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

Percentage Accurate: 73.1% → 83.6%

Time: 27.0s

Alternatives: 27

Speedup: 0.5×

• 58.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := a \cdot c - y \cdot i\\ \mathbf{if}\;j \cdot t\_2 + t\_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y} - i \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

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

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. fma-define 93.2%

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

      3. *-commutative 93.2%

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

      4. *-commutative 93.2%

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

   3. Simplified 93.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around -inf 41.4%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in c around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. *-commutative 52.1%

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

      3. associate-*r* 52.1%

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

      4. distribute-lft-neg-in 52.1%

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

      5. mul-1-neg 52.1%

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

      6. associate-*r* 53.9%

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

      7. distribute-rgt-in 61.0%

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

      8. +-commutative 61.0%

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

      9. mul-1-neg 61.0%

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

      10. unsub-neg 61.0%

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

   8. Simplified 61.0%

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

4. Final simplification 86.1%

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

Alternative 2: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + \left(b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y} - i \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around -inf 41.4%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in c around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. *-commutative 52.1%

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

      3. associate-*r* 52.1%

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

      4. distribute-lft-neg-in 52.1%

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

      5. mul-1-neg 52.1%

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

      6. associate-*r* 53.9%

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

      7. distribute-rgt-in 61.0%

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

      8. +-commutative 61.0%

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

      9. mul-1-neg 61.0%

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

      10. unsub-neg 61.0%

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

   8. Simplified 61.0%

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

4. Final simplification 86.1%

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

Alternative 3: 47.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-293}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(b \cdot i - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-34}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x y) (- z (* a (/ t y))))))
   (if (<= x -2.7e-36)
     t_1
     (if (<= x -9.5e-269)
       (* t (* b (- i (* c (/ z t)))))
       (if (<= x 3e-293)
         (* j (* y (- (/ (* a c) y) i)))
         (if (<= x 1.25e-238)
           (* t (- (* b i) (* b (/ (* z c) t))))
           (if (<= x 5.4e-151)
             (* y (- (* x z) (* i j)))
             (if (<= x 1.5e-69)
               (* a (* x (- (/ (* c j) x) t)))
               (if (<= x 4.7e-34)
                 (* i (* y (- (/ (* t b) y) j)))
                 (if (<= x 3e+73) (* t (- (* b i) (* 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 = (x * y) * (z - (a * (t / y)));
	double tmp;
	if (x <= -2.7e-36) {
		tmp = t_1;
	} else if (x <= -9.5e-269) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (x <= 3e-293) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (x <= 1.25e-238) {
		tmp = t * ((b * i) - (b * ((z * c) / t)));
	} else if (x <= 5.4e-151) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.5e-69) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (x <= 4.7e-34) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (x <= 3e+73) {
		tmp = t * ((b * i) - (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 = (x * y) * (z - (a * (t / y)))
    if (x <= (-2.7d-36)) then
        tmp = t_1
    else if (x <= (-9.5d-269)) then
        tmp = t * (b * (i - (c * (z / t))))
    else if (x <= 3d-293) then
        tmp = j * (y * (((a * c) / y) - i))
    else if (x <= 1.25d-238) then
        tmp = t * ((b * i) - (b * ((z * c) / t)))
    else if (x <= 5.4d-151) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 1.5d-69) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (x <= 4.7d-34) then
        tmp = i * (y * (((t * b) / y) - j))
    else if (x <= 3d+73) then
        tmp = t * ((b * i) - (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 = (x * y) * (z - (a * (t / y)));
	double tmp;
	if (x <= -2.7e-36) {
		tmp = t_1;
	} else if (x <= -9.5e-269) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (x <= 3e-293) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (x <= 1.25e-238) {
		tmp = t * ((b * i) - (b * ((z * c) / t)));
	} else if (x <= 5.4e-151) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.5e-69) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (x <= 4.7e-34) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (x <= 3e+73) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * y) * (z - (a * (t / y)))
	tmp = 0
	if x <= -2.7e-36:
		tmp = t_1
	elif x <= -9.5e-269:
		tmp = t * (b * (i - (c * (z / t))))
	elif x <= 3e-293:
		tmp = j * (y * (((a * c) / y) - i))
	elif x <= 1.25e-238:
		tmp = t * ((b * i) - (b * ((z * c) / t)))
	elif x <= 5.4e-151:
		tmp = y * ((x * z) - (i * j))
	elif x <= 1.5e-69:
		tmp = a * (x * (((c * j) / x) - t))
	elif x <= 4.7e-34:
		tmp = i * (y * (((t * b) / y) - j))
	elif x <= 3e+73:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))))
	tmp = 0.0
	if (x <= -2.7e-36)
		tmp = t_1;
	elseif (x <= -9.5e-269)
		tmp = Float64(t * Float64(b * Float64(i - Float64(c * Float64(z / t)))));
	elseif (x <= 3e-293)
		tmp = Float64(j * Float64(y * Float64(Float64(Float64(a * c) / y) - i)));
	elseif (x <= 1.25e-238)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(b * Float64(Float64(z * c) / t))));
	elseif (x <= 5.4e-151)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 1.5e-69)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (x <= 4.7e-34)
		tmp = Float64(i * Float64(y * Float64(Float64(Float64(t * b) / y) - j)));
	elseif (x <= 3e+73)
		tmp = Float64(t * Float64(Float64(b * i) - 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 = (x * y) * (z - (a * (t / y)));
	tmp = 0.0;
	if (x <= -2.7e-36)
		tmp = t_1;
	elseif (x <= -9.5e-269)
		tmp = t * (b * (i - (c * (z / t))));
	elseif (x <= 3e-293)
		tmp = j * (y * (((a * c) / y) - i));
	elseif (x <= 1.25e-238)
		tmp = t * ((b * i) - (b * ((z * c) / t)));
	elseif (x <= 5.4e-151)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 1.5e-69)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (x <= 4.7e-34)
		tmp = i * (y * (((t * b) / y) - j));
	elseif (x <= 3e+73)
		tmp = t * ((b * i) - (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[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e-36], t$95$1, If[LessEqual[x, -9.5e-269], N[(t * N[(b * N[(i - N[(c * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-293], N[(j * N[(y * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-238], N[(t * N[(N[(b * i), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.4e-151], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-69], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.7e-34], N[(i * N[(y * N[(N[(N[(t * b), $MachinePrecision] / y), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+73], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -2.70000000000000007e-36 or 3.00000000000000011e73 < x

   1. Initial program 71.3%

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

   3. Taylor expanded in y around -inf 69.4%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in x around inf 71.0%

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

      1. associate-*r* 72.5%

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

      2. *-commutative 72.5%

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

      3. mul-1-neg 72.5%

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

      4. unsub-neg 72.5%

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

      5. associate-/l* 74.1%

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

   8. Simplified 74.1%

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

   if -2.70000000000000007e-36 < x < -9.5000000000000006e-269

   1. Initial program 72.9%

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

   3. Taylor expanded in b around inf 56.2%

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

      1. *-commutative 56.2%

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

      2. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in t around inf 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. associate-/l* 52.8%

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

   8. Simplified 52.8%

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

   9. Taylor expanded in b around 0 56.7%

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

       1. associate-*r/ 58.5%

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

   11. Simplified 58.5%

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

   if -9.5000000000000006e-269 < x < 3.0000000000000002e-293

   1. Initial program 66.5%

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

   3. Taylor expanded in y around -inf 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in j around inf 73.8%

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

   if 3.0000000000000002e-293 < x < 1.25e-238

   1. Initial program 67.6%

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

   3. Taylor expanded in b around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in t around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. associate-/l* 72.2%

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

   8. Simplified 72.2%

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

   if 1.25e-238 < x < 5.40000000000000014e-151

   1. Initial program 77.0%

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

   3. Taylor expanded in y around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

      4. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   if 5.40000000000000014e-151 < x < 1.49999999999999995e-69

   1. Initial program 58.2%

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

   3. Taylor expanded in a around inf 83.2%

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

      1. +-commutative 83.2%

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

      2. mul-1-neg 83.2%

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

      3. unsub-neg 83.2%

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

      4. *-commutative 83.2%

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

      5. *-commutative 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in x around inf 83.3%

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

   if 1.49999999999999995e-69 < x < 4.70000000000000002e-34

   1. Initial program 83.1%

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

   3. Taylor expanded in y around -inf 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in i around inf 53.9%

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

   if 4.70000000000000002e-34 < x < 3.00000000000000011e73

   1. Initial program 90.8%

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

   3. Taylor expanded in j around 0 76.6%

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

      1. *-commutative 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in z around 0 45.0%

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

      1. associate-*r* 45.0%

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

      2. neg-mul-1 45.0%

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

      3. cancel-sign-sub 45.0%

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

      4. mul-1-neg 45.0%

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

      5. *-commutative 45.0%

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

      6. associate-*r* 54.3%

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

      7. distribute-lft-neg-in 54.3%

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

      8. mul-1-neg 54.3%

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

      9. associate-*r* 63.0%

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

      10. distribute-rgt-in 63.1%

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

      11. +-commutative 63.1%

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

      12. mul-1-neg 63.1%

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

      13. unsub-neg 63.1%

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

   8. Simplified 63.1%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i - a \cdot x\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-293}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(b \cdot i - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-34}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-236}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-34}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x y) (- z (* a (/ t y))))))
   (if (<= x -2.4e-31)
     t_1
     (if (<= x -2.7e-270)
       (* t (* b (- i (* c (/ z t)))))
       (if (<= x 3.4e-291)
         (* j (* y (- (/ (* a c) y) i)))
         (if (<= x 1.3e-236)
           (* b (- (* t i) (* z c)))
           (if (<= x 2.4e-146)
             (* y (- (* x z) (* i j)))
             (if (<= x 6.5e-71)
               (* a (* x (- (/ (* c j) x) t)))
               (if (<= x 4.8e-34)
                 (* i (* y (- (/ (* t b) y) j)))
                 (if (<= x 2.3e+73) (* t (- (* b i) (* 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 = (x * y) * (z - (a * (t / y)));
	double tmp;
	if (x <= -2.4e-31) {
		tmp = t_1;
	} else if (x <= -2.7e-270) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (x <= 3.4e-291) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (x <= 1.3e-236) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 2.4e-146) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 6.5e-71) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (x <= 4.8e-34) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (x <= 2.3e+73) {
		tmp = t * ((b * i) - (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 = (x * y) * (z - (a * (t / y)))
    if (x <= (-2.4d-31)) then
        tmp = t_1
    else if (x <= (-2.7d-270)) then
        tmp = t * (b * (i - (c * (z / t))))
    else if (x <= 3.4d-291) then
        tmp = j * (y * (((a * c) / y) - i))
    else if (x <= 1.3d-236) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 2.4d-146) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 6.5d-71) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (x <= 4.8d-34) then
        tmp = i * (y * (((t * b) / y) - j))
    else if (x <= 2.3d+73) then
        tmp = t * ((b * i) - (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 = (x * y) * (z - (a * (t / y)));
	double tmp;
	if (x <= -2.4e-31) {
		tmp = t_1;
	} else if (x <= -2.7e-270) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (x <= 3.4e-291) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (x <= 1.3e-236) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 2.4e-146) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 6.5e-71) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (x <= 4.8e-34) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (x <= 2.3e+73) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * y) * (z - (a * (t / y)))
	tmp = 0
	if x <= -2.4e-31:
		tmp = t_1
	elif x <= -2.7e-270:
		tmp = t * (b * (i - (c * (z / t))))
	elif x <= 3.4e-291:
		tmp = j * (y * (((a * c) / y) - i))
	elif x <= 1.3e-236:
		tmp = b * ((t * i) - (z * c))
	elif x <= 2.4e-146:
		tmp = y * ((x * z) - (i * j))
	elif x <= 6.5e-71:
		tmp = a * (x * (((c * j) / x) - t))
	elif x <= 4.8e-34:
		tmp = i * (y * (((t * b) / y) - j))
	elif x <= 2.3e+73:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))))
	tmp = 0.0
	if (x <= -2.4e-31)
		tmp = t_1;
	elseif (x <= -2.7e-270)
		tmp = Float64(t * Float64(b * Float64(i - Float64(c * Float64(z / t)))));
	elseif (x <= 3.4e-291)
		tmp = Float64(j * Float64(y * Float64(Float64(Float64(a * c) / y) - i)));
	elseif (x <= 1.3e-236)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 2.4e-146)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 6.5e-71)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (x <= 4.8e-34)
		tmp = Float64(i * Float64(y * Float64(Float64(Float64(t * b) / y) - j)));
	elseif (x <= 2.3e+73)
		tmp = Float64(t * Float64(Float64(b * i) - 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 = (x * y) * (z - (a * (t / y)));
	tmp = 0.0;
	if (x <= -2.4e-31)
		tmp = t_1;
	elseif (x <= -2.7e-270)
		tmp = t * (b * (i - (c * (z / t))));
	elseif (x <= 3.4e-291)
		tmp = j * (y * (((a * c) / y) - i));
	elseif (x <= 1.3e-236)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 2.4e-146)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 6.5e-71)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (x <= 4.8e-34)
		tmp = i * (y * (((t * b) / y) - j));
	elseif (x <= 2.3e+73)
		tmp = t * ((b * i) - (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[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e-31], t$95$1, If[LessEqual[x, -2.7e-270], N[(t * N[(b * N[(i - N[(c * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e-291], N[(j * N[(y * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-236], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-146], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-71], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e-34], N[(i * N[(y * N[(N[(N[(t * b), $MachinePrecision] / y), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+73], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -2.4e-31 or 2.3e73 < x

   1. Initial program 71.3%

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

   3. Taylor expanded in y around -inf 69.4%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in x around inf 71.0%

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

      1. associate-*r* 72.5%

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

      2. *-commutative 72.5%

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

      3. mul-1-neg 72.5%

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

      4. unsub-neg 72.5%

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

      5. associate-/l* 74.1%

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

   8. Simplified 74.1%

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

   if -2.4e-31 < x < -2.70000000000000007e-270

   1. Initial program 72.9%

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

   3. Taylor expanded in b around inf 56.2%

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

      1. *-commutative 56.2%

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

      2. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in t around inf 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. associate-/l* 52.8%

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

   8. Simplified 52.8%

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

   9. Taylor expanded in b around 0 56.7%

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

       1. associate-*r/ 58.5%

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

   11. Simplified 58.5%

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

   if -2.70000000000000007e-270 < x < 3.40000000000000026e-291

   1. Initial program 66.5%

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

   3. Taylor expanded in y around -inf 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in j around inf 73.8%

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

   if 3.40000000000000026e-291 < x < 1.3e-236

   1. Initial program 67.6%

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

   3. Taylor expanded in b around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   if 1.3e-236 < x < 2.4000000000000002e-146

   1. Initial program 77.0%

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

   3. Taylor expanded in y around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

      4. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   if 2.4000000000000002e-146 < x < 6.50000000000000005e-71

   1. Initial program 58.2%

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

   3. Taylor expanded in a around inf 83.2%

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

      1. +-commutative 83.2%

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

      2. mul-1-neg 83.2%

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

      3. unsub-neg 83.2%

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

      4. *-commutative 83.2%

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

      5. *-commutative 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in x around inf 83.3%

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

   if 6.50000000000000005e-71 < x < 4.79999999999999982e-34

   1. Initial program 83.1%

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

   3. Taylor expanded in y around -inf 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in i around inf 53.9%

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

   if 4.79999999999999982e-34 < x < 2.3e73

   1. Initial program 90.8%

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

   3. Taylor expanded in j around 0 76.6%

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

      1. *-commutative 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in z around 0 45.0%

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

      1. associate-*r* 45.0%

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

      2. neg-mul-1 45.0%

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

      3. cancel-sign-sub 45.0%

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

      4. mul-1-neg 45.0%

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

      5. *-commutative 45.0%

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

      6. associate-*r* 54.3%

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

      7. distribute-lft-neg-in 54.3%

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

      8. mul-1-neg 54.3%

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

      9. associate-*r* 63.0%

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

      10. distribute-rgt-in 63.1%

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

      11. +-commutative 63.1%

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

      12. mul-1-neg 63.1%

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

      13. unsub-neg 63.1%

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

   8. Simplified 63.1%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i - a \cdot x\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-31}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-236}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-34}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - i \cdot \left(j \cdot \frac{y}{t}\right)\right)\\ t_2 := \left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-290}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-249}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* i (* j (/ y t))))))
        (t_2 (* (* x y) (- z (* a (/ t y))))))
   (if (<= x -8e-32)
     t_2
     (if (<= x -4.2e-269)
       (* t (* b (- i (* c (/ z t)))))
       (if (<= x 4.2e-290)
         (* j (* y (- (/ (* a c) y) i)))
         (if (<= x 1.6e-249)
           (* b (- (* t i) (* z c)))
           (if (<= x 5.2e-147)
             t_1
             (if (<= x 1.25e-70)
               (* a (* x (- (/ (* c j) x) t)))
               (if (<= x 1.4e-8) 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 = t * ((b * i) - (i * (j * (y / t))));
	double t_2 = (x * y) * (z - (a * (t / y)));
	double tmp;
	if (x <= -8e-32) {
		tmp = t_2;
	} else if (x <= -4.2e-269) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (x <= 4.2e-290) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (x <= 1.6e-249) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 5.2e-147) {
		tmp = t_1;
	} else if (x <= 1.25e-70) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (x <= 1.4e-8) {
		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 = t * ((b * i) - (i * (j * (y / t))))
    t_2 = (x * y) * (z - (a * (t / y)))
    if (x <= (-8d-32)) then
        tmp = t_2
    else if (x <= (-4.2d-269)) then
        tmp = t * (b * (i - (c * (z / t))))
    else if (x <= 4.2d-290) then
        tmp = j * (y * (((a * c) / y) - i))
    else if (x <= 1.6d-249) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 5.2d-147) then
        tmp = t_1
    else if (x <= 1.25d-70) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (x <= 1.4d-8) 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 = t * ((b * i) - (i * (j * (y / t))));
	double t_2 = (x * y) * (z - (a * (t / y)));
	double tmp;
	if (x <= -8e-32) {
		tmp = t_2;
	} else if (x <= -4.2e-269) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (x <= 4.2e-290) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (x <= 1.6e-249) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 5.2e-147) {
		tmp = t_1;
	} else if (x <= 1.25e-70) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (x <= 1.4e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (i * (j * (y / t))))
	t_2 = (x * y) * (z - (a * (t / y)))
	tmp = 0
	if x <= -8e-32:
		tmp = t_2
	elif x <= -4.2e-269:
		tmp = t * (b * (i - (c * (z / t))))
	elif x <= 4.2e-290:
		tmp = j * (y * (((a * c) / y) - i))
	elif x <= 1.6e-249:
		tmp = b * ((t * i) - (z * c))
	elif x <= 5.2e-147:
		tmp = t_1
	elif x <= 1.25e-70:
		tmp = a * (x * (((c * j) / x) - t))
	elif x <= 1.4e-8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(i * Float64(j * Float64(y / t)))))
	t_2 = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))))
	tmp = 0.0
	if (x <= -8e-32)
		tmp = t_2;
	elseif (x <= -4.2e-269)
		tmp = Float64(t * Float64(b * Float64(i - Float64(c * Float64(z / t)))));
	elseif (x <= 4.2e-290)
		tmp = Float64(j * Float64(y * Float64(Float64(Float64(a * c) / y) - i)));
	elseif (x <= 1.6e-249)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 5.2e-147)
		tmp = t_1;
	elseif (x <= 1.25e-70)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (x <= 1.4e-8)
		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 = t * ((b * i) - (i * (j * (y / t))));
	t_2 = (x * y) * (z - (a * (t / y)));
	tmp = 0.0;
	if (x <= -8e-32)
		tmp = t_2;
	elseif (x <= -4.2e-269)
		tmp = t * (b * (i - (c * (z / t))));
	elseif (x <= 4.2e-290)
		tmp = j * (y * (((a * c) / y) - i));
	elseif (x <= 1.6e-249)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 5.2e-147)
		tmp = t_1;
	elseif (x <= 1.25e-70)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (x <= 1.4e-8)
		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[(t * N[(N[(b * i), $MachinePrecision] - N[(i * N[(j * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e-32], t$95$2, If[LessEqual[x, -4.2e-269], N[(t * N[(b * N[(i - N[(c * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-290], N[(j * N[(y * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-249], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e-147], t$95$1, If[LessEqual[x, 1.25e-70], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-8], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -8.00000000000000045e-32 or 1.4e-8 < x

   1. Initial program 73.4%

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

   3. Taylor expanded in y around -inf 69.0%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in x around inf 67.6%

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

      1. associate-*r* 69.0%

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

      2. *-commutative 69.0%

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

      3. mul-1-neg 69.0%

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

      4. unsub-neg 69.0%

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

      5. associate-/l* 70.4%

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

   8. Simplified 70.4%

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

   if -8.00000000000000045e-32 < x < -4.20000000000000009e-269

   1. Initial program 72.9%

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

   3. Taylor expanded in b around inf 56.2%

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

      1. *-commutative 56.2%

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

      2. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in t around inf 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. associate-/l* 52.8%

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

   8. Simplified 52.8%

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

   9. Taylor expanded in b around 0 56.7%

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

       1. associate-*r/ 58.5%

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

   11. Simplified 58.5%

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

   if -4.20000000000000009e-269 < x < 4.2000000000000002e-290

   1. Initial program 66.5%

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

   3. Taylor expanded in y around -inf 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in j around inf 73.8%

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

   if 4.2000000000000002e-290 < x < 1.6000000000000001e-249

   1. Initial program 84.0%

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

   3. Taylor expanded in b around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. *-commutative 74.6%

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

   5. Simplified 74.6%

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

   if 1.6000000000000001e-249 < x < 5.1999999999999997e-147 or 1.25e-70 < x < 1.4e-8

   1. Initial program 77.1%

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

   3. Taylor expanded in y around -inf 90.1%

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

   5. Simplified 90.1%

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

   6. Taylor expanded in i around inf 49.1%

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

   7. Taylor expanded in t around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. associate-/l* 61.7%

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

      5. associate-/l* 64.9%

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

   9. Simplified 64.9%

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

   if 5.1999999999999997e-147 < x < 1.25e-70

   1. Initial program 58.2%

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

   3. Taylor expanded in a around inf 83.2%

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

      1. +-commutative 83.2%

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

      2. mul-1-neg 83.2%

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

      3. unsub-neg 83.2%

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

      4. *-commutative 83.2%

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

      5. *-commutative 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in x around inf 83.3%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-32}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-290}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-249}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(b \cdot i - i \cdot \left(j \cdot \frac{y}{t}\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(b \cdot i - i \cdot \left(j \cdot \frac{y}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -2.5:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(b \cdot i - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (* y z)) (* b (- (* t i) (* z c))))))
   (if (<= a -2.3e+88)
     (* a (* x (- (/ (* c j) x) t)))
     (if (<= a -2.5)
       (* x (- (* y z) (* t a)))
       (if (<= a -1.95e-16)
         (* t (- (* b i) (* b (/ (* z c) t))))
         (if (<= a 9.5e-16)
           t_1
           (if (<= a 2.3e+49)
             (+ (* a (* c j)) (* y (- (* x z) (* i j))))
             (if (<= a 1.9e+70) t_1 (* a (- (* c j) (* x t)))))))))))

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)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (a <= -2.3e+88) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (a <= -2.5) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -1.95e-16) {
		tmp = t * ((b * i) - (b * ((z * c) / t)));
	} else if (a <= 9.5e-16) {
		tmp = t_1;
	} else if (a <= 2.3e+49) {
		tmp = (a * (c * j)) + (y * ((x * z) - (i * j)));
	} else if (a <= 1.9e+70) {
		tmp = t_1;
	} else {
		tmp = a * ((c * j) - (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) :: t_1
    real(8) :: tmp
    t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)))
    if (a <= (-2.3d+88)) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (a <= (-2.5d0)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= (-1.95d-16)) then
        tmp = t * ((b * i) - (b * ((z * c) / t)))
    else if (a <= 9.5d-16) then
        tmp = t_1
    else if (a <= 2.3d+49) then
        tmp = (a * (c * j)) + (y * ((x * z) - (i * j)))
    else if (a <= 1.9d+70) then
        tmp = t_1
    else
        tmp = a * ((c * j) - (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 t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (a <= -2.3e+88) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (a <= -2.5) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -1.95e-16) {
		tmp = t * ((b * i) - (b * ((z * c) / t)));
	} else if (a <= 9.5e-16) {
		tmp = t_1;
	} else if (a <= 2.3e+49) {
		tmp = (a * (c * j)) + (y * ((x * z) - (i * j)));
	} else if (a <= 1.9e+70) {
		tmp = t_1;
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if a <= -2.3e+88:
		tmp = a * (x * (((c * j) / x) - t))
	elif a <= -2.5:
		tmp = x * ((y * z) - (t * a))
	elif a <= -1.95e-16:
		tmp = t * ((b * i) - (b * ((z * c) / t)))
	elif a <= 9.5e-16:
		tmp = t_1
	elif a <= 2.3e+49:
		tmp = (a * (c * j)) + (y * ((x * z) - (i * j)))
	elif a <= 1.9e+70:
		tmp = t_1
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (a <= -2.3e+88)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (a <= -2.5)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= -1.95e-16)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(b * Float64(Float64(z * c) / t))));
	elseif (a <= 9.5e-16)
		tmp = t_1;
	elseif (a <= 2.3e+49)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (a <= 1.9e+70)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (a <= -2.3e+88)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (a <= -2.5)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= -1.95e-16)
		tmp = t * ((b * i) - (b * ((z * c) / t)));
	elseif (a <= 9.5e-16)
		tmp = t_1;
	elseif (a <= 2.3e+49)
		tmp = (a * (c * j)) + (y * ((x * z) - (i * j)));
	elseif (a <= 1.9e+70)
		tmp = t_1;
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+88], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.95e-16], N[(t * N[(N[(b * i), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-16], t$95$1, If[LessEqual[a, 2.3e+49], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+70], t$95$1, N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.3000000000000002e88

   1. Initial program 54.6%

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

   3. Taylor expanded in a around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. *-commutative 74.2%

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

      5. *-commutative 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in x around inf 74.9%

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

   if -2.3000000000000002e88 < a < -2.5

   1. Initial program 90.7%

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

   3. Taylor expanded in j around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. *-commutative 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in x around inf 81.3%

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

   if -2.5 < a < -1.94999999999999989e-16

   1. Initial program 49.6%

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

   3. Taylor expanded in b around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in t around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. associate-/l* 75.8%

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

   8. Simplified 75.8%

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

   if -1.94999999999999989e-16 < a < 9.5000000000000005e-16 or 2.30000000000000002e49 < a < 1.8999999999999999e70

   1. Initial program 80.1%

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

   3. Taylor expanded in j around 0 71.5%

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

      1. *-commutative 71.5%

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

      2. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in y around inf 68.6%

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

      1. *-commutative 68.6%

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

   8. Simplified 68.6%

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

   if 9.5000000000000005e-16 < a < 2.30000000000000002e49

   1. Initial program 100.0%

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

   3. Taylor expanded in y around -inf 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in j around inf 80.4%

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

      1. associate-*r* 80.4%

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

      2. *-commutative 80.4%

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

   8. Simplified 80.4%

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

   9. Taylor expanded in y around 0 89.9%

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

   if 1.8999999999999999e70 < a

   1. Initial program 64.1%

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

   3. Taylor expanded in a around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. unsub-neg 68.9%

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

      4. *-commutative 68.9%

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

      5. *-commutative 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -2.5:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(b \cdot i - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+77}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+110}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -3.2e+77)
     t_3
     (if (<= a -2.0)
       t_2
       (if (<= a 9.5e-99)
         t_1
         (if (<= a 8.5e-32)
           t_2
           (if (<= a 8.8e-16)
             t_1
             (if (<= a 2.5e+21)
               (* j (- (* a c) (* y i)))
               (if (<= a 9e+110) (* t (- (* b i) (* x a))) 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 * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.2e+77) {
		tmp = t_3;
	} else if (a <= -2.0) {
		tmp = t_2;
	} else if (a <= 9.5e-99) {
		tmp = t_1;
	} else if (a <= 8.5e-32) {
		tmp = t_2;
	} else if (a <= 8.8e-16) {
		tmp = t_1;
	} else if (a <= 2.5e+21) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 9e+110) {
		tmp = t * ((b * i) - (x * a));
	} 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 * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-3.2d+77)) then
        tmp = t_3
    else if (a <= (-2.0d0)) then
        tmp = t_2
    else if (a <= 9.5d-99) then
        tmp = t_1
    else if (a <= 8.5d-32) then
        tmp = t_2
    else if (a <= 8.8d-16) then
        tmp = t_1
    else if (a <= 2.5d+21) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= 9d+110) then
        tmp = t * ((b * i) - (x * a))
    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 * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.2e+77) {
		tmp = t_3;
	} else if (a <= -2.0) {
		tmp = t_2;
	} else if (a <= 9.5e-99) {
		tmp = t_1;
	} else if (a <= 8.5e-32) {
		tmp = t_2;
	} else if (a <= 8.8e-16) {
		tmp = t_1;
	} else if (a <= 2.5e+21) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 9e+110) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.2e+77:
		tmp = t_3
	elif a <= -2.0:
		tmp = t_2
	elif a <= 9.5e-99:
		tmp = t_1
	elif a <= 8.5e-32:
		tmp = t_2
	elif a <= 8.8e-16:
		tmp = t_1
	elif a <= 2.5e+21:
		tmp = j * ((a * c) - (y * i))
	elif a <= 9e+110:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.2e+77)
		tmp = t_3;
	elseif (a <= -2.0)
		tmp = t_2;
	elseif (a <= 9.5e-99)
		tmp = t_1;
	elseif (a <= 8.5e-32)
		tmp = t_2;
	elseif (a <= 8.8e-16)
		tmp = t_1;
	elseif (a <= 2.5e+21)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= 9e+110)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	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 * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.2e+77)
		tmp = t_3;
	elseif (a <= -2.0)
		tmp = t_2;
	elseif (a <= 9.5e-99)
		tmp = t_1;
	elseif (a <= 8.5e-32)
		tmp = t_2;
	elseif (a <= 8.8e-16)
		tmp = t_1;
	elseif (a <= 2.5e+21)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= 9e+110)
		tmp = t * ((b * i) - (x * a));
	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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+77], t$95$3, If[LessEqual[a, -2.0], t$95$2, If[LessEqual[a, 9.5e-99], t$95$1, If[LessEqual[a, 8.5e-32], t$95$2, If[LessEqual[a, 8.8e-16], t$95$1, If[LessEqual[a, 2.5e+21], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+110], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.2000000000000002e77 or 9.0000000000000005e110 < a

   1. Initial program 60.8%

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

   3. Taylor expanded in a around inf 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

      5. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -3.2000000000000002e77 < a < -2 or 9.5000000000000008e-99 < a < 8.5000000000000003e-32

   1. Initial program 77.5%

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

   3. Taylor expanded in j around 0 74.0%

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

      1. *-commutative 74.0%

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

      2. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in x around inf 78.3%

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

   if -2 < a < 9.5000000000000008e-99 or 8.5000000000000003e-32 < a < 8.80000000000000001e-16

   1. Initial program 79.7%

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

   3. Taylor expanded in b around inf 55.1%

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

      1. *-commutative 55.1%

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

      2. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   if 8.80000000000000001e-16 < a < 2.5e21

   1. Initial program 100.0%

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

   3. Taylor expanded in j around inf 83.7%

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

      1. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   if 2.5e21 < a < 9.0000000000000005e110

   1. Initial program 75.6%

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

   3. Taylor expanded in j around 0 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in z around 0 51.5%

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

      1. associate-*r* 51.5%

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

      2. neg-mul-1 51.5%

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

      3. cancel-sign-sub 51.5%

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

      4. mul-1-neg 51.5%

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

      5. *-commutative 51.5%

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

      6. associate-*r* 57.3%

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

      7. distribute-lft-neg-in 57.3%

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

      8. mul-1-neg 57.3%

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

      9. associate-*r* 63.2%

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

      10. distribute-rgt-in 63.2%

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

      11. +-commutative 63.2%

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

      12. mul-1-neg 63.2%

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

      13. unsub-neg 63.2%

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

   8. Simplified 63.2%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-16}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+110}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t\_1 - a \cdot \left(x \cdot t\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;j \leq -4 \cdot 10^{+72}:\\ \;\;\;\;t\_2 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-91}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;t\_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+211}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (- t_1 (* a (* x t))))
        (t_3 (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z))))))
   (if (<= j -4e+72)
     (+ t_2 (* b (* t i)))
     (if (<= j -8.5e-274)
       (* y (+ (* x z) (- (/ (* t (- (* b i) (* x a))) y) (* i j))))
       (if (<= j 3.6e-91)
         t_3
         (if (<= j 7.8e-16)
           (+ t_1 (* z (- (* x y) (* b c))))
           (if (<= j 4.5e+211) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 - (a * (x * t));
	double t_3 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -4e+72) {
		tmp = t_2 + (b * (t * i));
	} else if (j <= -8.5e-274) {
		tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)));
	} else if (j <= 3.6e-91) {
		tmp = t_3;
	} else if (j <= 7.8e-16) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else if (j <= 4.5e+211) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 - (a * (x * t))
    t_3 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
    if (j <= (-4d+72)) then
        tmp = t_2 + (b * (t * i))
    else if (j <= (-8.5d-274)) then
        tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)))
    else if (j <= 3.6d-91) then
        tmp = t_3
    else if (j <= 7.8d-16) then
        tmp = t_1 + (z * ((x * y) - (b * c)))
    else if (j <= 4.5d+211) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 - (a * (x * t));
	double t_3 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -4e+72) {
		tmp = t_2 + (b * (t * i));
	} else if (j <= -8.5e-274) {
		tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)));
	} else if (j <= 3.6e-91) {
		tmp = t_3;
	} else if (j <= 7.8e-16) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else if (j <= 4.5e+211) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 - (a * (x * t))
	t_3 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
	tmp = 0
	if j <= -4e+72:
		tmp = t_2 + (b * (t * i))
	elif j <= -8.5e-274:
		tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)))
	elif j <= 3.6e-91:
		tmp = t_3
	elif j <= 7.8e-16:
		tmp = t_1 + (z * ((x * y) - (b * c)))
	elif j <= 4.5e+211:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t_1 - Float64(a * Float64(x * t)))
	t_3 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (j <= -4e+72)
		tmp = Float64(t_2 + Float64(b * Float64(t * i)));
	elseif (j <= -8.5e-274)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) / y) - Float64(i * j))));
	elseif (j <= 3.6e-91)
		tmp = t_3;
	elseif (j <= 7.8e-16)
		tmp = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (j <= 4.5e+211)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 - (a * (x * t));
	t_3 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (j <= -4e+72)
		tmp = t_2 + (b * (t * i));
	elseif (j <= -8.5e-274)
		tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)));
	elseif (j <= 3.6e-91)
		tmp = t_3;
	elseif (j <= 7.8e-16)
		tmp = t_1 + (z * ((x * y) - (b * c)));
	elseif (j <= 4.5e+211)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4e+72], N[(t$95$2 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-274], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e-91], t$95$3, If[LessEqual[j, 7.8e-16], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e+211], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3.99999999999999978e72

   1. Initial program 70.3%

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

   3. Taylor expanded in z around 0 75.4%

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

   if -3.99999999999999978e72 < j < -8.49999999999999978e-274

   1. Initial program 65.3%

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

   3. Taylor expanded in y around -inf 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in c around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*r* 70.9%

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

      4. distribute-lft-neg-in 70.9%

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

      5. mul-1-neg 70.9%

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

      6. associate-*r* 75.3%

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

      7. distribute-rgt-in 75.3%

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

      8. +-commutative 75.3%

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

      9. mul-1-neg 75.3%

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

      10. unsub-neg 75.3%

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

   8. Simplified 75.3%

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

   if -8.49999999999999978e-274 < j < 3.6e-91 or 7.79999999999999954e-16 < j < 4.5e211

   1. Initial program 78.8%

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

   3. Taylor expanded in j around 0 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

   5. Simplified 79.0%

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

   if 3.6e-91 < j < 7.79999999999999954e-16

   1. Initial program 69.0%

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

   3. Taylor expanded in z around 0 81.2%

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

   4. Taylor expanded in t around 0 78.0%

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

   if 4.5e211 < j

   1. Initial program 76.4%

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

   3. Taylor expanded in z around 0 82.7%

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

   4. Taylor expanded in b around 0 71.2%

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

   5. Taylor expanded in z around 0 83.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+72}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-91}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+211}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+41} \lor \neg \left(t \leq -7.5 \cdot 10^{-31} \lor \neg \left(t \leq -1.3 \cdot 10^{-215}\right) \land t \leq 5.6 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -4.8e+41)
         (not
          (or (<= t -7.5e-31) (and (not (<= t -1.3e-215)) (<= t 5.6e+57)))))
   (* y (+ (* x z) (- (/ (* t (- (* b i) (* x a))) y) (* i j))))
   (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -4.8e+41) || !((t <= -7.5e-31) || (!(t <= -1.3e-215) && (t <= 5.6e+57)))) {
		tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-4.8d+41)) .or. (.not. (t <= (-7.5d-31)) .or. (.not. (t <= (-1.3d-215))) .and. (t <= 5.6d+57))) then
        tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)))
    else
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -4.8e+41) || !((t <= -7.5e-31) || (!(t <= -1.3e-215) && (t <= 5.6e+57)))) {
		tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -4.8e+41) or not ((t <= -7.5e-31) or (not (t <= -1.3e-215) and (t <= 5.6e+57))):
		tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)))
	else:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -4.8e+41) || !((t <= -7.5e-31) || (!(t <= -1.3e-215) && (t <= 5.6e+57))))
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) / y) - Float64(i * j))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -4.8e+41) || ~(((t <= -7.5e-31) || (~((t <= -1.3e-215)) && (t <= 5.6e+57)))))
		tmp = y * ((x * z) + (((t * ((b * i) - (x * a))) / y) - (i * j)));
	else
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -4.8e+41], N[Not[Or[LessEqual[t, -7.5e-31], And[N[Not[LessEqual[t, -1.3e-215]], $MachinePrecision], LessEqual[t, 5.6e+57]]]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8000000000000003e41 or -7.49999999999999975e-31 < t < -1.3e-215 or 5.59999999999999999e57 < t

   1. Initial program 65.1%

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

   3. Taylor expanded in y around -inf 72.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in c around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*r* 69.7%

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

      4. distribute-lft-neg-in 69.7%

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

      5. mul-1-neg 69.7%

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

      6. associate-*r* 72.1%

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

      7. distribute-rgt-in 74.8%

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

      8. +-commutative 74.8%

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

      9. mul-1-neg 74.8%

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

      10. unsub-neg 74.8%

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

   8. Simplified 74.8%

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

   if -4.8000000000000003e41 < t < -7.49999999999999975e-31 or -1.3e-215 < t < 5.59999999999999999e57

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 84.9%

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

   4. Taylor expanded in t around 0 76.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+41} \lor \neg \left(t \leq -7.5 \cdot 10^{-31} \lor \neg \left(t \leq -1.3 \cdot 10^{-215}\right) \land t \leq 5.6 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+119}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -0.39:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= a -2.4e+119)
     (* a (* x (- (/ (* c j) x) t)))
     (if (<= a -0.39)
       (- t_1 (* x (- (* t a) (* y z))))
       (if (<= a -1.9e-55)
         (* t (* b (- i (* c (/ z t)))))
         (if (<= a 1.52e-16)
           (+ (* x (* y z)) (* b (- (* t i) (* z c))))
           (- t_1 (* 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 t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -2.4e+119) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (a <= -0.39) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else if (a <= -1.9e-55) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (a <= 1.52e-16) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 - (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) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (a <= (-2.4d+119)) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (a <= (-0.39d0)) then
        tmp = t_1 - (x * ((t * a) - (y * z)))
    else if (a <= (-1.9d-55)) then
        tmp = t * (b * (i - (c * (z / t))))
    else if (a <= 1.52d-16) then
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1 - (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 t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -2.4e+119) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (a <= -0.39) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else if (a <= -1.9e-55) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (a <= 1.52e-16) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 - (a * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if a <= -2.4e+119:
		tmp = a * (x * (((c * j) / x) - t))
	elif a <= -0.39:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	elif a <= -1.9e-55:
		tmp = t * (b * (i - (c * (z / t))))
	elif a <= 1.52e-16:
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1 - (a * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (a <= -2.4e+119)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (a <= -0.39)
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (a <= -1.9e-55)
		tmp = Float64(t * Float64(b * Float64(i - Float64(c * Float64(z / t)))));
	elseif (a <= 1.52e-16)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (a <= -2.4e+119)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (a <= -0.39)
		tmp = t_1 - (x * ((t * a) - (y * z)));
	elseif (a <= -1.9e-55)
		tmp = t * (b * (i - (c * (z / t))));
	elseif (a <= 1.52e-16)
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1 - (a * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+119], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.39], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9e-55], N[(t * N[(b * N[(i - N[(c * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.52e-16], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.4e119

   1. Initial program 52.9%

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

   3. Taylor expanded in a around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. *-commutative 75.2%

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

      5. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in x around inf 76.0%

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

   if -2.4e119 < a < -0.39000000000000001

   1. Initial program 75.6%

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

   3. Taylor expanded in b around 0 80.8%

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

   if -0.39000000000000001 < a < -1.8999999999999998e-55

   1. Initial program 53.5%

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

   3. Taylor expanded in b around inf 74.3%

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

      1. *-commutative 74.3%

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

      2. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in t around inf 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

      4. associate-/l* 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in b around 0 80.4%

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

       1. associate-*r/ 80.5%

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

   11. Simplified 80.5%

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

   if -1.8999999999999998e-55 < a < 1.52e-16

   1. Initial program 81.8%

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

   3. Taylor expanded in j around 0 70.4%

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

      1. *-commutative 70.4%

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

      2. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if 1.52e-16 < a

   1. Initial program 71.1%

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

   3. Taylor expanded in z around 0 72.5%

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

   4. Taylor expanded in b around 0 71.2%

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

   5. Taylor expanded in z around 0 71.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+119}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -0.39:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -0.39:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(b \cdot i - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1e+88)
   (* a (* x (- (/ (* c j) x) t)))
   (if (<= a -0.39)
     (* x (- (* y z) (* t a)))
     (if (<= a -1.26e-13)
       (* t (- (* b i) (* b (/ (* z c) t))))
       (if (<= a 4.8e-15)
         (+ (* x (* y z)) (* b (- (* t i) (* z c))))
         (- (* j (- (* a c) (* y 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 (a <= -1e+88) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (a <= -0.39) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -1.26e-13) {
		tmp = t * ((b * i) - (b * ((z * c) / t)));
	} else if (a <= 4.8e-15) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (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 (a <= (-1d+88)) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (a <= (-0.39d0)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= (-1.26d-13)) then
        tmp = t * ((b * i) - (b * ((z * c) / t)))
    else if (a <= 4.8d-15) then
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    else
        tmp = (j * ((a * c) - (y * i))) - (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 (a <= -1e+88) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (a <= -0.39) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -1.26e-13) {
		tmp = t * ((b * i) - (b * ((z * c) / t)));
	} else if (a <= 4.8e-15) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1e+88:
		tmp = a * (x * (((c * j) / x) - t))
	elif a <= -0.39:
		tmp = x * ((y * z) - (t * a))
	elif a <= -1.26e-13:
		tmp = t * ((b * i) - (b * ((z * c) / t)))
	elif a <= 4.8e-15:
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	else:
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1e+88)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (a <= -0.39)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= -1.26e-13)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(b * Float64(Float64(z * c) / t))));
	elseif (a <= 4.8e-15)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - 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 (a <= -1e+88)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (a <= -0.39)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= -1.26e-13)
		tmp = t * ((b * i) - (b * ((z * c) / t)));
	elseif (a <= 4.8e-15)
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	else
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1e+88], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.39], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.26e-13], N[(t * N[(N[(b * i), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-15], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.99999999999999959e87

   1. Initial program 54.6%

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

   3. Taylor expanded in a around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. *-commutative 74.2%

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

      5. *-commutative 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in x around inf 74.9%

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

   if -9.99999999999999959e87 < a < -0.39000000000000001

   1. Initial program 90.7%

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

   3. Taylor expanded in j around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. *-commutative 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in x around inf 81.3%

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

   if -0.39000000000000001 < a < -1.25999999999999993e-13

   1. Initial program 49.6%

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

   3. Taylor expanded in b around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in t around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. associate-/l* 75.8%

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

   8. Simplified 75.8%

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

   if -1.25999999999999993e-13 < a < 4.7999999999999999e-15

   1. Initial program 79.4%

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

   3. Taylor expanded in j around 0 70.6%

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

      1. *-commutative 70.6%

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

      2. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in y around inf 67.6%

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

      1. *-commutative 67.6%

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

   8. Simplified 67.6%

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

   if 4.7999999999999999e-15 < a

   1. Initial program 71.1%

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

   3. Taylor expanded in z around 0 72.5%

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

   4. Taylor expanded in b around 0 71.2%

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

   5. Taylor expanded in z around 0 71.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -0.39:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(b \cdot i - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-224}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (* c j)) (* y (- (* x z) (* i j)))))
        (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -2.8e+100)
     t_2
     (if (<= t 1.7e-308)
       t_1
       (if (<= t 7e-224)
         (* z (- (* x y) (* b c)))
         (if (<= t 1.5e+57) 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 = (a * (c * j)) + (y * ((x * z) - (i * j)));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.8e+100) {
		tmp = t_2;
	} else if (t <= 1.7e-308) {
		tmp = t_1;
	} else if (t <= 7e-224) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.5e+57) {
		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 = (a * (c * j)) + (y * ((x * z) - (i * j)))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-2.8d+100)) then
        tmp = t_2
    else if (t <= 1.7d-308) then
        tmp = t_1
    else if (t <= 7d-224) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1.5d+57) 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 = (a * (c * j)) + (y * ((x * z) - (i * j)));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.8e+100) {
		tmp = t_2;
	} else if (t <= 1.7e-308) {
		tmp = t_1;
	} else if (t <= 7e-224) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.5e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * (c * j)) + (y * ((x * z) - (i * j)))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.8e+100:
		tmp = t_2
	elif t <= 1.7e-308:
		tmp = t_1
	elif t <= 7e-224:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1.5e+57:
		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(a * Float64(c * j)) + Float64(y * Float64(Float64(x * z) - Float64(i * j))))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.8e+100)
		tmp = t_2;
	elseif (t <= 1.7e-308)
		tmp = t_1;
	elseif (t <= 7e-224)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1.5e+57)
		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 = (a * (c * j)) + (y * ((x * z) - (i * j)));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.8e+100)
		tmp = t_2;
	elseif (t <= 1.7e-308)
		tmp = t_1;
	elseif (t <= 7e-224)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1.5e+57)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+100], t$95$2, If[LessEqual[t, 1.7e-308], t$95$1, If[LessEqual[t, 7e-224], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+57], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7999999999999998e100 or 1.5e57 < t

   1. Initial program 60.5%

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

   3. Taylor expanded in j around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in z around 0 59.5%

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

      1. associate-*r* 59.5%

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

      2. neg-mul-1 59.5%

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

      3. cancel-sign-sub 59.5%

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

      4. mul-1-neg 59.5%

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

      5. *-commutative 59.5%

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

      6. associate-*r* 61.5%

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

      7. distribute-lft-neg-in 61.5%

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

      8. mul-1-neg 61.5%

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

      9. associate-*r* 63.4%

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

      10. distribute-rgt-in 67.5%

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

      11. +-commutative 67.5%

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

      12. mul-1-neg 67.5%

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

      13. unsub-neg 67.5%

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

   8. Simplified 67.5%

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

   if -2.7999999999999998e100 < t < 1.7000000000000002e-308 or 7.00000000000000037e-224 < t < 1.5e57

   1. Initial program 79.9%

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

   3. Taylor expanded in y around -inf 77.0%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in j around inf 62.6%

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

      1. associate-*r* 63.9%

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

      2. *-commutative 63.9%

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

   8. Simplified 63.9%

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

   9. Taylor expanded in y around 0 66.7%

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

   if 1.7000000000000002e-308 < t < 7.00000000000000037e-224

   1. Initial program 86.0%

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

   3. Taylor expanded in z around inf 86.0%

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

      1. *-commutative 86.0%

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

   5. Simplified 86.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-224}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= b -8.2e-51)
     (* t (* b (- i (* c (/ z t)))))
     (if (<= b -7.4e-196)
       (* x (- (* y z) (* t a)))
       (if (<= b 8e-239)
         t_1
         (if (<= b 5e-121)
           (* a (- (* c j) (* x t)))
           (if (<= b 5.6e-12) t_1 (* b (- (* t i) (* z 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 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -8.2e-51) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (b <= -7.4e-196) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 8e-239) {
		tmp = t_1;
	} else if (b <= 5e-121) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 5.6e-12) {
		tmp = t_1;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (b <= (-8.2d-51)) then
        tmp = t * (b * (i - (c * (z / t))))
    else if (b <= (-7.4d-196)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 8d-239) then
        tmp = t_1
    else if (b <= 5d-121) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 5.6d-12) then
        tmp = t_1
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -8.2e-51) {
		tmp = t * (b * (i - (c * (z / t))));
	} else if (b <= -7.4e-196) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 8e-239) {
		tmp = t_1;
	} else if (b <= 5e-121) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 5.6e-12) {
		tmp = t_1;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if b <= -8.2e-51:
		tmp = t * (b * (i - (c * (z / t))))
	elif b <= -7.4e-196:
		tmp = x * ((y * z) - (t * a))
	elif b <= 8e-239:
		tmp = t_1
	elif b <= 5e-121:
		tmp = a * ((c * j) - (x * t))
	elif b <= 5.6e-12:
		tmp = t_1
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (b <= -8.2e-51)
		tmp = Float64(t * Float64(b * Float64(i - Float64(c * Float64(z / t)))));
	elseif (b <= -7.4e-196)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 8e-239)
		tmp = t_1;
	elseif (b <= 5e-121)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 5.6e-12)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (b <= -8.2e-51)
		tmp = t * (b * (i - (c * (z / t))));
	elseif (b <= -7.4e-196)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 8e-239)
		tmp = t_1;
	elseif (b <= 5e-121)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 5.6e-12)
		tmp = t_1;
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e-51], N[(t * N[(b * N[(i - N[(c * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.4e-196], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-239], t$95$1, If[LessEqual[b, 5e-121], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e-12], t$95$1, N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.19999999999999947e-51

   1. Initial program 71.0%

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

   3. Taylor expanded in b around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

      4. associate-/l* 57.6%

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

   8. Simplified 57.6%

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

   9. Taylor expanded in b around 0 60.5%

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

       1. associate-*r/ 60.5%

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

   11. Simplified 60.5%

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

   if -8.19999999999999947e-51 < b < -7.4000000000000002e-196

   1. Initial program 78.1%

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

   3. Taylor expanded in j around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in x around inf 61.6%

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

   if -7.4000000000000002e-196 < b < 8.0000000000000006e-239 or 4.99999999999999989e-121 < b < 5.6000000000000004e-12

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 65.8%

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

      1. +-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

      4. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   if 8.0000000000000006e-239 < b < 4.99999999999999989e-121

   1. Initial program 71.3%

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

   3. Taylor expanded in a around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   if 5.6000000000000004e-12 < b

   1. Initial program 72.9%

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

   3. Taylor expanded in b around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. *-commutative 65.4%

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

   5. Simplified 65.4%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(b \cdot \left(i - c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -7e-39)
     t_2
     (if (<= b -2.8e-196)
       (* x (- (* y z) (* t a)))
       (if (<= b 9.8e-238)
         t_1
         (if (<= b 4e-122)
           (* a (- (* c j) (* x t)))
           (if (<= b 3.1e-8) 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 = y * ((x * z) - (i * j));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7e-39) {
		tmp = t_2;
	} else if (b <= -2.8e-196) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 9.8e-238) {
		tmp = t_1;
	} else if (b <= 4e-122) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 3.1e-8) {
		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 = y * ((x * z) - (i * j))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-7d-39)) then
        tmp = t_2
    else if (b <= (-2.8d-196)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 9.8d-238) then
        tmp = t_1
    else if (b <= 4d-122) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 3.1d-8) 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 = y * ((x * z) - (i * j));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7e-39) {
		tmp = t_2;
	} else if (b <= -2.8e-196) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 9.8e-238) {
		tmp = t_1;
	} else if (b <= 4e-122) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 3.1e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7e-39:
		tmp = t_2
	elif b <= -2.8e-196:
		tmp = x * ((y * z) - (t * a))
	elif b <= 9.8e-238:
		tmp = t_1
	elif b <= 4e-122:
		tmp = a * ((c * j) - (x * t))
	elif b <= 3.1e-8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7e-39)
		tmp = t_2;
	elseif (b <= -2.8e-196)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 9.8e-238)
		tmp = t_1;
	elseif (b <= 4e-122)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 3.1e-8)
		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 = y * ((x * z) - (i * j));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7e-39)
		tmp = t_2;
	elseif (b <= -2.8e-196)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 9.8e-238)
		tmp = t_1;
	elseif (b <= 4e-122)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 3.1e-8)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e-39], t$95$2, If[LessEqual[b, -2.8e-196], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e-238], t$95$1, If[LessEqual[b, 4e-122], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-8], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.99999999999999999e-39 or 3.1e-8 < b

   1. Initial program 71.4%

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

   3. Taylor expanded in b around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   if -6.99999999999999999e-39 < b < -2.7999999999999998e-196

   1. Initial program 79.0%

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

   3. Taylor expanded in j around 0 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in x around inf 61.1%

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

   if -2.7999999999999998e-196 < b < 9.7999999999999996e-238 or 4.00000000000000024e-122 < b < 3.1e-8

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 65.8%

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

      1. +-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

      4. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   if 9.7999999999999996e-238 < b < 4.00000000000000024e-122

   1. Initial program 71.3%

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

   3. Taylor expanded in a around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. *-commutative 62.9%

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

   5. Simplified 62.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{if}\;a \leq -0.36:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-230}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-98}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* z (* c (- b)))))
   (if (<= a -0.36)
     t_1
     (if (<= a -1.35e-250)
       (* t (* b i))
       (if (<= a 2.7e-230)
         t_2
         (if (<= a 3.7e-175)
           (* i (* y (- j)))
           (if (<= a 1.02e-98) t_2 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 = a * ((c * j) - (x * t));
	double t_2 = z * (c * -b);
	double tmp;
	if (a <= -0.36) {
		tmp = t_1;
	} else if (a <= -1.35e-250) {
		tmp = t * (b * i);
	} else if (a <= 2.7e-230) {
		tmp = t_2;
	} else if (a <= 3.7e-175) {
		tmp = i * (y * -j);
	} else if (a <= 1.02e-98) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = z * (c * -b)
    if (a <= (-0.36d0)) then
        tmp = t_1
    else if (a <= (-1.35d-250)) then
        tmp = t * (b * i)
    else if (a <= 2.7d-230) then
        tmp = t_2
    else if (a <= 3.7d-175) then
        tmp = i * (y * -j)
    else if (a <= 1.02d-98) then
        tmp = t_2
    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 = a * ((c * j) - (x * t));
	double t_2 = z * (c * -b);
	double tmp;
	if (a <= -0.36) {
		tmp = t_1;
	} else if (a <= -1.35e-250) {
		tmp = t * (b * i);
	} else if (a <= 2.7e-230) {
		tmp = t_2;
	} else if (a <= 3.7e-175) {
		tmp = i * (y * -j);
	} else if (a <= 1.02e-98) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = z * (c * -b)
	tmp = 0
	if a <= -0.36:
		tmp = t_1
	elif a <= -1.35e-250:
		tmp = t * (b * i)
	elif a <= 2.7e-230:
		tmp = t_2
	elif a <= 3.7e-175:
		tmp = i * (y * -j)
	elif a <= 1.02e-98:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(z * Float64(c * Float64(-b)))
	tmp = 0.0
	if (a <= -0.36)
		tmp = t_1;
	elseif (a <= -1.35e-250)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 2.7e-230)
		tmp = t_2;
	elseif (a <= 3.7e-175)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 1.02e-98)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = z * (c * -b);
	tmp = 0.0;
	if (a <= -0.36)
		tmp = t_1;
	elseif (a <= -1.35e-250)
		tmp = t * (b * i);
	elseif (a <= 2.7e-230)
		tmp = t_2;
	elseif (a <= 3.7e-175)
		tmp = i * (y * -j);
	elseif (a <= 1.02e-98)
		tmp = t_2;
	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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.36], t$95$1, If[LessEqual[a, -1.35e-250], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-230], t$95$2, If[LessEqual[a, 3.7e-175], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-98], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.35999999999999999 or 1.02e-98 < a

   1. Initial program 66.6%

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

   3. Taylor expanded in a around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. *-commutative 62.4%

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

      5. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   if -0.35999999999999999 < a < -1.35000000000000001e-250

   1. Initial program 82.7%

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

   3. Taylor expanded in y around -inf 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in c around 0 66.4%

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

      1. mul-1-neg 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-*r* 71.6%

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

      4. distribute-lft-neg-in 71.6%

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

      5. mul-1-neg 71.6%

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

      6. associate-*r* 73.3%

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

      7. distribute-rgt-in 73.3%

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

      8. +-commutative 73.3%

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

      9. mul-1-neg 73.3%

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

      10. unsub-neg 73.3%

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

   8. Simplified 73.3%

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

   9. Taylor expanded in b around inf 40.8%

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

       1. associate-*r* 44.0%

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

   11. Simplified 44.0%

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

   if -1.35000000000000001e-250 < a < 2.70000000000000011e-230 or 3.69999999999999998e-175 < a < 1.02e-98

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 59.4%

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

      1. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in x around 0 41.3%

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

      1. mul-1-neg 41.3%

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

      2. distribute-rgt-neg-in 41.3%

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

   8. Simplified 41.3%

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

   if 2.70000000000000011e-230 < a < 3.69999999999999998e-175

   1. Initial program 83.9%

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

   3. Taylor expanded in y around -inf 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in c around 0 91.5%

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

      1. mul-1-neg 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r* 91.4%

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

      4. distribute-lft-neg-in 91.4%

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

      5. mul-1-neg 91.4%

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

      6. associate-*r* 91.4%

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

      7. distribute-rgt-in 91.4%

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

      8. +-commutative 91.4%

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

      9. mul-1-neg 91.4%

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

      10. unsub-neg 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in j around inf 52.6%

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

       1. associate-*r* 52.6%

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

       2. mul-1-neg 52.6%

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

       3. *-commutative 52.6%

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

   11. Simplified 52.6%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.36:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-230}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -0.42:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+19}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -0.42)
     t_1
     (if (<= a 2.4e-45)
       (* b (- (* t i) (* z c)))
       (if (<= a 3.3e-32)
         (* x (* y z))
         (if (<= a 7.2e+19) (* i (- (* t b) (* y j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -0.42) {
		tmp = t_1;
	} else if (a <= 2.4e-45) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 3.3e-32) {
		tmp = x * (y * z);
	} else if (a <= 7.2e+19) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-0.42d0)) then
        tmp = t_1
    else if (a <= 2.4d-45) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 3.3d-32) then
        tmp = x * (y * z)
    else if (a <= 7.2d+19) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -0.42) {
		tmp = t_1;
	} else if (a <= 2.4e-45) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 3.3e-32) {
		tmp = x * (y * z);
	} else if (a <= 7.2e+19) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -0.42:
		tmp = t_1
	elif a <= 2.4e-45:
		tmp = b * ((t * i) - (z * c))
	elif a <= 3.3e-32:
		tmp = x * (y * z)
	elif a <= 7.2e+19:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -0.42)
		tmp = t_1;
	elseif (a <= 2.4e-45)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 3.3e-32)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 7.2e+19)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -0.42)
		tmp = t_1;
	elseif (a <= 2.4e-45)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 3.3e-32)
		tmp = x * (y * z);
	elseif (a <= 7.2e+19)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.42], t$95$1, If[LessEqual[a, 2.4e-45], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-32], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+19], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.419999999999999984 or 7.2e19 < a

   1. Initial program 65.8%

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

   3. Taylor expanded in a around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

      5. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   if -0.419999999999999984 < a < 2.3999999999999999e-45

   1. Initial program 81.4%

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

   3. Taylor expanded in b around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   if 2.3999999999999999e-45 < a < 3.30000000000000025e-32

   1. Initial program 42.9%

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

   3. Taylor expanded in z around inf 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in x around inf 76.6%

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

      1. *-commutative 76.6%

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

   8. Simplified 76.6%

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

   if 3.30000000000000025e-32 < a < 7.2e19

   1. Initial program 77.8%

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

   3. Taylor expanded in y around -inf 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in i around inf 56.9%

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

   7. Taylor expanded in y around 0 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

      5. *-commutative 56.9%

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

   9. Simplified 56.9%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.42:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+19}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -0.9:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1050000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -0.9)
     t_2
     (if (<= a 2.65e-45)
       t_1
       (if (<= a 4.2e-32)
         (* x (* y z))
         (if (<= a 1050000000000.0) 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 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -0.9) {
		tmp = t_2;
	} else if (a <= 2.65e-45) {
		tmp = t_1;
	} else if (a <= 4.2e-32) {
		tmp = x * (y * z);
	} else if (a <= 1050000000000.0) {
		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 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-0.9d0)) then
        tmp = t_2
    else if (a <= 2.65d-45) then
        tmp = t_1
    else if (a <= 4.2d-32) then
        tmp = x * (y * z)
    else if (a <= 1050000000000.0d0) 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 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -0.9) {
		tmp = t_2;
	} else if (a <= 2.65e-45) {
		tmp = t_1;
	} else if (a <= 4.2e-32) {
		tmp = x * (y * z);
	} else if (a <= 1050000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -0.9:
		tmp = t_2
	elif a <= 2.65e-45:
		tmp = t_1
	elif a <= 4.2e-32:
		tmp = x * (y * z)
	elif a <= 1050000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -0.9)
		tmp = t_2;
	elseif (a <= 2.65e-45)
		tmp = t_1;
	elseif (a <= 4.2e-32)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 1050000000000.0)
		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 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -0.9)
		tmp = t_2;
	elseif (a <= 2.65e-45)
		tmp = t_1;
	elseif (a <= 4.2e-32)
		tmp = x * (y * z);
	elseif (a <= 1050000000000.0)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.9], t$95$2, If[LessEqual[a, 2.65e-45], t$95$1, If[LessEqual[a, 4.2e-32], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1050000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.900000000000000022 or 1.05e12 < a

   1. Initial program 66.4%

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

   3. Taylor expanded in a around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

      4. *-commutative 66.7%

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

      5. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if -0.900000000000000022 < a < 2.6499999999999999e-45 or 4.1999999999999998e-32 < a < 1.05e12

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf 54.5%

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

      1. *-commutative 54.5%

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

      2. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   if 2.6499999999999999e-45 < a < 4.1999999999999998e-32

   1. Initial program 42.9%

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

   3. Taylor expanded in z around inf 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in x around inf 76.6%

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

      1. *-commutative 76.6%

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

   8. Simplified 76.6%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.9:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1050000000000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+130} \lor \neg \left(t \leq 1.6 \cdot 10^{+78}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.8e+130) (not (<= t 1.6e+78)))
   (* t (- (* b i) (* x a)))
   (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.8e+130) || !(t <= 1.6e+78)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.8d+130)) .or. (.not. (t <= 1.6d+78))) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.8e+130) || !(t <= 1.6e+78)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.8e+130) or not (t <= 1.6e+78):
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.8e+130) || !(t <= 1.6e+78))
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.8e+130) || ~((t <= 1.6e+78)))
		tmp = t * ((b * i) - (x * a));
	else
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.8e+130], N[Not[LessEqual[t, 1.6e+78]], $MachinePrecision]], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8000000000000001e130 or 1.59999999999999997e78 < t

   1. Initial program 59.0%

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

   3. Taylor expanded in j around 0 67.9%

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

      1. *-commutative 67.9%

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

      2. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in z around 0 60.0%

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

      1. associate-*r* 60.0%

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

      2. neg-mul-1 60.0%

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

      3. cancel-sign-sub 60.0%

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

      4. mul-1-neg 60.0%

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

      5. *-commutative 60.0%

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

      6. associate-*r* 62.2%

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

      7. distribute-lft-neg-in 62.2%

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

      8. mul-1-neg 62.2%

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

      9. associate-*r* 64.2%

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

      10. distribute-rgt-in 68.6%

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

      11. +-commutative 68.6%

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

      12. mul-1-neg 68.6%

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

      13. unsub-neg 68.6%

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

   8. Simplified 68.6%

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

   if -1.8000000000000001e130 < t < 1.59999999999999997e78

   1. Initial program 80.5%

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

   3. Taylor expanded in z around 0 79.2%

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

   4. Taylor expanded in t around 0 68.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+130} \lor \neg \left(t \leq 1.6 \cdot 10^{+78}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.35 \cdot 10^{+79}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.35e+79)
     (- t_1 (* a (* x t)))
     (if (<= j 5.8e-93)
       (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z))))
       (+ 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.35e+79) {
		tmp = t_1 - (a * (x * t));
	} else if (j <= 5.8e-93) {
		tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-2.35d+79)) then
        tmp = t_1 - (a * (x * t))
    else if (j <= 5.8d-93) then
        tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
    else
        tmp = t_1 + (z * ((x * y) - (b * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.35e+79) {
		tmp = t_1 - (a * (x * t));
	} else if (j <= 5.8e-93) {
		tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.35e+79:
		tmp = t_1 - (a * (x * t))
	elif j <= 5.8e-93:
		tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
	else:
		tmp = t_1 + (z * ((x * y) - (b * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.35e+79)
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	elseif (j <= 5.8e-93)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.35e+79)
		tmp = t_1 - (a * (x * t));
	elseif (j <= 5.8e-93)
		tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	else
		tmp = t_1 + (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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.35e+79], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e-93], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.35000000000000011e79

   1. Initial program 69.2%

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

   3. Taylor expanded in z around 0 65.7%

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

   4. Taylor expanded in b around 0 71.2%

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

   5. Taylor expanded in z around 0 73.0%

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

   if -2.35000000000000011e79 < j < 5.7999999999999997e-93

   1. Initial program 74.0%

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

   3. Taylor expanded in j around 0 73.9%

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

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   if 5.7999999999999997e-93 < j

   1. Initial program 73.3%

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

   3. Taylor expanded in z around 0 76.1%

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

   4. Taylor expanded in t around 0 69.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.35 \cdot 10^{+79}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.06e+140)
   (* x (* t (- a)))
   (if (<= t -2.2e-64)
     (* i (* t b))
     (if (<= t 5.7e+60) (* z (* x y)) (* b (* t i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.06e+140) {
		tmp = x * (t * -a);
	} else if (t <= -2.2e-64) {
		tmp = i * (t * b);
	} else if (t <= 5.7e+60) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-1.06d+140)) then
        tmp = x * (t * -a)
    else if (t <= (-2.2d-64)) then
        tmp = i * (t * b)
    else if (t <= 5.7d+60) then
        tmp = z * (x * y)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.06e+140) {
		tmp = x * (t * -a);
	} else if (t <= -2.2e-64) {
		tmp = i * (t * b);
	} else if (t <= 5.7e+60) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.06e+140:
		tmp = x * (t * -a)
	elif t <= -2.2e-64:
		tmp = i * (t * b)
	elif t <= 5.7e+60:
		tmp = z * (x * y)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.06e+140)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (t <= -2.2e-64)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 5.7e+60)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.06e+140)
		tmp = x * (t * -a);
	elseif (t <= -2.2e-64)
		tmp = i * (t * b);
	elseif (t <= 5.7e+60)
		tmp = z * (x * y);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.06e+140], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.2e-64], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.7e+60], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.0600000000000001e140

   1. Initial program 63.7%

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

   3. Taylor expanded in j around 0 75.9%

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

      1. *-commutative 75.9%

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

      2. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in x around inf 52.9%

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

   7. Taylor expanded in y around 0 47.5%

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

      1. neg-mul-1 47.5%

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

      2. distribute-rgt-neg-in 47.5%

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

   9. Simplified 47.5%

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

   if -1.0600000000000001e140 < t < -2.2e-64

   1. Initial program 81.8%

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

   3. Taylor expanded in y around -inf 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in i around inf 51.6%

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

   7. Taylor expanded in y around 0 31.0%

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

      1. *-commutative 31.0%

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

   9. Simplified 31.0%

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

   if -2.2e-64 < t < 5.69999999999999978e60

   1. Initial program 79.6%

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

   3. Taylor expanded in z around inf 54.9%

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

      1. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in x around inf 40.9%

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

      1. *-commutative 40.9%

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

   8. Simplified 40.9%

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

   if 5.69999999999999978e60 < t

   1. Initial program 56.6%

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

   3. Taylor expanded in y around -inf 58.6%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in c around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. *-commutative 59.2%

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

      3. associate-*r* 64.5%

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

      4. distribute-lft-neg-in 64.5%

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

      5. mul-1-neg 64.5%

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

      6. associate-*r* 69.5%

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

      7. distribute-rgt-in 73.0%

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

      8. +-commutative 73.0%

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

      9. mul-1-neg 73.0%

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

      10. unsub-neg 73.0%

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

   8. Simplified 73.0%

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

   9. Taylor expanded in b around inf 45.6%

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

       1. *-commutative 45.6%

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

   11. Simplified 45.6%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+141}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-64}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.4e+141)
   (* (* x t) (- a))
   (if (<= t -1.65e-64)
     (* i (* t b))
     (if (<= t 2.5e+75) (* z (* x y)) (* b (* t i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.4e+141) {
		tmp = (x * t) * -a;
	} else if (t <= -1.65e-64) {
		tmp = i * (t * b);
	} else if (t <= 2.5e+75) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-1.4d+141)) then
        tmp = (x * t) * -a
    else if (t <= (-1.65d-64)) then
        tmp = i * (t * b)
    else if (t <= 2.5d+75) then
        tmp = z * (x * y)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.4e+141) {
		tmp = (x * t) * -a;
	} else if (t <= -1.65e-64) {
		tmp = i * (t * b);
	} else if (t <= 2.5e+75) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.4e+141:
		tmp = (x * t) * -a
	elif t <= -1.65e-64:
		tmp = i * (t * b)
	elif t <= 2.5e+75:
		tmp = z * (x * y)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.4e+141)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (t <= -1.65e-64)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 2.5e+75)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.4e+141)
		tmp = (x * t) * -a;
	elseif (t <= -1.65e-64)
		tmp = i * (t * b);
	elseif (t <= 2.5e+75)
		tmp = z * (x * y);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.4e+141], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[t, -1.65e-64], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+75], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.39999999999999996e141

   1. Initial program 63.7%

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

   3. Taylor expanded in a around inf 56.1%

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

      1. +-commutative 56.1%

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

      2. mul-1-neg 56.1%

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

      3. unsub-neg 56.1%

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

      4. *-commutative 56.1%

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

      5. *-commutative 56.1%

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

   5. Simplified 56.1%

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

   6. Taylor expanded in j around 0 46.8%

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

      1. mul-1-neg 46.8%

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

      2. *-commutative 46.8%

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

      3. distribute-rgt-neg-in 46.8%

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

      4. distribute-lft-neg-in 46.8%

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

      5. *-commutative 46.8%

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

   8. Simplified 46.8%

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

   if -1.39999999999999996e141 < t < -1.65e-64

   1. Initial program 81.8%

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

   3. Taylor expanded in y around -inf 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in i around inf 51.6%

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

   7. Taylor expanded in y around 0 31.0%

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

      1. *-commutative 31.0%

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

   9. Simplified 31.0%

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

   if -1.65e-64 < t < 2.5000000000000001e75

   1. Initial program 79.6%

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

   3. Taylor expanded in z around inf 54.9%

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

      1. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in x around inf 40.9%

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

      1. *-commutative 40.9%

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

   8. Simplified 40.9%

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

   if 2.5000000000000001e75 < t

   1. Initial program 56.6%

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

   3. Taylor expanded in y around -inf 58.6%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in c around 0 59.2%

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

      1. mul-1-neg 59.2%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      2. *-commutative 59.2%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-a \cdot \color{blue}{\left(x \cdot t\right)}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      3. associate-*r* 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-\color{blue}{\left(a \cdot x\right) \cdot t}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      4. distribute-lft-neg-in 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot x\right) \cdot t} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      5. mul-1-neg 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \cdot t + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      6. associate-*r* 69.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(b \cdot i\right) \cdot t}}{y}\right) - x \cdot z\right)\right) \]

      7. distribute-rgt-in 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)}}{y}\right) - x \cdot z\right)\right) \]

      8. +-commutative 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)}}{y}\right) - x \cdot z\right)\right) \]

      9. mul-1-neg 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right)}{y}\right) - x \cdot z\right)\right) \]

      10. unsub-neg 73.0%

          \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)}}{y}\right) - x \cdot z\right)\right) \]

   8. Simplified 73.0%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{t \cdot \left(b \cdot i - a \cdot x\right)}{y}}\right) - x \cdot z\right)\right) \]

   9. Taylor expanded in b around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 45.6%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 45.6%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+141}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-64}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-26} \lor \neg \left(b \leq 4.4 \cdot 10^{-102}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.5e-26) (not (<= b 4.4e-102))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.5e-26) || !(b <= 4.4e-102)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.5d-26)) .or. (.not. (b <= 4.4d-102))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.5e-26) || !(b <= 4.4e-102)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.5e-26) or not (b <= 4.4e-102):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.5e-26) || !(b <= 4.4e-102))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.5e-26) || ~((b <= 4.4e-102)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.5e-26], N[Not[LessEqual[b, 4.4e-102]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.50000000000000006e-26 or 4.40000000000000026e-102 < b

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 70.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 72.6%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)}{y}\right) - x \cdot z\right)\right)} \]

   6. Taylor expanded in c around 0 61.1%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + b \cdot \left(i \cdot t\right)}{y}}\right) - x \cdot z\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 61.1%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      2. *-commutative 61.1%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-a \cdot \color{blue}{\left(x \cdot t\right)}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      3. associate-*r* 61.1%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-\color{blue}{\left(a \cdot x\right) \cdot t}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      4. distribute-lft-neg-in 61.1%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot x\right) \cdot t} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      5. mul-1-neg 61.1%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \cdot t + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      6. associate-*r* 60.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(b \cdot i\right) \cdot t}}{y}\right) - x \cdot z\right)\right) \]

      7. distribute-rgt-in 63.3%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)}}{y}\right) - x \cdot z\right)\right) \]

      8. +-commutative 63.3%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)}}{y}\right) - x \cdot z\right)\right) \]

      9. mul-1-neg 63.3%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right)}{y}\right) - x \cdot z\right)\right) \]

      10. unsub-neg 63.3%

          \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)}}{y}\right) - x \cdot z\right)\right) \]

   8. Simplified 63.3%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{t \cdot \left(b \cdot i - a \cdot x\right)}{y}}\right) - x \cdot z\right)\right) \]

   9. Taylor expanded in b around inf 38.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 38.4%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 38.4%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -1.50000000000000006e-26 < b < 4.40000000000000026e-102

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 49.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 49.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 49.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 49.2%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 49.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-26} \lor \neg \left(b \leq 4.4 \cdot 10^{-102}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.9e-64)
   (* i (* t b))
   (if (<= t 2.25e+56) (* z (* x y)) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.9e-64) {
		tmp = i * (t * b);
	} else if (t <= 2.25e+56) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-1.9d-64)) then
        tmp = i * (t * b)
    else if (t <= 2.25d+56) then
        tmp = z * (x * y)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.9e-64) {
		tmp = i * (t * b);
	} else if (t <= 2.25e+56) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.9e-64:
		tmp = i * (t * b)
	elif t <= 2.25e+56:
		tmp = z * (x * y)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.9e-64)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 2.25e+56)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.9e-64)
		tmp = i * (t * b);
	elseif (t <= 2.25e+56)
		tmp = z * (x * y);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.9e-64], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+56], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9000000000000001e-64

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 78.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 79.6%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)}{y}\right) - x \cdot z\right)\right)} \]

   6. Taylor expanded in i around inf 47.9%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(\frac{b \cdot t}{y} - j\right)\right)} \]

   7. Taylor expanded in y around 0 31.3%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 31.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   9. Simplified 31.3%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   if -1.9000000000000001e-64 < t < 2.2500000000000002e56

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 54.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.9%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   5. Simplified 54.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   6. Taylor expanded in x around inf 40.9%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.9%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   8. Simplified 40.9%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   if 2.2500000000000002e56 < t

   1. Initial program 56.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 58.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 62.1%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)}{y}\right) - x \cdot z\right)\right)} \]

   6. Taylor expanded in c around 0 59.2%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + b \cdot \left(i \cdot t\right)}{y}}\right) - x \cdot z\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 59.2%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      2. *-commutative 59.2%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-a \cdot \color{blue}{\left(x \cdot t\right)}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      3. associate-*r* 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-\color{blue}{\left(a \cdot x\right) \cdot t}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      4. distribute-lft-neg-in 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot x\right) \cdot t} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      5. mul-1-neg 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \cdot t + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      6. associate-*r* 69.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(b \cdot i\right) \cdot t}}{y}\right) - x \cdot z\right)\right) \]

      7. distribute-rgt-in 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)}}{y}\right) - x \cdot z\right)\right) \]

      8. +-commutative 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)}}{y}\right) - x \cdot z\right)\right) \]

      9. mul-1-neg 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right)}{y}\right) - x \cdot z\right)\right) \]

      10. unsub-neg 73.0%

          \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)}}{y}\right) - x \cdot z\right)\right) \]

   8. Simplified 73.0%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{t \cdot \left(b \cdot i - a \cdot x\right)}{y}}\right) - x \cdot z\right)\right) \]

   9. Taylor expanded in b around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 45.6%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 45.6%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -2.2e-64)
   (* i (* t b))
   (if (<= t 2.6e+60) (* y (* x z)) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.2e-64) {
		tmp = i * (t * b);
	} else if (t <= 2.6e+60) {
		tmp = y * (x * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-2.2d-64)) then
        tmp = i * (t * b)
    else if (t <= 2.6d+60) then
        tmp = y * (x * z)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.2e-64) {
		tmp = i * (t * b);
	} else if (t <= 2.6e+60) {
		tmp = y * (x * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -2.2e-64:
		tmp = i * (t * b)
	elif t <= 2.6e+60:
		tmp = y * (x * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -2.2e-64)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 2.6e+60)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -2.2e-64)
		tmp = i * (t * b);
	elseif (t <= 2.6e+60)
		tmp = y * (x * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -2.2e-64], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+60], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2e-64

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 78.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 79.6%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)}{y}\right) - x \cdot z\right)\right)} \]

   6. Taylor expanded in i around inf 47.9%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(\frac{b \cdot t}{y} - j\right)\right)} \]

   7. Taylor expanded in y around 0 31.3%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 31.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   9. Simplified 31.3%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   if -2.2e-64 < t < 2.60000000000000008e60

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 80.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]

   4. Taylor expanded in b around 0 65.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right)} \]

   5. Taylor expanded in z around inf 38.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.9%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 40.9%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

      3. associate-*r* 40.1%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   7. Simplified 40.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 2.60000000000000008e60 < t

   1. Initial program 56.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 58.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 62.1%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)}{y}\right) - x \cdot z\right)\right)} \]

   6. Taylor expanded in c around 0 59.2%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + b \cdot \left(i \cdot t\right)}{y}}\right) - x \cdot z\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 59.2%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      2. *-commutative 59.2%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-a \cdot \color{blue}{\left(x \cdot t\right)}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      3. associate-*r* 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-\color{blue}{\left(a \cdot x\right) \cdot t}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      4. distribute-lft-neg-in 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot x\right) \cdot t} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      5. mul-1-neg 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \cdot t + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      6. associate-*r* 69.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(b \cdot i\right) \cdot t}}{y}\right) - x \cdot z\right)\right) \]

      7. distribute-rgt-in 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)}}{y}\right) - x \cdot z\right)\right) \]

      8. +-commutative 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)}}{y}\right) - x \cdot z\right)\right) \]

      9. mul-1-neg 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right)}{y}\right) - x \cdot z\right)\right) \]

      10. unsub-neg 73.0%

          \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)}}{y}\right) - x \cdot z\right)\right) \]

   8. Simplified 73.0%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{t \cdot \left(b \cdot i - a \cdot x\right)}{y}}\right) - x \cdot z\right)\right) \]

   9. Taylor expanded in b around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 45.6%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 45.6%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 25: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -6.6e-66)
   (* i (* t b))
   (if (<= t 3e+74) (* x (* y z)) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -6.6e-66) {
		tmp = i * (t * b);
	} else if (t <= 3e+74) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-6.6d-66)) then
        tmp = i * (t * b)
    else if (t <= 3d+74) then
        tmp = x * (y * z)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -6.6e-66) {
		tmp = i * (t * b);
	} else if (t <= 3e+74) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -6.6e-66:
		tmp = i * (t * b)
	elif t <= 3e+74:
		tmp = x * (y * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -6.6e-66)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 3e+74)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -6.6e-66)
		tmp = i * (t * b);
	elseif (t <= 3e+74)
		tmp = x * (y * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -6.6e-66], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+74], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5999999999999998e-66

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 78.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 79.6%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)}{y}\right) - x \cdot z\right)\right)} \]

   6. Taylor expanded in i around inf 47.9%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(\frac{b \cdot t}{y} - j\right)\right)} \]

   7. Taylor expanded in y around 0 31.3%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 31.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   9. Simplified 31.3%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   if -6.5999999999999998e-66 < t < 3e74

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 54.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.9%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   5. Simplified 54.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   6. Taylor expanded in x around inf 38.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   8. Simplified 38.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 3e74 < t

   1. Initial program 56.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 58.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 62.1%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)}{y}\right) - x \cdot z\right)\right)} \]

   6. Taylor expanded in c around 0 59.2%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + b \cdot \left(i \cdot t\right)}{y}}\right) - x \cdot z\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 59.2%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      2. *-commutative 59.2%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-a \cdot \color{blue}{\left(x \cdot t\right)}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      3. associate-*r* 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-\color{blue}{\left(a \cdot x\right) \cdot t}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      4. distribute-lft-neg-in 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot x\right) \cdot t} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      5. mul-1-neg 64.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \cdot t + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      6. associate-*r* 69.5%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(b \cdot i\right) \cdot t}}{y}\right) - x \cdot z\right)\right) \]

      7. distribute-rgt-in 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)}}{y}\right) - x \cdot z\right)\right) \]

      8. +-commutative 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)}}{y}\right) - x \cdot z\right)\right) \]

      9. mul-1-neg 73.0%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right)}{y}\right) - x \cdot z\right)\right) \]

      10. unsub-neg 73.0%

          \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)}}{y}\right) - x \cdot z\right)\right) \]

   8. Simplified 73.0%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{t \cdot \left(b \cdot i - a \cdot x\right)}{y}}\right) - x \cdot z\right)\right) \]

   9. Taylor expanded in b around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 45.6%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 45.6%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-31}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4.2e-31)
   (* i (* t b))
   (if (<= b 4.4e-102) (* a (* c j)) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.2e-31) {
		tmp = i * (t * b);
	} else if (b <= 4.4e-102) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-4.2d-31)) then
        tmp = i * (t * b)
    else if (b <= 4.4d-102) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.2e-31) {
		tmp = i * (t * b);
	} else if (b <= 4.4e-102) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4.2e-31:
		tmp = i * (t * b)
	elif b <= 4.4e-102:
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4.2e-31)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= 4.4e-102)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -4.2e-31)
		tmp = i * (t * b);
	elseif (b <= 4.4e-102)
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4.2e-31], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e-102], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.19999999999999982e-31

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 66.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 69.5%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)}{y}\right) - x \cdot z\right)\right)} \]

   6. Taylor expanded in i around inf 49.1%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(\frac{b \cdot t}{y} - j\right)\right)} \]

   7. Taylor expanded in y around 0 40.6%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   9. Simplified 40.6%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   if -4.19999999999999982e-31 < b < 4.40000000000000026e-102

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 49.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 49.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 49.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 49.2%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 49.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if 4.40000000000000026e-102 < b

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 73.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 75.1%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)}{y}\right) - x \cdot z\right)\right)} \]

   6. Taylor expanded in c around 0 63.7%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + b \cdot \left(i \cdot t\right)}{y}}\right) - x \cdot z\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 63.7%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      2. *-commutative 63.7%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-a \cdot \color{blue}{\left(x \cdot t\right)}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      3. associate-*r* 65.1%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-\color{blue}{\left(a \cdot x\right) \cdot t}\right) + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      4. distribute-lft-neg-in 65.1%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-a \cdot x\right) \cdot t} + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      5. mul-1-neg 65.1%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \cdot t + b \cdot \left(i \cdot t\right)}{y}\right) - x \cdot z\right)\right) \]

      6. associate-*r* 63.8%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(b \cdot i\right) \cdot t}}{y}\right) - x \cdot z\right)\right) \]

      7. distribute-rgt-in 66.4%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{\color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)}}{y}\right) - x \cdot z\right)\right) \]

      8. +-commutative 66.4%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)}}{y}\right) - x \cdot z\right)\right) \]

      9. mul-1-neg 66.4%

         \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right)}{y}\right) - x \cdot z\right)\right) \]

      10. unsub-neg 66.4%

          \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \frac{t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)}}{y}\right) - x \cdot z\right)\right) \]

   8. Simplified 66.4%

      \[\leadsto y \cdot \left(-\left(\left(j \cdot i - \color{blue}{\frac{t \cdot \left(b \cdot i - a \cdot x\right)}{y}}\right) - x \cdot z\right)\right) \]

   9. Taylor expanded in b around inf 36.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 36.7%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 36.7%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 27: 22.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.8%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 41.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 41.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 41.0%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 41.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 41.0%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. *-commutative 41.0%

      \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

5. Simplified 41.0%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

6. Taylor expanded in j around inf 20.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Add Preprocessing

Developer target: 59.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))