Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.6% → 98.1%

Time: 9.5s

Alternatives: 11

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.6% 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: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{2}{z}}{\frac{y - t}{x}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+197}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (<= t_1 (- INFINITY))
     (/ (/ 2.0 z) (/ (- y t) x))
     (if (<= t_1 5e+197)
       (/ (* 2.0 x) (* 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 <= -((double) INFINITY)) {
		tmp = (2.0 / z) / ((y - t) / x);
	} else if (t_1 <= 5e+197) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = (2.0 / z) / ((y - t) / x);
	} else if (t_1 <= 5e+197) {
		tmp = (2.0 * x) / (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 <= -math.inf:
		tmp = (2.0 / z) / ((y - t) / x)
	elif t_1 <= 5e+197:
		tmp = (2.0 * x) / (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 <= Float64(-Inf))
		tmp = Float64(Float64(2.0 / z) / Float64(Float64(y - t) / x));
	elseif (t_1 <= 5e+197)
		tmp = Float64(Float64(2.0 * x) / 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 <= -Inf)
		tmp = (2.0 / z) / ((y - t) / x);
	elseif (t_1 <= 5e+197)
		tmp = (2.0 * x) / (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, (-Infinity)], N[(N[(2.0 / z), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+197], N[(N[(2.0 * x), $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)) < -inf.0

   1. Initial program 44.5%

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

      1. *-commutative 44.5%

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

      2. associate-*r/ 44.5%

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

      3. distribute-rgt-out-- 44.5%

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

      4. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r* 44.5%

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

      2. associate-*r/ 44.5%

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

      3. frac-times 99.7%

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

      4. clear-num 99.6%

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

      5. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -inf.0 < (-.f64 (*.f64 y z) (*.f64 t z)) < 5.00000000000000009e197

   1. Initial program 97.6%

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

      1. distribute-rgt-out-- 97.6%

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

   3. Simplified 97.6%

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

   if 5.00000000000000009e197 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-*r/ 66.5%

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

      3. distribute-rgt-out-- 76.0%

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

      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 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{2}{z}}{\frac{y - t}{x}}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq 5 \cdot 10^{+197}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 95.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-201}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-38}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e-201)
   (* 2.0 (/ (/ x z) (- y t)))
   (if (<= z 5e-38) (/ (* 2.0 x) (* z (- y t))) (* (/ 2.0 z) (/ x (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-201) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else if (z <= 5e-38) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = (2.0 / z) * (x / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.2d-201)) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else if (z <= 5d-38) then
        tmp = (2.0d0 * x) / (z * (y - t))
    else
        tmp = (2.0d0 / z) * (x / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-201) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else if (z <= 5e-38) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = (2.0 / z) * (x / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e-201:
		tmp = 2.0 * ((x / z) / (y - t))
	elif z <= 5e-38:
		tmp = (2.0 * x) / (z * (y - t))
	else:
		tmp = (2.0 / z) * (x / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e-201)
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 5e-38)
		tmp = Float64(Float64(2.0 * x) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e-201)
		tmp = 2.0 * ((x / z) / (y - t));
	elseif (z <= 5e-38)
		tmp = (2.0 * x) / (z * (y - t));
	else
		tmp = (2.0 / z) * (x / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e-201], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-38], N[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000024e-201

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*r/ 81.8%

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

      3. distribute-rgt-out-- 85.4%

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

      4. associate-/r* 96.4%

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

   3. Simplified 96.4%

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

   if -4.20000000000000024e-201 < z < 5.00000000000000033e-38

   1. Initial program 97.0%

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

      1. distribute-rgt-out-- 97.0%

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

   3. Simplified 97.0%

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

   if 5.00000000000000033e-38 < z

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

      2. distribute-rgt-out-- 84.5%

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

      3. times-frac 98.4%

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

   3. Simplified 98.4%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-201}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-38}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \]

Alternative 3: 94.2% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* 2.0 x) -2e-81)
   (* (/ 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 ((2.0 * x) <= -2e-81) {
		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 ((2.0d0 * x) <= (-2d-81)) 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 ((2.0 * x) <= -2e-81) {
		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 (2.0 * x) <= -2e-81:
		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(2.0 * x) <= -2e-81)
		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 ((2.0 * x) <= -2e-81)
		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[LessEqual[N[(2.0 * x), $MachinePrecision], -2e-81], 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) < -1.9999999999999999e-81

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. distribute-rgt-out-- 81.6%

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

      3. times-frac 98.5%

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

   3. Simplified 98.5%

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

   if -1.9999999999999999e-81 < (*.f64 x 2)

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*r/ 89.4%

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

      3. distribute-rgt-out-- 92.6%

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

      4. associate-/r* 93.7%

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

   3. Simplified 93.7%

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

4. Final simplification 95.5%

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

Alternative 4: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{x}{z}}{t} \cdot -2\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-37}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} \cdot x}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.6e-31)
   (* (/ (/ x z) t) -2.0)
   (if (<= t 3.25e-37) (* (/ 2.0 z) (/ x y)) (/ (* (/ 2.0 z) x) (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.6e-31) {
		tmp = ((x / z) / t) * -2.0;
	} else if (t <= 3.25e-37) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = ((2.0 / z) * x) / -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 <= (-4.6d-31)) then
        tmp = ((x / z) / t) * (-2.0d0)
    else if (t <= 3.25d-37) then
        tmp = (2.0d0 / z) * (x / y)
    else
        tmp = ((2.0d0 / z) * x) / -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.6e-31) {
		tmp = ((x / z) / t) * -2.0;
	} else if (t <= 3.25e-37) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = ((2.0 / z) * x) / -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.6e-31:
		tmp = ((x / z) / t) * -2.0
	elif t <= 3.25e-37:
		tmp = (2.0 / z) * (x / y)
	else:
		tmp = ((2.0 / z) * x) / -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.6e-31)
		tmp = Float64(Float64(Float64(x / z) / t) * -2.0);
	elseif (t <= 3.25e-37)
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	else
		tmp = Float64(Float64(Float64(2.0 / z) * x) / Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.6e-31)
		tmp = ((x / z) / t) * -2.0;
	elseif (t <= 3.25e-37)
		tmp = (2.0 / z) * (x / y);
	else
		tmp = ((2.0 / z) * x) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.6e-31], N[(N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t, 3.25e-37], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 / z), $MachinePrecision] * x), $MachinePrecision] / (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5999999999999997e-31

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-*r/ 81.1%

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

      3. distribute-rgt-out-- 85.3%

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

      4. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   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* 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in x around 0 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/r* 84.2%

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

   9. Simplified 84.2%

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

   if -4.5999999999999997e-31 < t < 3.2500000000000001e-37

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*r/ 92.6%

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

      3. distribute-rgt-out-- 92.6%

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

      4. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. associate-*r/ 74.3%

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

      2. *-commutative 74.3%

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

      3. times-frac 77.8%

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

   6. Simplified 77.8%

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

   if 3.2500000000000001e-37 < t

   1. Initial program 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-*r/ 83.0%

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

      3. distribute-rgt-out-- 85.6%

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

      4. associate-/r* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around 0 74.6%

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

      1. associate-*r/ 74.6%

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

      2. metadata-eval 74.6%

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

      3. distribute-lft-neg-in 74.6%

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

      4. distribute-rgt-neg-in 74.6%

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

      5. *-commutative 74.6%

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

      6. frac-times 80.0%

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

      7. associate-*r/ 84.7%

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

      8. frac-2neg 84.7%

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

      9. add-sqr-sqrt 45.8%

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

      10. sqrt-unprod 53.4%

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

      11. sqr-neg 53.4%

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

      12. sqrt-unprod 17.0%

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

      13. add-sqr-sqrt 27.5%

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

      14. distribute-rgt-neg-out 27.5%

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

      15. add-sqr-sqrt 10.5%

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

      16. sqrt-unprod 42.0%

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

      17. sqr-neg 42.0%

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

      18. sqrt-unprod 38.6%

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

      19. add-sqr-sqrt 84.7%

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

   6. Applied egg-rr 84.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{x}{z}}{t} \cdot -2\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-37}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} \cdot x}{-t}\\ \end{array} \]

Alternative 5: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-32} \lor \neg \left(t \leq 3.05 \cdot 10^{-37}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8e-32) (not (<= t 3.05e-37)))
   (* -2.0 (/ x (* z t)))
   (* 2.0 (/ (/ x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e-32) || !(t <= 3.05e-37)) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = 2.0 * ((x / z) / 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 ((t <= (-8d-32)) .or. (.not. (t <= 3.05d-37))) then
        tmp = (-2.0d0) * (x / (z * t))
    else
        tmp = 2.0d0 * ((x / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e-32) || !(t <= 3.05e-37)) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = 2.0 * ((x / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8e-32) or not (t <= 3.05e-37):
		tmp = -2.0 * (x / (z * t))
	else:
		tmp = 2.0 * ((x / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8e-32) || !(t <= 3.05e-37))
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8e-32) || ~((t <= 3.05e-37)))
		tmp = -2.0 * (x / (z * t));
	else
		tmp = 2.0 * ((x / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8e-32], N[Not[LessEqual[t, 3.05e-37]], $MachinePrecision]], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.00000000000000045e-32 or 3.0500000000000002e-37 < t

   1. Initial program 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*r/ 82.1%

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

      3. distribute-rgt-out-- 85.4%

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

      4. associate-/r* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 75.1%

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

   if -8.00000000000000045e-32 < t < 3.0500000000000002e-37

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*r/ 92.6%

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

      3. distribute-rgt-out-- 92.6%

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

      4. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

      1. associate-*r/ 92.7%

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

      2. *-commutative 92.7%

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

      3. associate-*r/ 92.6%

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

      4. clear-num 92.5%

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

      5. frac-times 91.9%

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

      6. metadata-eval 91.9%

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

   5. Applied egg-rr 91.9%

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

   6. Taylor expanded in y around inf 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/r* 76.3%

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

   8. Simplified 76.3%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-32} \lor \neg \left(t \leq 3.05 \cdot 10^{-37}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 6: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-43} \lor \neg \left(t \leq 7.4 \cdot 10^{-37}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.9e-43) (not (<= t 7.4e-37)))
   (* -2.0 (/ x (* z t)))
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e-43) || !(t <= 7.4e-37)) {
		tmp = -2.0 * (x / (z * t));
	} 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 ((t <= (-2.9d-43)) .or. (.not. (t <= 7.4d-37))) then
        tmp = (-2.0d0) * (x / (z * t))
    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 ((t <= -2.9e-43) || !(t <= 7.4e-37)) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.9e-43) or not (t <= 7.4e-37):
		tmp = -2.0 * (x / (z * t))
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.9e-43) || !(t <= 7.4e-37))
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	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 ((t <= -2.9e-43) || ~((t <= 7.4e-37)))
		tmp = -2.0 * (x / (z * t));
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.9e-43], N[Not[LessEqual[t, 7.4e-37]], $MachinePrecision]], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9000000000000001e-43 or 7.4e-37 < t

   1. Initial program 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*r/ 82.1%

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

      3. distribute-rgt-out-- 85.4%

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

      4. associate-/r* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 75.1%

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

   if -2.9000000000000001e-43 < t < 7.4e-37

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*r/ 92.6%

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

      3. distribute-rgt-out-- 92.6%

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

      4. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. associate-*r/ 74.3%

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

      2. *-commutative 74.3%

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

      3. times-frac 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-43} \lor \neg \left(t \leq 7.4 \cdot 10^{-37}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-30} \lor \neg \left(t \leq 6 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.2e-30) (not (<= t 6e-37)))
   (* x (/ (/ -2.0 z) t))
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-30) || !(t <= 6e-37)) {
		tmp = x * ((-2.0 / z) / t);
	} 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 ((t <= (-6.2d-30)) .or. (.not. (t <= 6d-37))) then
        tmp = x * (((-2.0d0) / z) / t)
    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 ((t <= -6.2e-30) || !(t <= 6e-37)) {
		tmp = x * ((-2.0 / z) / t);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.2e-30) or not (t <= 6e-37):
		tmp = x * ((-2.0 / z) / t)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.2e-30) || !(t <= 6e-37))
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	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 ((t <= -6.2e-30) || ~((t <= 6e-37)))
		tmp = x * ((-2.0 / z) / t);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.2e-30], N[Not[LessEqual[t, 6e-37]], $MachinePrecision]], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.19999999999999982e-30 or 6e-37 < t

   1. Initial program 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*r/ 82.1%

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

      3. distribute-rgt-out-- 85.4%

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

      4. associate-/r* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/r* 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in x around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/r* 84.4%

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

   9. Simplified 84.4%

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

       1. *-commutative 84.4%

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

       2. clear-num 83.1%

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

       3. un-div-inv 83.1%

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

       4. div-inv 83.1%

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

       5. clear-num 83.3%

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

   11. Applied egg-rr 83.3%

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

       1. associate-*r/ 74.9%

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

       2. associate-*l/ 79.0%

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

       3. associate-/l/ 80.3%

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

       4. associate-/r/ 76.6%

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

   13. Applied egg-rr 76.6%

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

   if -6.19999999999999982e-30 < t < 6e-37

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*r/ 92.6%

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

      3. distribute-rgt-out-- 92.6%

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

      4. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. associate-*r/ 74.3%

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

      2. *-commutative 74.3%

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

      3. times-frac 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-30} \lor \neg \left(t \leq 6 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 8: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-44} \lor \neg \left(t \leq 3.8 \cdot 10^{-37}\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8e-44) (not (<= t 3.8e-37)))
   (* -2.0 (/ (/ x t) z))
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e-44) || !(t <= 3.8e-37)) {
		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 ((t <= (-8d-44)) .or. (.not. (t <= 3.8d-37))) 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 ((t <= -8e-44) || !(t <= 3.8e-37)) {
		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 (t <= -8e-44) or not (t <= 3.8e-37):
		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 ((t <= -8e-44) || !(t <= 3.8e-37))
		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 ((t <= -8e-44) || ~((t <= 3.8e-37)))
		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[Or[LessEqual[t, -8e-44], N[Not[LessEqual[t, 3.8e-37]], $MachinePrecision]], 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 2 regimes

2. if t < -7.99999999999999962e-44 or 3.8000000000000004e-37 < t

   1. Initial program 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*r/ 82.1%

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

      3. distribute-rgt-out-- 85.4%

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

      4. associate-/r* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/r* 81.9%

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

   6. Simplified 81.9%

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

   if -7.99999999999999962e-44 < t < 3.8000000000000004e-37

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*r/ 92.6%

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

      3. distribute-rgt-out-- 92.6%

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

      4. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. associate-*r/ 74.3%

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

      2. *-commutative 74.3%

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

      3. times-frac 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-44} \lor \neg \left(t \leq 3.8 \cdot 10^{-37}\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 9: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-31} \lor \neg \left(t \leq 6.2 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{t} \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.6e-31) (not (<= t 6.2e-37)))
   (* (/ (/ x z) t) -2.0)
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e-31) || !(t <= 6.2e-37)) {
		tmp = ((x / z) / t) * -2.0;
	} 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 ((t <= (-6.6d-31)) .or. (.not. (t <= 6.2d-37))) then
        tmp = ((x / z) / t) * (-2.0d0)
    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 ((t <= -6.6e-31) || !(t <= 6.2e-37)) {
		tmp = ((x / z) / t) * -2.0;
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.6e-31) or not (t <= 6.2e-37):
		tmp = ((x / z) / t) * -2.0
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.6e-31) || !(t <= 6.2e-37))
		tmp = Float64(Float64(Float64(x / z) / t) * -2.0);
	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 ((t <= -6.6e-31) || ~((t <= 6.2e-37)))
		tmp = ((x / z) / t) * -2.0;
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.6e-31], N[Not[LessEqual[t, 6.2e-37]], $MachinePrecision]], N[(N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision] * -2.0), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5999999999999998e-31 or 6.19999999999999987e-37 < t

   1. Initial program 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*r/ 82.1%

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

      3. distribute-rgt-out-- 85.4%

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

      4. associate-/r* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/r* 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in x around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/r* 84.4%

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

   9. Simplified 84.4%

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

   if -6.5999999999999998e-31 < t < 6.19999999999999987e-37

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*r/ 92.6%

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

      3. distribute-rgt-out-- 92.6%

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

      4. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. associate-*r/ 74.3%

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

      2. *-commutative 74.3%

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

      3. times-frac 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-31} \lor \neg \left(t \leq 6.2 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{t} \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 10: 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 86.4%

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

   1. *-commutative 86.4%

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

   2. associate-*r/ 86.4%

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

   3. distribute-rgt-out-- 88.4%

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

   4. associate-/r* 93.4%

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

3. Simplified 93.4%

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

4. Final simplification 93.4%

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

Alternative 11: 52.8% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.4%

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

   1. *-commutative 86.4%

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

   2. associate-*r/ 86.4%

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

   3. distribute-rgt-out-- 88.4%

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

   4. associate-/r* 93.4%

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

3. Simplified 93.4%

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

4. Taylor expanded in y around 0 57.3%

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

5. Final simplification 57.3%

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

Developer target: 97.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(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))))