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

Percentage Accurate: 73.6% → 82.3%

Time: 25.0s

Alternatives: 25

Speedup: 0.5×

• 57.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around -inf 52.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.0%

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

Alternative 2: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-159}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{+37}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{b \cdot i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -9.5e+61)
     t_2
     (if (<= b -5.7e-86)
       (* i (- (* t b) (* y j)))
       (if (<= b -1.6e-159)
         (* z (- (* x y) (* b c)))
         (if (<= b -1.15e-178)
           t_1
           (if (<= b 2e-211)
             (* a (- (* c j) (* x t)))
             (if (<= b 6.8e-127)
               t_1
               (if (<= b 1e+37) (* a (* t (- (/ (* b i) a) x))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9.5e+61) {
		tmp = t_2;
	} else if (b <= -5.7e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1.6e-159) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -1.15e-178) {
		tmp = t_1;
	} else if (b <= 2e-211) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 6.8e-127) {
		tmp = t_1;
	} else if (b <= 1e+37) {
		tmp = a * (t * (((b * i) / a) - x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-9.5d+61)) then
        tmp = t_2
    else if (b <= (-5.7d-86)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= (-1.6d-159)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-1.15d-178)) then
        tmp = t_1
    else if (b <= 2d-211) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 6.8d-127) then
        tmp = t_1
    else if (b <= 1d+37) then
        tmp = a * (t * (((b * i) / a) - x))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9.5e+61) {
		tmp = t_2;
	} else if (b <= -5.7e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1.6e-159) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -1.15e-178) {
		tmp = t_1;
	} else if (b <= 2e-211) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 6.8e-127) {
		tmp = t_1;
	} else if (b <= 1e+37) {
		tmp = a * (t * (((b * i) / a) - x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -9.5e+61:
		tmp = t_2
	elif b <= -5.7e-86:
		tmp = i * ((t * b) - (y * j))
	elif b <= -1.6e-159:
		tmp = z * ((x * y) - (b * c))
	elif b <= -1.15e-178:
		tmp = t_1
	elif b <= 2e-211:
		tmp = a * ((c * j) - (x * t))
	elif b <= 6.8e-127:
		tmp = t_1
	elif b <= 1e+37:
		tmp = a * (t * (((b * i) / a) - x))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9.5e+61)
		tmp = t_2;
	elseif (b <= -5.7e-86)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= -1.6e-159)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -1.15e-178)
		tmp = t_1;
	elseif (b <= 2e-211)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 6.8e-127)
		tmp = t_1;
	elseif (b <= 1e+37)
		tmp = Float64(a * Float64(t * Float64(Float64(Float64(b * i) / a) - x)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.5e+61)
		tmp = t_2;
	elseif (b <= -5.7e-86)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= -1.6e-159)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -1.15e-178)
		tmp = t_1;
	elseif (b <= 2e-211)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 6.8e-127)
		tmp = t_1;
	elseif (b <= 1e+37)
		tmp = a * (t * (((b * i) / a) - x));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.5e+61], t$95$2, If[LessEqual[b, -5.7e-86], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.6e-159], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.15e-178], t$95$1, If[LessEqual[b, 2e-211], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e-127], t$95$1, If[LessEqual[b, 1e+37], N[(a * N[(t * N[(N[(N[(b * i), $MachinePrecision] / a), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -9.49999999999999959e61 or 9.99999999999999954e36 < b

   1. Initial program 75.1%

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

   3. Taylor expanded in b around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -9.49999999999999959e61 < b < -5.7000000000000004e-86

   1. Initial program 71.8%

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

   3. Taylor expanded in i around inf 65.0%

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

      1. distribute-lft-out-- 65.0%

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

      2. *-commutative 65.0%

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

      3. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -5.7000000000000004e-86 < b < -1.6e-159

   1. Initial program 74.9%

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

   3. Taylor expanded in z around inf 63.1%

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

   if -1.6e-159 < b < -1.14999999999999997e-178 or 2.00000000000000017e-211 < b < 6.7999999999999997e-127

   1. Initial program 59.8%

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

   3. Taylor expanded in j around inf 67.0%

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

      1. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   if -1.14999999999999997e-178 < b < 2.00000000000000017e-211

   1. Initial program 59.3%

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

   3. Taylor expanded in a around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. mul-1-neg 61.7%

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

      3. unsub-neg 61.7%

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

      4. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   if 6.7999999999999997e-127 < b < 9.99999999999999954e36

   1. Initial program 78.7%

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

   3. Taylor expanded in a around -inf 78.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around inf 68.9%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-159}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-178}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-127}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 10^{+37}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{b \cdot i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-162}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(x \cdot \frac{y}{c} - b\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-178}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{b \cdot i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -5.6e+62)
     t_1
     (if (<= b -6.8e-86)
       (* i (- (* t b) (* y j)))
       (if (<= b -1.45e-162)
         (* (* z c) (- (* x (/ y c)) b))
         (if (<= b -2.4e-178)
           (* i (* y (- j)))
           (if (<= b 6.2e-212)
             (* a (- (* c j) (* x t)))
             (if (<= b 5.2e-122)
               (* j (- (* a c) (* y i)))
               (if (<= b 3.1e+36) (* a (* t (- (/ (* b i) a) x))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.6e+62) {
		tmp = t_1;
	} else if (b <= -6.8e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1.45e-162) {
		tmp = (z * c) * ((x * (y / c)) - b);
	} else if (b <= -2.4e-178) {
		tmp = i * (y * -j);
	} else if (b <= 6.2e-212) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 5.2e-122) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 3.1e+36) {
		tmp = a * (t * (((b * i) / a) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-5.6d+62)) then
        tmp = t_1
    else if (b <= (-6.8d-86)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= (-1.45d-162)) then
        tmp = (z * c) * ((x * (y / c)) - b)
    else if (b <= (-2.4d-178)) then
        tmp = i * (y * -j)
    else if (b <= 6.2d-212) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 5.2d-122) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 3.1d+36) then
        tmp = a * (t * (((b * i) / a) - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.6e+62) {
		tmp = t_1;
	} else if (b <= -6.8e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1.45e-162) {
		tmp = (z * c) * ((x * (y / c)) - b);
	} else if (b <= -2.4e-178) {
		tmp = i * (y * -j);
	} else if (b <= 6.2e-212) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 5.2e-122) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 3.1e+36) {
		tmp = a * (t * (((b * i) / a) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.6e+62:
		tmp = t_1
	elif b <= -6.8e-86:
		tmp = i * ((t * b) - (y * j))
	elif b <= -1.45e-162:
		tmp = (z * c) * ((x * (y / c)) - b)
	elif b <= -2.4e-178:
		tmp = i * (y * -j)
	elif b <= 6.2e-212:
		tmp = a * ((c * j) - (x * t))
	elif b <= 5.2e-122:
		tmp = j * ((a * c) - (y * i))
	elif b <= 3.1e+36:
		tmp = a * (t * (((b * i) / a) - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.6e+62)
		tmp = t_1;
	elseif (b <= -6.8e-86)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= -1.45e-162)
		tmp = Float64(Float64(z * c) * Float64(Float64(x * Float64(y / c)) - b));
	elseif (b <= -2.4e-178)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 6.2e-212)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 5.2e-122)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 3.1e+36)
		tmp = Float64(a * Float64(t * Float64(Float64(Float64(b * i) / a) - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.6e+62)
		tmp = t_1;
	elseif (b <= -6.8e-86)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= -1.45e-162)
		tmp = (z * c) * ((x * (y / c)) - b);
	elseif (b <= -2.4e-178)
		tmp = i * (y * -j);
	elseif (b <= 6.2e-212)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 5.2e-122)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 3.1e+36)
		tmp = a * (t * (((b * i) / a) - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.6e+62], t$95$1, If[LessEqual[b, -6.8e-86], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e-162], N[(N[(z * c), $MachinePrecision] * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e-178], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-212], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e-122], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e+36], N[(a * N[(t * N[(N[(N[(b * i), $MachinePrecision] / a), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -5.60000000000000029e62 or 3.0999999999999999e36 < b

   1. Initial program 75.1%

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

   3. Taylor expanded in b around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -5.60000000000000029e62 < b < -6.8000000000000001e-86

   1. Initial program 71.8%

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

   3. Taylor expanded in i around inf 65.0%

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

      1. distribute-lft-out-- 65.0%

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

      2. *-commutative 65.0%

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

      3. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -6.8000000000000001e-86 < b < -1.4500000000000001e-162

   1. Initial program 70.5%

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

   3. Taylor expanded in c around inf 82.2%

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

   4. Taylor expanded in z around inf 59.7%

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

      1. associate-*r* 65.2%

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

      2. associate-/l* 65.2%

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

   6. Simplified 65.2%

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

   if -1.4500000000000001e-162 < b < -2.40000000000000005e-178

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in x around 0 99.5%

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

      1. associate-*r* 99.5%

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

      2. neg-mul-1 99.5%

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

   8. Simplified 99.5%

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

   if -2.40000000000000005e-178 < b < 6.20000000000000011e-212

   1. Initial program 59.3%

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

   3. Taylor expanded in a around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. mul-1-neg 61.7%

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

      3. unsub-neg 61.7%

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

      4. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   if 6.20000000000000011e-212 < b < 5.1999999999999995e-122

   1. Initial program 56.6%

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

   3. Taylor expanded in j around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if 5.1999999999999995e-122 < b < 3.0999999999999999e36

   1. Initial program 78.7%

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

   3. Taylor expanded in a around -inf 78.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(\frac{b \cdot i}{a} - x\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-162}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(x \cdot \frac{y}{c} - b\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-178}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{b \cdot i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-222}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x a) (- (* y (/ z a)) t))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -7e+62)
     t_2
     (if (<= b -4e-86)
       (* i (- (* t b) (* y j)))
       (if (<= b -2.25e-160)
         t_1
         (if (<= b 8.5e-222)
           (* a (- (* c j) (* x t)))
           (if (<= b 8.5e-193)
             (* y (- (* x z) (* i j)))
             (if (<= b 8.4e-132)
               (* j (- (* a c) (* y i)))
               (if (<= b 1.45e+64) 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 * a) * ((y * (z / a)) - t);
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7e+62) {
		tmp = t_2;
	} else if (b <= -4e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -2.25e-160) {
		tmp = t_1;
	} else if (b <= 8.5e-222) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 8.5e-193) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 8.4e-132) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.45e+64) {
		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 * a) * ((y * (z / a)) - t)
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-7d+62)) then
        tmp = t_2
    else if (b <= (-4d-86)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= (-2.25d-160)) then
        tmp = t_1
    else if (b <= 8.5d-222) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 8.5d-193) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 8.4d-132) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 1.45d+64) 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 * a) * ((y * (z / a)) - t);
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7e+62) {
		tmp = t_2;
	} else if (b <= -4e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -2.25e-160) {
		tmp = t_1;
	} else if (b <= 8.5e-222) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 8.5e-193) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 8.4e-132) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.45e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * a) * ((y * (z / a)) - t)
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7e+62:
		tmp = t_2
	elif b <= -4e-86:
		tmp = i * ((t * b) - (y * j))
	elif b <= -2.25e-160:
		tmp = t_1
	elif b <= 8.5e-222:
		tmp = a * ((c * j) - (x * t))
	elif b <= 8.5e-193:
		tmp = y * ((x * z) - (i * j))
	elif b <= 8.4e-132:
		tmp = j * ((a * c) - (y * i))
	elif b <= 1.45e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * a) * Float64(Float64(y * Float64(z / a)) - t))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7e+62)
		tmp = t_2;
	elseif (b <= -4e-86)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= -2.25e-160)
		tmp = t_1;
	elseif (b <= 8.5e-222)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 8.5e-193)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 8.4e-132)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 1.45e+64)
		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 * a) * ((y * (z / a)) - t);
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7e+62)
		tmp = t_2;
	elseif (b <= -4e-86)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= -2.25e-160)
		tmp = t_1;
	elseif (b <= 8.5e-222)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 8.5e-193)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 8.4e-132)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 1.45e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+62], t$95$2, If[LessEqual[b, -4e-86], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.25e-160], t$95$1, If[LessEqual[b, 8.5e-222], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-193], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.4e-132], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e+64], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -6.99999999999999967e62 or 1.44999999999999997e64 < b

   1. Initial program 73.6%

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

   3. Taylor expanded in b around inf 73.2%

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

      1. *-commutative 73.2%

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

      2. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -6.99999999999999967e62 < b < -4.00000000000000034e-86

   1. Initial program 71.8%

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

   3. Taylor expanded in i around inf 65.0%

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

      1. distribute-lft-out-- 65.0%

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

      2. *-commutative 65.0%

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

      3. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -4.00000000000000034e-86 < b < -2.25000000000000013e-160 or 8.4000000000000004e-132 < b < 1.44999999999999997e64

   1. Initial program 80.4%

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

   3. Taylor expanded in a around -inf 78.4%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in x around inf 67.6%

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

      1. associate-*r* 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-/l* 69.5%

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

   8. Simplified 69.5%

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

   if -2.25000000000000013e-160 < b < 8.5000000000000003e-222

   1. Initial program 60.3%

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

   3. Taylor expanded in a around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   if 8.5000000000000003e-222 < b < 8.50000000000000004e-193

   1. Initial program 56.6%

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

   3. Taylor expanded in y around inf 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

   5. Simplified 71.9%

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

   if 8.50000000000000004e-193 < b < 8.4000000000000004e-132

   1. Initial program 54.9%

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

   3. Taylor expanded in j around inf 56.3%

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

      1. *-commutative 56.3%

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

   5. Simplified 56.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-160}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-222}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+64}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{-85}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.00023:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -5.8e-85)
     t_3
     (if (<= b -2.3e-178)
       t_2
       (if (<= b 2.7e-211)
         t_1
         (if (<= b 7.8e-125)
           (* j (- (* a c) (* y i)))
           (if (<= b 0.00023)
             (* (* x t) (- a))
             (if (<= b 1.4e+31) t_2 (if (<= b 3.3e+63) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.8e-85) {
		tmp = t_3;
	} else if (b <= -2.3e-178) {
		tmp = t_2;
	} else if (b <= 2.7e-211) {
		tmp = t_1;
	} else if (b <= 7.8e-125) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 0.00023) {
		tmp = (x * t) * -a;
	} else if (b <= 1.4e+31) {
		tmp = t_2;
	} else if (b <= 3.3e+63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = y * ((x * z) - (i * j))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-5.8d-85)) then
        tmp = t_3
    else if (b <= (-2.3d-178)) then
        tmp = t_2
    else if (b <= 2.7d-211) then
        tmp = t_1
    else if (b <= 7.8d-125) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 0.00023d0) then
        tmp = (x * t) * -a
    else if (b <= 1.4d+31) then
        tmp = t_2
    else if (b <= 3.3d+63) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.8e-85) {
		tmp = t_3;
	} else if (b <= -2.3e-178) {
		tmp = t_2;
	} else if (b <= 2.7e-211) {
		tmp = t_1;
	} else if (b <= 7.8e-125) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 0.00023) {
		tmp = (x * t) * -a;
	} else if (b <= 1.4e+31) {
		tmp = t_2;
	} else if (b <= 3.3e+63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = y * ((x * z) - (i * j))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.8e-85:
		tmp = t_3
	elif b <= -2.3e-178:
		tmp = t_2
	elif b <= 2.7e-211:
		tmp = t_1
	elif b <= 7.8e-125:
		tmp = j * ((a * c) - (y * i))
	elif b <= 0.00023:
		tmp = (x * t) * -a
	elif b <= 1.4e+31:
		tmp = t_2
	elif b <= 3.3e+63:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.8e-85)
		tmp = t_3;
	elseif (b <= -2.3e-178)
		tmp = t_2;
	elseif (b <= 2.7e-211)
		tmp = t_1;
	elseif (b <= 7.8e-125)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 0.00023)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= 1.4e+31)
		tmp = t_2;
	elseif (b <= 3.3e+63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = y * ((x * z) - (i * j));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.8e-85)
		tmp = t_3;
	elseif (b <= -2.3e-178)
		tmp = t_2;
	elseif (b <= 2.7e-211)
		tmp = t_1;
	elseif (b <= 7.8e-125)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 0.00023)
		tmp = (x * t) * -a;
	elseif (b <= 1.4e+31)
		tmp = t_2;
	elseif (b <= 3.3e+63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e-85], t$95$3, If[LessEqual[b, -2.3e-178], t$95$2, If[LessEqual[b, 2.7e-211], t$95$1, If[LessEqual[b, 7.8e-125], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00023], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, 1.4e+31], t$95$2, If[LessEqual[b, 3.3e+63], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.8000000000000004e-85 or 3.3000000000000002e63 < b

   1. Initial program 73.5%

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

   3. Taylor expanded in b around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if -5.8000000000000004e-85 < b < -2.29999999999999994e-178 or 2.3000000000000001e-4 < b < 1.40000000000000008e31

   1. Initial program 72.8%

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

   3. Taylor expanded in y around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

   if -2.29999999999999994e-178 < b < 2.6999999999999999e-211 or 1.40000000000000008e31 < b < 3.3000000000000002e63

   1. Initial program 65.7%

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

   3. Taylor expanded in a around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. mul-1-neg 61.7%

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

      3. unsub-neg 61.7%

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

      4. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   if 2.6999999999999999e-211 < b < 7.79999999999999965e-125

   1. Initial program 56.6%

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

   3. Taylor expanded in j around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if 7.79999999999999965e-125 < b < 2.3000000000000001e-4

   1. Initial program 75.1%

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

   3. Taylor expanded in a around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in c around 0 60.4%

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

      1. associate-*r* 60.4%

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

      2. mul-1-neg 60.4%

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

   8. Simplified 60.4%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.00023:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -9.2e-85)
     t_2
     (if (<= b -1.5e-178)
       (* y (- (* x z) (* i j)))
       (if (<= b 2e-211)
         t_1
         (if (<= b 1.65e-122)
           (* j (- (* a c) (* y i)))
           (if (<= b 1.7e-7)
             (* z (- (* x y) (* b c)))
             (if (<= b 2.1e+31)
               (* t (- (* b i) (* x a)))
               (if (<= b 4.9e+64) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9.2e-85) {
		tmp = t_2;
	} else if (b <= -1.5e-178) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2e-211) {
		tmp = t_1;
	} else if (b <= 1.65e-122) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.7e-7) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 2.1e+31) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 4.9e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-9.2d-85)) then
        tmp = t_2
    else if (b <= (-1.5d-178)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 2d-211) then
        tmp = t_1
    else if (b <= 1.65d-122) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 1.7d-7) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 2.1d+31) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= 4.9d+64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9.2e-85) {
		tmp = t_2;
	} else if (b <= -1.5e-178) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2e-211) {
		tmp = t_1;
	} else if (b <= 1.65e-122) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.7e-7) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 2.1e+31) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 4.9e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -9.2e-85:
		tmp = t_2
	elif b <= -1.5e-178:
		tmp = y * ((x * z) - (i * j))
	elif b <= 2e-211:
		tmp = t_1
	elif b <= 1.65e-122:
		tmp = j * ((a * c) - (y * i))
	elif b <= 1.7e-7:
		tmp = z * ((x * y) - (b * c))
	elif b <= 2.1e+31:
		tmp = t * ((b * i) - (x * a))
	elif b <= 4.9e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9.2e-85)
		tmp = t_2;
	elseif (b <= -1.5e-178)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 2e-211)
		tmp = t_1;
	elseif (b <= 1.65e-122)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 1.7e-7)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 2.1e+31)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= 4.9e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.2e-85)
		tmp = t_2;
	elseif (b <= -1.5e-178)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 2e-211)
		tmp = t_1;
	elseif (b <= 1.65e-122)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 1.7e-7)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 2.1e+31)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= 4.9e+64)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e-85], t$95$2, If[LessEqual[b, -1.5e-178], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-211], t$95$1, If[LessEqual[b, 1.65e-122], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-7], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+31], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.9e+64], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -9.2000000000000001e-85 or 4.9000000000000003e64 < b

   1. Initial program 73.5%

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

   3. Taylor expanded in b around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if -9.2000000000000001e-85 < b < -1.4999999999999999e-178

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   if -1.4999999999999999e-178 < b < 2.00000000000000017e-211 or 2.09999999999999979e31 < b < 4.9000000000000003e64

   1. Initial program 65.2%

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

   3. Taylor expanded in a around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if 2.00000000000000017e-211 < b < 1.65e-122

   1. Initial program 56.6%

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

   3. Taylor expanded in j around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if 1.65e-122 < b < 1.69999999999999987e-7

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf 61.9%

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

   if 1.69999999999999987e-7 < b < 2.09999999999999979e31

   1. Initial program 71.4%

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

   3. Taylor expanded in t around -inf 75.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-134}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i)))))
        (t_2 (+ (* j (* a c)) (* b (- (* t i) (* z c))))))
   (if (<= b -7.4e+61)
     t_2
     (if (<= b -9.6e-86)
       (* i (- (* t b) (* y j)))
       (if (<= b -9e-123)
         t_1
         (if (<= b -5.8e-134)
           (* (* x a) (- (* y (/ z a)) t))
           (if (<= b 2.6e+63) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	double t_2 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -7.4e+61) {
		tmp = t_2;
	} else if (b <= -9.6e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -9e-123) {
		tmp = t_1;
	} else if (b <= -5.8e-134) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else if (b <= 2.6e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    t_2 = (j * (a * c)) + (b * ((t * i) - (z * c)))
    if (b <= (-7.4d+61)) then
        tmp = t_2
    else if (b <= (-9.6d-86)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= (-9d-123)) then
        tmp = t_1
    else if (b <= (-5.8d-134)) then
        tmp = (x * a) * ((y * (z / a)) - t)
    else if (b <= 2.6d+63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	double t_2 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -7.4e+61) {
		tmp = t_2;
	} else if (b <= -9.6e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -9e-123) {
		tmp = t_1;
	} else if (b <= -5.8e-134) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else if (b <= 2.6e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	t_2 = (j * (a * c)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if b <= -7.4e+61:
		tmp = t_2
	elif b <= -9.6e-86:
		tmp = i * ((t * b) - (y * j))
	elif b <= -9e-123:
		tmp = t_1
	elif b <= -5.8e-134:
		tmp = (x * a) * ((y * (z / a)) - t)
	elif b <= 2.6e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_2 = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -7.4e+61)
		tmp = t_2;
	elseif (b <= -9.6e-86)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= -9e-123)
		tmp = t_1;
	elseif (b <= -5.8e-134)
		tmp = Float64(Float64(x * a) * Float64(Float64(y * Float64(z / a)) - t));
	elseif (b <= 2.6e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	t_2 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (b <= -7.4e+61)
		tmp = t_2;
	elseif (b <= -9.6e-86)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= -9e-123)
		tmp = t_1;
	elseif (b <= -5.8e-134)
		tmp = (x * a) * ((y * (z / a)) - t);
	elseif (b <= 2.6e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+61], t$95$2, If[LessEqual[b, -9.6e-86], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9e-123], t$95$1, If[LessEqual[b, -5.8e-134], N[(N[(x * a), $MachinePrecision] * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+63], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.40000000000000005e61 or 2.6000000000000001e63 < b

   1. Initial program 73.9%

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

   3. Taylor expanded in x around 0 76.2%

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

   4. Taylor expanded in y around 0 78.0%

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

      1. *-commutative 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*r* 80.0%

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

   6. Simplified 80.0%

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

   if -7.40000000000000005e61 < b < -9.60000000000000053e-86

   1. Initial program 71.8%

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

   3. Taylor expanded in i around inf 65.0%

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

      1. distribute-lft-out-- 65.0%

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

      2. *-commutative 65.0%

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

      3. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -9.60000000000000053e-86 < b < -8.99999999999999986e-123 or -5.79999999999999986e-134 < b < 2.6000000000000001e63

   1. Initial program 68.0%

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

   3. Taylor expanded in b around 0 65.9%

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

   if -8.99999999999999986e-123 < b < -5.79999999999999986e-134

   1. Initial program 56.9%

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

   3. Taylor expanded in a around -inf 57.1%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in x around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-134}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.48 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-159}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j - \left(x \cdot t + \frac{i \cdot \left(y \cdot j\right)}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (* a c)) (* b (- (* t i) (* z c))))))
   (if (<= b -2.1e+63)
     t_1
     (if (<= b -1.48e-86)
       (* i (- (* t b) (* y j)))
       (if (<= b -1.65e-106)
         t_1
         (if (<= b -4.6e-159)
           (* (* x a) (- (* y (/ z a)) t))
           (if (<= b 1.32e+14)
             (* a (- (* c j) (+ (* x t) (/ (* i (* y j)) a))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -2.1e+63) {
		tmp = t_1;
	} else if (b <= -1.48e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1.65e-106) {
		tmp = t_1;
	} else if (b <= -4.6e-159) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else if (b <= 1.32e+14) {
		tmp = a * ((c * j) - ((x * t) + ((i * (y * j)) / a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)))
    if (b <= (-2.1d+63)) then
        tmp = t_1
    else if (b <= (-1.48d-86)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= (-1.65d-106)) then
        tmp = t_1
    else if (b <= (-4.6d-159)) then
        tmp = (x * a) * ((y * (z / a)) - t)
    else if (b <= 1.32d+14) then
        tmp = a * ((c * j) - ((x * t) + ((i * (y * j)) / a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -2.1e+63) {
		tmp = t_1;
	} else if (b <= -1.48e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1.65e-106) {
		tmp = t_1;
	} else if (b <= -4.6e-159) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else if (b <= 1.32e+14) {
		tmp = a * ((c * j) - ((x * t) + ((i * (y * j)) / a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if b <= -2.1e+63:
		tmp = t_1
	elif b <= -1.48e-86:
		tmp = i * ((t * b) - (y * j))
	elif b <= -1.65e-106:
		tmp = t_1
	elif b <= -4.6e-159:
		tmp = (x * a) * ((y * (z / a)) - t)
	elif b <= 1.32e+14:
		tmp = a * ((c * j) - ((x * t) + ((i * (y * j)) / a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -2.1e+63)
		tmp = t_1;
	elseif (b <= -1.48e-86)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= -1.65e-106)
		tmp = t_1;
	elseif (b <= -4.6e-159)
		tmp = Float64(Float64(x * a) * Float64(Float64(y * Float64(z / a)) - t));
	elseif (b <= 1.32e+14)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(Float64(x * t) + Float64(Float64(i * Float64(y * j)) / a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (b <= -2.1e+63)
		tmp = t_1;
	elseif (b <= -1.48e-86)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= -1.65e-106)
		tmp = t_1;
	elseif (b <= -4.6e-159)
		tmp = (x * a) * ((y * (z / a)) - t);
	elseif (b <= 1.32e+14)
		tmp = a * ((c * j) - ((x * t) + ((i * (y * j)) / a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.1e+63], t$95$1, If[LessEqual[b, -1.48e-86], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.65e-106], t$95$1, If[LessEqual[b, -4.6e-159], N[(N[(x * a), $MachinePrecision] * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.32e+14], N[(a * N[(N[(c * j), $MachinePrecision] - N[(N[(x * t), $MachinePrecision] + N[(N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.1000000000000002e63 or -1.4800000000000001e-86 < b < -1.65000000000000008e-106 or 1.32e14 < b

   1. Initial program 76.8%

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

   3. Taylor expanded in x around 0 74.7%

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

   4. Taylor expanded in y around 0 76.2%

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

      1. *-commutative 76.2%

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

      2. *-commutative 76.2%

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

      3. associate-*r* 77.9%

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

   6. Simplified 77.9%

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

   if -2.1000000000000002e63 < b < -1.4800000000000001e-86

   1. Initial program 71.8%

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

   3. Taylor expanded in i around inf 65.0%

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

      1. distribute-lft-out-- 65.0%

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

      2. *-commutative 65.0%

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

      3. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -1.65000000000000008e-106 < b < -4.59999999999999957e-159

   1. Initial program 63.5%

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

   3. Taylor expanded in a around -inf 63.6%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in x around inf 82.9%

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

      1. associate-*r* 91.1%

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

      2. *-commutative 91.1%

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

      3. associate-/l* 90.8%

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

   8. Simplified 90.8%

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

   if -4.59999999999999957e-159 < b < 1.32e14

   1. Initial program 63.1%

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

   3. Taylor expanded in a around -inf 67.2%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in j around inf 63.4%

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

      1. associate-*r/ 63.4%

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

      2. associate-*r* 63.4%

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

      3. neg-mul-1 63.4%

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

   8. Simplified 63.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.48 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-106}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-159}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j - \left(x \cdot t + \frac{i \cdot \left(y \cdot j\right)}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-160}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(c \cdot j + t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (* a c)) (* b (- (* t i) (* z c))))))
   (if (<= b -7.5e+62)
     t_1
     (if (<= b -1.55e-86)
       (* i (- (* t b) (* y j)))
       (if (<= b -2.6e-113)
         t_1
         (if (<= b -9.2e-160)
           (* (* x a) (- (* y (/ z a)) t))
           (if (<= b 2e+36)
             (* a (+ (* c j) (* t (- (* b (/ i a)) x))))
             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 * (a * c)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -7.5e+62) {
		tmp = t_1;
	} else if (b <= -1.55e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -2.6e-113) {
		tmp = t_1;
	} else if (b <= -9.2e-160) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else if (b <= 2e+36) {
		tmp = a * ((c * j) + (t * ((b * (i / a)) - x)));
	} 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 * (a * c)) + (b * ((t * i) - (z * c)))
    if (b <= (-7.5d+62)) then
        tmp = t_1
    else if (b <= (-1.55d-86)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= (-2.6d-113)) then
        tmp = t_1
    else if (b <= (-9.2d-160)) then
        tmp = (x * a) * ((y * (z / a)) - t)
    else if (b <= 2d+36) then
        tmp = a * ((c * j) + (t * ((b * (i / a)) - x)))
    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 * (a * c)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -7.5e+62) {
		tmp = t_1;
	} else if (b <= -1.55e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -2.6e-113) {
		tmp = t_1;
	} else if (b <= -9.2e-160) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else if (b <= 2e+36) {
		tmp = a * ((c * j) + (t * ((b * (i / a)) - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if b <= -7.5e+62:
		tmp = t_1
	elif b <= -1.55e-86:
		tmp = i * ((t * b) - (y * j))
	elif b <= -2.6e-113:
		tmp = t_1
	elif b <= -9.2e-160:
		tmp = (x * a) * ((y * (z / a)) - t)
	elif b <= 2e+36:
		tmp = a * ((c * j) + (t * ((b * (i / a)) - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -7.5e+62)
		tmp = t_1;
	elseif (b <= -1.55e-86)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= -2.6e-113)
		tmp = t_1;
	elseif (b <= -9.2e-160)
		tmp = Float64(Float64(x * a) * Float64(Float64(y * Float64(z / a)) - t));
	elseif (b <= 2e+36)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(t * Float64(Float64(b * Float64(i / a)) - x))));
	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 * (a * c)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (b <= -7.5e+62)
		tmp = t_1;
	elseif (b <= -1.55e-86)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= -2.6e-113)
		tmp = t_1;
	elseif (b <= -9.2e-160)
		tmp = (x * a) * ((y * (z / a)) - t);
	elseif (b <= 2e+36)
		tmp = a * ((c * j) + (t * ((b * (i / a)) - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+62], t$95$1, If[LessEqual[b, -1.55e-86], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.6e-113], t$95$1, If[LessEqual[b, -9.2e-160], N[(N[(x * a), $MachinePrecision] * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+36], N[(a * N[(N[(c * j), $MachinePrecision] + N[(t * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.49999999999999998e62 or -1.54999999999999994e-86 < b < -2.5999999999999999e-113 or 2.00000000000000008e36 < b

   1. Initial program 76.3%

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

   3. Taylor expanded in x around 0 75.7%

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

   4. Taylor expanded in y around 0 77.4%

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

      1. *-commutative 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 79.2%

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

   6. Simplified 79.2%

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

   if -7.49999999999999998e62 < b < -1.54999999999999994e-86

   1. Initial program 71.8%

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

   3. Taylor expanded in i around inf 65.0%

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

      1. distribute-lft-out-- 65.0%

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

      2. *-commutative 65.0%

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

      3. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -2.5999999999999999e-113 < b < -9.19999999999999939e-160

   1. Initial program 63.5%

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

   3. Taylor expanded in a around -inf 63.6%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in x around inf 82.9%

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

      1. associate-*r* 91.1%

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

      2. *-commutative 91.1%

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

      3. associate-/l* 90.8%

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

   8. Simplified 90.8%

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

   if -9.19999999999999939e-160 < b < 2.00000000000000008e36

   1. Initial program 64.6%

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

   3. Taylor expanded in a around -inf 67.5%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in t around inf 55.6%

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

      1. associate-/l* 54.7%

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

      2. associate-/l* 55.5%

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

   8. Simplified 55.5%

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

   9. Taylor expanded in t around 0 55.5%

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

       1. distribute-lft-out 59.4%

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

       2. associate-/l* 60.3%

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

   11. Simplified 60.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-160}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(c \cdot j + t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-159}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (* a c)) (* b (- (* t i) (* z c))))))
   (if (<= b -7.2e+61)
     t_1
     (if (<= b -5.6e-86)
       (* i (- (* t b) (* y j)))
       (if (<= b -1e-103)
         t_1
         (if (<= b -6.2e-159)
           (* (* x a) (- (* y (/ z a)) t))
           (if (<= b 1.25e+37)
             (- (* j (- (* a c) (* y i))) (* a (* x t)))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -7.2e+61) {
		tmp = t_1;
	} else if (b <= -5.6e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1e-103) {
		tmp = t_1;
	} else if (b <= -6.2e-159) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else if (b <= 1.25e+37) {
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)))
    if (b <= (-7.2d+61)) then
        tmp = t_1
    else if (b <= (-5.6d-86)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= (-1d-103)) then
        tmp = t_1
    else if (b <= (-6.2d-159)) then
        tmp = (x * a) * ((y * (z / a)) - t)
    else if (b <= 1.25d+37) then
        tmp = (j * ((a * c) - (y * i))) - (a * (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -7.2e+61) {
		tmp = t_1;
	} else if (b <= -5.6e-86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1e-103) {
		tmp = t_1;
	} else if (b <= -6.2e-159) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else if (b <= 1.25e+37) {
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if b <= -7.2e+61:
		tmp = t_1
	elif b <= -5.6e-86:
		tmp = i * ((t * b) - (y * j))
	elif b <= -1e-103:
		tmp = t_1
	elif b <= -6.2e-159:
		tmp = (x * a) * ((y * (z / a)) - t)
	elif b <= 1.25e+37:
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -7.2e+61)
		tmp = t_1;
	elseif (b <= -5.6e-86)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= -1e-103)
		tmp = t_1;
	elseif (b <= -6.2e-159)
		tmp = Float64(Float64(x * a) * Float64(Float64(y * Float64(z / a)) - t));
	elseif (b <= 1.25e+37)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (b <= -7.2e+61)
		tmp = t_1;
	elseif (b <= -5.6e-86)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= -1e-103)
		tmp = t_1;
	elseif (b <= -6.2e-159)
		tmp = (x * a) * ((y * (z / a)) - t);
	elseif (b <= 1.25e+37)
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+61], t$95$1, If[LessEqual[b, -5.6e-86], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-103], t$95$1, If[LessEqual[b, -6.2e-159], N[(N[(x * a), $MachinePrecision] * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+37], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.20000000000000021e61 or -5.60000000000000019e-86 < b < -9.99999999999999958e-104 or 1.24999999999999997e37 < b

   1. Initial program 76.3%

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

   3. Taylor expanded in x around 0 75.7%

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

   4. Taylor expanded in y around 0 77.4%

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

      1. *-commutative 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 79.2%

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

   6. Simplified 79.2%

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

   if -7.20000000000000021e61 < b < -5.60000000000000019e-86

   1. Initial program 71.8%

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

   3. Taylor expanded in i around inf 65.0%

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

      1. distribute-lft-out-- 65.0%

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

      2. *-commutative 65.0%

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

      3. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -9.99999999999999958e-104 < b < -6.2e-159

   1. Initial program 63.5%

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

   3. Taylor expanded in a around -inf 63.6%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in x around inf 82.9%

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

      1. associate-*r* 91.1%

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

      2. *-commutative 91.1%

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

      3. associate-/l* 90.8%

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

   8. Simplified 90.8%

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

   if -6.2e-159 < b < 1.24999999999999997e37

   1. Initial program 64.6%

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

   3. Taylor expanded in b around 0 63.1%

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

   4. Taylor expanded in z around 0 62.2%

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

      1. +-commutative 62.2%

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

      2. *-commutative 62.2%

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

      3. mul-1-neg 62.2%

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

      4. unsub-neg 62.2%

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

   6. Simplified 62.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-159}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := \left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+159}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+66}:\\ \;\;\;\;\left(t\_1 - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+41}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* (* x a) (- (* y (/ z a)) t))))
   (if (<= x -2.5e+159)
     t_2
     (if (<= x -4.5e+66)
       (+ (- t_1 (* a (* x t))) (* b (* t i)))
       (if (<= x -1.3e+60)
         (* z (- (* x y) (* b c)))
         (if (<= x 3.1e+41) (+ t_1 (* b (- (* t i) (* z c)))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = (x * a) * ((y * (z / a)) - t);
	double tmp;
	if (x <= -2.5e+159) {
		tmp = t_2;
	} else if (x <= -4.5e+66) {
		tmp = (t_1 - (a * (x * t))) + (b * (t * i));
	} else if (x <= -1.3e+60) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= 3.1e+41) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = (x * a) * ((y * (z / a)) - t)
    if (x <= (-2.5d+159)) then
        tmp = t_2
    else if (x <= (-4.5d+66)) then
        tmp = (t_1 - (a * (x * t))) + (b * (t * i))
    else if (x <= (-1.3d+60)) then
        tmp = z * ((x * y) - (b * c))
    else if (x <= 3.1d+41) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = (x * a) * ((y * (z / a)) - t);
	double tmp;
	if (x <= -2.5e+159) {
		tmp = t_2;
	} else if (x <= -4.5e+66) {
		tmp = (t_1 - (a * (x * t))) + (b * (t * i));
	} else if (x <= -1.3e+60) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= 3.1e+41) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = (x * a) * ((y * (z / a)) - t)
	tmp = 0
	if x <= -2.5e+159:
		tmp = t_2
	elif x <= -4.5e+66:
		tmp = (t_1 - (a * (x * t))) + (b * (t * i))
	elif x <= -1.3e+60:
		tmp = z * ((x * y) - (b * c))
	elif x <= 3.1e+41:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(Float64(x * a) * Float64(Float64(y * Float64(z / a)) - t))
	tmp = 0.0
	if (x <= -2.5e+159)
		tmp = t_2;
	elseif (x <= -4.5e+66)
		tmp = Float64(Float64(t_1 - Float64(a * Float64(x * t))) + Float64(b * Float64(t * i)));
	elseif (x <= -1.3e+60)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (x <= 3.1e+41)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = (x * a) * ((y * (z / a)) - t);
	tmp = 0.0;
	if (x <= -2.5e+159)
		tmp = t_2;
	elseif (x <= -4.5e+66)
		tmp = (t_1 - (a * (x * t))) + (b * (t * i));
	elseif (x <= -1.3e+60)
		tmp = z * ((x * y) - (b * c));
	elseif (x <= 3.1e+41)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * a), $MachinePrecision] * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+159], t$95$2, If[LessEqual[x, -4.5e+66], N[(N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e+60], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+41], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.50000000000000002e159 or 3.1e41 < x

   1. Initial program 67.4%

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

   3. Taylor expanded in a around -inf 54.8%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in x around inf 68.0%

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

      1. associate-*r* 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-/l* 72.2%

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

   8. Simplified 72.2%

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

   if -2.50000000000000002e159 < x < -4.4999999999999998e66

   1. Initial program 82.2%

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

   3. Taylor expanded in z around 0 82.6%

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

   if -4.4999999999999998e66 < x < -1.30000000000000004e60

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 100.0%

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

   if -1.30000000000000004e60 < x < 3.1e41

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0 72.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+66}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{b \cdot i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -9e-85)
     t_1
     (if (<= b -1.9e-178)
       (* y (- (* x z) (* i j)))
       (if (<= b 2.8e-211)
         (* a (- (* c j) (* x t)))
         (if (<= b 9.5e-125)
           (* j (- (* a c) (* y i)))
           (if (<= b 1.15e+36) (* a (* t (- (/ (* b i) a) x))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9e-85) {
		tmp = t_1;
	} else if (b <= -1.9e-178) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.8e-211) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 9.5e-125) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.15e+36) {
		tmp = a * (t * (((b * i) / a) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-9d-85)) then
        tmp = t_1
    else if (b <= (-1.9d-178)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 2.8d-211) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 9.5d-125) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 1.15d+36) then
        tmp = a * (t * (((b * i) / a) - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9e-85) {
		tmp = t_1;
	} else if (b <= -1.9e-178) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.8e-211) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 9.5e-125) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.15e+36) {
		tmp = a * (t * (((b * i) / a) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -9e-85:
		tmp = t_1
	elif b <= -1.9e-178:
		tmp = y * ((x * z) - (i * j))
	elif b <= 2.8e-211:
		tmp = a * ((c * j) - (x * t))
	elif b <= 9.5e-125:
		tmp = j * ((a * c) - (y * i))
	elif b <= 1.15e+36:
		tmp = a * (t * (((b * i) / a) - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9e-85)
		tmp = t_1;
	elseif (b <= -1.9e-178)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 2.8e-211)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 9.5e-125)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 1.15e+36)
		tmp = Float64(a * Float64(t * Float64(Float64(Float64(b * i) / a) - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -9e-85)
		tmp = t_1;
	elseif (b <= -1.9e-178)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 2.8e-211)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 9.5e-125)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 1.15e+36)
		tmp = a * (t * (((b * i) / a) - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e-85], t$95$1, If[LessEqual[b, -1.9e-178], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-211], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-125], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+36], N[(a * N[(t * N[(N[(N[(b * i), $MachinePrecision] / a), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -9.00000000000000008e-85 or 1.14999999999999998e36 < b

   1. Initial program 74.7%

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

   3. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   if -9.00000000000000008e-85 < b < -1.90000000000000007e-178

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   if -1.90000000000000007e-178 < b < 2.7999999999999998e-211

   1. Initial program 59.3%

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

   3. Taylor expanded in a around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. mul-1-neg 61.7%

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

      3. unsub-neg 61.7%

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

      4. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   if 2.7999999999999998e-211 < b < 9.50000000000000031e-125

   1. Initial program 56.6%

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

   3. Taylor expanded in j around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if 9.50000000000000031e-125 < b < 1.14999999999999998e36

   1. Initial program 78.7%

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

   3. Taylor expanded in a around -inf 78.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around inf 68.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{b \cdot i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(x \cdot \frac{y}{c} - b\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+170}:\\ \;\;\;\;\left(c \cdot j\right) \cdot \left(a - i \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(c \cdot j + t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- (* x (/ y c)) b))))
   (if (<= z -7.2e+202)
     t_1
     (if (<= z -9.8e+170)
       (* (* c j) (- a (* i (/ y c))))
       (if (<= z -1.3e+46)
         t_1
         (if (<= z 3e+197)
           (* a (+ (* c j) (* t (- (* b (/ i a)) x))))
           (* z (- (* x y) (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * ((x * (y / c)) - b);
	double tmp;
	if (z <= -7.2e+202) {
		tmp = t_1;
	} else if (z <= -9.8e+170) {
		tmp = (c * j) * (a - (i * (y / c)));
	} else if (z <= -1.3e+46) {
		tmp = t_1;
	} else if (z <= 3e+197) {
		tmp = a * ((c * j) + (t * ((b * (i / a)) - x)));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * c) * ((x * (y / c)) - b)
    if (z <= (-7.2d+202)) then
        tmp = t_1
    else if (z <= (-9.8d+170)) then
        tmp = (c * j) * (a - (i * (y / c)))
    else if (z <= (-1.3d+46)) then
        tmp = t_1
    else if (z <= 3d+197) then
        tmp = a * ((c * j) + (t * ((b * (i / a)) - x)))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * ((x * (y / c)) - b);
	double tmp;
	if (z <= -7.2e+202) {
		tmp = t_1;
	} else if (z <= -9.8e+170) {
		tmp = (c * j) * (a - (i * (y / c)));
	} else if (z <= -1.3e+46) {
		tmp = t_1;
	} else if (z <= 3e+197) {
		tmp = a * ((c * j) + (t * ((b * (i / a)) - x)));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * ((x * (y / c)) - b)
	tmp = 0
	if z <= -7.2e+202:
		tmp = t_1
	elif z <= -9.8e+170:
		tmp = (c * j) * (a - (i * (y / c)))
	elif z <= -1.3e+46:
		tmp = t_1
	elif z <= 3e+197:
		tmp = a * ((c * j) + (t * ((b * (i / a)) - x)))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * c) * Float64(Float64(x * Float64(y / c)) - b))
	tmp = 0.0
	if (z <= -7.2e+202)
		tmp = t_1;
	elseif (z <= -9.8e+170)
		tmp = Float64(Float64(c * j) * Float64(a - Float64(i * Float64(y / c))));
	elseif (z <= -1.3e+46)
		tmp = t_1;
	elseif (z <= 3e+197)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(t * Float64(Float64(b * Float64(i / a)) - x))));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * c) * ((x * (y / c)) - b);
	tmp = 0.0;
	if (z <= -7.2e+202)
		tmp = t_1;
	elseif (z <= -9.8e+170)
		tmp = (c * j) * (a - (i * (y / c)));
	elseif (z <= -1.3e+46)
		tmp = t_1;
	elseif (z <= 3e+197)
		tmp = a * ((c * j) + (t * ((b * (i / a)) - x)));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * c), $MachinePrecision] * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+202], t$95$1, If[LessEqual[z, -9.8e+170], N[(N[(c * j), $MachinePrecision] * N[(a - N[(i * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e+46], t$95$1, If[LessEqual[z, 3e+197], N[(a * N[(N[(c * j), $MachinePrecision] + N[(t * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.20000000000000016e202 or -9.80000000000000079e170 < z < -1.30000000000000007e46

   1. Initial program 63.2%

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

   3. Taylor expanded in c around inf 54.8%

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

   4. Taylor expanded in z around inf 71.1%

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

      1. associate-*r* 71.2%

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

      2. associate-/l* 71.2%

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

   6. Simplified 71.2%

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

   if -7.20000000000000016e202 < z < -9.80000000000000079e170

   1. Initial program 56.9%

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

   3. Taylor expanded in c around inf 57.8%

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

   4. Taylor expanded in j around inf 86.1%

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

      1. associate-*r* 86.3%

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

      2. mul-1-neg 86.3%

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

      3. unsub-neg 86.3%

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

      4. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

   if -1.30000000000000007e46 < z < 3.0000000000000002e197

   1. Initial program 75.9%

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

   3. Taylor expanded in a around -inf 74.9%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in t around inf 62.7%

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

      1. associate-/l* 62.2%

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

      2. associate-/l* 62.7%

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

   8. Simplified 62.7%

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

   9. Taylor expanded in t around 0 63.8%

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

       1. distribute-lft-out 65.6%

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

       2. associate-/l* 66.2%

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

   11. Simplified 66.2%

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

   if 3.0000000000000002e197 < z

   1. Initial program 52.9%

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

   3. Taylor expanded in z around inf 74.7%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+202}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(x \cdot \frac{y}{c} - b\right)\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+170}:\\ \;\;\;\;\left(c \cdot j\right) \cdot \left(a - i \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(x \cdot \frac{y}{c} - b\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(c \cdot j + t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{-52}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{-296}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+45}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.6e-52)
   (* i (* t b))
   (if (<= b -1.45e-159)
     (* x (* y z))
     (if (<= b -1.42e-296)
       (* a (* c j))
       (if (<= b 8.5e-240)
         (* y (* x z))
         (if (<= b 3e+45) (* (* x t) (- a)) (* z (* b (- c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.6e-52) {
		tmp = i * (t * b);
	} else if (b <= -1.45e-159) {
		tmp = x * (y * z);
	} else if (b <= -1.42e-296) {
		tmp = a * (c * j);
	} else if (b <= 8.5e-240) {
		tmp = y * (x * z);
	} else if (b <= 3e+45) {
		tmp = (x * t) * -a;
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-5.6d-52)) then
        tmp = i * (t * b)
    else if (b <= (-1.45d-159)) then
        tmp = x * (y * z)
    else if (b <= (-1.42d-296)) then
        tmp = a * (c * j)
    else if (b <= 8.5d-240) then
        tmp = y * (x * z)
    else if (b <= 3d+45) then
        tmp = (x * t) * -a
    else
        tmp = z * (b * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.6e-52) {
		tmp = i * (t * b);
	} else if (b <= -1.45e-159) {
		tmp = x * (y * z);
	} else if (b <= -1.42e-296) {
		tmp = a * (c * j);
	} else if (b <= 8.5e-240) {
		tmp = y * (x * z);
	} else if (b <= 3e+45) {
		tmp = (x * t) * -a;
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.6e-52:
		tmp = i * (t * b)
	elif b <= -1.45e-159:
		tmp = x * (y * z)
	elif b <= -1.42e-296:
		tmp = a * (c * j)
	elif b <= 8.5e-240:
		tmp = y * (x * z)
	elif b <= 3e+45:
		tmp = (x * t) * -a
	else:
		tmp = z * (b * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.6e-52)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -1.45e-159)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -1.42e-296)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 8.5e-240)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 3e+45)
		tmp = Float64(Float64(x * t) * Float64(-a));
	else
		tmp = Float64(z * Float64(b * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.6e-52)
		tmp = i * (t * b);
	elseif (b <= -1.45e-159)
		tmp = x * (y * z);
	elseif (b <= -1.42e-296)
		tmp = a * (c * j);
	elseif (b <= 8.5e-240)
		tmp = y * (x * z);
	elseif (b <= 3e+45)
		tmp = (x * t) * -a;
	else
		tmp = z * (b * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.6e-52], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e-159], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.42e-296], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-240], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+45], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -5.59999999999999989e-52

   1. Initial program 74.8%

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

   3. Taylor expanded in x around 0 72.3%

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

   4. Taylor expanded in t around inf 47.7%

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

      1. associate-*r* 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*r* 47.9%

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

   6. Simplified 47.9%

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

   if -5.59999999999999989e-52 < b < -1.44999999999999995e-159

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in x around inf 48.9%

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

   if -1.44999999999999995e-159 < b < -1.4200000000000001e-296

   1. Initial program 65.2%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in c around inf 36.8%

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

   if -1.4200000000000001e-296 < b < 8.5e-240

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in x around inf 58.5%

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

      1. *-commutative 58.5%

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

   8. Simplified 58.5%

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

   if 8.5e-240 < b < 3.00000000000000011e45

   1. Initial program 66.7%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in c around 0 41.5%

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

      1. associate-*r* 41.5%

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

      2. mul-1-neg 41.5%

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

   8. Simplified 41.5%

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

   if 3.00000000000000011e45 < b

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0 74.8%

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

   4. Taylor expanded in z around inf 44.0%

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

      1. associate-*r* 49.0%

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

      2. associate-*r* 49.0%

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

      3. *-commutative 49.0%

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

      4. mul-1-neg 49.0%

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

      5. *-commutative 49.0%

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

      6. distribute-rgt-neg-in 49.0%

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

   6. Simplified 49.0%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{-52}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{-296}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+45}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-259}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-134}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{b \cdot i}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -7e-40)
     t_1
     (if (<= a -2.15e-259)
       (* b (* t i))
       (if (<= a 4.05e-237)
         (* x (* y z))
         (if (<= a 8.5e-134) (* a (* t (/ (* b i) a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7e-40) {
		tmp = t_1;
	} else if (a <= -2.15e-259) {
		tmp = b * (t * i);
	} else if (a <= 4.05e-237) {
		tmp = x * (y * z);
	} else if (a <= 8.5e-134) {
		tmp = a * (t * ((b * i) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-7d-40)) then
        tmp = t_1
    else if (a <= (-2.15d-259)) then
        tmp = b * (t * i)
    else if (a <= 4.05d-237) then
        tmp = x * (y * z)
    else if (a <= 8.5d-134) then
        tmp = a * (t * ((b * i) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7e-40) {
		tmp = t_1;
	} else if (a <= -2.15e-259) {
		tmp = b * (t * i);
	} else if (a <= 4.05e-237) {
		tmp = x * (y * z);
	} else if (a <= 8.5e-134) {
		tmp = a * (t * ((b * i) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -7e-40:
		tmp = t_1
	elif a <= -2.15e-259:
		tmp = b * (t * i)
	elif a <= 4.05e-237:
		tmp = x * (y * z)
	elif a <= 8.5e-134:
		tmp = a * (t * ((b * i) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7e-40)
		tmp = t_1;
	elseif (a <= -2.15e-259)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 4.05e-237)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 8.5e-134)
		tmp = Float64(a * Float64(t * Float64(Float64(b * i) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -7e-40)
		tmp = t_1;
	elseif (a <= -2.15e-259)
		tmp = b * (t * i);
	elseif (a <= 4.05e-237)
		tmp = x * (y * z);
	elseif (a <= 8.5e-134)
		tmp = a * (t * ((b * i) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e-40], t$95$1, If[LessEqual[a, -2.15e-259], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.05e-237], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-134], N[(a * N[(t * N[(N[(b * i), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.0000000000000003e-40 or 8.50000000000000015e-134 < a

   1. Initial program 67.0%

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

   3. Taylor expanded in a around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   if -7.0000000000000003e-40 < a < -2.15e-259

   1. Initial program 88.8%

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

   3. Taylor expanded in x around 0 89.1%

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

   4. Taylor expanded in t around inf 48.8%

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

   if -2.15e-259 < a < 4.05e-237

   1. Initial program 69.3%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in x around inf 39.7%

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

   if 4.05e-237 < a < 8.50000000000000015e-134

   1. Initial program 53.6%

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

   3. Taylor expanded in a around -inf 46.4%

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

   5. Simplified 46.4%

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

   6. Taylor expanded in t around inf 77.6%

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

   7. Taylor expanded in b around inf 77.8%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-259}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-134}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{b \cdot i}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-120}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -3.45e-43)
     t_2
     (if (<= b 9.4e-212)
       t_1
       (if (<= b 5e-120)
         (* j (- (* a c) (* y i)))
         (if (<= b 3.5e+63) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.45e-43) {
		tmp = t_2;
	} else if (b <= 9.4e-212) {
		tmp = t_1;
	} else if (b <= 5e-120) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 3.5e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-3.45d-43)) then
        tmp = t_2
    else if (b <= 9.4d-212) then
        tmp = t_1
    else if (b <= 5d-120) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 3.5d+63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.45e-43) {
		tmp = t_2;
	} else if (b <= 9.4e-212) {
		tmp = t_1;
	} else if (b <= 5e-120) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 3.5e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.45e-43:
		tmp = t_2
	elif b <= 9.4e-212:
		tmp = t_1
	elif b <= 5e-120:
		tmp = j * ((a * c) - (y * i))
	elif b <= 3.5e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.45e-43)
		tmp = t_2;
	elseif (b <= 9.4e-212)
		tmp = t_1;
	elseif (b <= 5e-120)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 3.5e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.45e-43)
		tmp = t_2;
	elseif (b <= 9.4e-212)
		tmp = t_1;
	elseif (b <= 5e-120)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 3.5e+63)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.45e-43], t$95$2, If[LessEqual[b, 9.4e-212], t$95$1, If[LessEqual[b, 5e-120], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.44999999999999982e-43 or 3.50000000000000029e63 < b

   1. Initial program 73.8%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if -3.44999999999999982e-43 < b < 9.39999999999999996e-212 or 5.00000000000000007e-120 < b < 3.50000000000000029e63

   1. Initial program 69.9%

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

   3. Taylor expanded in a around inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   if 9.39999999999999996e-212 < b < 5.00000000000000007e-120

   1. Initial program 53.6%

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

   3. Taylor expanded in j around inf 56.7%

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

      1. *-commutative 56.7%

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

   5. Simplified 56.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-120}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+118} \lor \neg \left(x \leq 2.8 \cdot 10^{+42}\right):\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -7.6e+118) (not (<= x 2.8e+42)))
   (* (* x a) (- (* y (/ z a)) t))
   (+ (* j (- (* a c) (* y i))) (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -7.6e+118) || !(x <= 2.8e+42)) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else {
		tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-7.6d+118)) .or. (.not. (x <= 2.8d+42))) then
        tmp = (x * a) * ((y * (z / a)) - t)
    else
        tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -7.6e+118) || !(x <= 2.8e+42)) {
		tmp = (x * a) * ((y * (z / a)) - t);
	} else {
		tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -7.6e+118) or not (x <= 2.8e+42):
		tmp = (x * a) * ((y * (z / a)) - t)
	else:
		tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -7.6e+118) || !(x <= 2.8e+42))
		tmp = Float64(Float64(x * a) * Float64(Float64(y * Float64(z / a)) - t));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -7.6e+118) || ~((x <= 2.8e+42)))
		tmp = (x * a) * ((y * (z / a)) - t);
	else
		tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -7.6e+118], N[Not[LessEqual[x, 2.8e+42]], $MachinePrecision]], N[(N[(x * a), $MachinePrecision] * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.60000000000000033e118 or 2.7999999999999999e42 < x

   1. Initial program 68.0%

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

   3. Taylor expanded in a around -inf 56.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in x around inf 65.8%

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

      1. associate-*r* 68.7%

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

      2. *-commutative 68.7%

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

      3. associate-/l* 69.7%

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

   8. Simplified 69.7%

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

   if -7.60000000000000033e118 < x < 2.7999999999999999e42

   1. Initial program 72.1%

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

   3. Taylor expanded in x around 0 72.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+118} \lor \neg \left(x \leq 2.8 \cdot 10^{+42}\right):\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot \frac{z}{a} - t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-51}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2.75 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.1e-51)
   (* i (* t b))
   (if (<= b -2.75e-160)
     (* x (* y z))
     (if (<= b -3.2e-297)
       (* a (* c j))
       (if (<= b 1.5e+63) (* z (* x y)) (* z (* b (- c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.1e-51) {
		tmp = i * (t * b);
	} else if (b <= -2.75e-160) {
		tmp = x * (y * z);
	} else if (b <= -3.2e-297) {
		tmp = a * (c * j);
	} else if (b <= 1.5e+63) {
		tmp = z * (x * y);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-5.1d-51)) then
        tmp = i * (t * b)
    else if (b <= (-2.75d-160)) then
        tmp = x * (y * z)
    else if (b <= (-3.2d-297)) then
        tmp = a * (c * j)
    else if (b <= 1.5d+63) then
        tmp = z * (x * y)
    else
        tmp = z * (b * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.1e-51) {
		tmp = i * (t * b);
	} else if (b <= -2.75e-160) {
		tmp = x * (y * z);
	} else if (b <= -3.2e-297) {
		tmp = a * (c * j);
	} else if (b <= 1.5e+63) {
		tmp = z * (x * y);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.1e-51:
		tmp = i * (t * b)
	elif b <= -2.75e-160:
		tmp = x * (y * z)
	elif b <= -3.2e-297:
		tmp = a * (c * j)
	elif b <= 1.5e+63:
		tmp = z * (x * y)
	else:
		tmp = z * (b * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.1e-51)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -2.75e-160)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -3.2e-297)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 1.5e+63)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(z * Float64(b * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.1e-51)
		tmp = i * (t * b);
	elseif (b <= -2.75e-160)
		tmp = x * (y * z);
	elseif (b <= -3.2e-297)
		tmp = a * (c * j);
	elseif (b <= 1.5e+63)
		tmp = z * (x * y);
	else
		tmp = z * (b * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.1e-51], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.75e-160], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.2e-297], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+63], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.0999999999999997e-51

   1. Initial program 74.8%

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

   3. Taylor expanded in x around 0 72.3%

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

   4. Taylor expanded in t around inf 47.7%

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

      1. associate-*r* 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*r* 47.9%

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

   6. Simplified 47.9%

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

   if -5.0999999999999997e-51 < b < -2.75e-160

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in x around inf 48.9%

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

   if -2.75e-160 < b < -3.19999999999999972e-297

   1. Initial program 65.2%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in c around inf 36.8%

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

   if -3.19999999999999972e-297 < b < 1.5e63

   1. Initial program 66.8%

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

   3. Taylor expanded in y around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in x around inf 28.1%

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

      1. associate-*r* 35.6%

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

      2. *-commutative 35.6%

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

   8. Simplified 35.6%

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

   if 1.5e63 < b

   1. Initial program 72.5%

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

   3. Taylor expanded in x around 0 76.6%

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

   4. Taylor expanded in z around inf 45.1%

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

      1. associate-*r* 50.6%

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

      2. associate-*r* 50.6%

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

      3. *-commutative 50.6%

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

      4. mul-1-neg 50.6%

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

      5. *-commutative 50.6%

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

      6. distribute-rgt-neg-in 50.6%

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

   6. Simplified 50.6%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-51}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2.75 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-165}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* i (* t b))))
   (if (<= b -6.2e-52)
     t_2
     (if (<= b -1.5e-160)
       t_1
       (if (<= b 1.02e-165) (* a (* c j)) (if (<= b 6.3e+63) 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);
	double t_2 = i * (t * b);
	double tmp;
	if (b <= -6.2e-52) {
		tmp = t_2;
	} else if (b <= -1.5e-160) {
		tmp = t_1;
	} else if (b <= 1.02e-165) {
		tmp = a * (c * j);
	} else if (b <= 6.3e+63) {
		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_2 = i * (t * b)
    if (b <= (-6.2d-52)) then
        tmp = t_2
    else if (b <= (-1.5d-160)) then
        tmp = t_1
    else if (b <= 1.02d-165) then
        tmp = a * (c * j)
    else if (b <= 6.3d+63) 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);
	double t_2 = i * (t * b);
	double tmp;
	if (b <= -6.2e-52) {
		tmp = t_2;
	} else if (b <= -1.5e-160) {
		tmp = t_1;
	} else if (b <= 1.02e-165) {
		tmp = a * (c * j);
	} else if (b <= 6.3e+63) {
		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_2 = i * (t * b)
	tmp = 0
	if b <= -6.2e-52:
		tmp = t_2
	elif b <= -1.5e-160:
		tmp = t_1
	elif b <= 1.02e-165:
		tmp = a * (c * j)
	elif b <= 6.3e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -6.2e-52)
		tmp = t_2;
	elseif (b <= -1.5e-160)
		tmp = t_1;
	elseif (b <= 1.02e-165)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 6.3e+63)
		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_2 = i * (t * b);
	tmp = 0.0;
	if (b <= -6.2e-52)
		tmp = t_2;
	elseif (b <= -1.5e-160)
		tmp = t_1;
	elseif (b <= 1.02e-165)
		tmp = a * (c * j);
	elseif (b <= 6.3e+63)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e-52], t$95$2, If[LessEqual[b, -1.5e-160], t$95$1, If[LessEqual[b, 1.02e-165], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.3e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.1999999999999998e-52 or 6.2999999999999998e63 < b

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 73.9%

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

   4. Taylor expanded in t around inf 45.4%

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

      1. associate-*r* 47.8%

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

      2. *-commutative 47.8%

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

      3. associate-*r* 47.1%

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

   6. Simplified 47.1%

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

   if -6.1999999999999998e-52 < b < -1.49999999999999998e-160 or 1.02e-165 < b < 6.2999999999999998e63

   1. Initial program 75.9%

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

   3. Taylor expanded in y around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in x around inf 40.8%

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

   if -1.49999999999999998e-160 < b < 1.02e-165

   1. Initial program 59.6%

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

   3. Taylor expanded in a around inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in c around inf 29.9%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-165}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -5.5e-51)
     t_1
     (if (<= b -4.5e-159)
       (* x (* y z))
       (if (<= b -8.6e-298)
         (* a (* c j))
         (if (<= b 3.1e+64) (* y (* x z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -5.5e-51) {
		tmp = t_1;
	} else if (b <= -4.5e-159) {
		tmp = x * (y * z);
	} else if (b <= -8.6e-298) {
		tmp = a * (c * j);
	} else if (b <= 3.1e+64) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (b <= (-5.5d-51)) then
        tmp = t_1
    else if (b <= (-4.5d-159)) then
        tmp = x * (y * z)
    else if (b <= (-8.6d-298)) then
        tmp = a * (c * j)
    else if (b <= 3.1d+64) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -5.5e-51) {
		tmp = t_1;
	} else if (b <= -4.5e-159) {
		tmp = x * (y * z);
	} else if (b <= -8.6e-298) {
		tmp = a * (c * j);
	} else if (b <= 3.1e+64) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -5.5e-51:
		tmp = t_1
	elif b <= -4.5e-159:
		tmp = x * (y * z)
	elif b <= -8.6e-298:
		tmp = a * (c * j)
	elif b <= 3.1e+64:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -5.5e-51)
		tmp = t_1;
	elseif (b <= -4.5e-159)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -8.6e-298)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 3.1e+64)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (b <= -5.5e-51)
		tmp = t_1;
	elseif (b <= -4.5e-159)
		tmp = x * (y * z);
	elseif (b <= -8.6e-298)
		tmp = a * (c * j);
	elseif (b <= 3.1e+64)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e-51], t$95$1, If[LessEqual[b, -4.5e-159], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.6e-298], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e+64], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.4999999999999997e-51 or 3.0999999999999999e64 < b

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 73.9%

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

   4. Taylor expanded in t around inf 45.4%

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

      1. associate-*r* 47.8%

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

      2. *-commutative 47.8%

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

      3. associate-*r* 47.1%

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

   6. Simplified 47.1%

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

   if -5.4999999999999997e-51 < b < -4.49999999999999989e-159

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in x around inf 48.9%

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

   if -4.49999999999999989e-159 < b < -8.600000000000001e-298

   1. Initial program 65.2%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in c around inf 36.8%

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

   if -8.600000000000001e-298 < b < 3.0999999999999999e64

   1. Initial program 67.2%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in x around inf 35.1%

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

      1. *-commutative 35.1%

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

   8. Simplified 35.1%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -1.5e-51)
     t_1
     (if (<= b -2.9e-159)
       (* x (* y z))
       (if (<= b -3.1e-298)
         (* a (* c j))
         (if (<= b 7.5e+64) (* z (* x y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -1.5e-51) {
		tmp = t_1;
	} else if (b <= -2.9e-159) {
		tmp = x * (y * z);
	} else if (b <= -3.1e-298) {
		tmp = a * (c * j);
	} else if (b <= 7.5e+64) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (b <= (-1.5d-51)) then
        tmp = t_1
    else if (b <= (-2.9d-159)) then
        tmp = x * (y * z)
    else if (b <= (-3.1d-298)) then
        tmp = a * (c * j)
    else if (b <= 7.5d+64) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -1.5e-51) {
		tmp = t_1;
	} else if (b <= -2.9e-159) {
		tmp = x * (y * z);
	} else if (b <= -3.1e-298) {
		tmp = a * (c * j);
	} else if (b <= 7.5e+64) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -1.5e-51:
		tmp = t_1
	elif b <= -2.9e-159:
		tmp = x * (y * z)
	elif b <= -3.1e-298:
		tmp = a * (c * j)
	elif b <= 7.5e+64:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -1.5e-51)
		tmp = t_1;
	elseif (b <= -2.9e-159)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -3.1e-298)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 7.5e+64)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (b <= -1.5e-51)
		tmp = t_1;
	elseif (b <= -2.9e-159)
		tmp = x * (y * z);
	elseif (b <= -3.1e-298)
		tmp = a * (c * j);
	elseif (b <= 7.5e+64)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.5e-51], t$95$1, If[LessEqual[b, -2.9e-159], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.1e-298], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+64], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.50000000000000001e-51 or 7.5000000000000005e64 < b

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 73.9%

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

   4. Taylor expanded in t around inf 45.4%

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

      1. associate-*r* 47.8%

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

      2. *-commutative 47.8%

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

      3. associate-*r* 47.1%

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

   6. Simplified 47.1%

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

   if -1.50000000000000001e-51 < b < -2.8999999999999999e-159

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in x around inf 48.9%

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

   if -2.8999999999999999e-159 < b < -3.1000000000000002e-298

   1. Initial program 65.2%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in c around inf 36.8%

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

   if -3.1000000000000002e-298 < b < 7.5000000000000005e64

   1. Initial program 67.2%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in x around inf 27.8%

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

      1. associate-*r* 35.2%

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

      2. *-commutative 35.2%

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

   8. Simplified 35.2%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-51}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 51.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-43} \lor \neg \left(b \leq 1.06 \cdot 10^{+64}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3e-43) (not (<= b 1.06e+64)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3e-43) || !(b <= 1.06e+64)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3d-43)) .or. (.not. (b <= 1.06d+64))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3e-43) || !(b <= 1.06e+64)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3e-43) or not (b <= 1.06e+64):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3e-43) || !(b <= 1.06e+64))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3e-43) || ~((b <= 1.06e+64)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3e-43], N[Not[LessEqual[b, 1.06e+64]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.00000000000000003e-43 or 1.06e64 < b

   1. Initial program 73.8%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if -3.00000000000000003e-43 < b < 1.06e64

   1. Initial program 67.6%

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

   3. Taylor expanded in a around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

      4. *-commutative 49.7%

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

   5. Simplified 49.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-43} \lor \neg \left(b \leq 1.06 \cdot 10^{+64}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-72} \lor \neg \left(t \leq 1.55 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.45e-72) (not (<= t 1.55e-41))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.45e-72) || !(t <= 1.55e-41)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.45d-72)) .or. (.not. (t <= 1.55d-41))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.45e-72) || !(t <= 1.55e-41)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.45e-72) or not (t <= 1.55e-41):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.45e-72) || !(t <= 1.55e-41))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.45e-72) || ~((t <= 1.55e-41)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.45e-72], N[Not[LessEqual[t, 1.55e-41]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999999e-72 or 1.55e-41 < t

   1. Initial program 65.3%

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

   3. Taylor expanded in x around 0 55.8%

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

   4. Taylor expanded in t around inf 37.9%

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

   if -1.44999999999999999e-72 < t < 1.55e-41

   1. Initial program 80.1%

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

   3. Taylor expanded in a around inf 38.5%

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

      1. +-commutative 38.5%

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

      2. mul-1-neg 38.5%

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

      3. unsub-neg 38.5%

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

      4. *-commutative 38.5%

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

   5. Simplified 38.5%

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

   6. Taylor expanded in c around inf 32.0%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-72} \lor \neg \left(t \leq 1.55 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-72}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.9e-72)
   (* b (* t i))
   (if (<= t 1.6e-40) (* a (* c j)) (* i (* t 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 (t <= -1.9e-72) {
		tmp = b * (t * i);
	} else if (t <= 1.6e-40) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * 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 (t <= (-1.9d-72)) then
        tmp = b * (t * i)
    else if (t <= 1.6d-40) then
        tmp = a * (c * j)
    else
        tmp = i * (t * 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 (t <= -1.9e-72) {
		tmp = b * (t * i);
	} else if (t <= 1.6e-40) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.9e-72:
		tmp = b * (t * i)
	elif t <= 1.6e-40:
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.9e-72)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 1.6e-40)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.9e-72)
		tmp = b * (t * i);
	elseif (t <= 1.6e-40)
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.9e-72], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-40], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.90000000000000001e-72

   1. Initial program 64.2%

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

   3. Taylor expanded in x around 0 57.2%

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

   4. Taylor expanded in t around inf 39.8%

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

   if -1.90000000000000001e-72 < t < 1.60000000000000001e-40

   1. Initial program 80.1%

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

   3. Taylor expanded in a around inf 38.5%

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

      1. +-commutative 38.5%

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

      2. mul-1-neg 38.5%

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

      3. unsub-neg 38.5%

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

      4. *-commutative 38.5%

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

   5. Simplified 38.5%

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

   6. Taylor expanded in c around inf 32.0%

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

   if 1.60000000000000001e-40 < t

   1. Initial program 66.7%

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

   3. Taylor expanded in x around 0 54.1%

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

   4. Taylor expanded in t around inf 35.5%

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

      1. associate-*r* 34.1%

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

      2. *-commutative 34.1%

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

      3. associate-*r* 38.1%

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

   6. Simplified 38.1%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-72}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.5%

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

3. Taylor expanded in a around inf 41.0%

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

   1. +-commutative 41.0%

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

   2. mul-1-neg 41.0%

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

   3. unsub-neg 41.0%

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

   4. *-commutative 41.0%

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

5. Simplified 41.0%

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

6. Taylor expanded in c around inf 22.2%

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

7. Final simplification 22.2%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Developer target: 59.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024081 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))