Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.8% → 97.0%

Time: 11.5s

Alternatives: 11

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \cdot 2 \leq 10000000000000:\\ \;\;\;\;\frac{x\_m \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y - t} \cdot \frac{2}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= (* x_m 2.0) 10000000000000.0)
    (/ (* x_m 2.0) (* z (- y t)))
    (* (/ x_m (- y t)) (/ 2.0 z)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((x_m * 2.0) <= 10000000000000.0) {
		tmp = (x_m * 2.0) / (z * (y - t));
	} else {
		tmp = (x_m / (y - t)) * (2.0 / z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x_m * 2.0d0) <= 10000000000000.0d0) then
        tmp = (x_m * 2.0d0) / (z * (y - t))
    else
        tmp = (x_m / (y - t)) * (2.0d0 / z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((x_m * 2.0) <= 10000000000000.0) {
		tmp = (x_m * 2.0) / (z * (y - t));
	} else {
		tmp = (x_m / (y - t)) * (2.0 / z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (x_m * 2.0) <= 10000000000000.0:
		tmp = (x_m * 2.0) / (z * (y - t))
	else:
		tmp = (x_m / (y - t)) * (2.0 / z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (Float64(x_m * 2.0) <= 10000000000000.0)
		tmp = Float64(Float64(x_m * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(Float64(x_m / Float64(y - t)) * Float64(2.0 / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((x_m * 2.0) <= 10000000000000.0)
		tmp = (x_m * 2.0) / (z * (y - t));
	else
		tmp = (x_m / (y - t)) * (2.0 / z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[N[(x$95$m * 2.0), $MachinePrecision], 10000000000000.0], N[(N[(x$95$m * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < 1e13

   1. Initial program 91.5%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 94.7%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   if 1e13 < (*.f64 x 2)

   1. Initial program 80.0%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 81.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 81.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{\left(y - t\right) \cdot z}} \]

      2. times-frac 98.1%

         \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{2}{z}} \]

   6. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{2}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq 10000000000000:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := -2 \cdot \frac{x\_m}{z \cdot t}\\ t_2 := 2 \cdot \frac{x\_m}{z \cdot y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -850:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 190:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x\_m}{y}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* -2.0 (/ x_m (* z t)))) (t_2 (* 2.0 (/ x_m (* z y)))))
   (*
    x_s
    (if (<= y -9e+43)
      t_2
      (if (<= y -850.0)
        t_1
        (if (<= y -3.85e-90)
          t_2
          (if (<= y 190.0) t_1 (* (/ 2.0 z) (/ x_m y)))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = -2.0 * (x_m / (z * t));
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -9e+43) {
		tmp = t_2;
	} else if (y <= -850.0) {
		tmp = t_1;
	} else if (y <= -3.85e-90) {
		tmp = t_2;
	} else if (y <= 190.0) {
		tmp = t_1;
	} else {
		tmp = (2.0 / z) * (x_m / y);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-2.0d0) * (x_m / (z * t))
    t_2 = 2.0d0 * (x_m / (z * y))
    if (y <= (-9d+43)) then
        tmp = t_2
    else if (y <= (-850.0d0)) then
        tmp = t_1
    else if (y <= (-3.85d-90)) then
        tmp = t_2
    else if (y <= 190.0d0) then
        tmp = t_1
    else
        tmp = (2.0d0 / z) * (x_m / y)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = -2.0 * (x_m / (z * t));
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -9e+43) {
		tmp = t_2;
	} else if (y <= -850.0) {
		tmp = t_1;
	} else if (y <= -3.85e-90) {
		tmp = t_2;
	} else if (y <= 190.0) {
		tmp = t_1;
	} else {
		tmp = (2.0 / z) * (x_m / y);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = -2.0 * (x_m / (z * t))
	t_2 = 2.0 * (x_m / (z * y))
	tmp = 0
	if y <= -9e+43:
		tmp = t_2
	elif y <= -850.0:
		tmp = t_1
	elif y <= -3.85e-90:
		tmp = t_2
	elif y <= 190.0:
		tmp = t_1
	else:
		tmp = (2.0 / z) * (x_m / y)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(-2.0 * Float64(x_m / Float64(z * t)))
	t_2 = Float64(2.0 * Float64(x_m / Float64(z * y)))
	tmp = 0.0
	if (y <= -9e+43)
		tmp = t_2;
	elseif (y <= -850.0)
		tmp = t_1;
	elseif (y <= -3.85e-90)
		tmp = t_2;
	elseif (y <= 190.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x_m / y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = -2.0 * (x_m / (z * t));
	t_2 = 2.0 * (x_m / (z * y));
	tmp = 0.0;
	if (y <= -9e+43)
		tmp = t_2;
	elseif (y <= -850.0)
		tmp = t_1;
	elseif (y <= -3.85e-90)
		tmp = t_2;
	elseif (y <= 190.0)
		tmp = t_1;
	else
		tmp = (2.0 / z) * (x_m / y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 * N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x$95$m / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -9e+43], t$95$2, If[LessEqual[y, -850.0], t$95$1, If[LessEqual[y, -3.85e-90], t$95$2, If[LessEqual[y, 190.0], t$95$1, N[(N[(2.0 / z), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e43 or -850 < y < -3.84999999999999986e-90

   1. Initial program 90.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 95.4%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 86.1%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{z \cdot y}} \]

   if -9e43 < y < -850 or -3.84999999999999986e-90 < y < 190

   1. Initial program 87.4%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 89.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 76.6%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 76.6%

         \[\leadsto -2 \cdot \frac{x}{\color{blue}{z \cdot t}} \]

   7. Simplified 76.6%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{z \cdot t}} \]

   if 190 < y

   1. Initial program 88.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 91.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 91.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{\left(y - t\right) \cdot z}} \]

      2. times-frac 94.0%

         \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{2}{z}} \]

   6. Applied egg-rr 94.0%

      \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{2}{z}} \]

   7. Taylor expanded in y around inf 80.9%

      \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{2}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq -850:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq 190:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{z} \cdot \frac{-2}{t}\\ t_2 := 2 \cdot \frac{x\_m}{z \cdot y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 28.5:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x\_m}{y}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (/ x_m z) (/ -2.0 t))) (t_2 (* 2.0 (/ x_m (* z y)))))
   (*
    x_s
    (if (<= y -1.15e+41)
      t_2
      (if (<= y -1200.0)
        t_1
        (if (<= y -2.4e-91)
          t_2
          (if (<= y 28.5) t_1 (* (/ 2.0 z) (/ x_m y)))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (-2.0 / t);
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -1.15e+41) {
		tmp = t_2;
	} else if (y <= -1200.0) {
		tmp = t_1;
	} else if (y <= -2.4e-91) {
		tmp = t_2;
	} else if (y <= 28.5) {
		tmp = t_1;
	} else {
		tmp = (2.0 / z) * (x_m / y);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x_m / z) * ((-2.0d0) / t)
    t_2 = 2.0d0 * (x_m / (z * y))
    if (y <= (-1.15d+41)) then
        tmp = t_2
    else if (y <= (-1200.0d0)) then
        tmp = t_1
    else if (y <= (-2.4d-91)) then
        tmp = t_2
    else if (y <= 28.5d0) then
        tmp = t_1
    else
        tmp = (2.0d0 / z) * (x_m / y)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (-2.0 / t);
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -1.15e+41) {
		tmp = t_2;
	} else if (y <= -1200.0) {
		tmp = t_1;
	} else if (y <= -2.4e-91) {
		tmp = t_2;
	} else if (y <= 28.5) {
		tmp = t_1;
	} else {
		tmp = (2.0 / z) * (x_m / y);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / z) * (-2.0 / t)
	t_2 = 2.0 * (x_m / (z * y))
	tmp = 0
	if y <= -1.15e+41:
		tmp = t_2
	elif y <= -1200.0:
		tmp = t_1
	elif y <= -2.4e-91:
		tmp = t_2
	elif y <= 28.5:
		tmp = t_1
	else:
		tmp = (2.0 / z) * (x_m / y)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / z) * Float64(-2.0 / t))
	t_2 = Float64(2.0 * Float64(x_m / Float64(z * y)))
	tmp = 0.0
	if (y <= -1.15e+41)
		tmp = t_2;
	elseif (y <= -1200.0)
		tmp = t_1;
	elseif (y <= -2.4e-91)
		tmp = t_2;
	elseif (y <= 28.5)
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x_m / y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / z) * (-2.0 / t);
	t_2 = 2.0 * (x_m / (z * y));
	tmp = 0.0;
	if (y <= -1.15e+41)
		tmp = t_2;
	elseif (y <= -1200.0)
		tmp = t_1;
	elseif (y <= -2.4e-91)
		tmp = t_2;
	elseif (y <= 28.5)
		tmp = t_1;
	else
		tmp = (2.0 / z) * (x_m / y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x$95$m / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -1.15e+41], t$95$2, If[LessEqual[y, -1200.0], t$95$1, If[LessEqual[y, -2.4e-91], t$95$2, If[LessEqual[y, 28.5], t$95$1, N[(N[(2.0 / z), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1499999999999999e41 or -1200 < y < -2.40000000000000011e-91

   1. Initial program 90.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 95.4%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 86.1%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{z \cdot y}} \]

   if -1.1499999999999999e41 < y < -1200 or -2.40000000000000011e-91 < y < 28.5

   1. Initial program 87.4%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 89.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. times-frac 89.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   6. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   7. Taylor expanded in y around 0 77.5%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-2}{t}} \]

   if 28.5 < y

   1. Initial program 88.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 91.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 91.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{\left(y - t\right) \cdot z}} \]

      2. times-frac 94.0%

         \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{2}{z}} \]

   6. Applied egg-rr 94.0%

      \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{2}{z}} \]

   7. Taylor expanded in y around inf 80.9%

      \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{2}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq -1200:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-91}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq 28.5:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{z} \cdot \frac{-2}{t}\\ t_2 := 2 \cdot \frac{x\_m}{z \cdot y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -950:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 9:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (/ x_m z) (/ -2.0 t))) (t_2 (* 2.0 (/ x_m (* z y)))))
   (*
    x_s
    (if (<= y -1.25e+42)
      t_2
      (if (<= y -950.0)
        t_1
        (if (<= y -3.1e-90)
          t_2
          (if (<= y 9.0) t_1 (* (/ x_m z) (/ 2.0 y)))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (-2.0 / t);
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -1.25e+42) {
		tmp = t_2;
	} else if (y <= -950.0) {
		tmp = t_1;
	} else if (y <= -3.1e-90) {
		tmp = t_2;
	} else if (y <= 9.0) {
		tmp = t_1;
	} else {
		tmp = (x_m / z) * (2.0 / y);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x_m / z) * ((-2.0d0) / t)
    t_2 = 2.0d0 * (x_m / (z * y))
    if (y <= (-1.25d+42)) then
        tmp = t_2
    else if (y <= (-950.0d0)) then
        tmp = t_1
    else if (y <= (-3.1d-90)) then
        tmp = t_2
    else if (y <= 9.0d0) then
        tmp = t_1
    else
        tmp = (x_m / z) * (2.0d0 / y)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (-2.0 / t);
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -1.25e+42) {
		tmp = t_2;
	} else if (y <= -950.0) {
		tmp = t_1;
	} else if (y <= -3.1e-90) {
		tmp = t_2;
	} else if (y <= 9.0) {
		tmp = t_1;
	} else {
		tmp = (x_m / z) * (2.0 / y);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / z) * (-2.0 / t)
	t_2 = 2.0 * (x_m / (z * y))
	tmp = 0
	if y <= -1.25e+42:
		tmp = t_2
	elif y <= -950.0:
		tmp = t_1
	elif y <= -3.1e-90:
		tmp = t_2
	elif y <= 9.0:
		tmp = t_1
	else:
		tmp = (x_m / z) * (2.0 / y)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / z) * Float64(-2.0 / t))
	t_2 = Float64(2.0 * Float64(x_m / Float64(z * y)))
	tmp = 0.0
	if (y <= -1.25e+42)
		tmp = t_2;
	elseif (y <= -950.0)
		tmp = t_1;
	elseif (y <= -3.1e-90)
		tmp = t_2;
	elseif (y <= 9.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_m / z) * Float64(2.0 / y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / z) * (-2.0 / t);
	t_2 = 2.0 * (x_m / (z * y));
	tmp = 0.0;
	if (y <= -1.25e+42)
		tmp = t_2;
	elseif (y <= -950.0)
		tmp = t_1;
	elseif (y <= -3.1e-90)
		tmp = t_2;
	elseif (y <= 9.0)
		tmp = t_1;
	else
		tmp = (x_m / z) * (2.0 / y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x$95$m / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -1.25e+42], t$95$2, If[LessEqual[y, -950.0], t$95$1, If[LessEqual[y, -3.1e-90], t$95$2, If[LessEqual[y, 9.0], t$95$1, N[(N[(x$95$m / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000002e42 or -950 < y < -3.1000000000000001e-90

   1. Initial program 90.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 95.4%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 86.1%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{z \cdot y}} \]

   if -1.25000000000000002e42 < y < -950 or -3.1000000000000001e-90 < y < 9

   1. Initial program 87.4%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 89.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. times-frac 89.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   6. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   7. Taylor expanded in y around 0 77.5%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-2}{t}} \]

   if 9 < y

   1. Initial program 88.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 91.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.6%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 80.6%

         \[\leadsto \color{blue}{\frac{2 \cdot x}{y \cdot z}} \]

      2. *-commutative 80.6%

         \[\leadsto \frac{\color{blue}{x \cdot 2}}{y \cdot z} \]

      3. *-commutative 80.6%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

      4. times-frac 83.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y}} \]

   7. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+42}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq -950:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq 9:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{z} \cdot \frac{-2}{t}\\ t_2 := 2 \cdot \frac{x\_m}{z \cdot y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -950:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 0.082:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m \cdot \frac{2}{z}}{y}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (/ x_m z) (/ -2.0 t))) (t_2 (* 2.0 (/ x_m (* z y)))))
   (*
    x_s
    (if (<= y -2e+44)
      t_2
      (if (<= y -950.0)
        t_1
        (if (<= y -3.85e-90)
          t_2
          (if (<= y 0.082) t_1 (/ (* x_m (/ 2.0 z)) y))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (-2.0 / t);
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -2e+44) {
		tmp = t_2;
	} else if (y <= -950.0) {
		tmp = t_1;
	} else if (y <= -3.85e-90) {
		tmp = t_2;
	} else if (y <= 0.082) {
		tmp = t_1;
	} else {
		tmp = (x_m * (2.0 / z)) / y;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x_m / z) * ((-2.0d0) / t)
    t_2 = 2.0d0 * (x_m / (z * y))
    if (y <= (-2d+44)) then
        tmp = t_2
    else if (y <= (-950.0d0)) then
        tmp = t_1
    else if (y <= (-3.85d-90)) then
        tmp = t_2
    else if (y <= 0.082d0) then
        tmp = t_1
    else
        tmp = (x_m * (2.0d0 / z)) / y
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (-2.0 / t);
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -2e+44) {
		tmp = t_2;
	} else if (y <= -950.0) {
		tmp = t_1;
	} else if (y <= -3.85e-90) {
		tmp = t_2;
	} else if (y <= 0.082) {
		tmp = t_1;
	} else {
		tmp = (x_m * (2.0 / z)) / y;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / z) * (-2.0 / t)
	t_2 = 2.0 * (x_m / (z * y))
	tmp = 0
	if y <= -2e+44:
		tmp = t_2
	elif y <= -950.0:
		tmp = t_1
	elif y <= -3.85e-90:
		tmp = t_2
	elif y <= 0.082:
		tmp = t_1
	else:
		tmp = (x_m * (2.0 / z)) / y
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / z) * Float64(-2.0 / t))
	t_2 = Float64(2.0 * Float64(x_m / Float64(z * y)))
	tmp = 0.0
	if (y <= -2e+44)
		tmp = t_2;
	elseif (y <= -950.0)
		tmp = t_1;
	elseif (y <= -3.85e-90)
		tmp = t_2;
	elseif (y <= 0.082)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_m * Float64(2.0 / z)) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / z) * (-2.0 / t);
	t_2 = 2.0 * (x_m / (z * y));
	tmp = 0.0;
	if (y <= -2e+44)
		tmp = t_2;
	elseif (y <= -950.0)
		tmp = t_1;
	elseif (y <= -3.85e-90)
		tmp = t_2;
	elseif (y <= 0.082)
		tmp = t_1;
	else
		tmp = (x_m * (2.0 / z)) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x$95$m / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -2e+44], t$95$2, If[LessEqual[y, -950.0], t$95$1, If[LessEqual[y, -3.85e-90], t$95$2, If[LessEqual[y, 0.082], t$95$1, N[(N[(x$95$m * N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0000000000000002e44 or -950 < y < -3.84999999999999986e-90

   1. Initial program 90.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 95.4%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 86.1%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{z \cdot y}} \]

   if -2.0000000000000002e44 < y < -950 or -3.84999999999999986e-90 < y < 0.0820000000000000034

   1. Initial program 87.4%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 89.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. times-frac 89.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   6. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   7. Taylor expanded in y around 0 77.5%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-2}{t}} \]

   if 0.0820000000000000034 < y

   1. Initial program 88.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 91.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.6%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 80.6%

         \[\leadsto \color{blue}{\frac{2 \cdot x}{y \cdot z}} \]

      2. *-commutative 80.6%

         \[\leadsto \frac{\color{blue}{x \cdot 2}}{y \cdot z} \]

      3. *-commutative 80.6%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

      4. times-frac 83.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y}} \]

   7. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y}} \]
   8. Step-by-step derivation

      1. frac-times 80.6%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot y}} \]

      2. associate-/r* 83.2%

         \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{z}}{y}} \]

      3. associate-*r/ 83.2%

         \[\leadsto \frac{\color{blue}{x \cdot \frac{2}{z}}}{y} \]

   9. Applied egg-rr 83.2%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{z}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+44}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq -950:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq 0.082:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{z} \cdot \frac{-2}{t}\\ t_2 := 2 \cdot \frac{x\_m}{z \cdot y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -980:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 90:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y}}{\frac{z}{x\_m}}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (/ x_m z) (/ -2.0 t))) (t_2 (* 2.0 (/ x_m (* z y)))))
   (*
    x_s
    (if (<= y -2.2e+40)
      t_2
      (if (<= y -980.0)
        t_1
        (if (<= y -3.85e-90)
          t_2
          (if (<= y 90.0) t_1 (/ (/ 2.0 y) (/ z x_m)))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (-2.0 / t);
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -2.2e+40) {
		tmp = t_2;
	} else if (y <= -980.0) {
		tmp = t_1;
	} else if (y <= -3.85e-90) {
		tmp = t_2;
	} else if (y <= 90.0) {
		tmp = t_1;
	} else {
		tmp = (2.0 / y) / (z / x_m);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x_m / z) * ((-2.0d0) / t)
    t_2 = 2.0d0 * (x_m / (z * y))
    if (y <= (-2.2d+40)) then
        tmp = t_2
    else if (y <= (-980.0d0)) then
        tmp = t_1
    else if (y <= (-3.85d-90)) then
        tmp = t_2
    else if (y <= 90.0d0) then
        tmp = t_1
    else
        tmp = (2.0d0 / y) / (z / x_m)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) * (-2.0 / t);
	double t_2 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -2.2e+40) {
		tmp = t_2;
	} else if (y <= -980.0) {
		tmp = t_1;
	} else if (y <= -3.85e-90) {
		tmp = t_2;
	} else if (y <= 90.0) {
		tmp = t_1;
	} else {
		tmp = (2.0 / y) / (z / x_m);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / z) * (-2.0 / t)
	t_2 = 2.0 * (x_m / (z * y))
	tmp = 0
	if y <= -2.2e+40:
		tmp = t_2
	elif y <= -980.0:
		tmp = t_1
	elif y <= -3.85e-90:
		tmp = t_2
	elif y <= 90.0:
		tmp = t_1
	else:
		tmp = (2.0 / y) / (z / x_m)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / z) * Float64(-2.0 / t))
	t_2 = Float64(2.0 * Float64(x_m / Float64(z * y)))
	tmp = 0.0
	if (y <= -2.2e+40)
		tmp = t_2;
	elseif (y <= -980.0)
		tmp = t_1;
	elseif (y <= -3.85e-90)
		tmp = t_2;
	elseif (y <= 90.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 / y) / Float64(z / x_m));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / z) * (-2.0 / t);
	t_2 = 2.0 * (x_m / (z * y));
	tmp = 0.0;
	if (y <= -2.2e+40)
		tmp = t_2;
	elseif (y <= -980.0)
		tmp = t_1;
	elseif (y <= -3.85e-90)
		tmp = t_2;
	elseif (y <= 90.0)
		tmp = t_1;
	else
		tmp = (2.0 / y) / (z / x_m);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x$95$m / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -2.2e+40], t$95$2, If[LessEqual[y, -980.0], t$95$1, If[LessEqual[y, -3.85e-90], t$95$2, If[LessEqual[y, 90.0], t$95$1, N[(N[(2.0 / y), $MachinePrecision] / N[(z / x$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1999999999999999e40 or -980 < y < -3.84999999999999986e-90

   1. Initial program 90.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 95.4%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 86.1%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{z \cdot y}} \]

   if -2.1999999999999999e40 < y < -980 or -3.84999999999999986e-90 < y < 90

   1. Initial program 87.4%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 89.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. times-frac 89.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   6. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   7. Taylor expanded in y around 0 77.5%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-2}{t}} \]

   if 90 < y

   1. Initial program 88.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 91.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.6%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 80.6%

         \[\leadsto \color{blue}{\frac{2 \cdot x}{y \cdot z}} \]

      2. *-commutative 80.6%

         \[\leadsto \frac{\color{blue}{x \cdot 2}}{y \cdot z} \]

      3. *-commutative 80.6%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

      4. times-frac 83.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y}} \]

   7. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 83.2%

         \[\leadsto \color{blue}{\frac{2}{y} \cdot \frac{x}{z}} \]

      2. clear-num 83.2%

         \[\leadsto \frac{2}{y} \cdot \color{blue}{\frac{1}{\frac{z}{x}}} \]

      3. un-div-inv 84.5%

         \[\leadsto \color{blue}{\frac{\frac{2}{y}}{\frac{z}{x}}} \]

   9. Applied egg-rr 84.5%

      \[\leadsto \color{blue}{\frac{\frac{2}{y}}{\frac{z}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+40}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq -980:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq 90:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y}}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := 2 \cdot \frac{x\_m}{z \cdot y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -980:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.365:\\ \;\;\;\;\frac{\frac{x\_m \cdot -2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y}}{\frac{z}{x\_m}}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ x_m (* z y)))))
   (*
    x_s
    (if (<= y -3.1e+43)
      t_1
      (if (<= y -980.0)
        (* (/ x_m z) (/ -2.0 t))
        (if (<= y -2.25e-91)
          t_1
          (if (<= y 0.365)
            (/ (/ (* x_m -2.0) t) z)
            (/ (/ 2.0 y) (/ z x_m)))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -3.1e+43) {
		tmp = t_1;
	} else if (y <= -980.0) {
		tmp = (x_m / z) * (-2.0 / t);
	} else if (y <= -2.25e-91) {
		tmp = t_1;
	} else if (y <= 0.365) {
		tmp = ((x_m * -2.0) / t) / z;
	} else {
		tmp = (2.0 / y) / (z / x_m);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x_m / (z * y))
    if (y <= (-3.1d+43)) then
        tmp = t_1
    else if (y <= (-980.0d0)) then
        tmp = (x_m / z) * ((-2.0d0) / t)
    else if (y <= (-2.25d-91)) then
        tmp = t_1
    else if (y <= 0.365d0) then
        tmp = ((x_m * (-2.0d0)) / t) / z
    else
        tmp = (2.0d0 / y) / (z / x_m)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = 2.0 * (x_m / (z * y));
	double tmp;
	if (y <= -3.1e+43) {
		tmp = t_1;
	} else if (y <= -980.0) {
		tmp = (x_m / z) * (-2.0 / t);
	} else if (y <= -2.25e-91) {
		tmp = t_1;
	} else if (y <= 0.365) {
		tmp = ((x_m * -2.0) / t) / z;
	} else {
		tmp = (2.0 / y) / (z / x_m);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = 2.0 * (x_m / (z * y))
	tmp = 0
	if y <= -3.1e+43:
		tmp = t_1
	elif y <= -980.0:
		tmp = (x_m / z) * (-2.0 / t)
	elif y <= -2.25e-91:
		tmp = t_1
	elif y <= 0.365:
		tmp = ((x_m * -2.0) / t) / z
	else:
		tmp = (2.0 / y) / (z / x_m)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(2.0 * Float64(x_m / Float64(z * y)))
	tmp = 0.0
	if (y <= -3.1e+43)
		tmp = t_1;
	elseif (y <= -980.0)
		tmp = Float64(Float64(x_m / z) * Float64(-2.0 / t));
	elseif (y <= -2.25e-91)
		tmp = t_1;
	elseif (y <= 0.365)
		tmp = Float64(Float64(Float64(x_m * -2.0) / t) / z);
	else
		tmp = Float64(Float64(2.0 / y) / Float64(z / x_m));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = 2.0 * (x_m / (z * y));
	tmp = 0.0;
	if (y <= -3.1e+43)
		tmp = t_1;
	elseif (y <= -980.0)
		tmp = (x_m / z) * (-2.0 / t);
	elseif (y <= -2.25e-91)
		tmp = t_1;
	elseif (y <= 0.365)
		tmp = ((x_m * -2.0) / t) / z;
	else
		tmp = (2.0 / y) / (z / x_m);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x$95$m / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -3.1e+43], t$95$1, If[LessEqual[y, -980.0], N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.25e-91], t$95$1, If[LessEqual[y, 0.365], N[(N[(N[(x$95$m * -2.0), $MachinePrecision] / t), $MachinePrecision] / z), $MachinePrecision], N[(N[(2.0 / y), $MachinePrecision] / N[(z / x$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if y < -3.1000000000000002e43 or -980 < y < -2.24999999999999988e-91

   1. Initial program 90.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 95.4%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 86.1%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{z \cdot y}} \]

   if -3.1000000000000002e43 < y < -980

   1. Initial program 89.0%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 89.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. times-frac 100.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   7. Taylor expanded in y around 0 89.6%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-2}{t}} \]

   if -2.24999999999999988e-91 < y < 0.36499999999999999

   1. Initial program 87.2%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 89.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 76.5%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 76.5%

         \[\leadsto -2 \cdot \frac{x}{\color{blue}{z \cdot t}} \]

   7. Simplified 76.5%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{z \cdot t}} \]
   8. Step-by-step derivation

      1. *-commutative 76.5%

         \[\leadsto \color{blue}{\frac{x}{z \cdot t} \cdot -2} \]

      2. associate-*l/ 76.5%

         \[\leadsto \color{blue}{\frac{x \cdot -2}{z \cdot t}} \]

      3. *-commutative 76.5%

         \[\leadsto \frac{x \cdot -2}{\color{blue}{t \cdot z}} \]

      4. associate-/r* 78.0%

         \[\leadsto \color{blue}{\frac{\frac{x \cdot -2}{t}}{z}} \]

   9. Applied egg-rr 78.0%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot -2}{t}}{z}} \]

   if 0.36499999999999999 < y

   1. Initial program 88.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 91.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.6%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 80.6%

         \[\leadsto \color{blue}{\frac{2 \cdot x}{y \cdot z}} \]

      2. *-commutative 80.6%

         \[\leadsto \frac{\color{blue}{x \cdot 2}}{y \cdot z} \]

      3. *-commutative 80.6%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

      4. times-frac 83.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y}} \]

   7. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 83.2%

         \[\leadsto \color{blue}{\frac{2}{y} \cdot \frac{x}{z}} \]

      2. clear-num 83.2%

         \[\leadsto \frac{2}{y} \cdot \color{blue}{\frac{1}{\frac{z}{x}}} \]

      3. un-div-inv 84.5%

         \[\leadsto \color{blue}{\frac{\frac{2}{y}}{\frac{z}{x}}} \]

   9. Applied egg-rr 84.5%

      \[\leadsto \color{blue}{\frac{\frac{2}{y}}{\frac{z}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq -980:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-91}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{elif}\;y \leq 0.365:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y}}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+70} \lor \neg \left(t \leq 4 \cdot 10^{-27}\right):\\ \;\;\;\;-2 \cdot \frac{x\_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x\_m}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= t -2.1e+70) (not (<= t 4e-27)))
    (* -2.0 (/ x_m (* z t)))
    (* 2.0 (/ x_m (* z y))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((t <= -2.1e+70) || !(t <= 4e-27)) {
		tmp = -2.0 * (x_m / (z * t));
	} else {
		tmp = 2.0 * (x_m / (z * y));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.1d+70)) .or. (.not. (t <= 4d-27))) then
        tmp = (-2.0d0) * (x_m / (z * t))
    else
        tmp = 2.0d0 * (x_m / (z * y))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((t <= -2.1e+70) || !(t <= 4e-27)) {
		tmp = -2.0 * (x_m / (z * t));
	} else {
		tmp = 2.0 * (x_m / (z * y));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (t <= -2.1e+70) or not (t <= 4e-27):
		tmp = -2.0 * (x_m / (z * t))
	else:
		tmp = 2.0 * (x_m / (z * y))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((t <= -2.1e+70) || !(t <= 4e-27))
		tmp = Float64(-2.0 * Float64(x_m / Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(x_m / Float64(z * y)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((t <= -2.1e+70) || ~((t <= 4e-27)))
		tmp = -2.0 * (x_m / (z * t));
	else
		tmp = 2.0 * (x_m / (z * y));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[t, -2.1e+70], N[Not[LessEqual[t, 4e-27]], $MachinePrecision]], N[(-2.0 * N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x$95$m / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -2.10000000000000008e70 or 4.0000000000000002e-27 < t

   1. Initial program 85.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 90.2%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.5%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 80.5%

         \[\leadsto -2 \cdot \frac{x}{\color{blue}{z \cdot t}} \]

   7. Simplified 80.5%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{z \cdot t}} \]

   if -2.10000000000000008e70 < t < 4.0000000000000002e-27

   1. Initial program 90.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 92.2%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 74.9%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 74.9%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

   7. Simplified 74.9%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{z \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+70} \lor \neg \left(t \leq 4 \cdot 10^{-27}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 96.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2 \cdot 10^{+41}:\\ \;\;\;\;2 \cdot \frac{\frac{x\_m}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y - t} \cdot \frac{2}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 2e+41)
    (* 2.0 (/ (/ x_m z) (- y t)))
    (* (/ x_m (- y t)) (/ 2.0 z)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 2e+41) {
		tmp = 2.0 * ((x_m / z) / (y - t));
	} else {
		tmp = (x_m / (y - t)) * (2.0 / z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x_m <= 2d+41) then
        tmp = 2.0d0 * ((x_m / z) / (y - t))
    else
        tmp = (x_m / (y - t)) * (2.0d0 / z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 2e+41) {
		tmp = 2.0 * ((x_m / z) / (y - t));
	} else {
		tmp = (x_m / (y - t)) * (2.0 / z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if x_m <= 2e+41:
		tmp = 2.0 * ((x_m / z) / (y - t))
	else:
		tmp = (x_m / (y - t)) * (2.0 / z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 2e+41)
		tmp = Float64(2.0 * Float64(Float64(x_m / z) / Float64(y - t)));
	else
		tmp = Float64(Float64(x_m / Float64(y - t)) * Float64(2.0 / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 2e+41)
		tmp = 2.0 * ((x_m / z) / (y - t));
	else
		tmp = (x_m / (y - t)) * (2.0 / z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 2e+41], N[(2.0 * N[(N[(x$95$m / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.00000000000000001e41

   1. Initial program 91.5%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 94.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 94.5%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{z \cdot \left(y - t\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 92.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   7. Simplified 92.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   if 2.00000000000000001e41 < x

   1. Initial program 78.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 80.1%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 80.1%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{\left(y - t\right) \cdot z}} \]

      2. times-frac 97.8%

         \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{2}{z}} \]

   6. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{2}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+41}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(2 \cdot \frac{\frac{x\_m}{z}}{y - t}\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (* 2.0 (/ (/ x_m z) (- y t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (2.0 * ((x_m / z) / (y - t)));
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * (2.0d0 * ((x_m / z) / (y - t)))
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (2.0 * ((x_m / z) / (y - t)));
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * (2.0 * ((x_m / z) / (y - t)))

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(2.0 * Float64(Float64(x_m / z) / Float64(y - t))))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * (2.0 * ((x_m / z) / (y - t)));
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(2.0 * N[(N[(x$95$m / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.5%

   \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
2. Step-by-step derivation

   1. distribute-rgt-out-- 91.3%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

3. Simplified 91.3%

   \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 91.3%

   \[\leadsto \color{blue}{2 \cdot \frac{x}{z \cdot \left(y - t\right)}} \]
6. Step-by-step derivation

   1. associate-/r* 91.0%

      \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

7. Simplified 91.0%

   \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

8. Final simplification 91.0%

   \[\leadsto 2 \cdot \frac{\frac{x}{z}}{y - t} \]
9. Add Preprocessing

Alternative 11: 53.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(-2 \cdot \frac{x\_m}{z \cdot t}\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t) :precision binary64 (* x_s (* -2.0 (/ x_m (* z t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (-2.0 * (x_m / (z * t)));
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * ((-2.0d0) * (x_m / (z * t)))
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (-2.0 * (x_m / (z * t)));
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * (-2.0 * (x_m / (z * t)))

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(-2.0 * Float64(x_m / Float64(z * t))))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * (-2.0 * (x_m / (z * t)));
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(-2.0 * N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.5%

   \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
2. Step-by-step derivation

   1. distribute-rgt-out-- 91.3%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

3. Simplified 91.3%

   \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 52.3%

   \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 52.3%

      \[\leadsto -2 \cdot \frac{x}{\color{blue}{z \cdot t}} \]

7. Simplified 52.3%

   \[\leadsto \color{blue}{-2 \cdot \frac{x}{z \cdot t}} \]

8. Final simplification 52.3%

   \[\leadsto -2 \cdot \frac{x}{z \cdot t} \]
9. Add Preprocessing

Developer target: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ t_2 := \frac{x \cdot 2}{y \cdot z - t \cdot z}\\ \mathbf{if}\;t\_2 < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.045027827330126 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x (* (- y t) z)) 2.0))
        (t_2 (/ (* x 2.0) (- (* y z) (* t z)))))
   (if (< t_2 -2.559141628295061e-13)
     t_1
     (if (< t_2 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / ((y - t) * z)) * 2.0d0
    t_2 = (x * 2.0d0) / ((y * z) - (t * z))
    if (t_2 < (-2.559141628295061d-13)) then
        tmp = t_1
    else if (t_2 < 1.045027827330126d-269) then
        tmp = ((x / z) * 2.0d0) / (y - 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 t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / ((y - t) * z)) * 2.0
	t_2 = (x * 2.0) / ((y * z) - (t * z))
	tmp = 0
	if t_2 < -2.559141628295061e-13:
		tmp = t_1
	elif t_2 < 1.045027827330126e-269:
		tmp = ((x / z) * 2.0) / (y - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(Float64(y - t) * z)) * 2.0)
	t_2 = Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
	tmp = 0.0
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = Float64(Float64(Float64(x / z) * 2.0) / Float64(y - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / ((y - t) * z)) * 2.0;
	t_2 = (x * 2.0) / ((y * z) - (t * z));
	tmp = 0.0;
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = ((x / z) * 2.0) / (y - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -2.559141628295061e-13], t$95$1, If[Less[t$95$2, 1.045027827330126e-269], N[(N[(N[(x / z), $MachinePrecision] * 2.0), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (if (< (/ (* x 2.0) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2.0) (if (< (/ (* x 2.0) (- (* y z) (* t z))) 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) (* (/ x (* (- y t) z)) 2.0)))

  (/ (* x 2.0) (- (* y z) (* t z))))