55.2%

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

   5. Taylor expanded in y around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. distribute-rgt-neg-in 45.4%

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

   7. Simplified 45.4%

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

   if -5.0000000000000004e-16 < c < -3.69999999999999999e-199 or -6.09999999999999957e-277 < c < -6.5999999999999997e-295

   1. Initial program 84.5%

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

      1. cancel-sign-sub 84.5%

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

      2. cancel-sign-sub-inv 84.5%

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

      3. *-commutative 84.5%

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

      4. *-commutative 84.5%

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

      5. remove-double-neg 84.5%

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

      6. *-commutative 84.5%

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

      7. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in i around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. sub-neg 60.7%

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

      3. mul-1-neg 60.7%

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

      4. remove-double-neg 60.7%

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

      5. +-commutative 60.7%

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

      6. mul-1-neg 60.7%

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

      7. unsub-neg 60.7%

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

      8. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in b around 0 47.4%

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

      1. associate-*r* 47.4%

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

      2. neg-mul-1 47.4%

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

   9. Simplified 47.4%

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

   if -3.69999999999999999e-199 < c < -6.09999999999999957e-277

   1. Initial program 94.2%

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

      1. cancel-sign-sub 94.2%

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

      2. cancel-sign-sub-inv 94.2%

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

      3. *-commutative 94.2%

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

      4. *-commutative 94.2%

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

      5. remove-double-neg 94.2%

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

      6. *-commutative 94.2%

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

      7. *-commutative 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in j around 0 81.8%

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

      1. *-commutative 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in c around inf 67.6%

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

   8. Taylor expanded in y around inf 40.0%

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

      1. associate-*r* 40.2%

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

      2. *-commutative 40.2%

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

      3. *-commutative 40.2%

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

      4. *-commutative 40.2%

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

   10. Simplified 40.2%

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

   if -6.5999999999999997e-295 < c < 3.3999999999999998e103

   1. Initial program 81.4%

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

      1. cancel-sign-sub 81.4%

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

      2. cancel-sign-sub-inv 81.4%

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

      3. *-commutative 81.4%

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

      4. *-commutative 81.4%

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

      5. remove-double-neg 81.4%

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

      6. *-commutative 81.4%

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

      7. *-commutative 81.4%

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

   3. Simplified 81.4%

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

   4. Taylor expanded in a around inf 45.5%

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

      1. associate-*r* 45.5%

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

      2. neg-mul-1 45.5%

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

      3. cancel-sign-sub 45.5%

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

      4. +-commutative 45.5%

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

      5. mul-1-neg 45.5%

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

      6. unsub-neg 45.5%

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

      7. *-commutative 45.5%

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

   6. Simplified 45.5%

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

   7. Taylor expanded in b around inf 27.4%

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

      1. associate-*r* 33.7%

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

      2. *-commutative 33.7%

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

   9. Simplified 33.7%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -6.1 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{-295}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 14: 30.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;c \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-276}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= c -4.5e-14)
     (* z (* b (- c)))
     (if (<= c -3.3e-199)
       t_1
       (if (<= c -5.2e-276)
         (* x (* y z))
         (if (<= c -5.2e-295)
           t_1
           (if (<= c 5.6e+101) (* b (* a i)) (* (* z c) (- b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double tmp;
	if (c <= -4.5e-14) {
		tmp = z * (b * -c);
	} else if (c <= -3.3e-199) {
		tmp = t_1;
	} else if (c <= -5.2e-276) {
		tmp = x * (y * z);
	} else if (c <= -5.2e-295) {
		tmp = t_1;
	} else if (c <= 5.6e+101) {
		tmp = b * (a * i);
	} else {
		tmp = (z * c) * -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) :: t_1
    real(8) :: tmp
    t_1 = i * (y * -j)
    if (c <= (-4.5d-14)) then
        tmp = z * (b * -c)
    else if (c <= (-3.3d-199)) then
        tmp = t_1
    else if (c <= (-5.2d-276)) then
        tmp = x * (y * z)
    else if (c <= (-5.2d-295)) then
        tmp = t_1
    else if (c <= 5.6d+101) then
        tmp = b * (a * i)
    else
        tmp = (z * c) * -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 t_1 = i * (y * -j);
	double tmp;
	if (c <= -4.5e-14) {
		tmp = z * (b * -c);
	} else if (c <= -3.3e-199) {
		tmp = t_1;
	} else if (c <= -5.2e-276) {
		tmp = x * (y * z);
	} else if (c <= -5.2e-295) {
		tmp = t_1;
	} else if (c <= 5.6e+101) {
		tmp = b * (a * i);
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if c <= -4.5e-14:
		tmp = z * (b * -c)
	elif c <= -3.3e-199:
		tmp = t_1
	elif c <= -5.2e-276:
		tmp = x * (y * z)
	elif c <= -5.2e-295:
		tmp = t_1
	elif c <= 5.6e+101:
		tmp = b * (a * i)
	else:
		tmp = (z * c) * -b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (c <= -4.5e-14)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (c <= -3.3e-199)
		tmp = t_1;
	elseif (c <= -5.2e-276)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -5.2e-295)
		tmp = t_1;
	elseif (c <= 5.6e+101)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(Float64(z * c) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	tmp = 0.0;
	if (c <= -4.5e-14)
		tmp = z * (b * -c);
	elseif (c <= -3.3e-199)
		tmp = t_1;
	elseif (c <= -5.2e-276)
		tmp = x * (y * z);
	elseif (c <= -5.2e-295)
		tmp = t_1;
	elseif (c <= 5.6e+101)
		tmp = b * (a * i);
	else
		tmp = (z * c) * -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.5e-14], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.3e-199], t$95$1, If[LessEqual[c, -5.2e-276], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.2e-295], t$95$1, If[LessEqual[c, 5.6e+101], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.4999999999999998e-14

   1. Initial program 68.0%

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

      1. cancel-sign-sub 68.0%

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

      2. cancel-sign-sub-inv 68.0%

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

      3. *-commutative 68.0%

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

      4. *-commutative 68.0%

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

      5. remove-double-neg 68.0%

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

      6. *-commutative 68.0%

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

      7. *-commutative 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in z around inf 56.7%

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

   5. Taylor expanded in y around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-rgt-neg-in 48.1%

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

   7. Simplified 48.1%

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

   if -4.4999999999999998e-14 < c < -3.3000000000000002e-199 or -5.19999999999999969e-276 < c < -5.1999999999999997e-295

   1. Initial program 84.5%

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

      1. cancel-sign-sub 84.5%

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

      2. cancel-sign-sub-inv 84.5%

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

      3. *-commutative 84.5%

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

      4. *-commutative 84.5%

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

      5. remove-double-neg 84.5%

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

      6. *-commutative 84.5%

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

      7. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in i around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. sub-neg 60.7%

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

      3. mul-1-neg 60.7%

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

      4. remove-double-neg 60.7%

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

      5. +-commutative 60.7%

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

      6. mul-1-neg 60.7%

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

      7. unsub-neg 60.7%

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

      8. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in b around 0 47.4%

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

      1. associate-*r* 47.4%

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

      2. neg-mul-1 47.4%

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

   9. Simplified 47.4%

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

   if -3.3000000000000002e-199 < c < -5.19999999999999969e-276

   1. Initial program 94.2%

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

      1. cancel-sign-sub 94.2%

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

      2. cancel-sign-sub-inv 94.2%

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

      3. *-commutative 94.2%

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

      4. *-commutative 94.2%

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

      5. remove-double-neg 94.2%

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

      6. *-commutative 94.2%

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

      7. *-commutative 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in j around 0 81.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 81.8%

         \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right) \]

   6. Simplified 81.8%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   7. Taylor expanded in c around inf 67.6%

      \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \color{blue}{c \cdot \left(z \cdot b\right)} \]

   8. Taylor expanded in y around inf 40.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 40.2%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 40.2%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

      3. *-commutative 40.2%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

      4. *-commutative 40.2%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   10. Simplified 40.2%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -5.1999999999999997e-295 < c < 5.59999999999999962e101

   1. Initial program 81.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 81.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 81.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 81.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 81.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 81.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 81.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 81.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 45.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 45.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 45.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 45.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 45.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 45.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 45.5%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 45.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 27.4%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 33.7%

         \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

      2. *-commutative 33.7%

         \[\leadsto \color{blue}{\left(a \cdot i\right)} \cdot b \]

   9. Simplified 33.7%

      \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

   if 5.59999999999999962e101 < c

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 64.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 64.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 50.4%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in a around 0 45.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \cdot b \]
   6. Step-by-step derivation

      1. neg-mul-1 45.8%

         \[\leadsto \color{blue}{\left(-c \cdot z\right)} \cdot b \]

      2. distribute-lft-neg-in 45.8%

         \[\leadsto \color{blue}{\left(\left(-c\right) \cdot z\right)} \cdot b \]

      3. *-commutative 45.8%

         \[\leadsto \color{blue}{\left(z \cdot \left(-c\right)\right)} \cdot b \]

   7. Simplified 45.8%

      \[\leadsto \color{blue}{\left(z \cdot \left(-c\right)\right)} \cdot b \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-276}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-295}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]

Alternative 15: 52.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.1 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{-233}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -3.1e-13)
     t_1
     (if (<= c 7.6e-233)
       (* i (- (* a b) (* y j)))
       (if (<= c 9.2e+20) (* a (- (* b i) (* 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.1e-13) {
		tmp = t_1;
	} else if (c <= 7.6e-233) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 9.2e+20) {
		tmp = a * ((b * i) - (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 = c * ((t * j) - (z * b))
    if (c <= (-3.1d-13)) then
        tmp = t_1
    else if (c <= 7.6d-233) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 9.2d+20) then
        tmp = a * ((b * i) - (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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.1e-13) {
		tmp = t_1;
	} else if (c <= 7.6e-233) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 9.2e+20) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.1e-13:
		tmp = t_1
	elif c <= 7.6e-233:
		tmp = i * ((a * b) - (y * j))
	elif c <= 9.2e+20:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.1e-13)
		tmp = t_1;
	elseif (c <= 7.6e-233)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 9.2e+20)
		tmp = Float64(a * Float64(Float64(b * i) - 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 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.1e-13)
		tmp = t_1;
	elseif (c <= 7.6e-233)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 9.2e+20)
		tmp = a * ((b * i) - (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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.1e-13], t$95$1, If[LessEqual[c, 7.6e-233], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e+20], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.0999999999999999e-13 or 9.2e20 < c

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 64.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -3.0999999999999999e-13 < c < 7.5999999999999999e-233

   1. Initial program 84.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 53.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]
   5. Step-by-step derivation

      1. *-commutative 53.2%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. sub-neg 53.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + \left(--1 \cdot \left(a \cdot b\right)\right)\right)} \]

      3. mul-1-neg 53.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \left(-\color{blue}{\left(-a \cdot b\right)}\right)\right) \]

      4. remove-double-neg 53.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \color{blue}{a \cdot b}\right) \]

      5. +-commutative 53.2%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      6. mul-1-neg 53.2%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      7. unsub-neg 53.2%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      8. *-commutative 53.2%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   6. Simplified 53.2%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if 7.5999999999999999e-233 < c < 9.2e20

   1. Initial program 85.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 85.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 85.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 85.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 85.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 85.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 85.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 50.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 50.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 50.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 50.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 50.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 50.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 50.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 50.3%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{-233}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 16: 30.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -1.02 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= j -1.02e+42)
     t_1
     (if (<= j 4e-190)
       (* a (* t (- x)))
       (if (<= j 8.5e+31) (* a (* 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 (j <= -1.02e+42) {
		tmp = t_1;
	} else if (j <= 4e-190) {
		tmp = a * (t * -x);
	} else if (j <= 8.5e+31) {
		tmp = a * (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 (j <= (-1.02d+42)) then
        tmp = t_1
    else if (j <= 4d-190) then
        tmp = a * (t * -x)
    else if (j <= 8.5d+31) then
        tmp = a * (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 (j <= -1.02e+42) {
		tmp = t_1;
	} else if (j <= 4e-190) {
		tmp = a * (t * -x);
	} else if (j <= 8.5e+31) {
		tmp = a * (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 j <= -1.02e+42:
		tmp = t_1
	elif j <= 4e-190:
		tmp = a * (t * -x)
	elif j <= 8.5e+31:
		tmp = a * (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 (j <= -1.02e+42)
		tmp = t_1;
	elseif (j <= 4e-190)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (j <= 8.5e+31)
		tmp = Float64(a * 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 (j <= -1.02e+42)
		tmp = t_1;
	elseif (j <= 4e-190)
		tmp = a * (t * -x);
	elseif (j <= 8.5e+31)
		tmp = a * (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[j, -1.02e+42], t$95$1, If[LessEqual[j, 4e-190], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+31], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.01999999999999996e42 or 8.49999999999999947e31 < j

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 44.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]
   5. Step-by-step derivation

      1. *-commutative 44.1%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. sub-neg 44.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + \left(--1 \cdot \left(a \cdot b\right)\right)\right)} \]

      3. mul-1-neg 44.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \left(-\color{blue}{\left(-a \cdot b\right)}\right)\right) \]

      4. remove-double-neg 44.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \color{blue}{a \cdot b}\right) \]

      5. +-commutative 44.1%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      6. mul-1-neg 44.1%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      7. unsub-neg 44.1%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      8. *-commutative 44.1%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   7. Taylor expanded in b around 0 40.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 40.8%

         \[\leadsto \color{blue}{-i \cdot \left(y \cdot j\right)} \]

      2. associate-*r* 36.9%

         \[\leadsto -\color{blue}{\left(i \cdot y\right) \cdot j} \]

      3. *-commutative 36.9%

         \[\leadsto -\color{blue}{\left(y \cdot i\right)} \cdot j \]

      4. associate-*r* 39.2%

         \[\leadsto -\color{blue}{y \cdot \left(i \cdot j\right)} \]

      5. distribute-rgt-neg-in 39.2%

         \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

      6. distribute-lft-neg-in 39.2%

         \[\leadsto y \cdot \color{blue}{\left(\left(-i\right) \cdot j\right)} \]

      7. *-commutative 39.2%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   9. Simplified 39.2%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   if -1.01999999999999996e42 < j < 4.0000000000000001e-190

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 77.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 43.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 43.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 43.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 43.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 43.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 43.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 43.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 43.3%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 43.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around 0 28.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 28.6%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 28.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 28.6%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 28.6%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 4.0000000000000001e-190 < j < 8.49999999999999947e31

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 57.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 57.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 57.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 57.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 57.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 57.7%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 57.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 57.7%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 57.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around -inf 48.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.02 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 17: 29.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+76} \lor \neg \left(z \leq 6.8 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -7e+76) (not (<= z 6.8e+66))) (* x (* y z)) (* i (* a 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 ((z <= -7e+76) || !(z <= 6.8e+66)) {
		tmp = x * (y * z);
	} else {
		tmp = i * (a * 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 ((z <= (-7d+76)) .or. (.not. (z <= 6.8d+66))) then
        tmp = x * (y * z)
    else
        tmp = i * (a * 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 ((z <= -7e+76) || !(z <= 6.8e+66)) {
		tmp = x * (y * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -7e+76) or not (z <= 6.8e+66):
		tmp = x * (y * z)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -7e+76) || !(z <= 6.8e+66))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -7e+76) || ~((z <= 6.8e+66)))
		tmp = x * (y * z);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -7e+76], N[Not[LessEqual[z, 6.8e+66]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000001e76 or 6.8000000000000006e66 < z

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 67.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 67.6%

         \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right) \]

   6. Simplified 67.6%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   7. Taylor expanded in c around inf 69.8%

      \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \color{blue}{c \cdot \left(z \cdot b\right)} \]

   8. Taylor expanded in y around inf 37.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.7%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 37.7%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

      3. *-commutative 37.7%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

      4. *-commutative 37.7%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   10. Simplified 37.7%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -7.00000000000000001e76 < z < 6.8000000000000006e66

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 41.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 41.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 41.0%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 41.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 41.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 41.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 41.0%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 41.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 26.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+76} \lor \neg \left(z \leq 6.8 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 18: 29.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -8e+76)
   (* x (* y z))
   (if (<= z 4.2e+63) (* i (* a b)) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -8e+76) {
		tmp = x * (y * z);
	} else if (z <= 4.2e+63) {
		tmp = i * (a * b);
	} else {
		tmp = y * (x * z);
	}
	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 (z <= (-8d+76)) then
        tmp = x * (y * z)
    else if (z <= 4.2d+63) then
        tmp = i * (a * b)
    else
        tmp = y * (x * z)
    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 (z <= -8e+76) {
		tmp = x * (y * z);
	} else if (z <= 4.2e+63) {
		tmp = i * (a * b);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -8e+76:
		tmp = x * (y * z)
	elif z <= 4.2e+63:
		tmp = i * (a * b)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -8e+76)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 4.2e+63)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -8e+76)
		tmp = x * (y * z);
	elseif (z <= 4.2e+63)
		tmp = i * (a * b);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -8e+76], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+63], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000004e76

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 73.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 73.8%

         \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right) \]

   6. Simplified 73.8%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   7. Taylor expanded in c around inf 71.7%

      \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \color{blue}{c \cdot \left(z \cdot b\right)} \]

   8. Taylor expanded in y around inf 35.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.0%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 37.0%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

      3. *-commutative 37.0%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

      4. *-commutative 37.0%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   10. Simplified 37.0%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -8.0000000000000004e76 < z < 4.2000000000000004e63

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 41.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 41.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 41.0%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 41.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 41.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 41.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 41.0%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 41.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 26.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if 4.2000000000000004e63 < z

   1. Initial program 59.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 59.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 59.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 49.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 49.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 49.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 49.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 40.1%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 19: 29.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -8e+76)
   (* x (* y z))
   (if (<= z 1.15e+66) (* b (* a i)) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -8e+76) {
		tmp = x * (y * z);
	} else if (z <= 1.15e+66) {
		tmp = b * (a * i);
	} else {
		tmp = y * (x * z);
	}
	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 (z <= (-8d+76)) then
        tmp = x * (y * z)
    else if (z <= 1.15d+66) then
        tmp = b * (a * i)
    else
        tmp = y * (x * z)
    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 (z <= -8e+76) {
		tmp = x * (y * z);
	} else if (z <= 1.15e+66) {
		tmp = b * (a * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -8e+76:
		tmp = x * (y * z)
	elif z <= 1.15e+66:
		tmp = b * (a * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -8e+76)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.15e+66)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -8e+76)
		tmp = x * (y * z);
	elseif (z <= 1.15e+66)
		tmp = b * (a * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -8e+76], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+66], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000004e76

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 73.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 73.8%

         \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right) \]

   6. Simplified 73.8%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   7. Taylor expanded in c around inf 71.7%

      \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \color{blue}{c \cdot \left(z \cdot b\right)} \]

   8. Taylor expanded in y around inf 35.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.0%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 37.0%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

      3. *-commutative 37.0%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

      4. *-commutative 37.0%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   10. Simplified 37.0%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -8.0000000000000004e76 < z < 1.15e66

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 41.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 41.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 41.0%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 41.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 41.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 41.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 41.0%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 41.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 26.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 26.1%

         \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

      2. *-commutative 26.1%

         \[\leadsto \color{blue}{\left(a \cdot i\right)} \cdot b \]

   9. Simplified 26.1%

      \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

   if 1.15e66 < z

   1. Initial program 59.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 59.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 59.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 59.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 49.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 49.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 49.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 49.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 40.1%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 20: 28.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -9e+15)
   (* a (* t (- x)))
   (if (<= a 4.7e+157) (* x (* y z)) (* i (* a 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 (a <= -9e+15) {
		tmp = a * (t * -x);
	} else if (a <= 4.7e+157) {
		tmp = x * (y * z);
	} else {
		tmp = i * (a * 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 (a <= (-9d+15)) then
        tmp = a * (t * -x)
    else if (a <= 4.7d+157) then
        tmp = x * (y * z)
    else
        tmp = i * (a * 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 (a <= -9e+15) {
		tmp = a * (t * -x);
	} else if (a <= 4.7e+157) {
		tmp = x * (y * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -9e+15:
		tmp = a * (t * -x)
	elif a <= 4.7e+157:
		tmp = x * (y * z)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -9e+15)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (a <= 4.7e+157)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -9e+15)
		tmp = a * (t * -x);
	elseif (a <= 4.7e+157)
		tmp = x * (y * z);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -9e+15], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e+157], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9e15

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 67.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 67.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 67.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 67.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 67.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 67.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 67.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 67.3%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 67.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around 0 44.2%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 44.2%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 44.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 44.2%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 44.2%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -9e15 < a < 4.7000000000000003e157

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 54.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 54.8%

         \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right) \]

   6. Simplified 54.8%

      \[\leadsto \color{blue}{\left(z \cdot y - a \cdot t\right) \cdot x - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   7. Taylor expanded in c around inf 46.5%

      \[\leadsto \left(z \cdot y - a \cdot t\right) \cdot x - \color{blue}{c \cdot \left(z \cdot b\right)} \]

   8. Taylor expanded in y around inf 24.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 24.9%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 24.9%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

      3. *-commutative 24.9%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

      4. *-commutative 24.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   10. Simplified 24.9%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 4.7000000000000003e157 < a

   1. Initial program 53.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 53.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 53.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 53.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 53.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 53.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 53.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 53.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 53.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 70.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 70.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 70.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 70.6%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 70.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 70.6%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 70.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 70.6%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 70.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 21: 21.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.8 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t 7.8e+105) (* a (* b i)) (* a (* x t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= 7.8e+105) {
		tmp = a * (b * i);
	} else {
		tmp = a * (x * t);
	}
	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 (t <= 7.8d+105) then
        tmp = a * (b * i)
    else
        tmp = a * (x * t)
    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 (t <= 7.8e+105) {
		tmp = a * (b * i);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= 7.8e+105:
		tmp = a * (b * i)
	else:
		tmp = a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= 7.8e+105)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(a * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= 7.8e+105)
		tmp = a * (b * i);
	else
		tmp = a * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, 7.8e+105], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 7.79999999999999957e105

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 77.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 35.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 35.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 35.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 35.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 35.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 35.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 35.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 35.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 35.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around -inf 21.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if 7.79999999999999957e105 < t

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 27.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 27.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 27.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 27.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 27.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 27.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 27.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 27.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 27.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around 0 20.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 20.3%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 20.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 20.3%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 20.3%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 8.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(x \cdot \left(-t\right)\right)\right)\right)} \]

       2. expm1-udef 8.3%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(x \cdot \left(-t\right)\right)\right)} - 1} \]

       3. *-commutative 8.3%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)}\right)} - 1 \]

       4. add-sqr-sqrt 0.0%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot x\right)\right)} - 1 \]

       5. sqrt-unprod 12.1%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot x\right)\right)} - 1 \]

       6. sqr-neg 12.1%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\sqrt{\color{blue}{t \cdot t}} \cdot x\right)\right)} - 1 \]

       7. sqrt-unprod 6.9%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot x\right)\right)} - 1 \]

       8. add-sqr-sqrt 6.9%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\color{blue}{t} \cdot x\right)\right)} - 1 \]

   11. Applied egg-rr 6.9%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(t \cdot x\right)\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 7.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(t \cdot x\right)\right)\right)} \]

       2. expm1-log1p 26.9%

          \[\leadsto \color{blue}{a \cdot \left(t \cdot x\right)} \]

   13. Simplified 26.9%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.8 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 22: 21.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.6 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t 3.6e+106) (* i (* a b)) (* a (* x t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= 3.6e+106) {
		tmp = i * (a * b);
	} else {
		tmp = a * (x * t);
	}
	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 (t <= 3.6d+106) then
        tmp = i * (a * b)
    else
        tmp = a * (x * t)
    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 (t <= 3.6e+106) {
		tmp = i * (a * b);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= 3.6e+106:
		tmp = i * (a * b)
	else:
		tmp = a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= 3.6e+106)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(a * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= 3.6e+106)
		tmp = i * (a * b);
	else
		tmp = a * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, 3.6e+106], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.6000000000000001e106

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 77.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 35.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 35.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 35.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 35.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 35.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 35.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 35.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 35.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 35.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 22.2%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if 3.6000000000000001e106 < t

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 27.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 27.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 27.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 27.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 27.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 27.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 27.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 27.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 27.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around 0 20.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 20.3%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 20.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 20.3%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 20.3%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 8.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(x \cdot \left(-t\right)\right)\right)\right)} \]

       2. expm1-udef 8.3%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(x \cdot \left(-t\right)\right)\right)} - 1} \]

       3. *-commutative 8.3%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)}\right)} - 1 \]

       4. add-sqr-sqrt 0.0%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot x\right)\right)} - 1 \]

       5. sqrt-unprod 12.1%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot x\right)\right)} - 1 \]

       6. sqr-neg 12.1%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\sqrt{\color{blue}{t \cdot t}} \cdot x\right)\right)} - 1 \]

       7. sqrt-unprod 6.9%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot x\right)\right)} - 1 \]

       8. add-sqr-sqrt 6.9%

          \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(\color{blue}{t} \cdot x\right)\right)} - 1 \]

   11. Applied egg-rr 6.9%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(t \cdot x\right)\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 7.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(t \cdot x\right)\right)\right)} \]

       2. expm1-log1p 26.9%

          \[\leadsto \color{blue}{a \cdot \left(t \cdot x\right)} \]

   13. Simplified 26.9%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.6 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 23: 22.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * 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 = a * (b * 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 a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub 76.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

   2. cancel-sign-sub-inv 76.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

   3. *-commutative 76.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

   4. *-commutative 76.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

   5. remove-double-neg 76.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

   6. *-commutative 76.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

   7. *-commutative 76.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

3. Simplified 76.5%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

4. Taylor expanded in a around inf 34.7%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. associate-*r* 34.7%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

   2. neg-mul-1 34.7%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

   3. cancel-sign-sub 34.7%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   4. +-commutative 34.7%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

   5. mul-1-neg 34.7%

      \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

   6. unsub-neg 34.7%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   7. *-commutative 34.7%

      \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

6. Simplified 34.7%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

7. Taylor expanded in b around -inf 20.2%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

8. Final simplification 20.2%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 67.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = 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[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023174 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))