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

Percentage Accurate: 74.1% → 82.4%

Time: 33.8s

Alternatives: 22

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.1% 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: 82.4% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $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 89.9%

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

      1. +-commutative 89.9%

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

      2. fma-define 89.9%

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

      3. *-commutative 89.9%

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

      4. *-commutative 89.9%

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

      5. *-commutative 89.9%

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

      6. *-commutative 89.9%

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

      7. *-commutative 89.9%

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

      8. *-commutative 89.9%

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

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   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 a around -inf 16.0%

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

   5. Simplified 21.1%

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

   6. Taylor expanded in t around inf 53.0%

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

4. Final simplification 81.7%

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

Alternative 2: 82.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $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 89.9%

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

   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 a around -inf 16.0%

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

   5. Simplified 21.1%

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

   6. Taylor expanded in t around inf 53.0%

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

4. Final simplification 81.6%

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

Alternative 3: 29.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+92}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-206}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-92}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{+103}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -6.2e+156)
     t_1
     (if (<= b -4.2e+92)
       (* (* z c) (- b))
       (if (<= b -4e+73)
         t_1
         (if (<= b -9.8e-206)
           (* z (* x y))
           (if (<= b 1.2e-92)
             (* a (* c j))
             (if (<= b 1.36e+19)
               (* x (* t (- a)))
               (if (<= b 6.3e+103)
                 (* y (* i (- j)))
                 (if (<= b 1.25e+112) (* x (* y z)) 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 = i * (t * b);
	double tmp;
	if (b <= -6.2e+156) {
		tmp = t_1;
	} else if (b <= -4.2e+92) {
		tmp = (z * c) * -b;
	} else if (b <= -4e+73) {
		tmp = t_1;
	} else if (b <= -9.8e-206) {
		tmp = z * (x * y);
	} else if (b <= 1.2e-92) {
		tmp = a * (c * j);
	} else if (b <= 1.36e+19) {
		tmp = x * (t * -a);
	} else if (b <= 6.3e+103) {
		tmp = y * (i * -j);
	} else if (b <= 1.25e+112) {
		tmp = x * (y * z);
	} 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 = i * (t * b)
    if (b <= (-6.2d+156)) then
        tmp = t_1
    else if (b <= (-4.2d+92)) then
        tmp = (z * c) * -b
    else if (b <= (-4d+73)) then
        tmp = t_1
    else if (b <= (-9.8d-206)) then
        tmp = z * (x * y)
    else if (b <= 1.2d-92) then
        tmp = a * (c * j)
    else if (b <= 1.36d+19) then
        tmp = x * (t * -a)
    else if (b <= 6.3d+103) then
        tmp = y * (i * -j)
    else if (b <= 1.25d+112) then
        tmp = x * (y * z)
    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 = i * (t * b);
	double tmp;
	if (b <= -6.2e+156) {
		tmp = t_1;
	} else if (b <= -4.2e+92) {
		tmp = (z * c) * -b;
	} else if (b <= -4e+73) {
		tmp = t_1;
	} else if (b <= -9.8e-206) {
		tmp = z * (x * y);
	} else if (b <= 1.2e-92) {
		tmp = a * (c * j);
	} else if (b <= 1.36e+19) {
		tmp = x * (t * -a);
	} else if (b <= 6.3e+103) {
		tmp = y * (i * -j);
	} else if (b <= 1.25e+112) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -6.2e+156:
		tmp = t_1
	elif b <= -4.2e+92:
		tmp = (z * c) * -b
	elif b <= -4e+73:
		tmp = t_1
	elif b <= -9.8e-206:
		tmp = z * (x * y)
	elif b <= 1.2e-92:
		tmp = a * (c * j)
	elif b <= 1.36e+19:
		tmp = x * (t * -a)
	elif b <= 6.3e+103:
		tmp = y * (i * -j)
	elif b <= 1.25e+112:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -6.2e+156)
		tmp = t_1;
	elseif (b <= -4.2e+92)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (b <= -4e+73)
		tmp = t_1;
	elseif (b <= -9.8e-206)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.2e-92)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 1.36e+19)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (b <= 6.3e+103)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (b <= 1.25e+112)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (b <= -6.2e+156)
		tmp = t_1;
	elseif (b <= -4.2e+92)
		tmp = (z * c) * -b;
	elseif (b <= -4e+73)
		tmp = t_1;
	elseif (b <= -9.8e-206)
		tmp = z * (x * y);
	elseif (b <= 1.2e-92)
		tmp = a * (c * j);
	elseif (b <= 1.36e+19)
		tmp = x * (t * -a);
	elseif (b <= 6.3e+103)
		tmp = y * (i * -j);
	elseif (b <= 1.25e+112)
		tmp = x * (y * z);
	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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e+156], t$95$1, If[LessEqual[b, -4.2e+92], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[b, -4e+73], t$95$1, If[LessEqual[b, -9.8e-206], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-92], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.36e+19], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.3e+103], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+112], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -6.2000000000000004e156 or -4.19999999999999972e92 < b < -3.99999999999999993e73 or 1.25e112 < b

   1. Initial program 69.4%

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

   3. Taylor expanded in a around -inf 69.4%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around inf 58.6%

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

   7. Taylor expanded in b around inf 51.1%

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

   8. Taylor expanded in t around 0 53.4%

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

      1. *-commutative 53.4%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

   10. Simplified 55.9%

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

   if -6.2000000000000004e156 < b < -4.19999999999999972e92

   1. Initial program 60.0%

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

      1. prod-diff 60.0%

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

      2. *-commutative 60.0%

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

      3. fma-neg 60.0%

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

      4. distribute-rgt-in 60.0%

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

      5. *-commutative 60.0%

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

      6. *-commutative 60.0%

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

      7. *-commutative 60.0%

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

      8. *-commutative 60.0%

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

   4. Applied egg-rr 60.0%

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

   5. Taylor expanded in x around 0 60.2%

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

      1. *-commutative 60.2%

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

      2. +-commutative 60.2%

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

      3. distribute-lft1-in 60.2%

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

      4. metadata-eval 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \left(\color{blue}{0} \cdot \left(i \cdot t\right)\right)\right) \]

      5. mul0-lft 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \color{blue}{0}\right) \]

      6. distribute-lft-in 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(\left(c \cdot z - i \cdot t\right) + 0\right)} \]

      7. add0 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in z around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-rgt-neg-in 54.3%

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

      3. distribute-rgt-neg-in 54.3%

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

   10. Simplified 54.3%

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

   if -3.99999999999999993e73 < b < -9.7999999999999999e-206

   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 y around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in z around inf 36.8%

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

      1. associate-*r* 38.3%

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

   8. Simplified 38.3%

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

   if -9.7999999999999999e-206 < b < 1.2000000000000001e-92

   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 a around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. unsub-neg 65.5%

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

      4. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in j around inf 43.7%

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

   if 1.2000000000000001e-92 < b < 1.36e19

   1. Initial program 52.4%

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

   3. Taylor expanded in a around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in j around 0 45.4%

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

      1. associate-*r* 45.4%

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

      2. neg-mul-1 45.4%

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

   8. Simplified 45.4%

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

      1. add0 45.4%

         \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x\right) + 0} \]

      2. associate-*r* 53.0%

         \[\leadsto \color{blue}{\left(\left(-a\right) \cdot t\right) \cdot x} + 0 \]

   10. Applied egg-rr 53.0%

       \[\leadsto \color{blue}{\left(\left(-a\right) \cdot t\right) \cdot x + 0} \]

   if 1.36e19 < b < 6.29999999999999969e103

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf 54.5%

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

      1. +-commutative 54.5%

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

      2. mul-1-neg 54.5%

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

      3. unsub-neg 54.5%

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

      4. *-commutative 54.5%

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

      5. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in z around 0 40.1%

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

      1. mul-1-neg 40.1%

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

      2. distribute-rgt-neg-in 40.1%

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

   8. Simplified 40.1%

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

   if 6.29999999999999969e103 < b < 1.25e112

   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 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+156}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+92}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-206}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-92}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{+103}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-75}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + t\_2\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i)))))
        (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1e+68)
     t_2
     (if (<= b -8.8e-27)
       t_1
       (if (<= b -4.2e-75)
         (+ (* j (* a c)) t_2)
         (if (<= b -1.4e-100)
           (* y (- (* x z) (* i j)))
           (if (<= b 1.6e+112) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1e+68) {
		tmp = t_2;
	} else if (b <= -8.8e-27) {
		tmp = t_1;
	} else if (b <= -4.2e-75) {
		tmp = (j * (a * c)) + t_2;
	} else if (b <= -1.4e-100) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.6e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1d+68)) then
        tmp = t_2
    else if (b <= (-8.8d-27)) then
        tmp = t_1
    else if (b <= (-4.2d-75)) then
        tmp = (j * (a * c)) + t_2
    else if (b <= (-1.4d-100)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1.6d+112) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1e+68) {
		tmp = t_2;
	} else if (b <= -8.8e-27) {
		tmp = t_1;
	} else if (b <= -4.2e-75) {
		tmp = (j * (a * c)) + t_2;
	} else if (b <= -1.4e-100) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.6e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1e+68:
		tmp = t_2
	elif b <= -8.8e-27:
		tmp = t_1
	elif b <= -4.2e-75:
		tmp = (j * (a * c)) + t_2
	elif b <= -1.4e-100:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1.6e+112:
		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(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1e+68)
		tmp = t_2;
	elseif (b <= -8.8e-27)
		tmp = t_1;
	elseif (b <= -4.2e-75)
		tmp = Float64(Float64(j * Float64(a * c)) + t_2);
	elseif (b <= -1.4e-100)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1.6e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1e+68)
		tmp = t_2;
	elseif (b <= -8.8e-27)
		tmp = t_1;
	elseif (b <= -4.2e-75)
		tmp = (j * (a * c)) + t_2;
	elseif (b <= -1.4e-100)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1.6e+112)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+68], t$95$2, If[LessEqual[b, -8.8e-27], t$95$1, If[LessEqual[b, -4.2e-75], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[b, -1.4e-100], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+112], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.99999999999999953e67 or 1.59999999999999993e112 < b

   1. Initial program 67.7%

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

   3. Taylor expanded in b around inf 77.3%

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

   if -9.99999999999999953e67 < b < -8.79999999999999948e-27 or -1.39999999999999998e-100 < b < 1.59999999999999993e112

   1. Initial program 69.3%

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

   3. Taylor expanded in b around 0 70.8%

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

   if -8.79999999999999948e-27 < b < -4.2000000000000002e-75

   1. Initial program 99.8%

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

      1. prod-diff 89.8%

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

      2. *-commutative 89.8%

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

      3. fma-neg 89.8%

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

      4. distribute-rgt-in 89.8%

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

      5. *-commutative 89.8%

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

      6. *-commutative 89.8%

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

      7. *-commutative 89.8%

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

      8. *-commutative 89.8%

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

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in x around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. +-commutative 80.3%

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

      3. distribute-lft1-in 80.3%

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

      4. metadata-eval 80.3%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \left(\color{blue}{0} \cdot \left(i \cdot t\right)\right)\right) \]

      5. mul0-lft 90.3%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \color{blue}{0}\right) \]

      6. distribute-lft-in 90.3%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(\left(c \cdot z - i \cdot t\right) + 0\right)} \]

      7. add0 90.3%

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

   7. Simplified 90.3%

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

   8. Taylor expanded in c around inf 90.3%

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

      1. associate-*r* 90.3%

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

      2. *-commutative 90.3%

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

      3. *-commutative 90.3%

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

      4. *-commutative 90.3%

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

   10. Simplified 90.3%

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

   if -4.2000000000000002e-75 < b < -1.39999999999999998e-100

   1. Initial program 67.7%

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

   3. Taylor expanded in y around inf 84.8%

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

      1. +-commutative 84.8%

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

      2. mul-1-neg 84.8%

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

      3. unsub-neg 84.8%

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

      4. *-commutative 84.8%

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

      5. *-commutative 84.8%

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

   5. Simplified 84.8%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-75}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+68}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{-64}:\\ \;\;\;\;t\_1 + t\_3\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ (* x (- (* y z) (* t a))) t_1))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -6.8e+68)
     t_3
     (if (<= b -2.2e-7)
       t_2
       (if (<= b -9.2e-21)
         (* z (- (* x y) (* b c)))
         (if (<= b -1.46e-64) (+ t_1 t_3) (if (<= b 7.5e+111) t_2 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 = j * ((a * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.8e+68) {
		tmp = t_3;
	} else if (b <= -2.2e-7) {
		tmp = t_2;
	} else if (b <= -9.2e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -1.46e-64) {
		tmp = t_1 + t_3;
	} else if (b <= 7.5e+111) {
		tmp = t_2;
	} 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 = j * ((a * c) - (y * i))
    t_2 = (x * ((y * z) - (t * a))) + t_1
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-6.8d+68)) then
        tmp = t_3
    else if (b <= (-2.2d-7)) then
        tmp = t_2
    else if (b <= (-9.2d-21)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-1.46d-64)) then
        tmp = t_1 + t_3
    else if (b <= 7.5d+111) then
        tmp = t_2
    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 = j * ((a * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.8e+68) {
		tmp = t_3;
	} else if (b <= -2.2e-7) {
		tmp = t_2;
	} else if (b <= -9.2e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -1.46e-64) {
		tmp = t_1 + t_3;
	} else if (b <= 7.5e+111) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = (x * ((y * z) - (t * a))) + t_1
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -6.8e+68:
		tmp = t_3
	elif b <= -2.2e-7:
		tmp = t_2
	elif b <= -9.2e-21:
		tmp = z * ((x * y) - (b * c))
	elif b <= -1.46e-64:
		tmp = t_1 + t_3
	elif b <= 7.5e+111:
		tmp = t_2
	else:
		tmp = t_3
	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(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -6.8e+68)
		tmp = t_3;
	elseif (b <= -2.2e-7)
		tmp = t_2;
	elseif (b <= -9.2e-21)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -1.46e-64)
		tmp = Float64(t_1 + t_3);
	elseif (b <= 7.5e+111)
		tmp = t_2;
	else
		tmp = t_3;
	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 = (x * ((y * z) - (t * a))) + t_1;
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -6.8e+68)
		tmp = t_3;
	elseif (b <= -2.2e-7)
		tmp = t_2;
	elseif (b <= -9.2e-21)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -1.46e-64)
		tmp = t_1 + t_3;
	elseif (b <= 7.5e+111)
		tmp = t_2;
	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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+68], t$95$3, If[LessEqual[b, -2.2e-7], t$95$2, If[LessEqual[b, -9.2e-21], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.46e-64], N[(t$95$1 + t$95$3), $MachinePrecision], If[LessEqual[b, 7.5e+111], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.8000000000000003e68 or 7.49999999999999948e111 < b

   1. Initial program 67.7%

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

   3. Taylor expanded in b around inf 77.3%

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

   if -6.8000000000000003e68 < b < -2.2000000000000001e-7 or -1.46e-64 < b < 7.49999999999999948e111

   1. Initial program 69.4%

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

   3. Taylor expanded in b around 0 71.5%

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

   if -2.2000000000000001e-7 < b < -9.19999999999999998e-21

   1. Initial program 33.3%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -9.19999999999999998e-21 < b < -1.46e-64

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 92.4%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{-64}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-82}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -4.2e+61)
     t_2
     (if (<= b -1.9e-6)
       (+ (* x (- (* y z) (* t a))) t_1)
       (if (<= b -9.2e-21)
         (* z (- (* x y) (* b c)))
         (if (<= b -2.9e-82)
           (+ t_1 t_2)
           (if (<= b 3.9e+112)
             (+ (* y (- (* x z) (* i j))) (* a (- (* c j) (* x t))))
             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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.2e+61) {
		tmp = t_2;
	} else if (b <= -1.9e-6) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= -9.2e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.9e-82) {
		tmp = t_1 + t_2;
	} else if (b <= 3.9e+112) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	} 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 * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-4.2d+61)) then
        tmp = t_2
    else if (b <= (-1.9d-6)) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else if (b <= (-9.2d-21)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-2.9d-82)) then
        tmp = t_1 + t_2
    else if (b <= 3.9d+112) then
        tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)))
    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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.2e+61) {
		tmp = t_2;
	} else if (b <= -1.9e-6) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= -9.2e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.9e-82) {
		tmp = t_1 + t_2;
	} else if (b <= 3.9e+112) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	} 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 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.2e+61:
		tmp = t_2
	elif b <= -1.9e-6:
		tmp = (x * ((y * z) - (t * a))) + t_1
	elif b <= -9.2e-21:
		tmp = z * ((x * y) - (b * c))
	elif b <= -2.9e-82:
		tmp = t_1 + t_2
	elif b <= 3.9e+112:
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)))
	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(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.2e+61)
		tmp = t_2;
	elseif (b <= -1.9e-6)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	elseif (b <= -9.2e-21)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -2.9e-82)
		tmp = Float64(t_1 + t_2);
	elseif (b <= 3.9e+112)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.2e+61)
		tmp = t_2;
	elseif (b <= -1.9e-6)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	elseif (b <= -9.2e-21)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -2.9e-82)
		tmp = t_1 + t_2;
	elseif (b <= 3.9e+112)
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+61], t$95$2, If[LessEqual[b, -1.9e-6], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, -9.2e-21], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.9e-82], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[b, 3.9e+112], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.2000000000000002e61 or 3.89999999999999968e112 < b

   1. Initial program 67.7%

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

   3. Taylor expanded in b around inf 77.3%

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

   if -4.2000000000000002e61 < b < -1.9e-6

   1. Initial program 92.3%

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

   3. Taylor expanded in b around 0 75.2%

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

   if -1.9e-6 < b < -9.19999999999999998e-21

   1. Initial program 33.3%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -9.19999999999999998e-21 < b < -2.89999999999999977e-82

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 93.4%

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

   if -2.89999999999999977e-82 < b < 3.89999999999999968e112

   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 70.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in b around 0 76.7%

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

      1. *-commutative 76.7%

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

   8. Simplified 76.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-82}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+52}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t\_2\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-82}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -7.6e+52)
     (+ (- (* a (* c j)) (* a (* x t))) t_2)
     (if (<= b -1.3e-5)
       (+ (* x (- (* y z) (* t a))) t_1)
       (if (<= b -6e-21)
         (* z (- (* x y) (* b c)))
         (if (<= b -5.8e-82)
           (+ t_1 t_2)
           (if (<= b 1.75e+113)
             (+ (* y (- (* x z) (* i j))) (* a (- (* c j) (* x t))))
             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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.6e+52) {
		tmp = ((a * (c * j)) - (a * (x * t))) + t_2;
	} else if (b <= -1.3e-5) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= -6e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -5.8e-82) {
		tmp = t_1 + t_2;
	} else if (b <= 1.75e+113) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	} 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 * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-7.6d+52)) then
        tmp = ((a * (c * j)) - (a * (x * t))) + t_2
    else if (b <= (-1.3d-5)) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else if (b <= (-6d-21)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-5.8d-82)) then
        tmp = t_1 + t_2
    else if (b <= 1.75d+113) then
        tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)))
    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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.6e+52) {
		tmp = ((a * (c * j)) - (a * (x * t))) + t_2;
	} else if (b <= -1.3e-5) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= -6e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -5.8e-82) {
		tmp = t_1 + t_2;
	} else if (b <= 1.75e+113) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	} 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 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7.6e+52:
		tmp = ((a * (c * j)) - (a * (x * t))) + t_2
	elif b <= -1.3e-5:
		tmp = (x * ((y * z) - (t * a))) + t_1
	elif b <= -6e-21:
		tmp = z * ((x * y) - (b * c))
	elif b <= -5.8e-82:
		tmp = t_1 + t_2
	elif b <= 1.75e+113:
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)))
	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(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.6e+52)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(a * Float64(x * t))) + t_2);
	elseif (b <= -1.3e-5)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	elseif (b <= -6e-21)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -5.8e-82)
		tmp = Float64(t_1 + t_2);
	elseif (b <= 1.75e+113)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.6e+52)
		tmp = ((a * (c * j)) - (a * (x * t))) + t_2;
	elseif (b <= -1.3e-5)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	elseif (b <= -6e-21)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -5.8e-82)
		tmp = t_1 + t_2;
	elseif (b <= 1.75e+113)
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.6e+52], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[b, -1.3e-5], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, -6e-21], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e-82], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[b, 1.75e+113], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -7.5999999999999999e52

   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 y around 0 72.8%

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

   if -7.5999999999999999e52 < b < -1.29999999999999992e-5

   1. Initial program 92.3%

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

   3. Taylor expanded in b around 0 75.2%

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

   if -1.29999999999999992e-5 < b < -5.99999999999999982e-21

   1. Initial program 33.3%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -5.99999999999999982e-21 < b < -5.79999999999999954e-82

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 93.4%

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

   if -5.79999999999999954e-82 < b < 1.75e113

   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 70.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in b around 0 76.7%

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

      1. *-commutative 76.7%

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

   8. Simplified 76.7%

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

   if 1.75e113 < b

   1. Initial program 62.0%

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

   3. Taylor expanded in b around inf 86.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+52}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-82}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c\right) + t\_1\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (+ (* j (* a c)) t_1)))
   (if (<= b -7.2e+34)
     t_2
     (if (<= b -1.3e-22)
       (* y (- (* x z) (* i j)))
       (if (<= b -6e-85)
         t_2
         (if (<= b -2e-189)
           (* z (- (* x y) (* b c)))
           (if (<= b 8.2e+111)
             (- (* j (- (* a c) (* y i))) (* a (* x t)))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (j * (a * c)) + t_1;
	double tmp;
	if (b <= -7.2e+34) {
		tmp = t_2;
	} else if (b <= -1.3e-22) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= -6e-85) {
		tmp = t_2;
	} else if (b <= -2e-189) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 8.2e+111) {
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = (j * (a * c)) + t_1
    if (b <= (-7.2d+34)) then
        tmp = t_2
    else if (b <= (-1.3d-22)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= (-6d-85)) then
        tmp = t_2
    else if (b <= (-2d-189)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 8.2d+111) then
        tmp = (j * ((a * c) - (y * i))) - (a * (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (j * (a * c)) + t_1;
	double tmp;
	if (b <= -7.2e+34) {
		tmp = t_2;
	} else if (b <= -1.3e-22) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= -6e-85) {
		tmp = t_2;
	} else if (b <= -2e-189) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 8.2e+111) {
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (j * (a * c)) + t_1
	tmp = 0
	if b <= -7.2e+34:
		tmp = t_2
	elif b <= -1.3e-22:
		tmp = y * ((x * z) - (i * j))
	elif b <= -6e-85:
		tmp = t_2
	elif b <= -2e-189:
		tmp = z * ((x * y) - (b * c))
	elif b <= 8.2e+111:
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t))
	else:
		tmp = t_1
	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(Float64(j * Float64(a * c)) + t_1)
	tmp = 0.0
	if (b <= -7.2e+34)
		tmp = t_2;
	elseif (b <= -1.3e-22)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= -6e-85)
		tmp = t_2;
	elseif (b <= -2e-189)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 8.2e+111)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = (j * (a * c)) + t_1;
	tmp = 0.0;
	if (b <= -7.2e+34)
		tmp = t_2;
	elseif (b <= -1.3e-22)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= -6e-85)
		tmp = t_2;
	elseif (b <= -2e-189)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 8.2e+111)
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[b, -7.2e+34], t$95$2, If[LessEqual[b, -1.3e-22], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6e-85], t$95$2, If[LessEqual[b, -2e-189], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+111], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.2000000000000001e34 or -1.3e-22 < b < -6.00000000000000044e-85

   1. Initial program 75.4%

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

      1. prod-diff 71.6%

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

      2. *-commutative 71.6%

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

      3. fma-neg 71.6%

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

      4. distribute-rgt-in 70.4%

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

      5. *-commutative 70.4%

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

      6. *-commutative 70.4%

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

      7. *-commutative 70.4%

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

      8. *-commutative 70.4%

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

   4. Applied egg-rr 70.4%

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

   5. Taylor expanded in x around 0 61.1%

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

      1. *-commutative 61.1%

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

      2. +-commutative 61.1%

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

      3. distribute-lft1-in 61.1%

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

      4. metadata-eval 61.1%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \left(\color{blue}{0} \cdot \left(i \cdot t\right)\right)\right) \]

      5. mul0-lft 67.4%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \color{blue}{0}\right) \]

      6. distribute-lft-in 67.4%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(\left(c \cdot z - i \cdot t\right) + 0\right)} \]

      7. add0 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in c around inf 64.9%

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

      1. associate-*r* 70.9%

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

      2. *-commutative 70.9%

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

      3. *-commutative 70.9%

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

      4. *-commutative 70.9%

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

   10. Simplified 70.9%

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

   if -7.2000000000000001e34 < b < -1.3e-22

   1. Initial program 84.6%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. *-commutative 63.0%

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

      5. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -6.00000000000000044e-85 < b < -2.00000000000000014e-189

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   if -2.00000000000000014e-189 < b < 8.19999999999999973e111

   1. Initial program 66.3%

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

   3. Taylor expanded in b around 0 73.4%

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

   4. Taylor expanded in z around 0 64.9%

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

      1. +-commutative 64.9%

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

      2. *-commutative 64.9%

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

      3. mul-1-neg 64.9%

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

      4. unsub-neg 64.9%

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

      5. *-commutative 64.9%

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

      6. *-commutative 64.9%

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

   6. Simplified 64.9%

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

   if 8.19999999999999973e111 < b

   1. Initial program 62.0%

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

   3. Taylor expanded in b around inf 86.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-85}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c\right) + t\_1\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (+ (* j (* a c)) t_1)))
   (if (<= b -9.5e+34)
     t_2
     (if (<= b -1e-22)
       (* y (- (* x z) (* i j)))
       (if (<= b -8.6e-85)
         t_2
         (if (<= b -3.3e-189)
           (* z (- (* x y) (* b c)))
           (if (<= b 8.2e+111)
             (- (* j (- (* a c) (* y i))) (* x (* t 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 = b * ((t * i) - (z * c));
	double t_2 = (j * (a * c)) + t_1;
	double tmp;
	if (b <= -9.5e+34) {
		tmp = t_2;
	} else if (b <= -1e-22) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= -8.6e-85) {
		tmp = t_2;
	} else if (b <= -3.3e-189) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 8.2e+111) {
		tmp = (j * ((a * c) - (y * i))) - (x * (t * 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) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = (j * (a * c)) + t_1
    if (b <= (-9.5d+34)) then
        tmp = t_2
    else if (b <= (-1d-22)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= (-8.6d-85)) then
        tmp = t_2
    else if (b <= (-3.3d-189)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 8.2d+111) then
        tmp = (j * ((a * c) - (y * i))) - (x * (t * 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 = b * ((t * i) - (z * c));
	double t_2 = (j * (a * c)) + t_1;
	double tmp;
	if (b <= -9.5e+34) {
		tmp = t_2;
	} else if (b <= -1e-22) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= -8.6e-85) {
		tmp = t_2;
	} else if (b <= -3.3e-189) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 8.2e+111) {
		tmp = (j * ((a * c) - (y * i))) - (x * (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (j * (a * c)) + t_1
	tmp = 0
	if b <= -9.5e+34:
		tmp = t_2
	elif b <= -1e-22:
		tmp = y * ((x * z) - (i * j))
	elif b <= -8.6e-85:
		tmp = t_2
	elif b <= -3.3e-189:
		tmp = z * ((x * y) - (b * c))
	elif b <= 8.2e+111:
		tmp = (j * ((a * c) - (y * i))) - (x * (t * a))
	else:
		tmp = t_1
	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(Float64(j * Float64(a * c)) + t_1)
	tmp = 0.0
	if (b <= -9.5e+34)
		tmp = t_2;
	elseif (b <= -1e-22)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= -8.6e-85)
		tmp = t_2;
	elseif (b <= -3.3e-189)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 8.2e+111)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(t * 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 = b * ((t * i) - (z * c));
	t_2 = (j * (a * c)) + t_1;
	tmp = 0.0;
	if (b <= -9.5e+34)
		tmp = t_2;
	elseif (b <= -1e-22)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= -8.6e-85)
		tmp = t_2;
	elseif (b <= -3.3e-189)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 8.2e+111)
		tmp = (j * ((a * c) - (y * i))) - (x * (t * 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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[b, -9.5e+34], t$95$2, If[LessEqual[b, -1e-22], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.6e-85], t$95$2, If[LessEqual[b, -3.3e-189], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+111], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -9.4999999999999999e34 or -1e-22 < b < -8.59999999999999998e-85

   1. Initial program 75.4%

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

      1. prod-diff 71.6%

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

      2. *-commutative 71.6%

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

      3. fma-neg 71.6%

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

      4. distribute-rgt-in 70.4%

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

      5. *-commutative 70.4%

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

      6. *-commutative 70.4%

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

      7. *-commutative 70.4%

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

      8. *-commutative 70.4%

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

   4. Applied egg-rr 70.4%

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

   5. Taylor expanded in x around 0 61.1%

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

      1. *-commutative 61.1%

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

      2. +-commutative 61.1%

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

      3. distribute-lft1-in 61.1%

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

      4. metadata-eval 61.1%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \left(\color{blue}{0} \cdot \left(i \cdot t\right)\right)\right) \]

      5. mul0-lft 67.4%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \color{blue}{0}\right) \]

      6. distribute-lft-in 67.4%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(\left(c \cdot z - i \cdot t\right) + 0\right)} \]

      7. add0 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in c around inf 64.9%

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

      1. associate-*r* 70.9%

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

      2. *-commutative 70.9%

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

      3. *-commutative 70.9%

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

      4. *-commutative 70.9%

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

   10. Simplified 70.9%

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

   if -9.4999999999999999e34 < b < -1e-22

   1. Initial program 84.6%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. *-commutative 63.0%

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

      5. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -8.59999999999999998e-85 < b < -3.3000000000000001e-189

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   if -3.3000000000000001e-189 < b < 8.19999999999999973e111

   1. Initial program 66.3%

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

   3. Taylor expanded in b around 0 73.4%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. neg-mul-1 65.9%

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

      2. distribute-lft-neg-in 65.9%

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

      3. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   if 8.19999999999999973e111 < b

   1. Initial program 62.0%

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

   3. Taylor expanded in b around inf 86.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-85}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c\right) + t\_1\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7.7 \cdot 10^{+111}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (* j (* a c)) t_1))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= b -7.4e+34)
     t_2
     (if (<= b -2.4e-22)
       t_3
       (if (<= b -7.6e-85)
         t_2
         (if (<= b -3.3e-192)
           (* z (- (* x y) (* b c)))
           (if (<= b 2.15e+20)
             (* a (- (* c j) (* x t)))
             (if (<= b 7.7e+111) t_3 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 = b * ((t * i) - (z * c));
	double t_2 = (j * (a * c)) + t_1;
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -7.4e+34) {
		tmp = t_2;
	} else if (b <= -2.4e-22) {
		tmp = t_3;
	} else if (b <= -7.6e-85) {
		tmp = t_2;
	} else if (b <= -3.3e-192) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 2.15e+20) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 7.7e+111) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = (j * (a * c)) + t_1
    t_3 = y * ((x * z) - (i * j))
    if (b <= (-7.4d+34)) then
        tmp = t_2
    else if (b <= (-2.4d-22)) then
        tmp = t_3
    else if (b <= (-7.6d-85)) then
        tmp = t_2
    else if (b <= (-3.3d-192)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 2.15d+20) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 7.7d+111) then
        tmp = t_3
    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 = b * ((t * i) - (z * c));
	double t_2 = (j * (a * c)) + t_1;
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -7.4e+34) {
		tmp = t_2;
	} else if (b <= -2.4e-22) {
		tmp = t_3;
	} else if (b <= -7.6e-85) {
		tmp = t_2;
	} else if (b <= -3.3e-192) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 2.15e+20) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 7.7e+111) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (j * (a * c)) + t_1
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if b <= -7.4e+34:
		tmp = t_2
	elif b <= -2.4e-22:
		tmp = t_3
	elif b <= -7.6e-85:
		tmp = t_2
	elif b <= -3.3e-192:
		tmp = z * ((x * y) - (b * c))
	elif b <= 2.15e+20:
		tmp = a * ((c * j) - (x * t))
	elif b <= 7.7e+111:
		tmp = t_3
	else:
		tmp = t_1
	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(Float64(j * Float64(a * c)) + t_1)
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (b <= -7.4e+34)
		tmp = t_2;
	elseif (b <= -2.4e-22)
		tmp = t_3;
	elseif (b <= -7.6e-85)
		tmp = t_2;
	elseif (b <= -3.3e-192)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 2.15e+20)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 7.7e+111)
		tmp = t_3;
	else
		tmp = t_1;
	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 = (j * (a * c)) + t_1;
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (b <= -7.4e+34)
		tmp = t_2;
	elseif (b <= -2.4e-22)
		tmp = t_3;
	elseif (b <= -7.6e-85)
		tmp = t_2;
	elseif (b <= -3.3e-192)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 2.15e+20)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 7.7e+111)
		tmp = t_3;
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+34], t$95$2, If[LessEqual[b, -2.4e-22], t$95$3, If[LessEqual[b, -7.6e-85], t$95$2, If[LessEqual[b, -3.3e-192], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+20], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.7e+111], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.40000000000000017e34 or -2.40000000000000002e-22 < b < -7.5999999999999997e-85

   1. Initial program 75.4%

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

      1. prod-diff 71.6%

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

      2. *-commutative 71.6%

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

      3. fma-neg 71.6%

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

      4. distribute-rgt-in 70.4%

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

      5. *-commutative 70.4%

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

      6. *-commutative 70.4%

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

      7. *-commutative 70.4%

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

      8. *-commutative 70.4%

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

   4. Applied egg-rr 70.4%

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

   5. Taylor expanded in x around 0 61.1%

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

      1. *-commutative 61.1%

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

      2. +-commutative 61.1%

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

      3. distribute-lft1-in 61.1%

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

      4. metadata-eval 61.1%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \left(\color{blue}{0} \cdot \left(i \cdot t\right)\right)\right) \]

      5. mul0-lft 67.4%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \color{blue}{0}\right) \]

      6. distribute-lft-in 67.4%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(\left(c \cdot z - i \cdot t\right) + 0\right)} \]

      7. add0 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in c around inf 64.9%

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

      1. associate-*r* 70.9%

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

      2. *-commutative 70.9%

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

      3. *-commutative 70.9%

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

      4. *-commutative 70.9%

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

   10. Simplified 70.9%

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

   if -7.40000000000000017e34 < b < -2.40000000000000002e-22 or 2.15e20 < b < 7.69999999999999955e111

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

      5. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   if -7.5999999999999997e-85 < b < -3.29999999999999989e-192

   1. Initial program 70.4%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   if -3.29999999999999989e-192 < b < 2.15e20

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

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

      3. unsub-neg 63.2%

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

      4. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   if 7.69999999999999955e111 < b

   1. Initial program 62.0%

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

   3. Taylor expanded in b around inf 86.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-85}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7.7 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+69} \lor \neg \left(t \leq 7 \cdot 10^{+102}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - \left(j \cdot \left(y \cdot i\right) - x \cdot \left(y \cdot z - t \cdot a\right)\right)\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -3.2e+69) (not (<= t 7e+102)))
   (* t (- (* b i) (* x a)))
   (-
    (- (* a (* c j)) (- (* j (* y i)) (* x (- (* y z) (* t a)))))
    (* b (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -3.2e+69) || !(t <= 7e+102)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = ((a * (c * j)) - ((j * (y * i)) - (x * ((y * z) - (t * a))))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-3.2d+69)) .or. (.not. (t <= 7d+102))) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = ((a * (c * j)) - ((j * (y * i)) - (x * ((y * z) - (t * a))))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -3.2e+69) || !(t <= 7e+102)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = ((a * (c * j)) - ((j * (y * i)) - (x * ((y * z) - (t * a))))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -3.2e+69) or not (t <= 7e+102):
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = ((a * (c * j)) - ((j * (y * i)) - (x * ((y * z) - (t * a))))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -3.2e+69) || !(t <= 7e+102))
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(Float64(j * Float64(y * i)) - Float64(x * Float64(Float64(y * z) - Float64(t * a))))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -3.2e+69) || ~((t <= 7e+102)))
		tmp = t * ((b * i) - (x * a));
	else
		tmp = ((a * (c * j)) - ((j * (y * i)) - (x * ((y * z) - (t * a))))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -3.2e+69], N[Not[LessEqual[t, 7e+102]], $MachinePrecision]], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999985e69 or 7.00000000000000021e102 < t

   1. Initial program 53.2%

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

   3. Taylor expanded in a around -inf 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in t around inf 75.4%

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

   if -3.19999999999999985e69 < t < 7.00000000000000021e102

   1. Initial program 81.6%

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

   3. Taylor expanded in i around 0 83.4%

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

   4. Taylor expanded in j around inf 72.9%

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

      1. associate-*r* 72.9%

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

      2. neg-mul-1 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-*r* 72.9%

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

      5. distribute-lft-neg-in 72.9%

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

      6. *-commutative 72.9%

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

      7. distribute-rgt-neg-in 72.9%

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

   6. Simplified 72.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+69} \lor \neg \left(t \leq 7 \cdot 10^{+102}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - \left(j \cdot \left(y \cdot i\right) - x \cdot \left(y \cdot z - t \cdot a\right)\right)\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+91}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 3.15 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -3.2e+158)
     t_1
     (if (<= b -9.2e+91)
       (* (* z c) (- b))
       (if (<= b -1.25e+71)
         t_1
         (if (<= b -1.75e-208)
           (* z (* x y))
           (if (<= b 1.7e-91)
             (* a (* c j))
             (if (<= b 3.15e+112) (* t (* 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 = i * (t * b);
	double tmp;
	if (b <= -3.2e+158) {
		tmp = t_1;
	} else if (b <= -9.2e+91) {
		tmp = (z * c) * -b;
	} else if (b <= -1.25e+71) {
		tmp = t_1;
	} else if (b <= -1.75e-208) {
		tmp = z * (x * y);
	} else if (b <= 1.7e-91) {
		tmp = a * (c * j);
	} else if (b <= 3.15e+112) {
		tmp = t * (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 = i * (t * b)
    if (b <= (-3.2d+158)) then
        tmp = t_1
    else if (b <= (-9.2d+91)) then
        tmp = (z * c) * -b
    else if (b <= (-1.25d+71)) then
        tmp = t_1
    else if (b <= (-1.75d-208)) then
        tmp = z * (x * y)
    else if (b <= 1.7d-91) then
        tmp = a * (c * j)
    else if (b <= 3.15d+112) then
        tmp = t * (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 = i * (t * b);
	double tmp;
	if (b <= -3.2e+158) {
		tmp = t_1;
	} else if (b <= -9.2e+91) {
		tmp = (z * c) * -b;
	} else if (b <= -1.25e+71) {
		tmp = t_1;
	} else if (b <= -1.75e-208) {
		tmp = z * (x * y);
	} else if (b <= 1.7e-91) {
		tmp = a * (c * j);
	} else if (b <= 3.15e+112) {
		tmp = t * (x * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -3.2e+158:
		tmp = t_1
	elif b <= -9.2e+91:
		tmp = (z * c) * -b
	elif b <= -1.25e+71:
		tmp = t_1
	elif b <= -1.75e-208:
		tmp = z * (x * y)
	elif b <= 1.7e-91:
		tmp = a * (c * j)
	elif b <= 3.15e+112:
		tmp = t * (x * -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -3.2e+158)
		tmp = t_1;
	elseif (b <= -9.2e+91)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (b <= -1.25e+71)
		tmp = t_1;
	elseif (b <= -1.75e-208)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.7e-91)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 3.15e+112)
		tmp = Float64(t * Float64(x * Float64(-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 = i * (t * b);
	tmp = 0.0;
	if (b <= -3.2e+158)
		tmp = t_1;
	elseif (b <= -9.2e+91)
		tmp = (z * c) * -b;
	elseif (b <= -1.25e+71)
		tmp = t_1;
	elseif (b <= -1.75e-208)
		tmp = z * (x * y);
	elseif (b <= 1.7e-91)
		tmp = a * (c * j);
	elseif (b <= 3.15e+112)
		tmp = t * (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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+158], t$95$1, If[LessEqual[b, -9.2e+91], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[b, -1.25e+71], t$95$1, If[LessEqual[b, -1.75e-208], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-91], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.15e+112], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.19999999999999995e158 or -9.19999999999999965e91 < b < -1.24999999999999993e71 or 3.1499999999999998e112 < b

   1. Initial program 69.4%

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

   3. Taylor expanded in a around -inf 69.4%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around inf 58.6%

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

   7. Taylor expanded in b around inf 51.1%

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

   8. Taylor expanded in t around 0 53.4%

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

      1. *-commutative 53.4%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

   10. Simplified 55.9%

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

   if -3.19999999999999995e158 < b < -9.19999999999999965e91

   1. Initial program 60.0%

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

      1. prod-diff 60.0%

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

      2. *-commutative 60.0%

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

      3. fma-neg 60.0%

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

      4. distribute-rgt-in 60.0%

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

      5. *-commutative 60.0%

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

      6. *-commutative 60.0%

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

      7. *-commutative 60.0%

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

      8. *-commutative 60.0%

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

   4. Applied egg-rr 60.0%

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

   5. Taylor expanded in x around 0 60.2%

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

      1. *-commutative 60.2%

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

      2. +-commutative 60.2%

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

      3. distribute-lft1-in 60.2%

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

      4. metadata-eval 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \left(\color{blue}{0} \cdot \left(i \cdot t\right)\right)\right) \]

      5. mul0-lft 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \color{blue}{0}\right) \]

      6. distribute-lft-in 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(\left(c \cdot z - i \cdot t\right) + 0\right)} \]

      7. add0 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in z around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-rgt-neg-in 54.3%

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

      3. distribute-rgt-neg-in 54.3%

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

   10. Simplified 54.3%

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

   if -1.24999999999999993e71 < b < -1.74999999999999996e-208

   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 y around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in z around inf 36.8%

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

      1. associate-*r* 38.3%

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

   8. Simplified 38.3%

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

   if -1.74999999999999996e-208 < b < 1.70000000000000013e-91

   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 a around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. unsub-neg 65.5%

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

      4. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in j around inf 43.7%

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

   if 1.70000000000000013e-91 < b < 3.1499999999999998e112

   1. Initial program 60.1%

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

   3. Taylor expanded in a around inf 48.3%

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

      1. +-commutative 48.3%

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

      2. mul-1-neg 48.3%

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

      3. unsub-neg 48.3%

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

      4. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in j around 0 33.9%

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

      1. associate-*r* 33.9%

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

      2. neg-mul-1 33.9%

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

   8. Simplified 33.9%

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

   9. Taylor expanded in a around 0 33.9%

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

       1. neg-mul-1 33.9%

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

       2. *-commutative 33.9%

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

       3. distribute-rgt-neg-in 33.9%

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

       4. associate-*l* 38.7%

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

       5. *-commutative 38.7%

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

       6. distribute-lft-neg-in 38.7%

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

       7. distribute-rgt-neg-in 38.7%

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

   11. Simplified 38.7%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+158}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+91}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 3.15 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+95}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -1.7e+158)
     t_1
     (if (<= b -3.5e+95)
       (* (* z c) (- b))
       (if (<= b -1e+72)
         t_1
         (if (<= b -3.3e-189)
           (* z (* x y))
           (if (<= b 9.8e+112) (* a (- (* c j) (* x t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -1.7e+158) {
		tmp = t_1;
	} else if (b <= -3.5e+95) {
		tmp = (z * c) * -b;
	} else if (b <= -1e+72) {
		tmp = t_1;
	} else if (b <= -3.3e-189) {
		tmp = z * (x * y);
	} else if (b <= 9.8e+112) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (b <= (-1.7d+158)) then
        tmp = t_1
    else if (b <= (-3.5d+95)) then
        tmp = (z * c) * -b
    else if (b <= (-1d+72)) then
        tmp = t_1
    else if (b <= (-3.3d-189)) then
        tmp = z * (x * y)
    else if (b <= 9.8d+112) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -1.7e+158) {
		tmp = t_1;
	} else if (b <= -3.5e+95) {
		tmp = (z * c) * -b;
	} else if (b <= -1e+72) {
		tmp = t_1;
	} else if (b <= -3.3e-189) {
		tmp = z * (x * y);
	} else if (b <= 9.8e+112) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -1.7e+158:
		tmp = t_1
	elif b <= -3.5e+95:
		tmp = (z * c) * -b
	elif b <= -1e+72:
		tmp = t_1
	elif b <= -3.3e-189:
		tmp = z * (x * y)
	elif b <= 9.8e+112:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -1.7e+158)
		tmp = t_1;
	elseif (b <= -3.5e+95)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (b <= -1e+72)
		tmp = t_1;
	elseif (b <= -3.3e-189)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 9.8e+112)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (b <= -1.7e+158)
		tmp = t_1;
	elseif (b <= -3.5e+95)
		tmp = (z * c) * -b;
	elseif (b <= -1e+72)
		tmp = t_1;
	elseif (b <= -3.3e-189)
		tmp = z * (x * y);
	elseif (b <= 9.8e+112)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.7e+158], t$95$1, If[LessEqual[b, -3.5e+95], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[b, -1e+72], t$95$1, If[LessEqual[b, -3.3e-189], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e+112], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.7e158 or -3.5e95 < b < -9.99999999999999944e71 or 9.80000000000000008e112 < b

   1. Initial program 69.4%

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

   3. Taylor expanded in a around -inf 69.4%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around inf 58.6%

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

   7. Taylor expanded in b around inf 51.1%

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

   8. Taylor expanded in t around 0 53.4%

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

      1. *-commutative 53.4%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

   10. Simplified 55.9%

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

   if -1.7e158 < b < -3.5e95

   1. Initial program 60.0%

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

      1. prod-diff 60.0%

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

      2. *-commutative 60.0%

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

      3. fma-neg 60.0%

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

      4. distribute-rgt-in 60.0%

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

      5. *-commutative 60.0%

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

      6. *-commutative 60.0%

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

      7. *-commutative 60.0%

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

      8. *-commutative 60.0%

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

   4. Applied egg-rr 60.0%

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

   5. Taylor expanded in x around 0 60.2%

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

      1. *-commutative 60.2%

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

      2. +-commutative 60.2%

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

      3. distribute-lft1-in 60.2%

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

      4. metadata-eval 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \left(\color{blue}{0} \cdot \left(i \cdot t\right)\right)\right) \]

      5. mul0-lft 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \color{blue}{0}\right) \]

      6. distribute-lft-in 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(\left(c \cdot z - i \cdot t\right) + 0\right)} \]

      7. add0 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in z around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-rgt-neg-in 54.3%

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

      3. distribute-rgt-neg-in 54.3%

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

   10. Simplified 54.3%

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

   if -9.99999999999999944e71 < b < -3.3000000000000001e-189

   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 y around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in z around inf 36.3%

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

      1. associate-*r* 37.9%

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

   8. Simplified 37.9%

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

   if -3.3000000000000001e-189 < b < 9.80000000000000008e112

   1. Initial program 66.3%

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

   3. Taylor expanded in a around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

   5. Simplified 58.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+158}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+95}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{+72}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+93}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-206}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -4.2e+157)
     t_1
     (if (<= b -7.2e+93)
       (* (* z c) (- b))
       (if (<= b -8.5e+70)
         t_1
         (if (<= b -3e-206)
           (* z (* x y))
           (if (<= b 1.15e+52) (* a (* c 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 = i * (t * b);
	double tmp;
	if (b <= -4.2e+157) {
		tmp = t_1;
	} else if (b <= -7.2e+93) {
		tmp = (z * c) * -b;
	} else if (b <= -8.5e+70) {
		tmp = t_1;
	} else if (b <= -3e-206) {
		tmp = z * (x * y);
	} else if (b <= 1.15e+52) {
		tmp = a * (c * 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 = i * (t * b)
    if (b <= (-4.2d+157)) then
        tmp = t_1
    else if (b <= (-7.2d+93)) then
        tmp = (z * c) * -b
    else if (b <= (-8.5d+70)) then
        tmp = t_1
    else if (b <= (-3d-206)) then
        tmp = z * (x * y)
    else if (b <= 1.15d+52) then
        tmp = a * (c * 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 = i * (t * b);
	double tmp;
	if (b <= -4.2e+157) {
		tmp = t_1;
	} else if (b <= -7.2e+93) {
		tmp = (z * c) * -b;
	} else if (b <= -8.5e+70) {
		tmp = t_1;
	} else if (b <= -3e-206) {
		tmp = z * (x * y);
	} else if (b <= 1.15e+52) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -4.2e+157:
		tmp = t_1
	elif b <= -7.2e+93:
		tmp = (z * c) * -b
	elif b <= -8.5e+70:
		tmp = t_1
	elif b <= -3e-206:
		tmp = z * (x * y)
	elif b <= 1.15e+52:
		tmp = a * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -4.2e+157)
		tmp = t_1;
	elseif (b <= -7.2e+93)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (b <= -8.5e+70)
		tmp = t_1;
	elseif (b <= -3e-206)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.15e+52)
		tmp = Float64(a * Float64(c * 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 = i * (t * b);
	tmp = 0.0;
	if (b <= -4.2e+157)
		tmp = t_1;
	elseif (b <= -7.2e+93)
		tmp = (z * c) * -b;
	elseif (b <= -8.5e+70)
		tmp = t_1;
	elseif (b <= -3e-206)
		tmp = z * (x * y);
	elseif (b <= 1.15e+52)
		tmp = a * (c * 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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+157], t$95$1, If[LessEqual[b, -7.2e+93], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[b, -8.5e+70], t$95$1, If[LessEqual[b, -3e-206], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+52], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.2e157 or -7.1999999999999998e93 < b < -8.4999999999999996e70 or 1.15e52 < b

   1. Initial program 68.8%

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

   3. Taylor expanded in a around -inf 69.9%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around inf 57.9%

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

   7. Taylor expanded in b around inf 48.9%

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

   8. Taylor expanded in t around 0 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-*r* 52.1%

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

      3. *-commutative 52.1%

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

   10. Simplified 52.1%

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

   if -4.2e157 < b < -7.1999999999999998e93

   1. Initial program 60.0%

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

      1. prod-diff 60.0%

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

      2. *-commutative 60.0%

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

      3. fma-neg 60.0%

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

      4. distribute-rgt-in 60.0%

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

      5. *-commutative 60.0%

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

      6. *-commutative 60.0%

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

      7. *-commutative 60.0%

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

      8. *-commutative 60.0%

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

   4. Applied egg-rr 60.0%

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

   5. Taylor expanded in x around 0 60.2%

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

      1. *-commutative 60.2%

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

      2. +-commutative 60.2%

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

      3. distribute-lft1-in 60.2%

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

      4. metadata-eval 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \left(\color{blue}{0} \cdot \left(i \cdot t\right)\right)\right) \]

      5. mul0-lft 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \left(b \cdot \left(c \cdot z - i \cdot t\right) + b \cdot \color{blue}{0}\right) \]

      6. distribute-lft-in 60.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(\left(c \cdot z - i \cdot t\right) + 0\right)} \]

      7. add0 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in z around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-rgt-neg-in 54.3%

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

      3. distribute-rgt-neg-in 54.3%

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

   10. Simplified 54.3%

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

   if -8.4999999999999996e70 < b < -3.0000000000000002e-206

   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 y around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in z around inf 36.8%

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

      1. associate-*r* 38.3%

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

   8. Simplified 38.3%

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

   if -3.0000000000000002e-206 < b < 1.15e52

   1. Initial program 65.9%

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

   3. Taylor expanded in a around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in j around inf 37.5%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+157}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+93}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-206}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -8e+35)
     t_2
     (if (<= b -3.4e-221)
       t_1
       (if (<= b 2.05e+20)
         (* a (- (* c j) (* x t)))
         (if (<= b 7.8e+111) 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 <= -8e+35) {
		tmp = t_2;
	} else if (b <= -3.4e-221) {
		tmp = t_1;
	} else if (b <= 2.05e+20) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 7.8e+111) {
		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 <= (-8d+35)) then
        tmp = t_2
    else if (b <= (-3.4d-221)) then
        tmp = t_1
    else if (b <= 2.05d+20) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 7.8d+111) 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 <= -8e+35) {
		tmp = t_2;
	} else if (b <= -3.4e-221) {
		tmp = t_1;
	} else if (b <= 2.05e+20) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 7.8e+111) {
		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 <= -8e+35:
		tmp = t_2
	elif b <= -3.4e-221:
		tmp = t_1
	elif b <= 2.05e+20:
		tmp = a * ((c * j) - (x * t))
	elif b <= 7.8e+111:
		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 <= -8e+35)
		tmp = t_2;
	elseif (b <= -3.4e-221)
		tmp = t_1;
	elseif (b <= 2.05e+20)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 7.8e+111)
		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 <= -8e+35)
		tmp = t_2;
	elseif (b <= -3.4e-221)
		tmp = t_1;
	elseif (b <= 2.05e+20)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 7.8e+111)
		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, -8e+35], t$95$2, If[LessEqual[b, -3.4e-221], t$95$1, If[LessEqual[b, 2.05e+20], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.9999999999999997e35 or 7.79999999999999958e111 < b

   1. Initial program 68.0%

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

   3. Taylor expanded in b around inf 75.3%

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

   if -7.9999999999999997e35 < b < -3.4000000000000001e-221 or 2.05e20 < b < 7.79999999999999958e111

   1. Initial program 80.4%

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

   3. Taylor expanded in y around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

      5. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   if -3.4000000000000001e-221 < b < 2.05e20

   1. Initial program 63.3%

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

   3. Taylor expanded in a around inf 64.5%

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

      1. +-commutative 64.5%

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

      2. mul-1-neg 64.5%

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

      3. unsub-neg 64.5%

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

      4. *-commutative 64.5%

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

   5. Simplified 64.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-221}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-196}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -5.5e+79)
     t_1
     (if (<= b -3e-196)
       (* z (- (* x y) (* b c)))
       (if (<= b 1.95e+20)
         (* a (- (* c j) (* x t)))
         (if (<= b 5.8e+113) (* y (- (* x z) (* i 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.5e+79) {
		tmp = t_1;
	} else if (b <= -3e-196) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 1.95e+20) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 5.8e+113) {
		tmp = y * ((x * z) - (i * 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 = b * ((t * i) - (z * c))
    if (b <= (-5.5d+79)) then
        tmp = t_1
    else if (b <= (-3d-196)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 1.95d+20) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 5.8d+113) then
        tmp = y * ((x * z) - (i * 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.5e+79) {
		tmp = t_1;
	} else if (b <= -3e-196) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 1.95e+20) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 5.8e+113) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.5e+79:
		tmp = t_1
	elif b <= -3e-196:
		tmp = z * ((x * y) - (b * c))
	elif b <= 1.95e+20:
		tmp = a * ((c * j) - (x * t))
	elif b <= 5.8e+113:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (b <= -5.5e+79)
		tmp = t_1;
	elseif (b <= -3e-196)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 1.95e+20)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 5.8e+113)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * 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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.5e+79)
		tmp = t_1;
	elseif (b <= -3e-196)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 1.95e+20)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 5.8e+113)
		tmp = y * ((x * z) - (i * 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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+79], t$95$1, If[LessEqual[b, -3e-196], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e+20], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+113], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.50000000000000007e79 or 5.79999999999999968e113 < b

   1. Initial program 67.3%

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

   3. Taylor expanded in b around inf 78.5%

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

   if -5.50000000000000007e79 < b < -3e-196

   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 z around inf 55.5%

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

      1. *-commutative 55.5%

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

      2. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if -3e-196 < b < 1.95e20

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

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

      3. unsub-neg 63.2%

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

      4. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   if 1.95e20 < b < 5.79999999999999968e113

   1. Initial program 78.3%

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

   3. Taylor expanded in y around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. *-commutative 64.8%

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

      5. *-commutative 64.8%

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

   5. Simplified 64.8%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-196}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -7.2e-85)
     t_1
     (if (<= b -3.2e-189)
       (* z (* x y))
       (if (<= b 3.6e+21) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.2e-85) {
		tmp = t_1;
	} else if (b <= -3.2e-189) {
		tmp = z * (x * y);
	} else if (b <= 3.6e+21) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-7.2d-85)) then
        tmp = t_1
    else if (b <= (-3.2d-189)) then
        tmp = z * (x * y)
    else if (b <= 3.6d+21) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.2e-85) {
		tmp = t_1;
	} else if (b <= -3.2e-189) {
		tmp = z * (x * y);
	} else if (b <= 3.6e+21) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7.2e-85:
		tmp = t_1
	elif b <= -3.2e-189:
		tmp = z * (x * y)
	elif b <= 3.6e+21:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.2e-85)
		tmp = t_1;
	elseif (b <= -3.2e-189)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 3.6e+21)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.2e-85)
		tmp = t_1;
	elseif (b <= -3.2e-189)
		tmp = z * (x * y);
	elseif (b <= 3.6e+21)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e-85], t$95$1, If[LessEqual[b, -3.2e-189], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+21], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.1999999999999996e-85 or 3.6e21 < b

   1. Initial program 73.1%

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

   3. Taylor expanded in b around inf 64.9%

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

   if -7.1999999999999996e-85 < b < -3.2000000000000001e-189

   1. Initial program 70.4%

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

   3. Taylor expanded in y around inf 53.7%

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

      1. +-commutative 53.7%

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

      2. mul-1-neg 53.7%

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

      3. unsub-neg 53.7%

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

      4. *-commutative 53.7%

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

      5. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in z around inf 45.0%

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

      1. associate-*r* 53.2%

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

   8. Simplified 53.2%

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

   if -3.2000000000000001e-189 < b < 3.6e21

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

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

      3. unsub-neg 63.2%

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

      4. *-commutative 63.2%

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

   5. Simplified 63.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -3.7e-55)
     t_1
     (if (<= b -1.05e-207)
       (* x (- (* y z) (* t a)))
       (if (<= b 7.5e+21) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e-55) {
		tmp = t_1;
	} else if (b <= -1.05e-207) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 7.5e+21) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-3.7d-55)) then
        tmp = t_1
    else if (b <= (-1.05d-207)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 7.5d+21) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e-55) {
		tmp = t_1;
	} else if (b <= -1.05e-207) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 7.5e+21) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.7e-55:
		tmp = t_1
	elif b <= -1.05e-207:
		tmp = x * ((y * z) - (t * a))
	elif b <= 7.5e+21:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.7e-55)
		tmp = t_1;
	elseif (b <= -1.05e-207)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 7.5e+21)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.7e-55)
		tmp = t_1;
	elseif (b <= -1.05e-207)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 7.5e+21)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e-55], t$95$1, If[LessEqual[b, -1.05e-207], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+21], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.69999999999999985e-55 or 7.5e21 < b

   1. Initial program 73.2%

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

   3. Taylor expanded in b around inf 66.2%

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

   if -3.69999999999999985e-55 < b < -1.05000000000000002e-207

   1. Initial program 72.4%

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

   3. Taylor expanded in x around inf 54.5%

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

   if -1.05000000000000002e-207 < b < 7.5e21

   1. Initial program 63.5%

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

   3. Taylor expanded in a around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

      4. *-commutative 63.4%

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

   5. Simplified 63.4%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -2.95 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 3.55 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -2.95e+187)
     t_1
     (if (<= b -2.1e-206)
       (* x (* y z))
       (if (<= b 3.55e+52) (* a (* c 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 = i * (t * b);
	double tmp;
	if (b <= -2.95e+187) {
		tmp = t_1;
	} else if (b <= -2.1e-206) {
		tmp = x * (y * z);
	} else if (b <= 3.55e+52) {
		tmp = a * (c * 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 = i * (t * b)
    if (b <= (-2.95d+187)) then
        tmp = t_1
    else if (b <= (-2.1d-206)) then
        tmp = x * (y * z)
    else if (b <= 3.55d+52) then
        tmp = a * (c * 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 = i * (t * b);
	double tmp;
	if (b <= -2.95e+187) {
		tmp = t_1;
	} else if (b <= -2.1e-206) {
		tmp = x * (y * z);
	} else if (b <= 3.55e+52) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -2.95e+187:
		tmp = t_1
	elif b <= -2.1e-206:
		tmp = x * (y * z)
	elif b <= 3.55e+52:
		tmp = a * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -2.95e+187)
		tmp = t_1;
	elseif (b <= -2.1e-206)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 3.55e+52)
		tmp = Float64(a * Float64(c * 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 = i * (t * b);
	tmp = 0.0;
	if (b <= -2.95e+187)
		tmp = t_1;
	elseif (b <= -2.1e-206)
		tmp = x * (y * z);
	elseif (b <= 3.55e+52)
		tmp = a * (c * 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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.95e+187], t$95$1, If[LessEqual[b, -2.1e-206], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.55e+52], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.95e187 or 3.54999999999999998e52 < b

   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 71.5%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in t around inf 56.8%

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

   7. Taylor expanded in b around inf 49.3%

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

   8. Taylor expanded in t around 0 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*r* 51.6%

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

      3. *-commutative 51.6%

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

   10. Simplified 51.6%

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

   if -2.95e187 < b < -2.1000000000000001e-206

   1. Initial program 77.4%

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

   3. Taylor expanded in y around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

      4. *-commutative 45.6%

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

      5. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in z around inf 37.3%

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

   if -2.1000000000000001e-206 < b < 3.54999999999999998e52

   1. Initial program 65.9%

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

   3. Taylor expanded in a around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in j around inf 37.5%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+187}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 3.55 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2050000 \lor \neg \left(b \leq 2.35 \cdot 10^{+52}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2050000.0) (not (<= b 2.35e+52))) (* 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 <= -2050000.0) || !(b <= 2.35e+52)) {
		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 <= (-2050000.0d0)) .or. (.not. (b <= 2.35d+52))) 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 <= -2050000.0) || !(b <= 2.35e+52)) {
		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 <= -2050000.0) or not (b <= 2.35e+52):
		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 <= -2050000.0) || !(b <= 2.35e+52))
		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 <= -2050000.0) || ~((b <= 2.35e+52)))
		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, -2050000.0], N[Not[LessEqual[b, 2.35e+52]], $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 < -2.05e6 or 2.35e52 < b

   1. Initial program 69.7%

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

   3. Taylor expanded in a around -inf 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in t around inf 51.0%

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

   7. Taylor expanded in b around inf 42.4%

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

   8. Taylor expanded in t around 0 44.0%

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

   if -2.05e6 < b < 2.35e52

   1. Initial program 69.9%

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

   3. Taylor expanded in a around inf 49.8%

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

      1. +-commutative 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

      4. *-commutative 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in j around inf 30.2%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2050000 \lor \neg \left(b \leq 2.35 \cdot 10^{+52}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.012 \lor \neg \left(b \leq 8.8 \cdot 10^{+51}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -0.012) (not (<= b 8.8e+51))) (* i (* t b)) (* 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 <= -0.012) || !(b <= 8.8e+51)) {
		tmp = i * (t * b);
	} 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 <= (-0.012d0)) .or. (.not. (b <= 8.8d+51))) then
        tmp = i * (t * b)
    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 <= -0.012) || !(b <= 8.8e+51)) {
		tmp = i * (t * b);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -0.012) or not (b <= 8.8e+51):
		tmp = i * (t * b)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -0.012) || !(b <= 8.8e+51))
		tmp = Float64(i * Float64(t * b));
	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 <= -0.012) || ~((b <= 8.8e+51)))
		tmp = i * (t * b);
	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, -0.012], N[Not[LessEqual[b, 8.8e+51]], $MachinePrecision]], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.012 or 8.79999999999999967e51 < b

   1. Initial program 69.7%

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

   3. Taylor expanded in a around -inf 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in t around inf 51.0%

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

   7. Taylor expanded in b around inf 42.4%

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

   8. Taylor expanded in t around 0 44.0%

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

      1. *-commutative 44.0%

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

      2. associate-*r* 44.8%

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

      3. *-commutative 44.8%

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

   10. Simplified 44.8%

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

   if -0.012 < b < 8.79999999999999967e51

   1. Initial program 69.9%

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

   3. Taylor expanded in a around inf 49.8%

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

      1. +-commutative 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

      4. *-commutative 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in j around inf 30.2%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.012 \lor \neg \left(b \leq 8.8 \cdot 10^{+51}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.8% 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 69.9%

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

3. Taylor expanded in a around inf 39.4%

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

   1. +-commutative 39.4%

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

   2. mul-1-neg 39.4%

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

   3. unsub-neg 39.4%

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

   4. *-commutative 39.4%

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

5. Simplified 39.4%

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

6. Taylor expanded in j around inf 21.7%

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

7. Final simplification 21.7%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Developer target: 59.3% 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 2024034 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))