Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.1% → 98.5%

Time: 7.0s

Alternatives: 9

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: 90.1% 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: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+197}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (<= t_1 -2e+220)
     (* (/ x z) (/ 2.0 (- y t)))
     (if (<= t_1 2e+197)
       (/ (* x 2.0) (* z (- y t)))
       (* 2.0 (/ (/ x z) (- y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -2e+220) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (t_1 <= 2e+197) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = 2.0 * ((x / z) / (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 = (y * z) - (z * t)
    if (t_1 <= (-2d+220)) then
        tmp = (x / z) * (2.0d0 / (y - t))
    else if (t_1 <= 2d+197) then
        tmp = (x * 2.0d0) / (z * (y - t))
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -2e+220) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (t_1 <= 2e+197) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - (z * t)
	tmp = 0
	if t_1 <= -2e+220:
		tmp = (x / z) * (2.0 / (y - t))
	elif t_1 <= 2e+197:
		tmp = (x * 2.0) / (z * (y - t))
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -2e+220)
		tmp = Float64(Float64(x / z) * Float64(2.0 / Float64(y - t)));
	elseif (t_1 <= 2e+197)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - (z * t);
	tmp = 0.0;
	if (t_1 <= -2e+220)
		tmp = (x / z) * (2.0 / (y - t));
	elseif (t_1 <= 2e+197)
		tmp = (x * 2.0) / (z * (y - t));
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+220], N[(N[(x / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+197], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -2e220

   1. Initial program 77.4%

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

      1. distribute-rgt-out-- 77.4%

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

   3. Simplified 77.4%

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

      1. times-frac 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -2e220 < (-.f64 (*.f64 y z) (*.f64 t z)) < 1.9999999999999999e197

   1. Initial program 98.0%

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

      1. distribute-rgt-out-- 98.0%

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

   3. Simplified 98.0%

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

   if 1.9999999999999999e197 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-*r/ 65.9%

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

      3. distribute-rgt-out-- 74.0%

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

      4. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq 2 \cdot 10^{+197}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 95.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{-154} \lor \neg \left(x \cdot 2 \leq 2 \cdot 10^{-141}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x 2.0) -5e-154) (not (<= (* x 2.0) 2e-141)))
   (* (/ 2.0 z) (/ x (- y t)))
   (* 2.0 (/ (/ x z) (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -5e-154) || !((x * 2.0) <= 2e-141)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = 2.0 * ((x / z) / (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) :: tmp
    if (((x * 2.0d0) <= (-5d-154)) .or. (.not. ((x * 2.0d0) <= 2d-141))) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    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) <= -5e-154) || !((x * 2.0) <= 2e-141)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * 2.0) <= -5e-154) or not ((x * 2.0) <= 2e-141):
		tmp = (2.0 / z) * (x / (y - t))
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x * 2.0) <= -5e-154) || !(Float64(x * 2.0) <= 2e-141))
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * 2.0) <= -5e-154) || ~(((x * 2.0) <= 2e-141)))
		tmp = (2.0 / z) * (x / (y - t));
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x * 2.0), $MachinePrecision], -5e-154], N[Not[LessEqual[N[(x * 2.0), $MachinePrecision], 2e-141]], $MachinePrecision]], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < -5.0000000000000002e-154 or 2.0000000000000001e-141 < (*.f64 x 2)

   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-- 88.4%

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

      3. times-frac 97.6%

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

   3. Simplified 97.6%

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

   if -5.0000000000000002e-154 < (*.f64 x 2) < 2.0000000000000001e-141

   1. Initial program 97.3%

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

      1. *-commutative 97.3%

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

      2. associate-*r/ 97.3%

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

      3. distribute-rgt-out-- 97.3%

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

      4. associate-/r* 97.1%

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

   3. Simplified 97.1%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{-154} \lor \neg \left(x \cdot 2 \leq 2 \cdot 10^{-141}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 3: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+30}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 2.0 y))))
   (if (<= y -4.8e-38)
     t_1
     (if (<= y 3.8e-63)
       (/ -2.0 (* t (/ z x)))
       (if (<= y 5.9e-5)
         t_1
         (if (<= y 1.02e+30) (* -2.0 (/ (/ x t) z)) (* (/ 2.0 z) (/ x y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (2.0 / y);
	double tmp;
	if (y <= -4.8e-38) {
		tmp = t_1;
	} else if (y <= 3.8e-63) {
		tmp = -2.0 / (t * (z / x));
	} else if (y <= 5.9e-5) {
		tmp = t_1;
	} else if (y <= 1.02e+30) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	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 / z) * (2.0d0 / y)
    if (y <= (-4.8d-38)) then
        tmp = t_1
    else if (y <= 3.8d-63) then
        tmp = (-2.0d0) / (t * (z / x))
    else if (y <= 5.9d-5) then
        tmp = t_1
    else if (y <= 1.02d+30) then
        tmp = (-2.0d0) * ((x / t) / z)
    else
        tmp = (2.0d0 / z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (2.0 / y);
	double tmp;
	if (y <= -4.8e-38) {
		tmp = t_1;
	} else if (y <= 3.8e-63) {
		tmp = -2.0 / (t * (z / x));
	} else if (y <= 5.9e-5) {
		tmp = t_1;
	} else if (y <= 1.02e+30) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * (2.0 / y)
	tmp = 0
	if y <= -4.8e-38:
		tmp = t_1
	elif y <= 3.8e-63:
		tmp = -2.0 / (t * (z / x))
	elif y <= 5.9e-5:
		tmp = t_1
	elif y <= 1.02e+30:
		tmp = -2.0 * ((x / t) / z)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(2.0 / y))
	tmp = 0.0
	if (y <= -4.8e-38)
		tmp = t_1;
	elseif (y <= 3.8e-63)
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	elseif (y <= 5.9e-5)
		tmp = t_1;
	elseif (y <= 1.02e+30)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (2.0 / y);
	tmp = 0.0;
	if (y <= -4.8e-38)
		tmp = t_1;
	elseif (y <= 3.8e-63)
		tmp = -2.0 / (t * (z / x));
	elseif (y <= 5.9e-5)
		tmp = t_1;
	elseif (y <= 1.02e+30)
		tmp = -2.0 * ((x / t) / z);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e-38], t$95$1, If[LessEqual[y, 3.8e-63], N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.9e-5], t$95$1, If[LessEqual[y, 1.02e+30], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.80000000000000044e-38 or 3.80000000000000017e-63 < y < 5.8999999999999998e-5

   1. Initial program 93.4%

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

      1. distribute-rgt-out-- 94.8%

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

   3. Simplified 94.8%

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

      1. times-frac 94.8%

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

   5. Applied egg-rr 94.8%

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

   6. Taylor expanded in y around inf 76.8%

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

   if -4.80000000000000044e-38 < y < 3.80000000000000017e-63

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*r/ 92.7%

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

      3. distribute-rgt-out-- 92.7%

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

      4. associate-/r* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/r* 74.9%

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

   6. Simplified 74.9%

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

      1. *-commutative 74.9%

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

      2. associate-/l/ 75.6%

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

      3. associate-*r/ 75.6%

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

      4. *-commutative 75.6%

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

      5. times-frac 77.1%

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

      6. clear-num 77.0%

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

      7. frac-times 77.2%

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

      8. metadata-eval 77.2%

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

   8. Applied egg-rr 77.2%

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

   if 5.8999999999999998e-5 < y < 1.02e30

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r/ 90.3%

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

      3. distribute-rgt-out-- 90.3%

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

      4. associate-/r* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-/r* 80.8%

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

   6. Simplified 80.8%

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

   if 1.02e30 < y

   1. Initial program 77.0%

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

      1. distribute-rgt-out-- 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

   6. Simplified 77.0%

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

      1. *-commutative 77.0%

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

      2. times-frac 85.4%

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

   8. Applied egg-rr 85.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+30}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-64}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 0.00016:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+30}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.25e-39)
   (/ (* x 2.0) (* y z))
   (if (<= y 7e-64)
     (/ -2.0 (* t (/ z x)))
     (if (<= y 0.00016)
       (* (/ x z) (/ 2.0 y))
       (if (<= y 1.1e+30) (* -2.0 (/ (/ x t) z)) (* (/ 2.0 z) (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-39) {
		tmp = (x * 2.0) / (y * z);
	} else if (y <= 7e-64) {
		tmp = -2.0 / (t * (z / x));
	} else if (y <= 0.00016) {
		tmp = (x / z) * (2.0 / y);
	} else if (y <= 1.1e+30) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	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 <= (-2.25d-39)) then
        tmp = (x * 2.0d0) / (y * z)
    else if (y <= 7d-64) then
        tmp = (-2.0d0) / (t * (z / x))
    else if (y <= 0.00016d0) then
        tmp = (x / z) * (2.0d0 / y)
    else if (y <= 1.1d+30) then
        tmp = (-2.0d0) * ((x / t) / z)
    else
        tmp = (2.0d0 / z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-39) {
		tmp = (x * 2.0) / (y * z);
	} else if (y <= 7e-64) {
		tmp = -2.0 / (t * (z / x));
	} else if (y <= 0.00016) {
		tmp = (x / z) * (2.0 / y);
	} else if (y <= 1.1e+30) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.25e-39:
		tmp = (x * 2.0) / (y * z)
	elif y <= 7e-64:
		tmp = -2.0 / (t * (z / x))
	elif y <= 0.00016:
		tmp = (x / z) * (2.0 / y)
	elif y <= 1.1e+30:
		tmp = -2.0 * ((x / t) / z)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.25e-39)
		tmp = Float64(Float64(x * 2.0) / Float64(y * z));
	elseif (y <= 7e-64)
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	elseif (y <= 0.00016)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	elseif (y <= 1.1e+30)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e-39)
		tmp = (x * 2.0) / (y * z);
	elseif (y <= 7e-64)
		tmp = -2.0 / (t * (z / x));
	elseif (y <= 0.00016)
		tmp = (x / z) * (2.0 / y);
	elseif (y <= 1.1e+30)
		tmp = -2.0 * ((x / t) / z);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.25e-39], N[(N[(x * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-64], N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00016], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+30], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.25e-39

   1. Initial program 92.6%

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

      1. distribute-rgt-out-- 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 76.1%

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

      1. *-commutative 76.1%

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

   6. Simplified 76.1%

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

   if -2.25e-39 < y < 7.0000000000000006e-64

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*r/ 92.7%

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

      3. distribute-rgt-out-- 92.7%

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

      4. associate-/r* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around 0 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-/r* 75.6%

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

   6. Simplified 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/l/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. *-commutative 76.2%

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

      5. times-frac 77.7%

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

      6. clear-num 77.6%

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

      7. frac-times 77.8%

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

      8. metadata-eval 77.8%

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

   8. Applied egg-rr 77.8%

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

   if 7.0000000000000006e-64 < y < 1.60000000000000013e-4

   1. Initial program 99.7%

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

      1. distribute-rgt-out-- 99.7%

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

   3. Simplified 99.7%

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

      1. times-frac 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 91.9%

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

   if 1.60000000000000013e-4 < y < 1.1e30

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r/ 90.3%

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

      3. distribute-rgt-out-- 90.3%

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

      4. associate-/r* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-/r* 80.8%

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

   6. Simplified 80.8%

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

   if 1.1e30 < y

   1. Initial program 77.0%

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

      1. distribute-rgt-out-- 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

   6. Simplified 77.0%

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

      1. *-commutative 77.0%

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

      2. times-frac 85.4%

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

   8. Applied egg-rr 85.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-64}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 0.00016:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+30}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+29}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e-39)
   (/ (* x 2.0) (* y z))
   (if (<= y 6.8e-63)
     (/ (* (/ x z) -2.0) t)
     (if (<= y 1.22e-5)
       (* (/ x z) (/ 2.0 y))
       (if (<= y 5.5e+29) (* -2.0 (/ (/ x t) z)) (* (/ 2.0 z) (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-39) {
		tmp = (x * 2.0) / (y * z);
	} else if (y <= 6.8e-63) {
		tmp = ((x / z) * -2.0) / t;
	} else if (y <= 1.22e-5) {
		tmp = (x / z) * (2.0 / y);
	} else if (y <= 5.5e+29) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	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 <= (-1.3d-39)) then
        tmp = (x * 2.0d0) / (y * z)
    else if (y <= 6.8d-63) then
        tmp = ((x / z) * (-2.0d0)) / t
    else if (y <= 1.22d-5) then
        tmp = (x / z) * (2.0d0 / y)
    else if (y <= 5.5d+29) then
        tmp = (-2.0d0) * ((x / t) / z)
    else
        tmp = (2.0d0 / z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-39) {
		tmp = (x * 2.0) / (y * z);
	} else if (y <= 6.8e-63) {
		tmp = ((x / z) * -2.0) / t;
	} else if (y <= 1.22e-5) {
		tmp = (x / z) * (2.0 / y);
	} else if (y <= 5.5e+29) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e-39:
		tmp = (x * 2.0) / (y * z)
	elif y <= 6.8e-63:
		tmp = ((x / z) * -2.0) / t
	elif y <= 1.22e-5:
		tmp = (x / z) * (2.0 / y)
	elif y <= 5.5e+29:
		tmp = -2.0 * ((x / t) / z)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e-39)
		tmp = Float64(Float64(x * 2.0) / Float64(y * z));
	elseif (y <= 6.8e-63)
		tmp = Float64(Float64(Float64(x / z) * -2.0) / t);
	elseif (y <= 1.22e-5)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	elseif (y <= 5.5e+29)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e-39)
		tmp = (x * 2.0) / (y * z);
	elseif (y <= 6.8e-63)
		tmp = ((x / z) * -2.0) / t;
	elseif (y <= 1.22e-5)
		tmp = (x / z) * (2.0 / y);
	elseif (y <= 5.5e+29)
		tmp = -2.0 * ((x / t) / z);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e-39], N[(N[(x * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-63], N[(N[(N[(x / z), $MachinePrecision] * -2.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 1.22e-5], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+29], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.3e-39

   1. Initial program 92.6%

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

      1. distribute-rgt-out-- 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 76.1%

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

      1. *-commutative 76.1%

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

   6. Simplified 76.1%

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

   if -1.3e-39 < y < 6.79999999999999997e-63

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*r/ 92.7%

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

      3. distribute-rgt-out-- 92.7%

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

      4. associate-/r* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around 0 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-/r* 75.6%

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

   6. Simplified 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/l/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. *-commutative 76.2%

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

      5. times-frac 77.7%

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

      6. associate-*r/ 78.6%

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

   8. Applied egg-rr 78.6%

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

   if 6.79999999999999997e-63 < y < 1.22000000000000001e-5

   1. Initial program 99.7%

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

      1. distribute-rgt-out-- 99.7%

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

   3. Simplified 99.7%

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

      1. times-frac 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 91.9%

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

   if 1.22000000000000001e-5 < y < 5.5e29

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r/ 90.3%

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

      3. distribute-rgt-out-- 90.3%

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

      4. associate-/r* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-/r* 80.8%

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

   6. Simplified 80.8%

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

   if 5.5e29 < y

   1. Initial program 77.0%

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

      1. distribute-rgt-out-- 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

   6. Simplified 77.0%

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

      1. *-commutative 77.0%

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

      2. times-frac 85.4%

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

   8. Applied egg-rr 85.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+29}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{if}\;t \leq -245000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq 0.0098:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -2.0 (/ (/ x t) z))))
   (if (<= t -245000.0)
     t_1
     (if (<= t -1.7e-260)
       (* (/ x z) (/ 2.0 y))
       (if (<= t 0.0098) (* (/ 2.0 z) (/ x y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 * ((x / t) / z);
	double tmp;
	if (t <= -245000.0) {
		tmp = t_1;
	} else if (t <= -1.7e-260) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= 0.0098) {
		tmp = (2.0 / z) * (x / y);
	} 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) :: tmp
    t_1 = (-2.0d0) * ((x / t) / z)
    if (t <= (-245000.0d0)) then
        tmp = t_1
    else if (t <= (-1.7d-260)) then
        tmp = (x / z) * (2.0d0 / y)
    else if (t <= 0.0098d0) then
        tmp = (2.0d0 / z) * (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 * ((x / t) / z);
	double tmp;
	if (t <= -245000.0) {
		tmp = t_1;
	} else if (t <= -1.7e-260) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= 0.0098) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 * ((x / t) / z)
	tmp = 0
	if t <= -245000.0:
		tmp = t_1
	elif t <= -1.7e-260:
		tmp = (x / z) * (2.0 / y)
	elif t <= 0.0098:
		tmp = (2.0 / z) * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 * Float64(Float64(x / t) / z))
	tmp = 0.0
	if (t <= -245000.0)
		tmp = t_1;
	elseif (t <= -1.7e-260)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	elseif (t <= 0.0098)
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 * ((x / t) / z);
	tmp = 0.0;
	if (t <= -245000.0)
		tmp = t_1;
	elseif (t <= -1.7e-260)
		tmp = (x / z) * (2.0 / y);
	elseif (t <= 0.0098)
		tmp = (2.0 / z) * (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -245000.0], t$95$1, If[LessEqual[t, -1.7e-260], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0098], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -245000 or 0.0097999999999999997 < t

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*r/ 86.6%

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

      3. distribute-rgt-out-- 89.8%

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

      4. associate-/r* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/r* 72.8%

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

   6. Simplified 72.8%

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

   if -245000 < t < -1.6999999999999999e-260

   1. Initial program 92.4%

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

      1. distribute-rgt-out-- 92.4%

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

   3. Simplified 92.4%

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

      1. times-frac 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in y around inf 82.2%

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

   if -1.6999999999999999e-260 < t < 0.0097999999999999997

   1. Initial program 90.7%

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

      1. distribute-rgt-out-- 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. *-commutative 74.3%

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

   6. Simplified 74.3%

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

      1. *-commutative 74.3%

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

      2. times-frac 82.0%

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

   8. Applied egg-rr 82.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -245000:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq 0.0098:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 7: 58.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+38} \lor \neg \left(x \leq 2 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1e+38) (not (<= x 2e+26)))
   (* (/ 2.0 z) (/ x y))
   (* (/ x z) (/ 2.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1e+38) || !(x <= 2e+26)) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	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 <= (-1d+38)) .or. (.not. (x <= 2d+26))) then
        tmp = (2.0d0 / z) * (x / y)
    else
        tmp = (x / z) * (2.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1e+38) || !(x <= 2e+26)) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1e+38) or not (x <= 2e+26):
		tmp = (2.0 / z) * (x / y)
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1e+38) || !(x <= 2e+26))
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	else
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1e+38) || ~((x <= 2e+26)))
		tmp = (2.0 / z) * (x / y);
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1e+38], N[Not[LessEqual[x, 2e+26]], $MachinePrecision]], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999977e37 or 2.0000000000000001e26 < x

   1. Initial program 81.6%

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

      1. distribute-rgt-out-- 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in y around inf 49.4%

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

      1. *-commutative 49.4%

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

   6. Simplified 49.4%

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

      1. *-commutative 49.4%

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

      2. times-frac 58.7%

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

   8. Applied egg-rr 58.7%

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

   if -9.99999999999999977e37 < x < 2.0000000000000001e26

   1. Initial program 95.7%

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

      1. distribute-rgt-out-- 97.1%

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

   3. Simplified 97.1%

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

      1. times-frac 97.1%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in y around inf 66.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+38} \lor \neg \left(x \leq 2 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 8: 92.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

   1. *-commutative 89.0%

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

   2. associate-*r/ 89.0%

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

   3. distribute-rgt-out-- 90.7%

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

   4. associate-/r* 92.1%

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

3. Simplified 92.1%

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

4. Final simplification 92.1%

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

Alternative 9: 53.6% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

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)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

   1. distribute-rgt-out-- 90.7%

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

3. Simplified 90.7%

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

4. Taylor expanded in y around inf 55.5%

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

   1. *-commutative 55.5%

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

6. Simplified 55.5%

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

   1. *-commutative 55.5%

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

   2. times-frac 56.5%

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

8. Applied egg-rr 56.5%

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

9. Final simplification 56.5%

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

Developer target: 97.4% 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 2023293 
(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))))