Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.4% → 94.4%

Time: 10.0s

Alternatives: 15

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: 89.4% 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: 94.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -2 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{elif}\;x \cdot 2 \leq 2 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x 2.0) -2e-67)
   (* (/ x (- y t)) (/ 2.0 z))
   (if (<= (* x 2.0) 2e+173)
     (* x (/ 2.0 (* z (- 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) <= -2e-67) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else if ((x * 2.0) <= 2e+173) {
		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) :: tmp
    if ((x * 2.0d0) <= (-2d-67)) then
        tmp = (x / (y - t)) * (2.0d0 / z)
    else if ((x * 2.0d0) <= 2d+173) 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 tmp;
	if ((x * 2.0) <= -2e-67) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else if ((x * 2.0) <= 2e+173) {
		tmp = x * (2.0 / (z * (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) <= -2e-67:
		tmp = (x / (y - t)) * (2.0 / z)
	elif (x * 2.0) <= 2e+173:
		tmp = x * (2.0 / (z * (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) <= -2e-67)
		tmp = Float64(Float64(x / Float64(y - t)) * Float64(2.0 / z));
	elseif (Float64(x * 2.0) <= 2e+173)
		tmp = Float64(x * Float64(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)
	tmp = 0.0;
	if ((x * 2.0) <= -2e-67)
		tmp = (x / (y - t)) * (2.0 / z);
	elseif ((x * 2.0) <= 2e+173)
		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_] := If[LessEqual[N[(x * 2.0), $MachinePrecision], -2e-67], N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 2.0), $MachinePrecision], 2e+173], N[(x * N[(2.0 / N[(z * N[(y - t), $MachinePrecision]), $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 x 2) < -1.99999999999999989e-67

   1. Initial program 84.7%

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

      1. distribute-rgt-out-- 88.9%

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

   3. Simplified 88.9%

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

      1. *-commutative 88.9%

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

      2. times-frac 98.6%

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

   5. Applied egg-rr 98.6%

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

   if -1.99999999999999989e-67 < (*.f64 x 2) < 2e173

   1. Initial program 99.2%

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

      1. associate-*r/ 99.0%

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

      2. distribute-rgt-out-- 99.0%

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

   3. Simplified 99.0%

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

   if 2e173 < (*.f64 x 2)

   1. Initial program 68.7%

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

      1. associate-*l/ 68.7%

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

      2. *-commutative 68.7%

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

      3. distribute-rgt-out-- 72.7%

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

      4. associate-/r* 96.4%

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

   3. Simplified 96.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -2 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{elif}\;x \cdot 2 \leq 2 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq -1 \cdot 10^{-279}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x 2.0) (- (* y z) (* z t))) -1e-279)
   (/ (* x 2.0) (* z (- y t)))
   (* (/ x (- y t)) (/ 2.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) / ((y * z) - (z * t))) <= -1e-279) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = (x / (y - t)) * (2.0 / 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 (((x * 2.0d0) / ((y * z) - (z * t))) <= (-1d-279)) then
        tmp = (x * 2.0d0) / (z * (y - t))
    else
        tmp = (x / (y - t)) * (2.0d0 / z)
    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) / ((y * z) - (z * t))) <= -1e-279) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = (x / (y - t)) * (2.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * 2.0) / ((y * z) - (z * t))) <= -1e-279:
		tmp = (x * 2.0) / (z * (y - t))
	else:
		tmp = (x / (y - t)) * (2.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(z * t))) <= -1e-279)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(Float64(x / Float64(y - t)) * Float64(2.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * 2.0) / ((y * z) - (z * t))) <= -1e-279)
		tmp = (x * 2.0) / (z * (y - t));
	else
		tmp = (x / (y - t)) * (2.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1e-279], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z))) < -1.00000000000000006e-279

   1. Initial program 97.4%

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

      1. distribute-rgt-out-- 99.6%

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

   3. Simplified 99.6%

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

   if -1.00000000000000006e-279 < (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z)))

   1. Initial program 86.8%

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

      1. distribute-rgt-out-- 88.7%

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

   3. Simplified 88.7%

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

      1. *-commutative 88.7%

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

      2. times-frac 96.9%

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

   5. Applied egg-rr 96.9%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq -1 \cdot 10^{-279}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \end{array} \]

Alternative 3: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= t -3.6e-80)
     (* x (/ (/ -2.0 t) z))
     (if (<= t 3.1e-259)
       t_1
       (if (<= t 4.6e-215)
         (* x (/ 2.0 (* y z)))
         (if (<= t 4.4e-16) t_1 (* x (/ -2.0 (* z t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -3.6e-80) {
		tmp = x * ((-2.0 / t) / z);
	} else if (t <= 3.1e-259) {
		tmp = t_1;
	} else if (t <= 4.6e-215) {
		tmp = x * (2.0 / (y * z));
	} else if (t <= 4.4e-16) {
		tmp = t_1;
	} else {
		tmp = x * (-2.0 / (z * 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 = (2.0d0 / z) * (x / y)
    if (t <= (-3.6d-80)) then
        tmp = x * (((-2.0d0) / t) / z)
    else if (t <= 3.1d-259) then
        tmp = t_1
    else if (t <= 4.6d-215) then
        tmp = x * (2.0d0 / (y * z))
    else if (t <= 4.4d-16) then
        tmp = t_1
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -3.6e-80) {
		tmp = x * ((-2.0 / t) / z);
	} else if (t <= 3.1e-259) {
		tmp = t_1;
	} else if (t <= 4.6e-215) {
		tmp = x * (2.0 / (y * z));
	} else if (t <= 4.4e-16) {
		tmp = t_1;
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if t <= -3.6e-80:
		tmp = x * ((-2.0 / t) / z)
	elif t <= 3.1e-259:
		tmp = t_1
	elif t <= 4.6e-215:
		tmp = x * (2.0 / (y * z))
	elif t <= 4.4e-16:
		tmp = t_1
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (t <= -3.6e-80)
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	elseif (t <= 3.1e-259)
		tmp = t_1;
	elseif (t <= 4.6e-215)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (t <= 4.4e-16)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (t <= -3.6e-80)
		tmp = x * ((-2.0 / t) / z);
	elseif (t <= 3.1e-259)
		tmp = t_1;
	elseif (t <= 4.6e-215)
		tmp = x * (2.0 / (y * z));
	elseif (t <= 4.4e-16)
		tmp = t_1;
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e-80], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-259], t$95$1, If[LessEqual[t, 4.6e-215], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-16], t$95$1, N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.6e-80

   1. Initial program 92.4%

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

      1. associate-*r/ 92.3%

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

      2. distribute-rgt-out-- 93.7%

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

      3. associate-/l/ 93.7%

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

      4. sub-neg 93.7%

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

      5. +-commutative 93.7%

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

      6. neg-sub0 93.7%

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

      7. associate-+l- 93.7%

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

      8. sub0-neg 93.7%

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

      9. neg-mul-1 93.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{-1 \cdot \left(t - y\right)}}}{z} \]

      10. associate-/r* 93.7%

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

      11. metadata-eval 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 75.5%

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

   if -3.6e-80 < t < 3.0999999999999998e-259 or 4.5999999999999998e-215 < t < 4.40000000000000001e-16

   1. Initial program 88.6%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. distribute-rgt-out-- 91.6%

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

      4. associate-/r* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 75.3%

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

      1. associate-*r/ 75.3%

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

      2. *-commutative 75.3%

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

   6. Simplified 75.3%

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

      1. times-frac 81.5%

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

   8. Applied egg-rr 81.5%

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

   if 3.0999999999999998e-259 < t < 4.5999999999999998e-215

   1. Initial program 93.1%

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

      1. associate-*r/ 93.2%

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

      2. distribute-rgt-out-- 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 93.2%

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

   if 4.40000000000000001e-16 < t

   1. Initial program 90.7%

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

      1. associate-*r/ 90.8%

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

      2. distribute-rgt-out-- 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in y around 0 78.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-259}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= t -3.5e-80)
     (* (/ x z) (/ -2.0 t))
     (if (<= t 1.32e-257)
       t_1
       (if (<= t 3.2e-215)
         (* x (/ 2.0 (* y z)))
         (if (<= t 3.6e-15) t_1 (* x (/ -2.0 (* z t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -3.5e-80) {
		tmp = (x / z) * (-2.0 / t);
	} else if (t <= 1.32e-257) {
		tmp = t_1;
	} else if (t <= 3.2e-215) {
		tmp = x * (2.0 / (y * z));
	} else if (t <= 3.6e-15) {
		tmp = t_1;
	} else {
		tmp = x * (-2.0 / (z * 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 = (2.0d0 / z) * (x / y)
    if (t <= (-3.5d-80)) then
        tmp = (x / z) * ((-2.0d0) / t)
    else if (t <= 1.32d-257) then
        tmp = t_1
    else if (t <= 3.2d-215) then
        tmp = x * (2.0d0 / (y * z))
    else if (t <= 3.6d-15) then
        tmp = t_1
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -3.5e-80) {
		tmp = (x / z) * (-2.0 / t);
	} else if (t <= 1.32e-257) {
		tmp = t_1;
	} else if (t <= 3.2e-215) {
		tmp = x * (2.0 / (y * z));
	} else if (t <= 3.6e-15) {
		tmp = t_1;
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if t <= -3.5e-80:
		tmp = (x / z) * (-2.0 / t)
	elif t <= 1.32e-257:
		tmp = t_1
	elif t <= 3.2e-215:
		tmp = x * (2.0 / (y * z))
	elif t <= 3.6e-15:
		tmp = t_1
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (t <= -3.5e-80)
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	elseif (t <= 1.32e-257)
		tmp = t_1;
	elseif (t <= 3.2e-215)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (t <= 3.6e-15)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (t <= -3.5e-80)
		tmp = (x / z) * (-2.0 / t);
	elseif (t <= 1.32e-257)
		tmp = t_1;
	elseif (t <= 3.2e-215)
		tmp = x * (2.0 / (y * z));
	elseif (t <= 3.6e-15)
		tmp = t_1;
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-80], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e-257], t$95$1, If[LessEqual[t, 3.2e-215], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-15], t$95$1, N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.50000000000000015e-80

   1. Initial program 92.4%

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

      1. associate-*l/ 92.4%

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

      2. *-commutative 92.4%

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

      3. distribute-rgt-out-- 93.8%

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

      4. associate-/r* 93.5%

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

   3. Simplified 93.5%

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

   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. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. *-commutative 75.6%

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

      4. times-frac 79.3%

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

   6. Simplified 79.3%

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

   if -3.50000000000000015e-80 < t < 1.32e-257 or 3.2000000000000001e-215 < t < 3.6000000000000001e-15

   1. Initial program 88.6%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. distribute-rgt-out-- 91.6%

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

      4. associate-/r* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 75.3%

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

      1. associate-*r/ 75.3%

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

      2. *-commutative 75.3%

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

   6. Simplified 75.3%

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

      1. times-frac 81.5%

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

   8. Applied egg-rr 81.5%

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

   if 1.32e-257 < t < 3.2000000000000001e-215

   1. Initial program 93.1%

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

      1. associate-*r/ 93.2%

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

      2. distribute-rgt-out-- 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 93.2%

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

   if 3.6000000000000001e-15 < t

   1. Initial program 90.7%

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

      1. associate-*r/ 90.8%

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

      2. distribute-rgt-out-- 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in y around 0 78.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-257}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 5: 96.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+51} \lor \neg \left(z \leq 9.2 \cdot 10^{+118}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e+51) (not (<= z 9.2e+118)))
   (* 2.0 (/ (/ x z) (- y t)))
   (* x (/ 2.0 (* z (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e+51) || !(z <= 9.2e+118)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * (2.0 / (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 ((z <= (-2d+51)) .or. (.not. (z <= 9.2d+118))) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = x * (2.0d0 / (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 ((z <= -2e+51) || !(z <= 9.2e+118)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * (2.0 / (z * (y - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e+51) or not (z <= 9.2e+118):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = x * (2.0 / (z * (y - t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e+51) || !(z <= 9.2e+118))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(x * Float64(2.0 / Float64(z * Float64(y - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e+51) || ~((z <= 9.2e+118)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = x * (2.0 / (z * (y - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e+51], N[Not[LessEqual[z, 9.2e+118]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e51 or 9.20000000000000063e118 < z

   1. Initial program 83.1%

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

      1. associate-*l/ 83.1%

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

      2. *-commutative 83.1%

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

      3. distribute-rgt-out-- 85.0%

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

      4. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   if -2e51 < z < 9.20000000000000063e118

   1. Initial program 96.5%

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

      1. associate-*r/ 96.2%

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

      2. distribute-rgt-out-- 98.3%

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

   3. Simplified 98.3%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+51} \lor \neg \left(z \leq 9.2 \cdot 10^{+118}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 6: 94.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -1 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(y - t\right) \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x 2.0) -1e-74)
   (* (/ x (- y t)) (/ 2.0 z))
   (/ 2.0 (* (- y t) (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * 2.0) <= -1e-74) {
		tmp = (x / (y - t)) * (2.0 / z);
	} 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-74)) then
        tmp = (x / (y - t)) * (2.0d0 / z)
    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-74) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else {
		tmp = 2.0 / ((y - t) * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * 2.0) <= -1e-74:
		tmp = (x / (y - t)) * (2.0 / z)
	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-74)
		tmp = Float64(Float64(x / Float64(y - t)) * Float64(2.0 / z));
	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-74)
		tmp = (x / (y - t)) * (2.0 / z);
	else
		tmp = 2.0 / ((y - t) * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * 2.0), $MachinePrecision], -1e-74], N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $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) < -9.99999999999999958e-75

   1. Initial program 85.0%

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

      1. distribute-rgt-out-- 89.2%

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

   3. Simplified 89.2%

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

      1. *-commutative 89.2%

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

      2. times-frac 98.6%

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

   5. Applied egg-rr 98.6%

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

   if -9.99999999999999958e-75 < (*.f64 x 2)

   1. Initial program 93.9%

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

      1. associate-*l/ 93.8%

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

      2. *-commutative 93.8%

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

      3. distribute-rgt-out-- 94.5%

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

      4. associate-/r* 95.9%

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

   3. Simplified 95.9%

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

      1. *-commutative 95.9%

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

      2. associate-*l/ 95.9%

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

      3. associate-*r/ 95.9%

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

      4. clear-num 95.6%

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

      5. frac-times 96.4%

         \[\leadsto \color{blue}{\frac{1 \cdot 2}{\frac{z}{x} \cdot \left(y - t\right)}} \]

      6. metadata-eval 96.4%

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

   5. Applied egg-rr 96.4%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -1 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(y - t\right) \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 7: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-81} \lor \neg \left(t \leq 7.8 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.8e-81) (not (<= t 7.8e-21)))
   (* x (/ -2.0 (* z t)))
   (* x (/ 2.0 (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e-81) || !(t <= 7.8e-21)) {
		tmp = x * (-2.0 / (z * t));
	} else {
		tmp = x * (2.0 / (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 ((t <= (-3.8d-81)) .or. (.not. (t <= 7.8d-21))) then
        tmp = x * ((-2.0d0) / (z * t))
    else
        tmp = x * (2.0d0 / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e-81) || !(t <= 7.8e-21)) {
		tmp = x * (-2.0 / (z * t));
	} else {
		tmp = x * (2.0 / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.8e-81) or not (t <= 7.8e-21):
		tmp = x * (-2.0 / (z * t))
	else:
		tmp = x * (2.0 / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.8e-81) || !(t <= 7.8e-21))
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	else
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.8e-81) || ~((t <= 7.8e-21)))
		tmp = x * (-2.0 / (z * t));
	else
		tmp = x * (2.0 / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.8e-81], N[Not[LessEqual[t, 7.8e-21]], $MachinePrecision]], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7999999999999999e-81 or 7.8000000000000001e-21 < t

   1. Initial program 91.7%

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

      1. associate-*r/ 91.6%

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

      2. distribute-rgt-out-- 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around 0 76.9%

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

   if -3.7999999999999999e-81 < t < 7.8000000000000001e-21

   1. Initial program 89.2%

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

      1. associate-*r/ 88.8%

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

      2. distribute-rgt-out-- 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around inf 77.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-81} \lor \neg \left(t \leq 7.8 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \]

Alternative 8: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.3e-80)
   (* x (/ (/ -2.0 t) z))
   (if (<= t 1.2e-17) (* x (/ 2.0 (* y z))) (* x (/ -2.0 (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-80) {
		tmp = x * ((-2.0 / t) / z);
	} else if (t <= 1.2e-17) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * (-2.0 / (z * 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 (t <= (-2.3d-80)) then
        tmp = x * (((-2.0d0) / t) / z)
    else if (t <= 1.2d-17) then
        tmp = x * (2.0d0 / (y * z))
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-80) {
		tmp = x * ((-2.0 / t) / z);
	} else if (t <= 1.2e-17) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.3e-80:
		tmp = x * ((-2.0 / t) / z)
	elif t <= 1.2e-17:
		tmp = x * (2.0 / (y * z))
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.3e-80)
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	elseif (t <= 1.2e-17)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.3e-80)
		tmp = x * ((-2.0 / t) / z);
	elseif (t <= 1.2e-17)
		tmp = x * (2.0 / (y * z));
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.3e-80], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-17], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2999999999999998e-80

   1. Initial program 92.4%

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

      1. associate-*r/ 92.3%

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

      2. distribute-rgt-out-- 93.7%

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

      3. associate-/l/ 93.7%

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

      4. sub-neg 93.7%

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

      5. +-commutative 93.7%

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

      6. neg-sub0 93.7%

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

      7. associate-+l- 93.7%

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

      8. sub0-neg 93.7%

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

      9. neg-mul-1 93.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{-1 \cdot \left(t - y\right)}}}{z} \]

      10. associate-/r* 93.7%

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

      11. metadata-eval 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 75.5%

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

   if -2.2999999999999998e-80 < t < 1.19999999999999993e-17

   1. Initial program 89.2%

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

      1. associate-*r/ 88.8%

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

      2. distribute-rgt-out-- 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around inf 77.2%

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

   if 1.19999999999999993e-17 < t

   1. Initial program 90.7%

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

      1. associate-*r/ 90.8%

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

      2. distribute-rgt-out-- 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in y around 0 78.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 9: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.3e-80)
   (* (/ x z) (/ -2.0 t))
   (if (<= t 4.4e-42) (* (/ x z) (/ 2.0 y)) (* x (/ -2.0 (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-80) {
		tmp = (x / z) * (-2.0 / t);
	} else if (t <= 4.4e-42) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = x * (-2.0 / (z * 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 (t <= (-2.3d-80)) then
        tmp = (x / z) * ((-2.0d0) / t)
    else if (t <= 4.4d-42) then
        tmp = (x / z) * (2.0d0 / y)
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-80) {
		tmp = (x / z) * (-2.0 / t);
	} else if (t <= 4.4e-42) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.3e-80:
		tmp = (x / z) * (-2.0 / t)
	elif t <= 4.4e-42:
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.3e-80)
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	elseif (t <= 4.4e-42)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.3e-80)
		tmp = (x / z) * (-2.0 / t);
	elseif (t <= 4.4e-42)
		tmp = (x / z) * (2.0 / y);
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.3e-80], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-42], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2999999999999998e-80

   1. Initial program 92.4%

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

      1. associate-*l/ 92.4%

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

      2. *-commutative 92.4%

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

      3. distribute-rgt-out-- 93.8%

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

      4. associate-/r* 93.5%

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

   3. Simplified 93.5%

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

   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. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. *-commutative 75.6%

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

      4. times-frac 79.3%

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

   6. Simplified 79.3%

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

   if -2.2999999999999998e-80 < t < 4.4000000000000001e-42

   1. Initial program 88.7%

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

      1. associate-*l/ 88.7%

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

      2. *-commutative 88.7%

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

      3. distribute-rgt-out-- 91.4%

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

      4. associate-/r* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in y around inf 78.2%

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

      1. associate-*r/ 78.2%

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

      2. *-commutative 78.2%

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

   6. Simplified 78.2%

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

      1. *-commutative 78.2%

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

      2. times-frac 85.7%

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

   8. Applied egg-rr 85.7%

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

   if 4.4000000000000001e-42 < t

   1. Initial program 91.4%

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

      1. associate-*r/ 91.4%

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

      2. distribute-rgt-out-- 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 77.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 10: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-80}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.6e-80)
   (/ -2.0 (* t (/ z x)))
   (if (<= t 4.4e-42) (* (/ x z) (/ 2.0 y)) (* x (/ -2.0 (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e-80) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 4.4e-42) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = x * (-2.0 / (z * 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 (t <= (-3.6d-80)) then
        tmp = (-2.0d0) / (t * (z / x))
    else if (t <= 4.4d-42) then
        tmp = (x / z) * (2.0d0 / y)
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e-80) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 4.4e-42) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.6e-80:
		tmp = -2.0 / (t * (z / x))
	elif t <= 4.4e-42:
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.6e-80)
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	elseif (t <= 4.4e-42)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.6e-80)
		tmp = -2.0 / (t * (z / x));
	elseif (t <= 4.4e-42)
		tmp = (x / z) * (2.0 / y);
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.6e-80], N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-42], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6e-80

   1. Initial program 92.4%

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

      1. associate-*r/ 92.3%

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

      2. distribute-rgt-out-- 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. frac-times 79.3%

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

      4. clear-num 80.5%

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

      5. frac-times 82.7%

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

      6. metadata-eval 82.7%

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

   6. Applied egg-rr 82.7%

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

   if -3.6e-80 < t < 4.4000000000000001e-42

   1. Initial program 88.7%

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

      1. associate-*l/ 88.7%

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

      2. *-commutative 88.7%

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

      3. distribute-rgt-out-- 91.4%

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

      4. associate-/r* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in y around inf 78.2%

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

      1. associate-*r/ 78.2%

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

      2. *-commutative 78.2%

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

   6. Simplified 78.2%

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

      1. *-commutative 78.2%

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

      2. times-frac 85.7%

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

   8. Applied egg-rr 85.7%

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

   if 4.4000000000000001e-42 < t

   1. Initial program 91.4%

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

      1. associate-*r/ 91.4%

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

      2. distribute-rgt-out-- 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 77.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-80}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 11: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.8e-81)
   (/ -2.0 (* t (/ z x)))
   (if (<= t 4.4e-42) (/ 2.0 (/ y (/ x z))) (* x (/ -2.0 (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e-81) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 4.4e-42) {
		tmp = 2.0 / (y / (x / z));
	} else {
		tmp = x * (-2.0 / (z * 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 (t <= (-3.8d-81)) then
        tmp = (-2.0d0) / (t * (z / x))
    else if (t <= 4.4d-42) then
        tmp = 2.0d0 / (y / (x / z))
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e-81) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 4.4e-42) {
		tmp = 2.0 / (y / (x / z));
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.8e-81:
		tmp = -2.0 / (t * (z / x))
	elif t <= 4.4e-42:
		tmp = 2.0 / (y / (x / z))
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.8e-81)
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	elseif (t <= 4.4e-42)
		tmp = Float64(2.0 / Float64(y / Float64(x / z)));
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.8e-81)
		tmp = -2.0 / (t * (z / x));
	elseif (t <= 4.4e-42)
		tmp = 2.0 / (y / (x / z));
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.8e-81], N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-42], N[(2.0 / N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7999999999999999e-81

   1. Initial program 92.4%

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

      1. associate-*r/ 92.3%

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

      2. distribute-rgt-out-- 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. frac-times 79.3%

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

      4. clear-num 80.5%

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

      5. frac-times 82.7%

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

      6. metadata-eval 82.7%

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

   6. Applied egg-rr 82.7%

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

   if -3.7999999999999999e-81 < t < 4.4000000000000001e-42

   1. Initial program 88.7%

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

      1. associate-*l/ 88.7%

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

      2. *-commutative 88.7%

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

      3. distribute-rgt-out-- 91.4%

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

      4. associate-/r* 96.3%

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

   3. Simplified 96.3%

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

      1. *-commutative 96.3%

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

      2. associate-*l/ 96.3%

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

      3. associate-*r/ 96.2%

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

      4. clear-num 95.4%

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

      5. frac-times 95.4%

         \[\leadsto \color{blue}{\frac{1 \cdot 2}{\frac{z}{x} \cdot \left(y - t\right)}} \]

      6. metadata-eval 95.4%

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

   5. Applied egg-rr 95.4%

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

   6. Taylor expanded in y around inf 78.2%

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

      1. associate-/l* 85.7%

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

   8. Simplified 85.7%

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

   if 4.4000000000000001e-42 < t

   1. Initial program 91.4%

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

      1. associate-*r/ 91.4%

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

      2. distribute-rgt-out-- 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 77.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 12: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-80}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t \cdot -0.5}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.1e-80)
   (/ -2.0 (* t (/ z x)))
   (if (<= t 4.4e-42) (/ 2.0 (/ y (/ x z))) (/ (/ x (* t -0.5)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.1e-80) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 4.4e-42) {
		tmp = 2.0 / (y / (x / z));
	} else {
		tmp = (x / (t * -0.5)) / 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 (t <= (-3.1d-80)) then
        tmp = (-2.0d0) / (t * (z / x))
    else if (t <= 4.4d-42) then
        tmp = 2.0d0 / (y / (x / z))
    else
        tmp = (x / (t * (-0.5d0))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.1e-80) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 4.4e-42) {
		tmp = 2.0 / (y / (x / z));
	} else {
		tmp = (x / (t * -0.5)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.1e-80:
		tmp = -2.0 / (t * (z / x))
	elif t <= 4.4e-42:
		tmp = 2.0 / (y / (x / z))
	else:
		tmp = (x / (t * -0.5)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.1e-80)
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	elseif (t <= 4.4e-42)
		tmp = Float64(2.0 / Float64(y / Float64(x / z)));
	else
		tmp = Float64(Float64(x / Float64(t * -0.5)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.1e-80)
		tmp = -2.0 / (t * (z / x));
	elseif (t <= 4.4e-42)
		tmp = 2.0 / (y / (x / z));
	else
		tmp = (x / (t * -0.5)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.1e-80], N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-42], N[(2.0 / N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(t * -0.5), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.10000000000000016e-80

   1. Initial program 92.4%

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

      1. associate-*r/ 92.3%

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

      2. distribute-rgt-out-- 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. frac-times 79.3%

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

      4. clear-num 80.5%

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

      5. frac-times 82.7%

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

      6. metadata-eval 82.7%

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

   6. Applied egg-rr 82.7%

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

   if -3.10000000000000016e-80 < t < 4.4000000000000001e-42

   1. Initial program 88.7%

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

      1. associate-*l/ 88.7%

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

      2. *-commutative 88.7%

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

      3. distribute-rgt-out-- 91.4%

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

      4. associate-/r* 96.3%

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

   3. Simplified 96.3%

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

      1. *-commutative 96.3%

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

      2. associate-*l/ 96.3%

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

      3. associate-*r/ 96.2%

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

      4. clear-num 95.4%

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

      5. frac-times 95.4%

         \[\leadsto \color{blue}{\frac{1 \cdot 2}{\frac{z}{x} \cdot \left(y - t\right)}} \]

      6. metadata-eval 95.4%

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

   5. Applied egg-rr 95.4%

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

   6. Taylor expanded in y around inf 78.2%

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

      1. associate-/l* 85.7%

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

   8. Simplified 85.7%

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

   if 4.4000000000000001e-42 < t

   1. Initial program 91.4%

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

      1. associate-*r/ 91.4%

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

      2. distribute-rgt-out-- 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 77.3%

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

      1. associate-/r* 77.2%

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

      2. associate-*r/ 78.9%

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

      3. clear-num 78.9%

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

      4. un-div-inv 79.0%

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

      5. div-inv 79.0%

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

      6. metadata-eval 79.0%

         \[\leadsto \frac{\frac{x}{t \cdot \color{blue}{-0.5}}}{z} \]

   6. Applied egg-rr 79.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t \cdot -0.5}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-80}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t \cdot -0.5}}{z}\\ \end{array} \]

Alternative 13: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-80}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{z \cdot 0.5}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t \cdot -0.5}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.36e-80)
   (/ -2.0 (* t (/ z x)))
   (if (<= t 4.4e-42) (/ (/ x (* z 0.5)) y) (/ (/ x (* t -0.5)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.36e-80) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 4.4e-42) {
		tmp = (x / (z * 0.5)) / y;
	} else {
		tmp = (x / (t * -0.5)) / 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 (t <= (-1.36d-80)) then
        tmp = (-2.0d0) / (t * (z / x))
    else if (t <= 4.4d-42) then
        tmp = (x / (z * 0.5d0)) / y
    else
        tmp = (x / (t * (-0.5d0))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.36e-80) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 4.4e-42) {
		tmp = (x / (z * 0.5)) / y;
	} else {
		tmp = (x / (t * -0.5)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.36e-80:
		tmp = -2.0 / (t * (z / x))
	elif t <= 4.4e-42:
		tmp = (x / (z * 0.5)) / y
	else:
		tmp = (x / (t * -0.5)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.36e-80)
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	elseif (t <= 4.4e-42)
		tmp = Float64(Float64(x / Float64(z * 0.5)) / y);
	else
		tmp = Float64(Float64(x / Float64(t * -0.5)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.36e-80)
		tmp = -2.0 / (t * (z / x));
	elseif (t <= 4.4e-42)
		tmp = (x / (z * 0.5)) / y;
	else
		tmp = (x / (t * -0.5)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.36e-80], N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-42], N[(N[(x / N[(z * 0.5), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(t * -0.5), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3599999999999999e-80

   1. Initial program 92.4%

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

      1. associate-*r/ 92.3%

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

      2. distribute-rgt-out-- 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. frac-times 79.3%

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

      4. clear-num 80.5%

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

      5. frac-times 82.7%

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

      6. metadata-eval 82.7%

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

   6. Applied egg-rr 82.7%

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

   if -1.3599999999999999e-80 < t < 4.4000000000000001e-42

   1. Initial program 88.7%

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

      1. associate-*r/ 88.4%

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

      2. distribute-rgt-out-- 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around inf 77.9%

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

      1. associate-*r/ 78.2%

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

      2. frac-times 79.7%

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

      3. associate-*l/ 85.7%

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

      4. clear-num 85.7%

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

      5. un-div-inv 85.8%

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

      6. div-inv 85.8%

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

      7. metadata-eval 85.8%

         \[\leadsto \frac{\frac{x}{z \cdot \color{blue}{0.5}}}{y} \]

   6. Applied egg-rr 85.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{z \cdot 0.5}}{y}} \]

   if 4.4000000000000001e-42 < t

   1. Initial program 91.4%

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

      1. associate-*r/ 91.4%

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

      2. distribute-rgt-out-- 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 77.3%

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

      1. associate-/r* 77.2%

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

      2. associate-*r/ 78.9%

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

      3. clear-num 78.9%

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

      4. un-div-inv 79.0%

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

      5. div-inv 79.0%

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

      6. metadata-eval 79.0%

         \[\leadsto \frac{\frac{x}{t \cdot \color{blue}{-0.5}}}{z} \]

   6. Applied egg-rr 79.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t \cdot -0.5}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-80}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{z \cdot 0.5}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t \cdot -0.5}}{z}\\ \end{array} \]

Alternative 14: 91.9% 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 90.5%

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

   1. associate-*l/ 90.5%

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

   2. *-commutative 90.5%

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

   3. distribute-rgt-out-- 92.5%

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

   4. associate-/r* 94.2%

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

3. Simplified 94.2%

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

4. Final simplification 94.2%

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

Alternative 15: 52.7% accurate, 1.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * (-2.0 / (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 = x * ((-2.0d0) / (z * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

   1. associate-*r/ 90.4%

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

   2. distribute-rgt-out-- 92.4%

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

3. Simplified 92.4%

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

4. Taylor expanded in y around 0 55.0%

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

5. Final simplification 55.0%

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

Developer target: 97.2% 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 2023185 
(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))))