Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.7% → 81.8%

Time: 33.9s

Alternatives: 23

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (y * ((x * z) - (i * j))) - (t * (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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * 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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 93.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around 0 26.0%

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

   4. Taylor expanded in c around 0 44.1%

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

   6. Simplified 62.2%

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

4. Final simplification 87.0%

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

Alternative 2: 29.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;j \leq -2.65 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* t (* x (- a)))))
   (if (<= j -2.65e+64)
     (* c (* t j))
     (if (<= j -1.55e-55)
       t_2
       (if (<= j -8.5e-256)
         (* i (* a b))
         (if (<= j 5.2e-255)
           t_1
           (if (<= j 1.05e-193)
             t_2
             (if (<= j 4.7e-160)
               t_1
               (if (<= j 1.2e-59)
                 (* b (* a i))
                 (if (<= j 5.2e-23)
                   (* y (* x z))
                   (if (<= j 1.6e+85)
                     (* i (* y (- j)))
                     (* t (* c j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = t * (x * -a);
	double tmp;
	if (j <= -2.65e+64) {
		tmp = c * (t * j);
	} else if (j <= -1.55e-55) {
		tmp = t_2;
	} else if (j <= -8.5e-256) {
		tmp = i * (a * b);
	} else if (j <= 5.2e-255) {
		tmp = t_1;
	} else if (j <= 1.05e-193) {
		tmp = t_2;
	} else if (j <= 4.7e-160) {
		tmp = t_1;
	} else if (j <= 1.2e-59) {
		tmp = b * (a * i);
	} else if (j <= 5.2e-23) {
		tmp = y * (x * z);
	} else if (j <= 1.6e+85) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = t * (x * -a)
    if (j <= (-2.65d+64)) then
        tmp = c * (t * j)
    else if (j <= (-1.55d-55)) then
        tmp = t_2
    else if (j <= (-8.5d-256)) then
        tmp = i * (a * b)
    else if (j <= 5.2d-255) then
        tmp = t_1
    else if (j <= 1.05d-193) then
        tmp = t_2
    else if (j <= 4.7d-160) then
        tmp = t_1
    else if (j <= 1.2d-59) then
        tmp = b * (a * i)
    else if (j <= 5.2d-23) then
        tmp = y * (x * z)
    else if (j <= 1.6d+85) then
        tmp = i * (y * -j)
    else
        tmp = t * (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 t_1 = x * (y * z);
	double t_2 = t * (x * -a);
	double tmp;
	if (j <= -2.65e+64) {
		tmp = c * (t * j);
	} else if (j <= -1.55e-55) {
		tmp = t_2;
	} else if (j <= -8.5e-256) {
		tmp = i * (a * b);
	} else if (j <= 5.2e-255) {
		tmp = t_1;
	} else if (j <= 1.05e-193) {
		tmp = t_2;
	} else if (j <= 4.7e-160) {
		tmp = t_1;
	} else if (j <= 1.2e-59) {
		tmp = b * (a * i);
	} else if (j <= 5.2e-23) {
		tmp = y * (x * z);
	} else if (j <= 1.6e+85) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = t * (x * -a)
	tmp = 0
	if j <= -2.65e+64:
		tmp = c * (t * j)
	elif j <= -1.55e-55:
		tmp = t_2
	elif j <= -8.5e-256:
		tmp = i * (a * b)
	elif j <= 5.2e-255:
		tmp = t_1
	elif j <= 1.05e-193:
		tmp = t_2
	elif j <= 4.7e-160:
		tmp = t_1
	elif j <= 1.2e-59:
		tmp = b * (a * i)
	elif j <= 5.2e-23:
		tmp = y * (x * z)
	elif j <= 1.6e+85:
		tmp = i * (y * -j)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (j <= -2.65e+64)
		tmp = Float64(c * Float64(t * j));
	elseif (j <= -1.55e-55)
		tmp = t_2;
	elseif (j <= -8.5e-256)
		tmp = Float64(i * Float64(a * b));
	elseif (j <= 5.2e-255)
		tmp = t_1;
	elseif (j <= 1.05e-193)
		tmp = t_2;
	elseif (j <= 4.7e-160)
		tmp = t_1;
	elseif (j <= 1.2e-59)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= 5.2e-23)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.6e+85)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = t * (x * -a);
	tmp = 0.0;
	if (j <= -2.65e+64)
		tmp = c * (t * j);
	elseif (j <= -1.55e-55)
		tmp = t_2;
	elseif (j <= -8.5e-256)
		tmp = i * (a * b);
	elseif (j <= 5.2e-255)
		tmp = t_1;
	elseif (j <= 1.05e-193)
		tmp = t_2;
	elseif (j <= 4.7e-160)
		tmp = t_1;
	elseif (j <= 1.2e-59)
		tmp = b * (a * i);
	elseif (j <= 5.2e-23)
		tmp = y * (x * z);
	elseif (j <= 1.6e+85)
		tmp = i * (y * -j);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.65e+64], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.55e-55], t$95$2, If[LessEqual[j, -8.5e-256], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.2e-255], t$95$1, If[LessEqual[j, 1.05e-193], t$95$2, If[LessEqual[j, 4.7e-160], t$95$1, If[LessEqual[j, 1.2e-59], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.2e-23], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e+85], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -2.6500000000000001e64

   1. Initial program 77.3%

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

   3. Taylor expanded in b around 0 66.3%

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

   4. Taylor expanded in c around inf 41.8%

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

      1. *-commutative 41.8%

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

   6. Simplified 41.8%

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

   if -2.6500000000000001e64 < j < -1.54999999999999998e-55 or 5.20000000000000041e-255 < j < 1.05e-193

   1. Initial program 74.9%

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

   3. Taylor expanded in t around inf 57.0%

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

   4. Taylor expanded in a around inf 54.2%

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

      1. associate-*r* 54.2%

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

      2. neg-mul-1 54.2%

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

   6. Simplified 54.2%

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

   if -1.54999999999999998e-55 < j < -8.49999999999999959e-256

   1. Initial program 74.3%

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

   3. Taylor expanded in b around inf 46.2%

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

   4. Taylor expanded in a around inf 37.2%

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

      1. associate-*r* 39.7%

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

   6. Simplified 39.7%

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

   if -8.49999999999999959e-256 < j < 5.20000000000000041e-255 or 1.05e-193 < j < 4.6999999999999998e-160

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in y around inf 49.4%

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

      1. *-commutative 49.4%

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

   8. Simplified 49.4%

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

   if 4.6999999999999998e-160 < j < 1.20000000000000008e-59

   1. Initial program 78.9%

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

   3. Taylor expanded in b around inf 74.9%

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

   4. Taylor expanded in a around inf 36.3%

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

      1. *-commutative 36.3%

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

      2. associate-*l* 40.2%

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

      3. *-commutative 40.2%

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

   6. Simplified 40.2%

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

   if 1.20000000000000008e-59 < j < 5.2e-23

   1. Initial program 56.4%

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

   3. Taylor expanded in y around -inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. *-commutative 65.4%

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

      3. distribute-rgt-neg-in 65.4%

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

      4. +-commutative 65.4%

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

      5. mul-1-neg 65.4%

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

      6. unsub-neg 65.4%

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

      7. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in i around 0 44.7%

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

      1. *-commutative 44.7%

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

      2. associate-*l* 65.5%

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

      3. *-commutative 65.5%

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

   8. Simplified 65.5%

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

   if 5.2e-23 < j < 1.60000000000000009e85

   1. Initial program 71.4%

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

   3. Taylor expanded in i around inf 63.8%

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

      1. distribute-lft-out-- 63.8%

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

      2. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in j around inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. *-commutative 47.6%

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

      3. distribute-rgt-neg-in 47.6%

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

   8. Simplified 47.6%

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

   if 1.60000000000000009e85 < j

   1. Initial program 74.4%

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

   3. Taylor expanded in b around 0 73.3%

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

   4. Taylor expanded in c around inf 49.0%

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

      1. *-commutative 49.0%

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

      2. *-commutative 49.0%

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

      3. associate-*r* 52.0%

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

   6. Simplified 52.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.65 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-219}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+81}:\\ \;\;\;\;\left(\left(t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - a \cdot \left(x \cdot t\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+127}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -7e+115)
     t_2
     (if (<= b -1.1e-132)
       t_1
       (if (<= b -3.9e-219)
         (- (* y (- (* x z) (* i j))) (* t (* x a)))
         (if (<= b 9.6e-69)
           t_1
           (if (<= b 8e+81)
             (-
              (- (+ (* t (* c j)) (* x (* y z))) (* a (* x t)))
              (* b (* z c)))
             (if (<= b 7.5e+127) (* i (- (* a b) (* y j))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7e+115) {
		tmp = t_2;
	} else if (b <= -1.1e-132) {
		tmp = t_1;
	} else if (b <= -3.9e-219) {
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a));
	} else if (b <= 9.6e-69) {
		tmp = t_1;
	} else if (b <= 8e+81) {
		tmp = (((t * (c * j)) + (x * (y * z))) - (a * (x * t))) - (b * (z * c));
	} else if (b <= 7.5e+127) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-7d+115)) then
        tmp = t_2
    else if (b <= (-1.1d-132)) then
        tmp = t_1
    else if (b <= (-3.9d-219)) then
        tmp = (y * ((x * z) - (i * j))) - (t * (x * a))
    else if (b <= 9.6d-69) then
        tmp = t_1
    else if (b <= 8d+81) then
        tmp = (((t * (c * j)) + (x * (y * z))) - (a * (x * t))) - (b * (z * c))
    else if (b <= 7.5d+127) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7e+115) {
		tmp = t_2;
	} else if (b <= -1.1e-132) {
		tmp = t_1;
	} else if (b <= -3.9e-219) {
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a));
	} else if (b <= 9.6e-69) {
		tmp = t_1;
	} else if (b <= 8e+81) {
		tmp = (((t * (c * j)) + (x * (y * z))) - (a * (x * t))) - (b * (z * c));
	} else if (b <= 7.5e+127) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -7e+115:
		tmp = t_2
	elif b <= -1.1e-132:
		tmp = t_1
	elif b <= -3.9e-219:
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a))
	elif b <= 9.6e-69:
		tmp = t_1
	elif b <= 8e+81:
		tmp = (((t * (c * j)) + (x * (y * z))) - (a * (x * t))) - (b * (z * c))
	elif b <= 7.5e+127:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7e+115)
		tmp = t_2;
	elseif (b <= -1.1e-132)
		tmp = t_1;
	elseif (b <= -3.9e-219)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(t * Float64(x * a)));
	elseif (b <= 9.6e-69)
		tmp = t_1;
	elseif (b <= 8e+81)
		tmp = Float64(Float64(Float64(Float64(t * Float64(c * j)) + Float64(x * Float64(y * z))) - Float64(a * Float64(x * t))) - Float64(b * Float64(z * c)));
	elseif (b <= 7.5e+127)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -7e+115)
		tmp = t_2;
	elseif (b <= -1.1e-132)
		tmp = t_1;
	elseif (b <= -3.9e-219)
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a));
	elseif (b <= 9.6e-69)
		tmp = t_1;
	elseif (b <= 8e+81)
		tmp = (((t * (c * j)) + (x * (y * z))) - (a * (x * t))) - (b * (z * c));
	elseif (b <= 7.5e+127)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+115], t$95$2, If[LessEqual[b, -1.1e-132], t$95$1, If[LessEqual[b, -3.9e-219], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.6e-69], t$95$1, If[LessEqual[b, 8e+81], N[(N[(N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+127], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.00000000000000011e115 or 7.4999999999999996e127 < b

   1. Initial program 71.3%

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

   3. Taylor expanded in b around inf 81.0%

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

   if -7.00000000000000011e115 < b < -1.09999999999999995e-132 or -3.89999999999999987e-219 < b < 9.6000000000000005e-69

   1. Initial program 77.8%

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

   3. Taylor expanded in b around 0 75.6%

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

   if -1.09999999999999995e-132 < b < -3.89999999999999987e-219

   1. Initial program 56.0%

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

   3. Taylor expanded in b around 0 45.7%

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

   4. Taylor expanded in c around 0 51.5%

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

   6. Simplified 71.2%

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

   if 9.6000000000000005e-69 < b < 7.99999999999999937e81

   1. Initial program 90.4%

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

   3. Taylor expanded in a around -inf 93.8%

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

   4. Taylor expanded in c around inf 86.6%

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

      1. associate-*r* 92.6%

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

      2. *-commutative 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in t around inf 87.6%

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

   if 7.99999999999999937e81 < b < 7.4999999999999996e127

   1. Initial program 54.4%

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

   3. Taylor expanded in i around inf 90.8%

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

      1. distribute-lft-out-- 90.8%

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

      2. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in i around 0 90.8%

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

      1. mul-1-neg 90.8%

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

      2. *-commutative 90.8%

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

      3. *-commutative 90.8%

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

      4. distribute-rgt-neg-in 90.8%

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

   8. Simplified 90.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+115}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-219}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-69}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+81}:\\ \;\;\;\;\left(\left(t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - a \cdot \left(x \cdot t\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+127}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.9 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-258}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.1 \cdot 10^{-50}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -1.9e+15)
     t_2
     (if (<= j -8.6e-253)
       (* a (- (* b i) (* x t)))
       (if (<= j 6.2e-258)
         t_1
         (if (<= j 3.8e-210)
           (* x (- (* y z) (* t a)))
           (if (<= j 2.1e-159)
             t_1
             (if (<= j 7.1e-50)
               (* b (- (* a i) (* z c)))
               (if (<= j 8.5e+22) (* y (- (* x z) (* i j))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.9e+15) {
		tmp = t_2;
	} else if (j <= -8.6e-253) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 6.2e-258) {
		tmp = t_1;
	} else if (j <= 3.8e-210) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 2.1e-159) {
		tmp = t_1;
	} else if (j <= 7.1e-50) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 8.5e+22) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-1.9d+15)) then
        tmp = t_2
    else if (j <= (-8.6d-253)) then
        tmp = a * ((b * i) - (x * t))
    else if (j <= 6.2d-258) then
        tmp = t_1
    else if (j <= 3.8d-210) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 2.1d-159) then
        tmp = t_1
    else if (j <= 7.1d-50) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 8.5d+22) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.9e+15) {
		tmp = t_2;
	} else if (j <= -8.6e-253) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 6.2e-258) {
		tmp = t_1;
	} else if (j <= 3.8e-210) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 2.1e-159) {
		tmp = t_1;
	} else if (j <= 7.1e-50) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 8.5e+22) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.9e+15:
		tmp = t_2
	elif j <= -8.6e-253:
		tmp = a * ((b * i) - (x * t))
	elif j <= 6.2e-258:
		tmp = t_1
	elif j <= 3.8e-210:
		tmp = x * ((y * z) - (t * a))
	elif j <= 2.1e-159:
		tmp = t_1
	elif j <= 7.1e-50:
		tmp = b * ((a * i) - (z * c))
	elif j <= 8.5e+22:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.9e+15)
		tmp = t_2;
	elseif (j <= -8.6e-253)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (j <= 6.2e-258)
		tmp = t_1;
	elseif (j <= 3.8e-210)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 2.1e-159)
		tmp = t_1;
	elseif (j <= 7.1e-50)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 8.5e+22)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.9e+15)
		tmp = t_2;
	elseif (j <= -8.6e-253)
		tmp = a * ((b * i) - (x * t));
	elseif (j <= 6.2e-258)
		tmp = t_1;
	elseif (j <= 3.8e-210)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 2.1e-159)
		tmp = t_1;
	elseif (j <= 7.1e-50)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 8.5e+22)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.9e+15], t$95$2, If[LessEqual[j, -8.6e-253], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-258], t$95$1, If[LessEqual[j, 3.8e-210], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.1e-159], t$95$1, If[LessEqual[j, 7.1e-50], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+22], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.9e15 or 8.49999999999999979e22 < j

   1. Initial program 76.3%

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

   3. Taylor expanded in b around 0 71.6%

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

   4. Taylor expanded in j around inf 68.5%

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

      1. sub-neg 68.5%

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

      2. *-commutative 68.5%

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

      3. *-commutative 68.5%

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

      4. sub-neg 68.5%

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

   6. Simplified 68.5%

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

   if -1.9e15 < j < -8.6000000000000003e-253

   1. Initial program 78.4%

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

   3. Taylor expanded in a around inf 48.8%

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

      1. distribute-lft-out-- 48.8%

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

   5. Simplified 48.8%

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

   if -8.6000000000000003e-253 < j < 6.19999999999999997e-258 or 3.80000000000000003e-210 < j < 2.0999999999999999e-159

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   if 6.19999999999999997e-258 < j < 3.80000000000000003e-210

   1. Initial program 62.7%

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

   3. Taylor expanded in x around inf 77.0%

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

      1. *-commutative 77.0%

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

   5. Simplified 77.0%

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

   if 2.0999999999999999e-159 < j < 7.0999999999999998e-50

   1. Initial program 80.5%

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

   3. Taylor expanded in b around inf 73.0%

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

   if 7.0999999999999998e-50 < j < 8.49999999999999979e22

   1. Initial program 53.8%

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

   3. Taylor expanded in y around -inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. *-commutative 73.4%

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

      3. distribute-rgt-neg-in 73.4%

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

      4. +-commutative 73.4%

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

      5. mul-1-neg 73.4%

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

      6. unsub-neg 73.4%

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

      7. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in i around 0 53.1%

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

      1. +-commutative 53.1%

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

      2. *-commutative 53.1%

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

      3. associate-*l* 62.9%

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

      4. mul-1-neg 62.9%

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

      5. associate-*r* 62.9%

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

      6. *-commutative 62.9%

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

      7. distribute-rgt-neg-in 62.9%

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

      8. distribute-lft-in 73.4%

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

      9. unsub-neg 73.4%

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

      10. *-commutative 73.4%

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

   8. Simplified 73.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-258}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-159}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 7.1 \cdot 10^{-50}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -17500000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -17500000000000.0)
     t_2
     (if (<= j -7.8e-255)
       (* a (- (* b i) (* x t)))
       (if (<= j 1.5e-253)
         t_1
         (if (<= j 2.6e-194)
           (* t (- (* c j) (* x a)))
           (if (<= j 6.2e-158)
             t_1
             (if (<= j 5.3e-51)
               (* b (- (* a i) (* z c)))
               (if (<= j 1.9e+23) (* y (- (* x z) (* i j))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -17500000000000.0) {
		tmp = t_2;
	} else if (j <= -7.8e-255) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 1.5e-253) {
		tmp = t_1;
	} else if (j <= 2.6e-194) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= 6.2e-158) {
		tmp = t_1;
	} else if (j <= 5.3e-51) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 1.9e+23) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-17500000000000.0d0)) then
        tmp = t_2
    else if (j <= (-7.8d-255)) then
        tmp = a * ((b * i) - (x * t))
    else if (j <= 1.5d-253) then
        tmp = t_1
    else if (j <= 2.6d-194) then
        tmp = t * ((c * j) - (x * a))
    else if (j <= 6.2d-158) then
        tmp = t_1
    else if (j <= 5.3d-51) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 1.9d+23) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -17500000000000.0) {
		tmp = t_2;
	} else if (j <= -7.8e-255) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 1.5e-253) {
		tmp = t_1;
	} else if (j <= 2.6e-194) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= 6.2e-158) {
		tmp = t_1;
	} else if (j <= 5.3e-51) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 1.9e+23) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -17500000000000.0:
		tmp = t_2
	elif j <= -7.8e-255:
		tmp = a * ((b * i) - (x * t))
	elif j <= 1.5e-253:
		tmp = t_1
	elif j <= 2.6e-194:
		tmp = t * ((c * j) - (x * a))
	elif j <= 6.2e-158:
		tmp = t_1
	elif j <= 5.3e-51:
		tmp = b * ((a * i) - (z * c))
	elif j <= 1.9e+23:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -17500000000000.0)
		tmp = t_2;
	elseif (j <= -7.8e-255)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (j <= 1.5e-253)
		tmp = t_1;
	elseif (j <= 2.6e-194)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (j <= 6.2e-158)
		tmp = t_1;
	elseif (j <= 5.3e-51)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 1.9e+23)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -17500000000000.0)
		tmp = t_2;
	elseif (j <= -7.8e-255)
		tmp = a * ((b * i) - (x * t));
	elseif (j <= 1.5e-253)
		tmp = t_1;
	elseif (j <= 2.6e-194)
		tmp = t * ((c * j) - (x * a));
	elseif (j <= 6.2e-158)
		tmp = t_1;
	elseif (j <= 5.3e-51)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 1.9e+23)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -17500000000000.0], t$95$2, If[LessEqual[j, -7.8e-255], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e-253], t$95$1, If[LessEqual[j, 2.6e-194], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-158], t$95$1, If[LessEqual[j, 5.3e-51], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e+23], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.75e13 or 1.89999999999999987e23 < j

   1. Initial program 76.3%

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

   3. Taylor expanded in b around 0 71.6%

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

   4. Taylor expanded in j around inf 68.5%

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

      1. sub-neg 68.5%

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

      2. *-commutative 68.5%

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

      3. *-commutative 68.5%

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

      4. sub-neg 68.5%

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

   6. Simplified 68.5%

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

   if -1.75e13 < j < -7.8000000000000001e-255

   1. Initial program 78.4%

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

   3. Taylor expanded in a around inf 48.8%

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

      1. distribute-lft-out-- 48.8%

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

   5. Simplified 48.8%

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

   if -7.8000000000000001e-255 < j < 1.5000000000000001e-253 or 2.60000000000000002e-194 < j < 6.20000000000000036e-158

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   if 1.5000000000000001e-253 < j < 2.60000000000000002e-194

   1. Initial program 62.0%

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

   3. Taylor expanded in t around inf 77.6%

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

   if 6.20000000000000036e-158 < j < 5.29999999999999974e-51

   1. Initial program 80.5%

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

   3. Taylor expanded in b around inf 73.0%

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

   if 5.29999999999999974e-51 < j < 1.89999999999999987e23

   1. Initial program 53.8%

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

   3. Taylor expanded in y around -inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. *-commutative 73.4%

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

      3. distribute-rgt-neg-in 73.4%

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

      4. +-commutative 73.4%

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

      5. mul-1-neg 73.4%

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

      6. unsub-neg 73.4%

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

      7. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in i around 0 53.1%

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

      1. +-commutative 53.1%

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

      2. *-commutative 53.1%

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

      3. associate-*l* 62.9%

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

      4. mul-1-neg 62.9%

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

      5. associate-*r* 62.9%

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

      6. *-commutative 62.9%

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

      7. distribute-rgt-neg-in 62.9%

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

      8. distribute-lft-in 73.4%

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

      9. unsub-neg 73.4%

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

      10. *-commutative 73.4%

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

   8. Simplified 73.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -17500000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-158}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - t \cdot \left(x \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.2 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.4 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+152}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* t (* x a))))
        (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -2.2e+36)
     t_2
     (if (<= c -1.6e-308)
       t_1
       (if (<= c 9.4e-54)
         (* a (- (* b i) (* x t)))
         (if (<= c 6.8e-7)
           t_1
           (if (<= c 1.95e+31)
             t_2
             (if (<= c 2.05e+74)
               (* z (- (* x y) (* b c)))
               (if (<= c 1.05e+152) (* j (- (* t c) (* y i))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (t * (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.2e+36) {
		tmp = t_2;
	} else if (c <= -1.6e-308) {
		tmp = t_1;
	} else if (c <= 9.4e-54) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 6.8e-7) {
		tmp = t_1;
	} else if (c <= 1.95e+31) {
		tmp = t_2;
	} else if (c <= 2.05e+74) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= 1.05e+152) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (t * (x * a))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-2.2d+36)) then
        tmp = t_2
    else if (c <= (-1.6d-308)) then
        tmp = t_1
    else if (c <= 9.4d-54) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 6.8d-7) then
        tmp = t_1
    else if (c <= 1.95d+31) then
        tmp = t_2
    else if (c <= 2.05d+74) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= 1.05d+152) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (t * (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.2e+36) {
		tmp = t_2;
	} else if (c <= -1.6e-308) {
		tmp = t_1;
	} else if (c <= 9.4e-54) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 6.8e-7) {
		tmp = t_1;
	} else if (c <= 1.95e+31) {
		tmp = t_2;
	} else if (c <= 2.05e+74) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= 1.05e+152) {
		tmp = j * ((t * c) - (y * i));
	} 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 * (x * a))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.2e+36:
		tmp = t_2
	elif c <= -1.6e-308:
		tmp = t_1
	elif c <= 9.4e-54:
		tmp = a * ((b * i) - (x * t))
	elif c <= 6.8e-7:
		tmp = t_1
	elif c <= 1.95e+31:
		tmp = t_2
	elif c <= 2.05e+74:
		tmp = z * ((x * y) - (b * c))
	elif c <= 1.05e+152:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(t * Float64(x * a)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.2e+36)
		tmp = t_2;
	elseif (c <= -1.6e-308)
		tmp = t_1;
	elseif (c <= 9.4e-54)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 6.8e-7)
		tmp = t_1;
	elseif (c <= 1.95e+31)
		tmp = t_2;
	elseif (c <= 2.05e+74)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= 1.05e+152)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) - (t * (x * a));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.2e+36)
		tmp = t_2;
	elseif (c <= -1.6e-308)
		tmp = t_1;
	elseif (c <= 9.4e-54)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 6.8e-7)
		tmp = t_1;
	elseif (c <= 1.95e+31)
		tmp = t_2;
	elseif (c <= 2.05e+74)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= 1.05e+152)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.2e+36], t$95$2, If[LessEqual[c, -1.6e-308], t$95$1, If[LessEqual[c, 9.4e-54], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e-7], t$95$1, If[LessEqual[c, 1.95e+31], t$95$2, If[LessEqual[c, 2.05e+74], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e+152], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.2e36 or 6.79999999999999948e-7 < c < 1.95e31 or 1.0500000000000001e152 < c

   1. Initial program 71.6%

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

   3. Taylor expanded in c around inf 71.8%

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

   if -2.2e36 < c < -1.6000000000000001e-308 or 9.4e-54 < c < 6.79999999999999948e-7

   1. Initial program 81.5%

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

   3. Taylor expanded in b around 0 70.6%

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

   4. Taylor expanded in c around 0 66.9%

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

   6. Simplified 73.1%

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

   if -1.6000000000000001e-308 < c < 9.4e-54

   1. Initial program 76.6%

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

   3. Taylor expanded in a around inf 62.9%

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

      1. distribute-lft-out-- 62.9%

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

   5. Simplified 62.9%

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

   if 1.95e31 < c < 2.05e74

   1. Initial program 51.0%

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

   3. Taylor expanded in z around inf 59.2%

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

      1. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if 2.05e74 < c < 1.0500000000000001e152

   1. Initial program 75.0%

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

   3. Taylor expanded in b around 0 83.7%

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

   4. Taylor expanded in j around inf 92.0%

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

      1. sub-neg 92.0%

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

      2. *-commutative 92.0%

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

      3. *-commutative 92.0%

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

      4. sub-neg 92.0%

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

   6. Simplified 92.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;c \leq 9.4 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+31}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+152}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -330000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-257}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -330000000000.0)
     t_2
     (if (<= j -8.5e-253)
       t_1
       (if (<= j 2.35e-257)
         (* z (- (* x y) (* b c)))
         (if (<= j 4.4e-175)
           (* x (- (* y z) (* t a)))
           (if (<= j 7.4e-51)
             t_1
             (if (<= j 5.3e+22) (* y (- (* x z) (* i j))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -330000000000.0) {
		tmp = t_2;
	} else if (j <= -8.5e-253) {
		tmp = t_1;
	} else if (j <= 2.35e-257) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 4.4e-175) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 7.4e-51) {
		tmp = t_1;
	} else if (j <= 5.3e+22) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-330000000000.0d0)) then
        tmp = t_2
    else if (j <= (-8.5d-253)) then
        tmp = t_1
    else if (j <= 2.35d-257) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 4.4d-175) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 7.4d-51) then
        tmp = t_1
    else if (j <= 5.3d+22) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -330000000000.0) {
		tmp = t_2;
	} else if (j <= -8.5e-253) {
		tmp = t_1;
	} else if (j <= 2.35e-257) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 4.4e-175) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 7.4e-51) {
		tmp = t_1;
	} else if (j <= 5.3e+22) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -330000000000.0:
		tmp = t_2
	elif j <= -8.5e-253:
		tmp = t_1
	elif j <= 2.35e-257:
		tmp = z * ((x * y) - (b * c))
	elif j <= 4.4e-175:
		tmp = x * ((y * z) - (t * a))
	elif j <= 7.4e-51:
		tmp = t_1
	elif j <= 5.3e+22:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -330000000000.0)
		tmp = t_2;
	elseif (j <= -8.5e-253)
		tmp = t_1;
	elseif (j <= 2.35e-257)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 4.4e-175)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 7.4e-51)
		tmp = t_1;
	elseif (j <= 5.3e+22)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -330000000000.0)
		tmp = t_2;
	elseif (j <= -8.5e-253)
		tmp = t_1;
	elseif (j <= 2.35e-257)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 4.4e-175)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 7.4e-51)
		tmp = t_1;
	elseif (j <= 5.3e+22)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -330000000000.0], t$95$2, If[LessEqual[j, -8.5e-253], t$95$1, If[LessEqual[j, 2.35e-257], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-175], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.4e-51], t$95$1, If[LessEqual[j, 5.3e+22], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3.3e11 or 5.2999999999999998e22 < j

   1. Initial program 76.3%

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

   3. Taylor expanded in b around 0 71.6%

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

   4. Taylor expanded in j around inf 68.5%

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

      1. sub-neg 68.5%

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

      2. *-commutative 68.5%

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

      3. *-commutative 68.5%

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

      4. sub-neg 68.5%

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

   6. Simplified 68.5%

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

   if -3.3e11 < j < -8.4999999999999999e-253 or 4.4e-175 < j < 7.39999999999999946e-51

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf 55.8%

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

   if -8.4999999999999999e-253 < j < 2.3499999999999999e-257

   1. Initial program 74.2%

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

   3. Taylor expanded in z around inf 78.5%

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

      1. *-commutative 78.5%

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

   5. Simplified 78.5%

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

   if 2.3499999999999999e-257 < j < 4.4e-175

   1. Initial program 70.2%

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

   3. Taylor expanded in x around inf 69.7%

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

      1. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   if 7.39999999999999946e-51 < j < 5.2999999999999998e22

   1. Initial program 53.8%

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

   3. Taylor expanded in y around -inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. *-commutative 73.4%

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

      3. distribute-rgt-neg-in 73.4%

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

      4. +-commutative 73.4%

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

      5. mul-1-neg 73.4%

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

      6. unsub-neg 73.4%

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

      7. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in i around 0 53.1%

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

      1. +-commutative 53.1%

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

      2. *-commutative 53.1%

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

      3. associate-*l* 62.9%

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

      4. mul-1-neg 62.9%

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

      5. associate-*r* 62.9%

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

      6. *-commutative 62.9%

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

      7. distribute-rgt-neg-in 62.9%

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

      8. distribute-lft-in 73.4%

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

      9. unsub-neg 73.4%

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

      10. *-commutative 73.4%

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

   8. Simplified 73.4%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -330000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-253}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-257}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;b \leq 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+124}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -4.2e+116)
     t_2
     (if (<= b -1e-132)
       t_1
       (if (<= b -9.2e-228)
         (- (* y (- (* x z) (* i j))) (* t (* x a)))
         (if (<= b 1e+82)
           t_1
           (if (<= b 5.1e+124) (* i (- (* a b) (* y j))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.2e+116) {
		tmp = t_2;
	} else if (b <= -1e-132) {
		tmp = t_1;
	} else if (b <= -9.2e-228) {
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a));
	} else if (b <= 1e+82) {
		tmp = t_1;
	} else if (b <= 5.1e+124) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-4.2d+116)) then
        tmp = t_2
    else if (b <= (-1d-132)) then
        tmp = t_1
    else if (b <= (-9.2d-228)) then
        tmp = (y * ((x * z) - (i * j))) - (t * (x * a))
    else if (b <= 1d+82) then
        tmp = t_1
    else if (b <= 5.1d+124) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.2e+116) {
		tmp = t_2;
	} else if (b <= -1e-132) {
		tmp = t_1;
	} else if (b <= -9.2e-228) {
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a));
	} else if (b <= 1e+82) {
		tmp = t_1;
	} else if (b <= 5.1e+124) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.2e+116:
		tmp = t_2
	elif b <= -1e-132:
		tmp = t_1
	elif b <= -9.2e-228:
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a))
	elif b <= 1e+82:
		tmp = t_1
	elif b <= 5.1e+124:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.2e+116)
		tmp = t_2;
	elseif (b <= -1e-132)
		tmp = t_1;
	elseif (b <= -9.2e-228)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(t * Float64(x * a)));
	elseif (b <= 1e+82)
		tmp = t_1;
	elseif (b <= 5.1e+124)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.2e+116)
		tmp = t_2;
	elseif (b <= -1e-132)
		tmp = t_1;
	elseif (b <= -9.2e-228)
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a));
	elseif (b <= 1e+82)
		tmp = t_1;
	elseif (b <= 5.1e+124)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+116], t$95$2, If[LessEqual[b, -1e-132], t$95$1, If[LessEqual[b, -9.2e-228], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+82], t$95$1, If[LessEqual[b, 5.1e+124], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.2000000000000002e116 or 5.0999999999999998e124 < b

   1. Initial program 71.3%

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

   3. Taylor expanded in b around inf 81.0%

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

   if -4.2000000000000002e116 < b < -9.9999999999999999e-133 or -9.1999999999999995e-228 < b < 9.9999999999999996e81

   1. Initial program 80.4%

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

   3. Taylor expanded in b around 0 75.0%

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

   if -9.9999999999999999e-133 < b < -9.1999999999999995e-228

   1. Initial program 56.0%

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

   3. Taylor expanded in b around 0 45.7%

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

   4. Taylor expanded in c around 0 51.5%

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

   6. Simplified 71.2%

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

   if 9.9999999999999996e81 < b < 5.0999999999999998e124

   1. Initial program 54.4%

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

   3. Taylor expanded in i around inf 90.8%

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

      1. distribute-lft-out-- 90.8%

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

      2. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in i around 0 90.8%

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

      1. mul-1-neg 90.8%

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

      2. *-commutative 90.8%

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

      3. *-commutative 90.8%

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

      4. distribute-rgt-neg-in 90.8%

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

   8. Simplified 90.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;b \leq 10^{+82}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+124}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.05e-13)
   (* c (* t j))
   (if (<= j -6.8e-254)
     (* i (* a b))
     (if (<= j 5.8e-158)
       (* x (* y z))
       (if (<= j 3e-49)
         (* b (* a i))
         (if (<= j 1.25e-22)
           (* y (* x z))
           (if (<= j 1.2e+85) (* i (* y (- j))) (* t (* 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 (j <= -1.05e-13) {
		tmp = c * (t * j);
	} else if (j <= -6.8e-254) {
		tmp = i * (a * b);
	} else if (j <= 5.8e-158) {
		tmp = x * (y * z);
	} else if (j <= 3e-49) {
		tmp = b * (a * i);
	} else if (j <= 1.25e-22) {
		tmp = y * (x * z);
	} else if (j <= 1.2e+85) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (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 (j <= (-1.05d-13)) then
        tmp = c * (t * j)
    else if (j <= (-6.8d-254)) then
        tmp = i * (a * b)
    else if (j <= 5.8d-158) then
        tmp = x * (y * z)
    else if (j <= 3d-49) then
        tmp = b * (a * i)
    else if (j <= 1.25d-22) then
        tmp = y * (x * z)
    else if (j <= 1.2d+85) then
        tmp = i * (y * -j)
    else
        tmp = t * (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 (j <= -1.05e-13) {
		tmp = c * (t * j);
	} else if (j <= -6.8e-254) {
		tmp = i * (a * b);
	} else if (j <= 5.8e-158) {
		tmp = x * (y * z);
	} else if (j <= 3e-49) {
		tmp = b * (a * i);
	} else if (j <= 1.25e-22) {
		tmp = y * (x * z);
	} else if (j <= 1.2e+85) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.05e-13:
		tmp = c * (t * j)
	elif j <= -6.8e-254:
		tmp = i * (a * b)
	elif j <= 5.8e-158:
		tmp = x * (y * z)
	elif j <= 3e-49:
		tmp = b * (a * i)
	elif j <= 1.25e-22:
		tmp = y * (x * z)
	elif j <= 1.2e+85:
		tmp = i * (y * -j)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.05e-13)
		tmp = Float64(c * Float64(t * j));
	elseif (j <= -6.8e-254)
		tmp = Float64(i * Float64(a * b));
	elseif (j <= 5.8e-158)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 3e-49)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= 1.25e-22)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.2e+85)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(t * 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 (j <= -1.05e-13)
		tmp = c * (t * j);
	elseif (j <= -6.8e-254)
		tmp = i * (a * b);
	elseif (j <= 5.8e-158)
		tmp = x * (y * z);
	elseif (j <= 3e-49)
		tmp = b * (a * i);
	elseif (j <= 1.25e-22)
		tmp = y * (x * z);
	elseif (j <= 1.2e+85)
		tmp = i * (y * -j);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.05e-13], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.8e-254], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e-158], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e-49], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.25e-22], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.2e+85], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.04999999999999994e-13

   1. Initial program 77.8%

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

   3. Taylor expanded in b around 0 67.0%

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

   4. Taylor expanded in c around inf 37.8%

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

      1. *-commutative 37.8%

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

   6. Simplified 37.8%

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

   if -1.04999999999999994e-13 < j < -6.79999999999999986e-254

   1. Initial program 77.0%

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

   3. Taylor expanded in b around inf 48.1%

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

   4. Taylor expanded in a around inf 34.6%

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

      1. associate-*r* 34.7%

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

   6. Simplified 34.7%

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

   if -6.79999999999999986e-254 < j < 5.79999999999999961e-158

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf 65.3%

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

      1. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around inf 38.7%

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

      1. *-commutative 38.7%

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

   8. Simplified 38.7%

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

   if 5.79999999999999961e-158 < j < 3e-49

   1. Initial program 80.5%

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

   3. Taylor expanded in b around inf 73.0%

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

   4. Taylor expanded in a around inf 37.6%

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

      1. *-commutative 37.6%

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

      2. associate-*l* 41.1%

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

      3. *-commutative 41.1%

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

   6. Simplified 41.1%

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

   if 3e-49 < j < 1.24999999999999988e-22

   1. Initial program 44.1%

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

   3. Taylor expanded in y around -inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. *-commutative 69.7%

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

      3. distribute-rgt-neg-in 69.7%

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

      4. +-commutative 69.7%

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

      5. mul-1-neg 69.7%

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

      6. unsub-neg 69.7%

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

      7. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in i around 0 42.9%

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

      1. *-commutative 42.9%

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

      2. associate-*l* 69.7%

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

      3. *-commutative 69.7%

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

   8. Simplified 69.7%

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

   if 1.24999999999999988e-22 < j < 1.19999999999999998e85

   1. Initial program 71.4%

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

   3. Taylor expanded in i around inf 63.8%

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

      1. distribute-lft-out-- 63.8%

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

      2. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in j around inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. *-commutative 47.6%

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

      3. distribute-rgt-neg-in 47.6%

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

   8. Simplified 47.6%

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

   if 1.19999999999999998e85 < j

   1. Initial program 74.4%

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

   3. Taylor expanded in b around 0 73.3%

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

   4. Taylor expanded in c around inf 49.0%

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

      1. *-commutative 49.0%

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

      2. *-commutative 49.0%

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

      3. associate-*r* 52.0%

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

   6. Simplified 52.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{if}\;c \leq -1.35 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-308}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+152} \lor \neg \left(c \leq 3.15 \cdot 10^{+240}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b)))))
   (if (<= c -1.35e-15)
     t_1
     (if (<= c -4.8e-308)
       (* i (* y (- j)))
       (if (<= c 5.4e-7)
         (* b (* a i))
         (if (or (<= c 1.25e+152) (not (<= c 3.15e+240)))
           (* j (* t c))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double tmp;
	if (c <= -1.35e-15) {
		tmp = t_1;
	} else if (c <= -4.8e-308) {
		tmp = i * (y * -j);
	} else if (c <= 5.4e-7) {
		tmp = b * (a * i);
	} else if ((c <= 1.25e+152) || !(c <= 3.15e+240)) {
		tmp = j * (t * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (c * -b)
    if (c <= (-1.35d-15)) then
        tmp = t_1
    else if (c <= (-4.8d-308)) then
        tmp = i * (y * -j)
    else if (c <= 5.4d-7) then
        tmp = b * (a * i)
    else if ((c <= 1.25d+152) .or. (.not. (c <= 3.15d+240))) then
        tmp = j * (t * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double tmp;
	if (c <= -1.35e-15) {
		tmp = t_1;
	} else if (c <= -4.8e-308) {
		tmp = i * (y * -j);
	} else if (c <= 5.4e-7) {
		tmp = b * (a * i);
	} else if ((c <= 1.25e+152) || !(c <= 3.15e+240)) {
		tmp = j * (t * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	tmp = 0
	if c <= -1.35e-15:
		tmp = t_1
	elif c <= -4.8e-308:
		tmp = i * (y * -j)
	elif c <= 5.4e-7:
		tmp = b * (a * i)
	elif (c <= 1.25e+152) or not (c <= 3.15e+240):
		tmp = j * (t * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	tmp = 0.0
	if (c <= -1.35e-15)
		tmp = t_1;
	elseif (c <= -4.8e-308)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 5.4e-7)
		tmp = Float64(b * Float64(a * i));
	elseif ((c <= 1.25e+152) || !(c <= 3.15e+240))
		tmp = Float64(j * Float64(t * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * -b);
	tmp = 0.0;
	if (c <= -1.35e-15)
		tmp = t_1;
	elseif (c <= -4.8e-308)
		tmp = i * (y * -j);
	elseif (c <= 5.4e-7)
		tmp = b * (a * i);
	elseif ((c <= 1.25e+152) || ~((c <= 3.15e+240)))
		tmp = j * (t * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.35e-15], t$95$1, If[LessEqual[c, -4.8e-308], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.4e-7], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 1.25e+152], N[Not[LessEqual[c, 3.15e+240]], $MachinePrecision]], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.35000000000000005e-15 or 1.25e152 < c < 3.14999999999999985e240

   1. Initial program 70.1%

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

   3. Taylor expanded in z around inf 53.0%

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

      1. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in y around 0 44.2%

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

      1. neg-mul-1 44.2%

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

      2. distribute-rgt-neg-in 44.2%

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

   8. Simplified 44.2%

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

   if -1.35000000000000005e-15 < c < -4.80000000000000016e-308

   1. Initial program 81.9%

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

   3. Taylor expanded in i around inf 48.6%

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

      1. distribute-lft-out-- 48.6%

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

      2. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in j around inf 40.4%

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

      1. mul-1-neg 40.4%

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

      2. *-commutative 40.4%

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

      3. distribute-rgt-neg-in 40.4%

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

   8. Simplified 40.4%

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

   if -4.80000000000000016e-308 < c < 5.40000000000000018e-7

   1. Initial program 78.8%

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

   3. Taylor expanded in b around inf 49.7%

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

   4. Taylor expanded in a around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. associate-*l* 44.2%

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

      3. *-commutative 44.2%

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

   6. Simplified 44.2%

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

   if 5.40000000000000018e-7 < c < 1.25e152 or 3.14999999999999985e240 < c

   1. Initial program 69.8%

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

   3. Taylor expanded in b around 0 66.5%

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

   4. Taylor expanded in c around inf 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*l* 46.0%

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

   6. Simplified 46.0%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-308}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+152} \lor \neg \left(c \leq 3.15 \cdot 10^{+240}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-305}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+152} \lor \neg \left(c \leq 9.2 \cdot 10^{+240}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.25e-14)
   (* b (* z (- c)))
   (if (<= c -1.8e-305)
     (* i (* y (- j)))
     (if (<= c 9.2e-7)
       (* b (* a i))
       (if (or (<= c 3.8e+152) (not (<= c 9.2e+240)))
         (* j (* t c))
         (* z (* c (- b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.25e-14) {
		tmp = b * (z * -c);
	} else if (c <= -1.8e-305) {
		tmp = i * (y * -j);
	} else if (c <= 9.2e-7) {
		tmp = b * (a * i);
	} else if ((c <= 3.8e+152) || !(c <= 9.2e+240)) {
		tmp = j * (t * c);
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.25d-14)) then
        tmp = b * (z * -c)
    else if (c <= (-1.8d-305)) then
        tmp = i * (y * -j)
    else if (c <= 9.2d-7) then
        tmp = b * (a * i)
    else if ((c <= 3.8d+152) .or. (.not. (c <= 9.2d+240))) then
        tmp = j * (t * c)
    else
        tmp = z * (c * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.25e-14) {
		tmp = b * (z * -c);
	} else if (c <= -1.8e-305) {
		tmp = i * (y * -j);
	} else if (c <= 9.2e-7) {
		tmp = b * (a * i);
	} else if ((c <= 3.8e+152) || !(c <= 9.2e+240)) {
		tmp = j * (t * c);
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.25e-14:
		tmp = b * (z * -c)
	elif c <= -1.8e-305:
		tmp = i * (y * -j)
	elif c <= 9.2e-7:
		tmp = b * (a * i)
	elif (c <= 3.8e+152) or not (c <= 9.2e+240):
		tmp = j * (t * c)
	else:
		tmp = z * (c * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.25e-14)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -1.8e-305)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 9.2e-7)
		tmp = Float64(b * Float64(a * i));
	elseif ((c <= 3.8e+152) || !(c <= 9.2e+240))
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(z * Float64(c * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.25e-14)
		tmp = b * (z * -c);
	elseif (c <= -1.8e-305)
		tmp = i * (y * -j);
	elseif (c <= 9.2e-7)
		tmp = b * (a * i);
	elseif ((c <= 3.8e+152) || ~((c <= 9.2e+240)))
		tmp = j * (t * c);
	else
		tmp = z * (c * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.25e-14], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.8e-305], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e-7], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 3.8e+152], N[Not[LessEqual[c, 9.2e+240]], $MachinePrecision]], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.25e-14

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 48.1%

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

   4. Taylor expanded in a around 0 45.4%

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

      1. associate-*r* 45.4%

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

      2. neg-mul-1 45.4%

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

   6. Simplified 45.4%

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

   if -1.25e-14 < c < -1.80000000000000002e-305

   1. Initial program 81.9%

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

   3. Taylor expanded in i around inf 48.6%

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

      1. distribute-lft-out-- 48.6%

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

      2. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in j around inf 40.4%

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

      1. mul-1-neg 40.4%

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

      2. *-commutative 40.4%

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

      3. distribute-rgt-neg-in 40.4%

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

   8. Simplified 40.4%

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

   if -1.80000000000000002e-305 < c < 9.1999999999999998e-7

   1. Initial program 78.8%

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

   3. Taylor expanded in b around inf 49.7%

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

   4. Taylor expanded in a around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. associate-*l* 44.2%

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

      3. *-commutative 44.2%

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

   6. Simplified 44.2%

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

   if 9.1999999999999998e-7 < c < 3.8e152 or 9.20000000000000005e240 < c

   1. Initial program 69.8%

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

   3. Taylor expanded in b around 0 66.5%

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

   4. Taylor expanded in c around inf 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*l* 46.0%

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

   6. Simplified 46.0%

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

   if 3.8e152 < c < 9.20000000000000005e240

   1. Initial program 69.3%

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

   3. Taylor expanded in z around inf 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in y around 0 59.5%

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

      1. neg-mul-1 59.5%

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

      2. distribute-rgt-neg-in 59.5%

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

   8. Simplified 59.5%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-305}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+152} \lor \neg \left(c \leq 9.2 \cdot 10^{+240}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-307}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+156} \lor \neg \left(c \leq 1.58 \cdot 10^{+240}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -4.6e-15)
   (* b (* z (- c)))
   (if (<= c -9.2e-307)
     (* (* i j) (- y))
     (if (<= c 8.2e-7)
       (* b (* a i))
       (if (or (<= c 2e+156) (not (<= c 1.58e+240)))
         (* j (* t c))
         (* z (* c (- b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -4.6e-15) {
		tmp = b * (z * -c);
	} else if (c <= -9.2e-307) {
		tmp = (i * j) * -y;
	} else if (c <= 8.2e-7) {
		tmp = b * (a * i);
	} else if ((c <= 2e+156) || !(c <= 1.58e+240)) {
		tmp = j * (t * c);
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-4.6d-15)) then
        tmp = b * (z * -c)
    else if (c <= (-9.2d-307)) then
        tmp = (i * j) * -y
    else if (c <= 8.2d-7) then
        tmp = b * (a * i)
    else if ((c <= 2d+156) .or. (.not. (c <= 1.58d+240))) then
        tmp = j * (t * c)
    else
        tmp = z * (c * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -4.6e-15) {
		tmp = b * (z * -c);
	} else if (c <= -9.2e-307) {
		tmp = (i * j) * -y;
	} else if (c <= 8.2e-7) {
		tmp = b * (a * i);
	} else if ((c <= 2e+156) || !(c <= 1.58e+240)) {
		tmp = j * (t * c);
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -4.6e-15:
		tmp = b * (z * -c)
	elif c <= -9.2e-307:
		tmp = (i * j) * -y
	elif c <= 8.2e-7:
		tmp = b * (a * i)
	elif (c <= 2e+156) or not (c <= 1.58e+240):
		tmp = j * (t * c)
	else:
		tmp = z * (c * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -4.6e-15)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -9.2e-307)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (c <= 8.2e-7)
		tmp = Float64(b * Float64(a * i));
	elseif ((c <= 2e+156) || !(c <= 1.58e+240))
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(z * Float64(c * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -4.6e-15)
		tmp = b * (z * -c);
	elseif (c <= -9.2e-307)
		tmp = (i * j) * -y;
	elseif (c <= 8.2e-7)
		tmp = b * (a * i);
	elseif ((c <= 2e+156) || ~((c <= 1.58e+240)))
		tmp = j * (t * c);
	else
		tmp = z * (c * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -4.6e-15], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9.2e-307], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[c, 8.2e-7], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 2e+156], N[Not[LessEqual[c, 1.58e+240]], $MachinePrecision]], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.59999999999999981e-15

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 48.1%

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

   4. Taylor expanded in a around 0 45.4%

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

      1. associate-*r* 45.4%

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

      2. neg-mul-1 45.4%

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

   6. Simplified 45.4%

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

   if -4.59999999999999981e-15 < c < -9.1999999999999996e-307

   1. Initial program 81.9%

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

   3. Taylor expanded in y around -inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. *-commutative 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

      4. +-commutative 67.4%

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

      5. mul-1-neg 67.4%

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

      6. unsub-neg 67.4%

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

      7. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in i around inf 43.5%

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

   if -9.1999999999999996e-307 < c < 8.1999999999999998e-7

   1. Initial program 78.8%

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

   3. Taylor expanded in b around inf 49.7%

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

   4. Taylor expanded in a around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. associate-*l* 44.2%

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

      3. *-commutative 44.2%

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

   6. Simplified 44.2%

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

   if 8.1999999999999998e-7 < c < 2e156 or 1.58e240 < c

   1. Initial program 69.8%

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

   3. Taylor expanded in b around 0 66.5%

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

   4. Taylor expanded in c around inf 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*l* 46.0%

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

   6. Simplified 46.0%

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

   if 2e156 < c < 1.58e240

   1. Initial program 69.3%

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

   3. Taylor expanded in z around inf 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in y around 0 59.5%

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

      1. neg-mul-1 59.5%

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

      2. distribute-rgt-neg-in 59.5%

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

   8. Simplified 59.5%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-307}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+156} \lor \neg \left(c \leq 1.58 \cdot 10^{+240}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+115}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= y -3.2e+115)
     (* (* i j) (- y))
     (if (<= y 1.5e-226)
       t_1
       (if (<= y 5.2e-183)
         (* j (* t c))
         (if (<= y 3.9e+111) t_1 (* z (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -3.2e+115) {
		tmp = (i * j) * -y;
	} else if (y <= 1.5e-226) {
		tmp = t_1;
	} else if (y <= 5.2e-183) {
		tmp = j * (t * c);
	} else if (y <= 3.9e+111) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (y <= (-3.2d+115)) then
        tmp = (i * j) * -y
    else if (y <= 1.5d-226) then
        tmp = t_1
    else if (y <= 5.2d-183) then
        tmp = j * (t * c)
    else if (y <= 3.9d+111) then
        tmp = t_1
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -3.2e+115) {
		tmp = (i * j) * -y;
	} else if (y <= 1.5e-226) {
		tmp = t_1;
	} else if (y <= 5.2e-183) {
		tmp = j * (t * c);
	} else if (y <= 3.9e+111) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if y <= -3.2e+115:
		tmp = (i * j) * -y
	elif y <= 1.5e-226:
		tmp = t_1
	elif y <= 5.2e-183:
		tmp = j * (t * c)
	elif y <= 3.9e+111:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (y <= -3.2e+115)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (y <= 1.5e-226)
		tmp = t_1;
	elseif (y <= 5.2e-183)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 3.9e+111)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (y <= -3.2e+115)
		tmp = (i * j) * -y;
	elseif (y <= 1.5e-226)
		tmp = t_1;
	elseif (y <= 5.2e-183)
		tmp = j * (t * c);
	elseif (y <= 3.9e+111)
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+115], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 1.5e-226], t$95$1, If[LessEqual[y, 5.2e-183], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+111], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.2e115

   1. Initial program 84.7%

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

   3. Taylor expanded in y around -inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. *-commutative 64.6%

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

      3. distribute-rgt-neg-in 64.6%

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

      4. +-commutative 64.6%

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

      5. mul-1-neg 64.6%

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

      6. unsub-neg 64.6%

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

      7. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in i around inf 47.4%

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

   if -3.2e115 < y < 1.49999999999999998e-226 or 5.1999999999999998e-183 < y < 3.89999999999999979e111

   1. Initial program 79.1%

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

   3. Taylor expanded in b around inf 50.5%

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

   if 1.49999999999999998e-226 < y < 5.1999999999999998e-183

   1. Initial program 81.8%

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

   3. Taylor expanded in b around 0 72.2%

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

   4. Taylor expanded in c around inf 47.6%

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

      1. *-commutative 47.6%

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

      2. associate-*l* 53.3%

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

   6. Simplified 53.3%

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

   if 3.89999999999999979e111 < y

   1. Initial program 54.1%

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

   3. Taylor expanded in z around inf 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in y around inf 60.5%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+115}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -140000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -140000000000.0)
     t_1
     (if (<= j 1.2e-173)
       (* x (- (* y z) (* t a)))
       (if (<= j 6.4e-54)
         (* b (- (* a i) (* z c)))
         (if (<= j 8e+22) (* 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -140000000000.0) {
		tmp = t_1;
	} else if (j <= 1.2e-173) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 6.4e-54) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 8e+22) {
		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 = j * ((t * c) - (y * i))
    if (j <= (-140000000000.0d0)) then
        tmp = t_1
    else if (j <= 1.2d-173) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 6.4d-54) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 8d+22) 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -140000000000.0) {
		tmp = t_1;
	} else if (j <= 1.2e-173) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 6.4e-54) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 8e+22) {
		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 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -140000000000.0:
		tmp = t_1
	elif j <= 1.2e-173:
		tmp = x * ((y * z) - (t * a))
	elif j <= 6.4e-54:
		tmp = b * ((a * i) - (z * c))
	elif j <= 8e+22:
		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(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -140000000000.0)
		tmp = t_1;
	elseif (j <= 1.2e-173)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 6.4e-54)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 8e+22)
		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 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -140000000000.0)
		tmp = t_1;
	elseif (j <= 1.2e-173)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 6.4e-54)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 8e+22)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -140000000000.0], t$95$1, If[LessEqual[j, 1.2e-173], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.4e-54], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e+22], 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 j < -1.4e11 or 8e22 < j

   1. Initial program 76.3%

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

   3. Taylor expanded in b around 0 71.6%

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

   4. Taylor expanded in j around inf 68.5%

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

      1. sub-neg 68.5%

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

      2. *-commutative 68.5%

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

      3. *-commutative 68.5%

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

      4. sub-neg 68.5%

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

   6. Simplified 68.5%

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

   if -1.4e11 < j < 1.20000000000000008e-173

   1. Initial program 75.4%

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

   3. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   if 1.20000000000000008e-173 < j < 6.39999999999999997e-54

   1. Initial program 81.9%

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

   3. Taylor expanded in b around inf 71.4%

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

   if 6.39999999999999997e-54 < j < 8e22

   1. Initial program 53.8%

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

   3. Taylor expanded in y around -inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. *-commutative 73.4%

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

      3. distribute-rgt-neg-in 73.4%

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

      4. +-commutative 73.4%

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

      5. mul-1-neg 73.4%

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

      6. unsub-neg 73.4%

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

      7. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in i around 0 53.1%

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

      1. +-commutative 53.1%

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

      2. *-commutative 53.1%

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

      3. associate-*l* 62.9%

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

      4. mul-1-neg 62.9%

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

      5. associate-*r* 62.9%

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

      6. *-commutative 62.9%

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

      7. distribute-rgt-neg-in 62.9%

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

      8. distribute-lft-in 73.4%

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

      9. unsub-neg 73.4%

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

      10. *-commutative 73.4%

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

   8. Simplified 73.4%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -140000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* b (* a i))))
   (if (<= b -2.3e+96)
     t_2
     (if (<= b -1.76e-40)
       t_1
       (if (<= b -2.2e-176) t_2 (if (<= b 4.6e+82) t_1 (* a (* b i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = b * (a * i);
	double tmp;
	if (b <= -2.3e+96) {
		tmp = t_2;
	} else if (b <= -1.76e-40) {
		tmp = t_1;
	} else if (b <= -2.2e-176) {
		tmp = t_2;
	} else if (b <= 4.6e+82) {
		tmp = t_1;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = b * (a * i)
    if (b <= (-2.3d+96)) then
        tmp = t_2
    else if (b <= (-1.76d-40)) then
        tmp = t_1
    else if (b <= (-2.2d-176)) then
        tmp = t_2
    else if (b <= 4.6d+82) then
        tmp = t_1
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = b * (a * i);
	double tmp;
	if (b <= -2.3e+96) {
		tmp = t_2;
	} else if (b <= -1.76e-40) {
		tmp = t_1;
	} else if (b <= -2.2e-176) {
		tmp = t_2;
	} else if (b <= 4.6e+82) {
		tmp = t_1;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = b * (a * i)
	tmp = 0
	if b <= -2.3e+96:
		tmp = t_2
	elif b <= -1.76e-40:
		tmp = t_1
	elif b <= -2.2e-176:
		tmp = t_2
	elif b <= 4.6e+82:
		tmp = t_1
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (b <= -2.3e+96)
		tmp = t_2;
	elseif (b <= -1.76e-40)
		tmp = t_1;
	elseif (b <= -2.2e-176)
		tmp = t_2;
	elseif (b <= 4.6e+82)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = b * (a * i);
	tmp = 0.0;
	if (b <= -2.3e+96)
		tmp = t_2;
	elseif (b <= -1.76e-40)
		tmp = t_1;
	elseif (b <= -2.2e-176)
		tmp = t_2;
	elseif (b <= 4.6e+82)
		tmp = t_1;
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+96], t$95$2, If[LessEqual[b, -1.76e-40], t$95$1, If[LessEqual[b, -2.2e-176], t$95$2, If[LessEqual[b, 4.6e+82], t$95$1, N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.30000000000000015e96 or -1.76e-40 < b < -2.1999999999999999e-176

   1. Initial program 65.2%

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

   3. Taylor expanded in b around inf 58.8%

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

   4. Taylor expanded in a around inf 36.5%

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

      1. *-commutative 36.5%

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

      2. associate-*l* 40.4%

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

      3. *-commutative 40.4%

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

   6. Simplified 40.4%

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

   if -2.30000000000000015e96 < b < -1.76e-40 or -2.1999999999999999e-176 < b < 4.59999999999999976e82

   1. Initial program 82.1%

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

   3. Taylor expanded in b around 0 76.0%

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

   4. Taylor expanded in c around inf 34.6%

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

      1. *-commutative 34.6%

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

   6. Simplified 34.6%

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

   if 4.59999999999999976e82 < b

   1. Initial program 68.8%

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

   3. Taylor expanded in b around inf 74.9%

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

   4. Taylor expanded in a around inf 48.3%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+96}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-176}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+82}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-175}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))) (t_2 (* b (* a i))))
   (if (<= b -1.05e+97)
     t_2
     (if (<= b -6.2e-37)
       t_1
       (if (<= b -1.4e-175) t_2 (if (<= b 6.8e+82) t_1 (* a (* b i))))))))

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 * (t * c);
	double t_2 = b * (a * i);
	double tmp;
	if (b <= -1.05e+97) {
		tmp = t_2;
	} else if (b <= -6.2e-37) {
		tmp = t_1;
	} else if (b <= -1.4e-175) {
		tmp = t_2;
	} else if (b <= 6.8e+82) {
		tmp = t_1;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (t * c)
    t_2 = b * (a * i)
    if (b <= (-1.05d+97)) then
        tmp = t_2
    else if (b <= (-6.2d-37)) then
        tmp = t_1
    else if (b <= (-1.4d-175)) then
        tmp = t_2
    else if (b <= 6.8d+82) then
        tmp = t_1
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double t_2 = b * (a * i);
	double tmp;
	if (b <= -1.05e+97) {
		tmp = t_2;
	} else if (b <= -6.2e-37) {
		tmp = t_1;
	} else if (b <= -1.4e-175) {
		tmp = t_2;
	} else if (b <= 6.8e+82) {
		tmp = t_1;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	t_2 = b * (a * i)
	tmp = 0
	if b <= -1.05e+97:
		tmp = t_2
	elif b <= -6.2e-37:
		tmp = t_1
	elif b <= -1.4e-175:
		tmp = t_2
	elif b <= 6.8e+82:
		tmp = t_1
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	t_2 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (b <= -1.05e+97)
		tmp = t_2;
	elseif (b <= -6.2e-37)
		tmp = t_1;
	elseif (b <= -1.4e-175)
		tmp = t_2;
	elseif (b <= 6.8e+82)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	t_2 = b * (a * i);
	tmp = 0.0;
	if (b <= -1.05e+97)
		tmp = t_2;
	elseif (b <= -6.2e-37)
		tmp = t_1;
	elseif (b <= -1.4e-175)
		tmp = t_2;
	elseif (b <= 6.8e+82)
		tmp = t_1;
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+97], t$95$2, If[LessEqual[b, -6.2e-37], t$95$1, If[LessEqual[b, -1.4e-175], t$95$2, If[LessEqual[b, 6.8e+82], t$95$1, N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05000000000000006e97 or -6.19999999999999987e-37 < b < -1.4e-175

   1. Initial program 65.2%

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

   3. Taylor expanded in b around inf 58.8%

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

   4. Taylor expanded in a around inf 36.5%

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

      1. *-commutative 36.5%

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

      2. associate-*l* 40.4%

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

      3. *-commutative 40.4%

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

   6. Simplified 40.4%

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

   if -1.05000000000000006e97 < b < -6.19999999999999987e-37 or -1.4e-175 < b < 6.79999999999999989e82

   1. Initial program 82.1%

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

   3. Taylor expanded in b around 0 76.0%

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

   4. Taylor expanded in c around inf 34.6%

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

      1. *-commutative 34.6%

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

      2. associate-*l* 35.3%

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

   6. Simplified 35.3%

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

   if 6.79999999999999989e82 < b

   1. Initial program 68.8%

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

   3. Taylor expanded in b around inf 74.9%

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

   4. Taylor expanded in a around inf 48.3%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+97}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-37}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+82}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-305}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -1.1e-89)
     t_1
     (if (<= c -3.2e-305)
       (* (* i j) (- y))
       (if (<= c 7e-7) (* b (- (* a i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.1e-89) {
		tmp = t_1;
	} else if (c <= -3.2e-305) {
		tmp = (i * j) * -y;
	} else if (c <= 7e-7) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-1.1d-89)) then
        tmp = t_1
    else if (c <= (-3.2d-305)) then
        tmp = (i * j) * -y
    else if (c <= 7d-7) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.1e-89) {
		tmp = t_1;
	} else if (c <= -3.2e-305) {
		tmp = (i * j) * -y;
	} else if (c <= 7e-7) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.1e-89:
		tmp = t_1
	elif c <= -3.2e-305:
		tmp = (i * j) * -y
	elif c <= 7e-7:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.1e-89)
		tmp = t_1;
	elseif (c <= -3.2e-305)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (c <= 7e-7)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.1e-89)
		tmp = t_1;
	elseif (c <= -3.2e-305)
		tmp = (i * j) * -y;
	elseif (c <= 7e-7)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.1e-89], t$95$1, If[LessEqual[c, -3.2e-305], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[c, 7e-7], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.10000000000000006e-89 or 6.99999999999999968e-7 < c

   1. Initial program 71.8%

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

   3. Taylor expanded in c around inf 63.4%

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

   if -1.10000000000000006e-89 < c < -3.20000000000000009e-305

   1. Initial program 79.5%

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

   3. Taylor expanded in y around -inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. *-commutative 71.4%

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

      3. distribute-rgt-neg-in 71.4%

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

      4. +-commutative 71.4%

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

      5. mul-1-neg 71.4%

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

      6. unsub-neg 71.4%

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

      7. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in i around inf 43.6%

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

   if -3.20000000000000009e-305 < c < 6.99999999999999968e-7

   1. Initial program 78.8%

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

   3. Taylor expanded in b around inf 49.7%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{-89}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-305}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1250000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1250000000000.0)
     t_1
     (if (<= j 2.7e-171)
       (* x (- (* y z) (* t a)))
       (if (<= j 1.35e-41) (* b (- (* a i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1250000000000.0) {
		tmp = t_1;
	} else if (j <= 2.7e-171) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.35e-41) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1250000000000.0d0)) then
        tmp = t_1
    else if (j <= 2.7d-171) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 1.35d-41) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1250000000000.0) {
		tmp = t_1;
	} else if (j <= 2.7e-171) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.35e-41) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1250000000000.0:
		tmp = t_1
	elif j <= 2.7e-171:
		tmp = x * ((y * z) - (t * a))
	elif j <= 1.35e-41:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1250000000000.0)
		tmp = t_1;
	elseif (j <= 2.7e-171)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 1.35e-41)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1250000000000.0)
		tmp = t_1;
	elseif (j <= 2.7e-171)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 1.35e-41)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1250000000000.0], t$95$1, If[LessEqual[j, 2.7e-171], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.35e-41], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.25e12 or 1.35e-41 < j

   1. Initial program 73.6%

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

   3. Taylor expanded in b around 0 70.3%

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

   4. Taylor expanded in j around inf 64.7%

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

      1. sub-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. *-commutative 64.7%

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

      4. sub-neg 64.7%

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

   6. Simplified 64.7%

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

   if -1.25e12 < j < 2.70000000000000014e-171

   1. Initial program 75.4%

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

   3. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   if 2.70000000000000014e-171 < j < 1.35e-41

   1. Initial program 79.0%

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

   3. Taylor expanded in b around inf 72.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1250000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-133}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -5.8e+16)
     t_1
     (if (<= y -1.4e-133)
       (* b (* a i))
       (if (<= y 1.5e-56) (* j (* t c)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -5.8e+16) {
		tmp = t_1;
	} else if (y <= -1.4e-133) {
		tmp = b * (a * i);
	} else if (y <= 1.5e-56) {
		tmp = j * (t * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (y <= (-5.8d+16)) then
        tmp = t_1
    else if (y <= (-1.4d-133)) then
        tmp = b * (a * i)
    else if (y <= 1.5d-56) then
        tmp = j * (t * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -5.8e+16) {
		tmp = t_1;
	} else if (y <= -1.4e-133) {
		tmp = b * (a * i);
	} else if (y <= 1.5e-56) {
		tmp = j * (t * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if y <= -5.8e+16:
		tmp = t_1
	elif y <= -1.4e-133:
		tmp = b * (a * i)
	elif y <= 1.5e-56:
		tmp = j * (t * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -5.8e+16)
		tmp = t_1;
	elseif (y <= -1.4e-133)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 1.5e-56)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (y <= -5.8e+16)
		tmp = t_1;
	elseif (y <= -1.4e-133)
		tmp = b * (a * i);
	elseif (y <= 1.5e-56)
		tmp = j * (t * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+16], t$95$1, If[LessEqual[y, -1.4e-133], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-56], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8e16 or 1.49999999999999995e-56 < y

   1. Initial program 67.8%

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

   3. Taylor expanded in z around inf 49.0%

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

      1. *-commutative 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in y around inf 38.1%

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

      1. *-commutative 38.1%

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

   8. Simplified 38.1%

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

   if -5.8e16 < y < -1.3999999999999999e-133

   1. Initial program 79.0%

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

   3. Taylor expanded in b around inf 58.1%

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

   4. Taylor expanded in a around inf 37.2%

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

      1. *-commutative 37.2%

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

      2. associate-*l* 43.9%

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

      3. *-commutative 43.9%

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

   6. Simplified 43.9%

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

   if -1.3999999999999999e-133 < y < 1.49999999999999995e-56

   1. Initial program 84.1%

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

   3. Taylor expanded in b around 0 58.0%

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

   4. Taylor expanded in c around inf 35.7%

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

      1. *-commutative 35.7%

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

      2. associate-*l* 37.9%

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

   6. Simplified 37.9%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-133}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -7.8e+16)
   (* x (* y z))
   (if (<= y -3.2e-138)
     (* b (* a i))
     (if (<= y 4.6e-55) (* j (* t c)) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.8e+16) {
		tmp = x * (y * z);
	} else if (y <= -3.2e-138) {
		tmp = b * (a * i);
	} else if (y <= 4.6e-55) {
		tmp = j * (t * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-7.8d+16)) then
        tmp = x * (y * z)
    else if (y <= (-3.2d-138)) then
        tmp = b * (a * i)
    else if (y <= 4.6d-55) then
        tmp = j * (t * c)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.8e+16) {
		tmp = x * (y * z);
	} else if (y <= -3.2e-138) {
		tmp = b * (a * i);
	} else if (y <= 4.6e-55) {
		tmp = j * (t * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -7.8e+16:
		tmp = x * (y * z)
	elif y <= -3.2e-138:
		tmp = b * (a * i)
	elif y <= 4.6e-55:
		tmp = j * (t * c)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -7.8e+16)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -3.2e-138)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 4.6e-55)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -7.8e+16)
		tmp = x * (y * z);
	elseif (y <= -3.2e-138)
		tmp = b * (a * i);
	elseif (y <= 4.6e-55)
		tmp = j * (t * c);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -7.8e+16], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-138], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-55], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.8e16

   1. Initial program 77.8%

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

   3. Taylor expanded in z around inf 35.1%

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

      1. *-commutative 35.1%

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

   5. Simplified 35.1%

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

   6. Taylor expanded in y around inf 29.3%

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

      1. *-commutative 29.3%

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

   8. Simplified 29.3%

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

   if -7.8e16 < y < -3.2000000000000001e-138

   1. Initial program 79.0%

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

   3. Taylor expanded in b around inf 58.1%

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

   4. Taylor expanded in a around inf 37.2%

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

      1. *-commutative 37.2%

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

      2. associate-*l* 43.9%

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

      3. *-commutative 43.9%

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

   6. Simplified 43.9%

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

   if -3.2000000000000001e-138 < y < 4.60000000000000023e-55

   1. Initial program 84.1%

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

   3. Taylor expanded in b around 0 58.0%

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

   4. Taylor expanded in c around inf 35.7%

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

      1. *-commutative 35.7%

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

      2. associate-*l* 37.9%

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

   6. Simplified 37.9%

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

   if 4.60000000000000023e-55 < y

   1. Initial program 61.3%

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

   3. Taylor expanded in z around inf 58.1%

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

      1. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in y around inf 46.3%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+31} \lor \neg \left(b \leq 1.45 \cdot 10^{+82}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -9.5e+31) (not (<= b 1.45e+82)))
   (* b (- (* a i) (* z c)))
   (* j (- (* t c) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -9.5e+31) || !(b <= 1.45e+82)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-9.5d+31)) .or. (.not. (b <= 1.45d+82))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = j * ((t * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -9.5e+31) || !(b <= 1.45e+82)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -9.5e+31) or not (b <= 1.45e+82):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = j * ((t * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -9.5e+31) || !(b <= 1.45e+82))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -9.5e+31) || ~((b <= 1.45e+82)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = j * ((t * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -9.5e+31], N[Not[LessEqual[b, 1.45e+82]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.5000000000000008e31 or 1.4500000000000001e82 < b

   1. Initial program 70.4%

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

   3. Taylor expanded in b around inf 70.4%

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

   if -9.5000000000000008e31 < b < 1.4500000000000001e82

   1. Initial program 77.7%

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

   3. Taylor expanded in b around 0 72.4%

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

   4. Taylor expanded in j around inf 53.6%

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

      1. sub-neg 53.6%

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

      2. *-commutative 53.6%

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

      3. *-commutative 53.6%

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

      4. sub-neg 53.6%

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

   6. Simplified 53.6%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+31} \lor \neg \left(b \leq 1.45 \cdot 10^{+82}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.9%

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

3. Taylor expanded in b around inf 40.9%

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

4. Taylor expanded in a around inf 23.7%

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

5. Final simplification 23.7%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
6. Add Preprocessing

Alternative 23: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.9%

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

3. Taylor expanded in b around inf 40.9%

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

4. Taylor expanded in a around inf 23.7%

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

   1. *-commutative 23.7%

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

   2. associate-*l* 24.8%

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

   3. *-commutative 24.8%

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

6. Simplified 24.8%

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

7. Final simplification 24.8%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
8. Add Preprocessing

Developer target: 67.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024045 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))