Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.0% → 97.0%

Time: 7.5s

Alternatives: 9

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+169}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t - y}}{z}\\ \mathbf{elif}\;t_1 \leq 10^{+74}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (<= t_1 -1e+169)
     (/ (/ (* x -2.0) (- t y)) z)
     (if (<= t_1 1e+74)
       (/ (* x 2.0) (* z (- y t)))
       (* 2.0 (/ (/ x z) (- y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -1e+169) {
		tmp = ((x * -2.0) / (t - y)) / z;
	} else if (t_1 <= 1e+74) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - (z * t)
    if (t_1 <= (-1d+169)) then
        tmp = ((x * (-2.0d0)) / (t - y)) / z
    else if (t_1 <= 1d+74) then
        tmp = (x * 2.0d0) / (z * (y - t))
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -1e+169) {
		tmp = ((x * -2.0) / (t - y)) / z;
	} else if (t_1 <= 1e+74) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - (z * t)
	tmp = 0
	if t_1 <= -1e+169:
		tmp = ((x * -2.0) / (t - y)) / z
	elif t_1 <= 1e+74:
		tmp = (x * 2.0) / (z * (y - t))
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -1e+169)
		tmp = Float64(Float64(Float64(x * -2.0) / Float64(t - y)) / z);
	elseif (t_1 <= 1e+74)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - (z * t);
	tmp = 0.0;
	if (t_1 <= -1e+169)
		tmp = ((x * -2.0) / (t - y)) / z;
	elseif (t_1 <= 1e+74)
		tmp = (x * 2.0) / (z * (y - t));
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+169], N[(N[(N[(x * -2.0), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+74], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -9.99999999999999934e168

   1. Initial program 82.4%

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

      1. associate-*r/ 82.3%

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

      2. distribute-rgt-out-- 82.3%

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

      3. associate-/l/ 85.5%

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

      4. sub-neg 85.5%

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

      5. +-commutative 85.5%

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

      6. neg-sub0 85.5%

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

      7. associate-+l- 85.5%

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

      8. sub0-neg 85.5%

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

      9. neg-mul-1 85.5%

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

      10. associate-/r* 85.5%

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

      11. metadata-eval 85.5%

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

   3. Simplified 85.5%

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

      1. associate-*r/ 99.7%

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

      2. associate-*r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -9.99999999999999934e168 < (-.f64 (*.f64 y z) (*.f64 t z)) < 9.99999999999999952e73

   1. Initial program 97.6%

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

      1. distribute-rgt-out-- 98.3%

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

   3. Simplified 98.3%

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

   if 9.99999999999999952e73 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 82.2%

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

      1. associate-*l/ 82.2%

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

      2. *-commutative 82.2%

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

      3. distribute-rgt-out-- 88.9%

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

      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 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -1 \cdot 10^{+169}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t - y}}{z}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq 10^{+74}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 96.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+116} \lor \neg \left(z \leq 2.2 \cdot 10^{-59}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.1e+116) (not (<= z 2.2e-59)))
   (* 2.0 (/ (/ x z) (- y t)))
   (* x (/ (/ -2.0 (- t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e+116) || !(z <= 2.2e-59)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * ((-2.0 / (t - 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 ((z <= (-5.1d+116)) .or. (.not. (z <= 2.2d-59))) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = x * (((-2.0d0) / (t - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e+116) || !(z <= 2.2e-59)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * ((-2.0 / (t - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.1e+116) or not (z <= 2.2e-59):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = x * ((-2.0 / (t - y)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.1e+116) || !(z <= 2.2e-59))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / Float64(t - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.1e+116) || ~((z <= 2.2e-59)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = x * ((-2.0 / (t - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.1e+116], N[Not[LessEqual[z, 2.2e-59]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.09999999999999999e116 or 2.1999999999999999e-59 < z

   1. Initial program 83.5%

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

      1. associate-*l/ 83.5%

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

      2. *-commutative 83.5%

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

      3. distribute-rgt-out-- 87.7%

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

      4. associate-/r* 98.1%

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

   3. Simplified 98.1%

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

   if -5.09999999999999999e116 < z < 2.1999999999999999e-59

   1. Initial program 96.2%

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

      1. associate-*r/ 96.1%

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

      2. distribute-rgt-out-- 96.8%

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

      3. associate-/l/ 97.4%

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

      4. sub-neg 97.4%

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

      5. +-commutative 97.4%

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

      6. neg-sub0 97.4%

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

      7. associate-+l- 97.4%

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

      8. sub0-neg 97.4%

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

      9. neg-mul-1 97.4%

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

      10. associate-/r* 97.4%

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

      11. metadata-eval 97.4%

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

   3. Simplified 97.4%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+116} \lor \neg \left(z \leq 2.2 \cdot 10^{-59}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \end{array} \]

Alternative 3: 96.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.4e+27)
   (/ (* x (/ 2.0 (- y t))) z)
   (if (<= z 2.5e-59)
     (/ (* 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 (z <= -3.4e+27) {
		tmp = (x * (2.0 / (y - t))) / z;
	} else if (z <= 2.5e-59) {
		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 (z <= (-3.4d+27)) then
        tmp = (x * (2.0d0 / (y - t))) / z
    else if (z <= 2.5d-59) 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 (z <= -3.4e+27) {
		tmp = (x * (2.0 / (y - t))) / z;
	} else if (z <= 2.5e-59) {
		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 z <= -3.4e+27:
		tmp = (x * (2.0 / (y - t))) / z
	elif z <= 2.5e-59:
		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 (z <= -3.4e+27)
		tmp = Float64(Float64(x * Float64(2.0 / Float64(y - t))) / z);
	elseif (z <= 2.5e-59)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.4e+27)
		tmp = (x * (2.0 / (y - t))) / z;
	elseif (z <= 2.5e-59)
		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[z, -3.4e+27], N[(N[(x * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.5e-59], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4e27

   1. Initial program 82.7%

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

      1. associate-*l/ 82.7%

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

      2. *-commutative 82.7%

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

      3. distribute-rgt-out-- 88.3%

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

      4. associate-/r* 94.7%

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

   3. Simplified 94.7%

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

      1. *-commutative 94.7%

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

      2. associate-*l/ 94.7%

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

      3. associate-*r/ 94.7%

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

      4. associate-*l/ 98.5%

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

   5. Applied egg-rr 98.5%

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

   if -3.4e27 < z < 2.5000000000000001e-59

   1. Initial program 97.2%

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

      1. distribute-rgt-out-- 98.1%

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

   3. Simplified 98.1%

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

   if 2.5000000000000001e-59 < z

   1. Initial program 86.8%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

      3. distribute-rgt-out-- 88.4%

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

      4. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 4: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-41} \lor \neg \left(t \leq 6 \cdot 10^{+27}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.75e-41) (not (<= t 6e+27)))
   (* x (/ (/ -2.0 t) z))
   (* x (/ (/ 2.0 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.75e-41) || !(t <= 6e+27)) {
		tmp = x * ((-2.0 / t) / z);
	} 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 <= (-1.75d-41)) .or. (.not. (t <= 6d+27))) then
        tmp = x * (((-2.0d0) / t) / z)
    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 <= -1.75e-41) || !(t <= 6e+27)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.75e-41) or not (t <= 6e+27):
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = x * ((2.0 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.75e-41) || !(t <= 6e+27))
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.75e-41) || ~((t <= 6e+27)))
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = x * ((2.0 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.75e-41], N[Not[LessEqual[t, 6e+27]], $MachinePrecision]], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75e-41 or 5.99999999999999953e27 < t

   1. Initial program 85.7%

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

      1. associate-*r/ 85.6%

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

      2. distribute-rgt-out-- 89.6%

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

      3. associate-/l/ 90.6%

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

      4. sub-neg 90.6%

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

      5. +-commutative 90.6%

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

      6. neg-sub0 90.6%

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

      7. associate-+l- 90.6%

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

      8. sub0-neg 90.6%

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

      9. neg-mul-1 90.6%

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

      10. associate-/r* 90.6%

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

      11. metadata-eval 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in t around inf 75.7%

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

      1. associate-/r* 76.7%

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

   6. Simplified 76.7%

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

   if -1.75e-41 < t < 5.99999999999999953e27

   1. Initial program 94.6%

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

      1. associate-*r/ 94.5%

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

      2. distribute-rgt-out-- 95.3%

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

      3. associate-/l/ 95.5%

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

      4. sub-neg 95.5%

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

      5. +-commutative 95.5%

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

      6. neg-sub0 95.5%

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

      7. associate-+l- 95.5%

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

      8. sub0-neg 95.5%

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

      9. neg-mul-1 95.5%

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

      10. associate-/r* 95.5%

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

      11. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 81.1%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-41} \lor \neg \left(t \leq 6 \cdot 10^{+27}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \]

Alternative 5: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+82} \lor \neg \left(t \leq 2.2 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.5e+82) (not (<= t 2.2e-22)))
   (* x (/ (/ -2.0 t) z))
   (* (/ x z) (/ 2.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.5e+82) || !(t <= 2.2e-22)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.5d+82)) .or. (.not. (t <= 2.2d-22))) then
        tmp = x * (((-2.0d0) / t) / z)
    else
        tmp = (x / z) * (2.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.5e+82) || !(t <= 2.2e-22)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.5e+82) or not (t <= 2.2e-22):
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.5e+82) || !(t <= 2.2e-22))
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	else
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.5e+82) || ~((t <= 2.2e-22)))
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.5e+82], N[Not[LessEqual[t, 2.2e-22]], $MachinePrecision]], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4999999999999997e82 or 2.2000000000000001e-22 < t

   1. Initial program 85.2%

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

      1. associate-*r/ 85.2%

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

      2. distribute-rgt-out-- 89.5%

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

      3. associate-/l/ 90.7%

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

      4. sub-neg 90.7%

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

      5. +-commutative 90.7%

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

      6. neg-sub0 90.7%

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

      7. associate-+l- 90.7%

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

      8. sub0-neg 90.7%

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

      9. neg-mul-1 90.7%

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

      10. associate-/r* 90.7%

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

      11. metadata-eval 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in t around inf 77.5%

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

      1. associate-/r* 78.6%

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

   6. Simplified 78.6%

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

   if -4.4999999999999997e82 < t < 2.2000000000000001e-22

   1. Initial program 94.3%

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

      1. associate-*r/ 94.2%

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

      2. distribute-rgt-out-- 94.9%

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

      3. associate-/l/ 95.1%

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

      4. sub-neg 95.1%

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

      5. +-commutative 95.1%

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

      6. neg-sub0 95.1%

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

      7. associate-+l- 95.1%

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

      8. sub0-neg 95.1%

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

      9. neg-mul-1 95.1%

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

      10. associate-/r* 95.1%

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

      11. metadata-eval 95.1%

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

   3. Simplified 95.1%

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

      1. associate-*r/ 93.9%

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

      2. associate-*r/ 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in t around 0 76.5%

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

      1. associate-*r/ 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-/l/ 77.5%

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

      4. times-frac 81.5%

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

   8. Applied egg-rr 81.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+82} \lor \neg \left(t \leq 2.2 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 6: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+82}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.5e+82)
   (* -2.0 (/ (/ x z) t))
   (if (<= t 3.7e-22) (* (/ x z) (/ 2.0 y)) (* x (/ (/ -2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e+82) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= 3.7e-22) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = x * ((-2.0 / t) / 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 <= (-4.5d+82)) then
        tmp = (-2.0d0) * ((x / z) / t)
    else if (t <= 3.7d-22) then
        tmp = (x / z) * (2.0d0 / y)
    else
        tmp = x * (((-2.0d0) / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e+82) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= 3.7e-22) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.5e+82:
		tmp = -2.0 * ((x / z) / t)
	elif t <= 3.7e-22:
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = x * ((-2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.5e+82)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	elseif (t <= 3.7e-22)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.5e+82)
		tmp = -2.0 * ((x / z) / t);
	elseif (t <= 3.7e-22)
		tmp = (x / z) * (2.0 / y);
	else
		tmp = x * ((-2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.5e+82], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-22], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4999999999999997e82

   1. Initial program 81.3%

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

      1. associate-*l/ 81.3%

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

      2. *-commutative 81.3%

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

      3. distribute-rgt-out-- 87.3%

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

      4. associate-/r* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. *-commutative 74.8%

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

      3. associate-/r* 78.5%

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

   6. Simplified 78.5%

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

   if -4.4999999999999997e82 < t < 3.7e-22

   1. Initial program 94.3%

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

      1. associate-*r/ 94.2%

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

      2. distribute-rgt-out-- 94.9%

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

      3. associate-/l/ 95.1%

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

      4. sub-neg 95.1%

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

      5. +-commutative 95.1%

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

      6. neg-sub0 95.1%

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

      7. associate-+l- 95.1%

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

      8. sub0-neg 95.1%

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

      9. neg-mul-1 95.1%

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

      10. associate-/r* 95.1%

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

      11. metadata-eval 95.1%

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

   3. Simplified 95.1%

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

      1. associate-*r/ 93.9%

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

      2. associate-*r/ 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in t around 0 76.5%

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

      1. associate-*r/ 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-/l/ 77.5%

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

      4. times-frac 81.5%

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

   8. Applied egg-rr 81.5%

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

   if 3.7e-22 < t

   1. Initial program 88.3%

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

      1. associate-*r/ 88.2%

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

      2. distribute-rgt-out-- 91.3%

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

      3. associate-/l/ 92.1%

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

      4. sub-neg 92.1%

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

      5. +-commutative 92.1%

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

      6. neg-sub0 92.1%

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

      7. associate-+l- 92.1%

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

      8. sub0-neg 92.1%

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

      9. neg-mul-1 92.1%

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

      10. associate-/r* 92.1%

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

      11. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around inf 79.5%

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

      1. associate-/r* 80.3%

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

   6. Simplified 80.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+82}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \]

Alternative 7: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+84}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.3e+84)
   (* -2.0 (/ (/ x z) t))
   (if (<= t 1.25e-22) (* (/ x z) (/ 2.0 y)) (/ (* -2.0 (/ x t)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.3e+84) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= 1.25e-22) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = (-2.0 * (x / t)) / 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 <= (-3.3d+84)) then
        tmp = (-2.0d0) * ((x / z) / t)
    else if (t <= 1.25d-22) then
        tmp = (x / z) * (2.0d0 / y)
    else
        tmp = ((-2.0d0) * (x / t)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.3e+84) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= 1.25e-22) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = (-2.0 * (x / t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.3e+84:
		tmp = -2.0 * ((x / z) / t)
	elif t <= 1.25e-22:
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = (-2.0 * (x / t)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.3e+84)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	elseif (t <= 1.25e-22)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	else
		tmp = Float64(Float64(-2.0 * Float64(x / t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.3e+84)
		tmp = -2.0 * ((x / z) / t);
	elseif (t <= 1.25e-22)
		tmp = (x / z) * (2.0 / y);
	else
		tmp = (-2.0 * (x / t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.3e+84], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-22], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.30000000000000017e84

   1. Initial program 81.3%

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

      1. associate-*l/ 81.3%

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

      2. *-commutative 81.3%

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

      3. distribute-rgt-out-- 87.3%

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

      4. associate-/r* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. *-commutative 74.8%

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

      3. associate-/r* 78.5%

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

   6. Simplified 78.5%

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

   if -3.30000000000000017e84 < t < 1.24999999999999988e-22

   1. Initial program 94.3%

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

      1. associate-*r/ 94.2%

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

      2. distribute-rgt-out-- 94.9%

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

      3. associate-/l/ 95.1%

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

      4. sub-neg 95.1%

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

      5. +-commutative 95.1%

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

      6. neg-sub0 95.1%

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

      7. associate-+l- 95.1%

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

      8. sub0-neg 95.1%

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

      9. neg-mul-1 95.1%

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

      10. associate-/r* 95.1%

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

      11. metadata-eval 95.1%

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

   3. Simplified 95.1%

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

      1. associate-*r/ 93.9%

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

      2. associate-*r/ 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in t around 0 76.5%

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

      1. associate-*r/ 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-/l/ 77.5%

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

      4. times-frac 81.5%

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

   8. Applied egg-rr 81.5%

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

   if 1.24999999999999988e-22 < t

   1. Initial program 88.3%

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

      1. associate-*r/ 88.2%

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

      2. distribute-rgt-out-- 91.3%

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

      3. associate-/l/ 92.1%

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

      4. sub-neg 92.1%

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

      5. +-commutative 92.1%

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

      6. neg-sub0 92.1%

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

      7. associate-+l- 92.1%

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

      8. sub0-neg 92.1%

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

      9. neg-mul-1 92.1%

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

      10. associate-/r* 92.1%

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

      11. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around inf 79.5%

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

      1. associate-/r* 80.3%

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

   6. Simplified 80.3%

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

      1. associate-*r/ 81.2%

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

      2. associate-*r/ 81.3%

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

      3. associate-/r* 79.6%

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

      4. associate-*l/ 79.6%

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

      5. associate-/r* 81.3%

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

      6. associate-*l/ 81.3%

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

   8. Applied egg-rr 81.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+84}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{x}{t}}{z}\\ \end{array} \]

Alternative 8: 92.2% 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 90.1%

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

   1. associate-*l/ 90.1%

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

   2. *-commutative 90.1%

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

   3. distribute-rgt-out-- 92.5%

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

   4. associate-/r* 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. Final simplification 93.5%

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

Alternative 9: 53.5% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.1%

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

   1. associate-*r/ 90.0%

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

   2. distribute-rgt-out-- 92.4%

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

   3. associate-/l/ 93.0%

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

   4. sub-neg 93.0%

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

   5. +-commutative 93.0%

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

   6. neg-sub0 93.0%

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

   7. associate-+l- 93.0%

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

   8. sub0-neg 93.0%

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

   9. neg-mul-1 93.0%

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

   10. associate-/r* 93.0%

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

   11. metadata-eval 93.0%

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

3. Simplified 93.0%

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

4. Taylor expanded in t around inf 51.4%

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

   1. associate-/r* 52.0%

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

6. Simplified 52.0%

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

7. Final simplification 52.0%

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

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 2023221 
(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))))