Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.7% → 97.3%

Time: 9.5s

Alternatives: 8

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: 89.7% 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: 97.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot z - z \cdot t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-276}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (- (* y z) (* z t)))))
   (if (<= t_1 -1e-276)
     (/ (* x 2.0) (* z (- y t)))
     (if (<= t_1 4e-97)
       (/ (/ (* x -2.0) z) (- t y))
       (* (/ 2.0 z) (/ x (- y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * 2.0) / ((y * z) - (z * t));
	double tmp;
	if (t_1 <= -1e-276) {
		tmp = (x * 2.0) / (z * (y - t));
	} else if (t_1 <= 4e-97) {
		tmp = ((x * -2.0) / z) / (t - y);
	} else {
		tmp = (2.0 / z) * (x / (y - t));
	}
	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) :: tmp
    t_1 = (x * 2.0d0) / ((y * z) - (z * t))
    if (t_1 <= (-1d-276)) then
        tmp = (x * 2.0d0) / (z * (y - t))
    else if (t_1 <= 4d-97) then
        tmp = ((x * (-2.0d0)) / z) / (t - y)
    else
        tmp = (2.0d0 / z) * (x / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * 2.0) / ((y * z) - (z * t));
	double tmp;
	if (t_1 <= -1e-276) {
		tmp = (x * 2.0) / (z * (y - t));
	} else if (t_1 <= 4e-97) {
		tmp = ((x * -2.0) / z) / (t - y);
	} else {
		tmp = (2.0 / z) * (x / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * 2.0) / ((y * z) - (z * t))
	tmp = 0
	if t_1 <= -1e-276:
		tmp = (x * 2.0) / (z * (y - t))
	elif t_1 <= 4e-97:
		tmp = ((x * -2.0) / z) / (t - y)
	else:
		tmp = (2.0 / z) * (x / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(z * t)))
	tmp = 0.0
	if (t_1 <= -1e-276)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	elseif (t_1 <= 4e-97)
		tmp = Float64(Float64(Float64(x * -2.0) / z) / Float64(t - y));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * 2.0) / ((y * z) - (z * t));
	tmp = 0.0;
	if (t_1 <= -1e-276)
		tmp = (x * 2.0) / (z * (y - t));
	elseif (t_1 <= 4e-97)
		tmp = ((x * -2.0) / z) / (t - y);
	else
		tmp = (2.0 / z) * (x / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-276], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-97], N[(N[(N[(x * -2.0), $MachinePrecision] / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z))) < -1e-276

   1. Initial program 95.6%

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

      1. distribute-rgt-out-- 97.8%

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

   3. Simplified 97.8%

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

   if -1e-276 < (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z))) < 4.00000000000000014e-97

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. distribute-rgt-out-- 87.5%

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

      3. times-frac 91.7%

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

   3. Simplified 91.7%

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

      1. frac-2neg 91.7%

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

      2. associate-*r/ 99.0%

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

      3. *-commutative 99.0%

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

      4. associate-*r/ 99.1%

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

      5. distribute-lft-neg-in 99.1%

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

      6. distribute-rgt-neg-in 99.1%

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

      7. metadata-eval 99.1%

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

      8. neg-sub0 99.1%

         \[\leadsto \frac{\frac{x \cdot -2}{z}}{\color{blue}{0 - \left(y - t\right)}} \]

      9. sub-neg 99.1%

         \[\leadsto \frac{\frac{x \cdot -2}{z}}{0 - \color{blue}{\left(y + \left(-t\right)\right)}} \]

      10. +-commutative 99.1%

          \[\leadsto \frac{\frac{x \cdot -2}{z}}{0 - \color{blue}{\left(\left(-t\right) + y\right)}} \]

      11. associate--r+ 99.1%

          \[\leadsto \frac{\frac{x \cdot -2}{z}}{\color{blue}{\left(0 - \left(-t\right)\right) - y}} \]

      12. neg-sub0 99.1%

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

      13. remove-double-neg 99.1%

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

   5. Applied egg-rr 99.1%

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

   if 4.00000000000000014e-97 < (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z)))

   1. Initial program 78.7%

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

      1. *-commutative 78.7%

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

      2. distribute-rgt-out-- 87.0%

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

      3. times-frac 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq -1 \cdot 10^{-276}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq 4 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \]

Alternative 2: 95.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -1 \cdot 10^{-78} \lor \neg \left(x \cdot 2 \leq 5 \cdot 10^{-117}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(y - t\right) \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x 2.0) -1e-78) (not (<= (* x 2.0) 5e-117)))
   (* (/ 2.0 z) (/ x (- y t)))
   (/ 2.0 (* (- y t) (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -1e-78) || !((x * 2.0) <= 5e-117)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = 2.0 / ((y - t) * (z / x));
	}
	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) :: tmp
    if (((x * 2.0d0) <= (-1d-78)) .or. (.not. ((x * 2.0d0) <= 5d-117))) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else
        tmp = 2.0d0 / ((y - t) * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -1e-78) || !((x * 2.0) <= 5e-117)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = 2.0 / ((y - t) * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * 2.0) <= -1e-78) or not ((x * 2.0) <= 5e-117):
		tmp = (2.0 / z) * (x / (y - t))
	else:
		tmp = 2.0 / ((y - t) * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x * 2.0) <= -1e-78) || !(Float64(x * 2.0) <= 5e-117))
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	else
		tmp = Float64(2.0 / Float64(Float64(y - t) * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * 2.0) <= -1e-78) || ~(((x * 2.0) <= 5e-117)))
		tmp = (2.0 / z) * (x / (y - t));
	else
		tmp = 2.0 / ((y - t) * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x * 2.0), $MachinePrecision], -1e-78], N[Not[LessEqual[N[(x * 2.0), $MachinePrecision], 5e-117]], $MachinePrecision]], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(y - t), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < -9.99999999999999999e-79 or 5e-117 < (*.f64 x 2)

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

      2. distribute-rgt-out-- 89.8%

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

      3. times-frac 99.0%

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

   3. Simplified 99.0%

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

   if -9.99999999999999999e-79 < (*.f64 x 2) < 5e-117

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

      2. distribute-rgt-out-- 92.9%

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

      3. times-frac 81.6%

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

   3. Simplified 81.6%

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

      1. associate-*r/ 97.2%

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

      2. associate-/r/ 97.0%

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

      3. associate-/l/ 96.6%

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

   5. Applied egg-rr 96.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -1 \cdot 10^{-78} \lor \neg \left(x \cdot 2 \leq 5 \cdot 10^{-117}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(y - t\right) \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 3: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{\frac{x}{y}}{z}\\ t_2 := -2 \cdot \frac{x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-72}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (/ x y) z))) (t_2 (* -2.0 (/ x (* z t)))))
   (if (<= t -1.25e-91)
     t_2
     (if (<= t 9e-116)
       t_1
       (if (<= t 1.06e-72)
         (* -2.0 (/ (/ x t) z))
         (if (<= t 2.7e-55) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / y) / z);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.25e-91) {
		tmp = t_2;
	} else if (t <= 9e-116) {
		tmp = t_1;
	} else if (t <= 1.06e-72) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= 2.7e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = 2.0d0 * ((x / y) / z)
    t_2 = (-2.0d0) * (x / (z * t))
    if (t <= (-1.25d-91)) then
        tmp = t_2
    else if (t <= 9d-116) then
        tmp = t_1
    else if (t <= 1.06d-72) then
        tmp = (-2.0d0) * ((x / t) / z)
    else if (t <= 2.7d-55) 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 t_1 = 2.0 * ((x / y) / z);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.25e-91) {
		tmp = t_2;
	} else if (t <= 9e-116) {
		tmp = t_1;
	} else if (t <= 1.06e-72) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= 2.7e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((x / y) / z)
	t_2 = -2.0 * (x / (z * t))
	tmp = 0
	if t <= -1.25e-91:
		tmp = t_2
	elif t <= 9e-116:
		tmp = t_1
	elif t <= 1.06e-72:
		tmp = -2.0 * ((x / t) / z)
	elif t <= 2.7e-55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(x / y) / z))
	t_2 = Float64(-2.0 * Float64(x / Float64(z * t)))
	tmp = 0.0
	if (t <= -1.25e-91)
		tmp = t_2;
	elseif (t <= 9e-116)
		tmp = t_1;
	elseif (t <= 1.06e-72)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	elseif (t <= 2.7e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((x / y) / z);
	t_2 = -2.0 * (x / (z * t));
	tmp = 0.0;
	if (t <= -1.25e-91)
		tmp = t_2;
	elseif (t <= 9e-116)
		tmp = t_1;
	elseif (t <= 1.06e-72)
		tmp = -2.0 * ((x / t) / z);
	elseif (t <= 2.7e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e-91], t$95$2, If[LessEqual[t, 9e-116], t$95$1, If[LessEqual[t, 1.06e-72], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-55], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.24999999999999999e-91 or 2.70000000000000004e-55 < t

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

      2. distribute-rgt-out-- 93.5%

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

      3. times-frac 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around 0 78.4%

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

      1. *-commutative 78.4%

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

   6. Simplified 78.4%

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

   if -1.24999999999999999e-91 < t < 9.00000000000000023e-116 or 1.05999999999999994e-72 < t < 2.70000000000000004e-55

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

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

      2. distribute-rgt-out-- 87.5%

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

      3. times-frac 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 80.6%

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

      1. associate-/r* 85.2%

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

   6. Simplified 85.2%

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

   if 9.00000000000000023e-116 < t < 1.05999999999999994e-72

   1. Initial program 77.5%

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

      1. *-commutative 77.5%

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

      2. distribute-rgt-out-- 85.2%

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

      3. times-frac 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 62.1%

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

      1. associate-/r* 76.7%

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

   6. Simplified 76.7%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-91}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-116}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-72}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-55}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 4: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-102}:\\ \;\;\;\;\frac{2}{y} \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e-102)
   (* (/ 2.0 y) (/ x z))
   (if (<= y 4.5e+55) (* -2.0 (/ x (* z t))) (* 2.0 (/ (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-102) {
		tmp = (2.0 / y) * (x / z);
	} else if (y <= 4.5e+55) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = 2.0 * ((x / y) / z);
	}
	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) :: tmp
    if (y <= (-1.7d-102)) then
        tmp = (2.0d0 / y) * (x / z)
    else if (y <= 4.5d+55) then
        tmp = (-2.0d0) * (x / (z * t))
    else
        tmp = 2.0d0 * ((x / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-102) {
		tmp = (2.0 / y) * (x / z);
	} else if (y <= 4.5e+55) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = 2.0 * ((x / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e-102:
		tmp = (2.0 / y) * (x / z)
	elif y <= 4.5e+55:
		tmp = -2.0 * (x / (z * t))
	else:
		tmp = 2.0 * ((x / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e-102)
		tmp = Float64(Float64(2.0 / y) * Float64(x / z));
	elseif (y <= 4.5e+55)
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e-102)
		tmp = (2.0 / y) * (x / z);
	elseif (y <= 4.5e+55)
		tmp = -2.0 * (x / (z * t));
	else
		tmp = 2.0 * ((x / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e-102], N[(N[(2.0 / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+55], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000006e-102

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. distribute-rgt-out-- 88.9%

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

      3. times-frac 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around inf 69.2%

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

      1. associate-/r* 70.0%

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

   6. Simplified 70.0%

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

      1. associate-*r/ 70.0%

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

      2. associate-/l* 68.7%

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

      3. associate-/r/ 70.0%

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

      4. *-commutative 70.0%

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

   8. Applied egg-rr 70.0%

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

      1. associate-*r/ 68.9%

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

      2. associate-/l* 69.9%

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

      3. associate-/r/ 71.2%

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

   10. Simplified 71.2%

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

   if -1.70000000000000006e-102 < y < 4.49999999999999998e55

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

      2. distribute-rgt-out-- 93.3%

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

      3. times-frac 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around 0 80.5%

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

      1. *-commutative 80.5%

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

   6. Simplified 80.5%

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

   if 4.49999999999999998e55 < y

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

      2. distribute-rgt-out-- 89.0%

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

      3. times-frac 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in y around inf 76.3%

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

      1. associate-/r* 81.6%

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

   6. Simplified 81.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-102}:\\ \;\;\;\;\frac{2}{y} \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \end{array} \]

Alternative 5: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-66}:\\ \;\;\;\;\frac{2}{y} \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-66)
   (* (/ 2.0 y) (/ x z))
   (if (<= y 4.8e+26) (* (/ x z) (/ -2.0 t)) (* 2.0 (/ (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-66) {
		tmp = (2.0 / y) * (x / z);
	} else if (y <= 4.8e+26) {
		tmp = (x / z) * (-2.0 / t);
	} else {
		tmp = 2.0 * ((x / y) / z);
	}
	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) :: tmp
    if (y <= (-1.05d-66)) then
        tmp = (2.0d0 / y) * (x / z)
    else if (y <= 4.8d+26) then
        tmp = (x / z) * ((-2.0d0) / t)
    else
        tmp = 2.0d0 * ((x / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-66) {
		tmp = (2.0 / y) * (x / z);
	} else if (y <= 4.8e+26) {
		tmp = (x / z) * (-2.0 / t);
	} else {
		tmp = 2.0 * ((x / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-66:
		tmp = (2.0 / y) * (x / z)
	elif y <= 4.8e+26:
		tmp = (x / z) * (-2.0 / t)
	else:
		tmp = 2.0 * ((x / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-66)
		tmp = Float64(Float64(2.0 / y) * Float64(x / z));
	elseif (y <= 4.8e+26)
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	else
		tmp = Float64(2.0 * Float64(Float64(x / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e-66)
		tmp = (2.0 / y) * (x / z);
	elseif (y <= 4.8e+26)
		tmp = (x / z) * (-2.0 / t);
	else
		tmp = 2.0 * ((x / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e-66], N[(N[(2.0 / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+26], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e-66

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

      2. distribute-rgt-out-- 90.4%

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

      3. times-frac 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around inf 71.1%

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

      1. associate-/r* 70.6%

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

   6. Simplified 70.6%

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

      1. associate-*r/ 70.6%

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

      2. associate-/l* 69.3%

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

      3. associate-/r/ 70.6%

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

      4. *-commutative 70.6%

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

   8. Applied egg-rr 70.6%

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

      1. associate-*r/ 70.7%

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

      2. associate-/l* 70.6%

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

      3. associate-/r/ 71.9%

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

   10. Simplified 71.9%

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

   if -1.05e-66 < y < 4.80000000000000009e26

   1. Initial program 89.6%

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

      1. distribute-rgt-out-- 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around 0 79.4%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{-1 \cdot \left(t \cdot z\right)}} \]
   5. Step-by-step derivation

      1. mul-1-neg 79.4%

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

      2. *-commutative 79.4%

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

      3. distribute-rgt-neg-out 79.4%

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

   6. Simplified 79.4%

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

      1. times-frac 81.3%

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

      2. metadata-eval 81.3%

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

      3. frac-2neg 81.3%

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

   8. Applied egg-rr 81.3%

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

   if 4.80000000000000009e26 < y

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

      2. distribute-rgt-out-- 89.6%

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

      3. times-frac 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. associate-/r* 80.8%

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

   6. Simplified 80.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-66}:\\ \;\;\;\;\frac{2}{y} \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \end{array} \]

Alternative 6: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-64}:\\ \;\;\;\;\frac{2}{y} \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.45e-64)
   (* (/ 2.0 y) (/ x z))
   (if (<= y 4.4e+32) (* (/ x z) (/ -2.0 t)) (/ (/ 2.0 z) (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.45e-64) {
		tmp = (2.0 / y) * (x / z);
	} else if (y <= 4.4e+32) {
		tmp = (x / z) * (-2.0 / t);
	} else {
		tmp = (2.0 / z) / (y / x);
	}
	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) :: tmp
    if (y <= (-2.45d-64)) then
        tmp = (2.0d0 / y) * (x / z)
    else if (y <= 4.4d+32) then
        tmp = (x / z) * ((-2.0d0) / t)
    else
        tmp = (2.0d0 / z) / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.45e-64) {
		tmp = (2.0 / y) * (x / z);
	} else if (y <= 4.4e+32) {
		tmp = (x / z) * (-2.0 / t);
	} else {
		tmp = (2.0 / z) / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.45e-64:
		tmp = (2.0 / y) * (x / z)
	elif y <= 4.4e+32:
		tmp = (x / z) * (-2.0 / t)
	else:
		tmp = (2.0 / z) / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.45e-64)
		tmp = Float64(Float64(2.0 / y) * Float64(x / z));
	elseif (y <= 4.4e+32)
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	else
		tmp = Float64(Float64(2.0 / z) / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.45e-64)
		tmp = (2.0 / y) * (x / z);
	elseif (y <= 4.4e+32)
		tmp = (x / z) * (-2.0 / t);
	else
		tmp = (2.0 / z) / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.45e-64], N[(N[(2.0 / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+32], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4500000000000001e-64

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

      2. distribute-rgt-out-- 90.4%

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

      3. times-frac 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around inf 71.1%

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

      1. associate-/r* 70.6%

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

   6. Simplified 70.6%

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

      1. associate-*r/ 70.6%

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

      2. associate-/l* 69.3%

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

      3. associate-/r/ 70.6%

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

      4. *-commutative 70.6%

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

   8. Applied egg-rr 70.6%

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

      1. associate-*r/ 70.7%

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

      2. associate-/l* 70.6%

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

      3. associate-/r/ 71.9%

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

   10. Simplified 71.9%

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

   if -2.4500000000000001e-64 < y < 4.40000000000000002e32

   1. Initial program 89.6%

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

      1. distribute-rgt-out-- 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around 0 79.4%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{-1 \cdot \left(t \cdot z\right)}} \]
   5. Step-by-step derivation

      1. mul-1-neg 79.4%

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

      2. *-commutative 79.4%

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

      3. distribute-rgt-neg-out 79.4%

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

   6. Simplified 79.4%

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

      1. times-frac 81.3%

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

      2. metadata-eval 81.3%

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

      3. frac-2neg 81.3%

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

   8. Applied egg-rr 81.3%

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

   if 4.40000000000000002e32 < y

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

      2. distribute-rgt-out-- 89.6%

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

      3. times-frac 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. associate-/r* 80.8%

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

   6. Simplified 80.8%

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

      1. associate-*r/ 80.8%

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

      2. associate-/l* 80.1%

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

      3. div-inv 80.1%

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

      4. clear-num 80.2%

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

      5. associate-/r* 80.8%

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

   8. Applied egg-rr 80.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-64}:\\ \;\;\;\;\frac{2}{y} \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{\frac{y}{x}}\\ \end{array} \]

Alternative 7: 92.2% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 = (2.0d0 / z) * (x / (y - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.3%

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

   1. *-commutative 88.3%

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

   2. distribute-rgt-out-- 91.1%

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

   3. times-frac 91.9%

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

3. Simplified 91.9%

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

4. Final simplification 91.9%

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

Alternative 8: 53.0% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

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 = (-2.0d0) * (x / (z * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.3%

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

   1. *-commutative 88.3%

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

   2. distribute-rgt-out-- 91.1%

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

   3. times-frac 91.9%

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

3. Simplified 91.9%

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

4. Taylor expanded in y around 0 56.4%

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

   1. *-commutative 56.4%

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

6. Simplified 56.4%

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

7. Final simplification 56.4%

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

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 2023297 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (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))))