Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.6% → 96.5%

Time: 11.8s

Alternatives: 12

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: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot z - z \cdot t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-312}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t_1 \leq 10^{-203}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t - y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (- (* y z) (* z t)))))
   (if (<= t_1 -2e-312)
     (/ (* x 2.0) (* z (- y t)))
     (if (<= t_1 1e-203)
       (/ (/ (* x 2.0) z) (- y t))
       (/ (/ (* x -2.0) (- t y)) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * 2.0) / ((y * z) - (z * t));
	double tmp;
	if (t_1 <= -2e-312) {
		tmp = (x * 2.0) / (z * (y - t));
	} else if (t_1 <= 1e-203) {
		tmp = ((x * 2.0) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) / ((y * z) - (z * t))
    if (t_1 <= (-2d-312)) then
        tmp = (x * 2.0d0) / (z * (y - t))
    else if (t_1 <= 1d-203) then
        tmp = ((x * 2.0d0) / 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 t_1 = (x * 2.0) / ((y * z) - (z * t));
	double tmp;
	if (t_1 <= -2e-312) {
		tmp = (x * 2.0) / (z * (y - t));
	} else if (t_1 <= 1e-203) {
		tmp = ((x * 2.0) / z) / (y - t);
	} else {
		tmp = ((x * -2.0) / (t - y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * 2.0) / ((y * z) - (z * t))
	tmp = 0
	if t_1 <= -2e-312:
		tmp = (x * 2.0) / (z * (y - t))
	elif t_1 <= 1e-203:
		tmp = ((x * 2.0) / z) / (y - t)
	else:
		tmp = ((x * -2.0) / (t - y)) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(z * t)))
	tmp = 0.0
	if (t_1 <= -2e-312)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	elseif (t_1 <= 1e-203)
		tmp = Float64(Float64(Float64(x * 2.0) / z) / Float64(y - t));
	else
		tmp = Float64(Float64(Float64(x * -2.0) / Float64(t - y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * 2.0) / ((y * z) - (z * t));
	tmp = 0.0;
	if (t_1 <= -2e-312)
		tmp = (x * 2.0) / (z * (y - t));
	elseif (t_1 <= 1e-203)
		tmp = ((x * 2.0) / z) / (y - t);
	else
		tmp = ((x * -2.0) / (t - y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-312], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-203], N[(N[(N[(x * 2.0), $MachinePrecision] / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -2.0), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z))) < -2.0000000000019e-312

   1. Initial program 96.3%

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

      1. distribute-rgt-out-- 98.6%

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

   3. Simplified 98.6%

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

   if -2.0000000000019e-312 < (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z))) < 1e-203

   1. Initial program 77.5%

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

      1. distribute-rgt-out-- 77.5%

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

      2. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   if 1e-203 < (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z)))

   1. Initial program 85.7%

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

      1. associate-*l/ 85.7%

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

      2. *-commutative 85.7%

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

      3. distribute-rgt-out-- 94.6%

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

      4. associate-/l/ 96.1%

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

   3. Simplified 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-/l/ 94.6%

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

      3. associate-*l/ 94.6%

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

      4. times-frac 80.5%

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

      5. associate-*l/ 95.9%

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

   5. Applied egg-rr 95.9%

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

      1. frac-2neg 95.9%

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

      2. metadata-eval 95.9%

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

      3. associate-*r/ 96.1%

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

      4. neg-sub0 96.1%

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

      5. sub-neg 96.1%

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

      6. +-commutative 96.1%

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

      7. associate--r+ 96.1%

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

      8. add-sqr-sqrt 42.6%

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

      9. sqrt-unprod 67.0%

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

      10. sqr-neg 67.0%

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

      11. sqrt-unprod 28.1%

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

      12. add-sqr-sqrt 53.9%

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

      13. neg-sub0 53.9%

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

      14. add-sqr-sqrt 25.8%

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

      15. sqrt-unprod 73.2%

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

      16. sqr-neg 73.2%

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

      17. sqrt-unprod 53.3%

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

      18. add-sqr-sqrt 96.1%

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

   7. Applied egg-rr 96.1%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq -2 \cdot 10^{-312}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq 10^{-203}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t - y}}{z}\\ \end{array} \]

Alternative 2: 96.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -1 \cdot 10^{-19} \lor \neg \left(x \cdot 2 \leq 5 \cdot 10^{-128}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x 2.0) -1e-19) (not (<= (* x 2.0) 5e-128)))
   (* 2.0 (/ (/ x (- y t)) z))
   (* x (/ (/ 2.0 z) (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -1e-19) || !((x * 2.0) <= 5e-128)) {
		tmp = 2.0 * ((x / (y - t)) / z);
	} else {
		tmp = x * ((2.0 / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x * 2.0d0) <= (-1d-19)) .or. (.not. ((x * 2.0d0) <= 5d-128))) then
        tmp = 2.0d0 * ((x / (y - t)) / z)
    else
        tmp = x * ((2.0d0 / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -1e-19) || !((x * 2.0) <= 5e-128)) {
		tmp = 2.0 * ((x / (y - t)) / z);
	} else {
		tmp = x * ((2.0 / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * 2.0) <= -1e-19) or not ((x * 2.0) <= 5e-128):
		tmp = 2.0 * ((x / (y - t)) / z)
	else:
		tmp = x * ((2.0 / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x * 2.0) <= -1e-19) || !(Float64(x * 2.0) <= 5e-128))
		tmp = Float64(2.0 * Float64(Float64(x / Float64(y - t)) / z));
	else
		tmp = Float64(x * Float64(Float64(2.0 / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * 2.0) <= -1e-19) || ~(((x * 2.0) <= 5e-128)))
		tmp = 2.0 * ((x / (y - t)) / z);
	else
		tmp = x * ((2.0 / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x * 2.0), $MachinePrecision], -1e-19], N[Not[LessEqual[N[(x * 2.0), $MachinePrecision], 5e-128]], $MachinePrecision]], N[(2.0 * N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < -9.9999999999999998e-20 or 5.0000000000000001e-128 < (*.f64 x 2)

   1. Initial program 84.5%

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

      1. associate-*l/ 84.5%

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

      2. *-commutative 84.5%

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

      3. distribute-rgt-out-- 86.8%

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

      4. associate-/l/ 97.5%

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

   3. Simplified 97.5%

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

   if -9.9999999999999998e-20 < (*.f64 x 2) < 5.0000000000000001e-128

   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-- 95.6%

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

      4. associate-/l/ 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in x around 0 95.6%

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

      1. associate-/r* 95.6%

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

      2. associate-*r/ 95.6%

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

      3. associate-*r/ 95.6%

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

      4. *-commutative 95.6%

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

      5. associate-*r/ 95.5%

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

      6. associate-*r/ 95.4%

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

   6. Simplified 95.4%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -1 \cdot 10^{-19} \lor \neg \left(x \cdot 2 \leq 5 \cdot 10^{-128}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{z}}{y - t}\\ \end{array} \]

Alternative 3: 96.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{\frac{2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y - t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.4e+68)
   (* (/ x z) (/ 2.0 (- y t)))
   (if (<= z 1.1e-34)
     (* x (/ (/ 2.0 z) (- y t)))
     (* 2.0 (/ (/ x (- y t)) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e+68) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (z <= 1.1e-34) {
		tmp = x * ((2.0 / z) / (y - t));
	} else {
		tmp = 2.0 * ((x / (y - 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 (z <= (-1.4d+68)) then
        tmp = (x / z) * (2.0d0 / (y - t))
    else if (z <= 1.1d-34) then
        tmp = x * ((2.0d0 / z) / (y - t))
    else
        tmp = 2.0d0 * ((x / (y - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e+68) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (z <= 1.1e-34) {
		tmp = x * ((2.0 / z) / (y - t));
	} else {
		tmp = 2.0 * ((x / (y - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.4e+68:
		tmp = (x / z) * (2.0 / (y - t))
	elif z <= 1.1e-34:
		tmp = x * ((2.0 / z) / (y - t))
	else:
		tmp = 2.0 * ((x / (y - t)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.4e+68)
		tmp = Float64(Float64(x / z) * Float64(2.0 / Float64(y - t)));
	elseif (z <= 1.1e-34)
		tmp = Float64(x * Float64(Float64(2.0 / z) / Float64(y - t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x / Float64(y - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.4e+68)
		tmp = (x / z) * (2.0 / (y - t));
	elseif (z <= 1.1e-34)
		tmp = x * ((2.0 / z) / (y - t));
	else
		tmp = 2.0 * ((x / (y - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.4e+68], N[(N[(x / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-34], N[(x * N[(N[(2.0 / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e68

   1. Initial program 72.6%

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

      1. distribute-rgt-out-- 78.1%

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

   3. Simplified 78.1%

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

      1. times-frac 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -1.4e68 < z < 1.0999999999999999e-34

   1. Initial program 93.8%

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

      1. associate-*l/ 93.8%

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

      2. *-commutative 93.8%

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

      3. distribute-rgt-out-- 95.6%

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

      4. associate-/l/ 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in x around 0 95.6%

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

      1. associate-/r* 84.2%

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

      2. associate-*r/ 84.2%

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

      3. associate-*r/ 84.2%

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

      4. *-commutative 84.2%

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

      5. associate-*r/ 84.1%

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

      6. associate-*r/ 95.4%

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

   6. Simplified 95.4%

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

   if 1.0999999999999999e-34 < z

   1. Initial program 85.5%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. distribute-rgt-out-- 89.9%

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

      4. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{\frac{2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y - t}}{z}\\ \end{array} \]

Alternative 4: 97.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y - t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+46)
   (* (/ x z) (/ 2.0 (- y t)))
   (if (<= z 1.1e-34)
     (/ (* x 2.0) (* z (- y t)))
     (* 2.0 (/ (/ x (- y t)) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+46) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (z <= 1.1e-34) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = 2.0 * ((x / (y - 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 (z <= (-2.7d+46)) then
        tmp = (x / z) * (2.0d0 / (y - t))
    else if (z <= 1.1d-34) then
        tmp = (x * 2.0d0) / (z * (y - t))
    else
        tmp = 2.0d0 * ((x / (y - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+46) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (z <= 1.1e-34) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = 2.0 * ((x / (y - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+46:
		tmp = (x / z) * (2.0 / (y - t))
	elif z <= 1.1e-34:
		tmp = (x * 2.0) / (z * (y - t))
	else:
		tmp = 2.0 * ((x / (y - t)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+46)
		tmp = Float64(Float64(x / z) * Float64(2.0 / Float64(y - t)));
	elseif (z <= 1.1e-34)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x / Float64(y - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.7e+46)
		tmp = (x / z) * (2.0 / (y - t));
	elseif (z <= 1.1e-34)
		tmp = (x * 2.0) / (z * (y - t));
	else
		tmp = 2.0 * ((x / (y - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+46], N[(N[(x / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-34], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000002e46

   1. Initial program 74.4%

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

      1. distribute-rgt-out-- 79.6%

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

   3. Simplified 79.6%

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

      1. times-frac 99.7%

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

   5. Applied egg-rr 99.7%

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

   if -2.7000000000000002e46 < z < 1.0999999999999999e-34

   1. Initial program 93.6%

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

      1. distribute-rgt-out-- 95.4%

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

   3. Simplified 95.4%

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

   if 1.0999999999999999e-34 < z

   1. Initial program 85.5%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. distribute-rgt-out-- 89.9%

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

      4. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y - t}}{z}\\ \end{array} \]

Alternative 5: 97.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t - y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+46)
   (* (/ x z) (/ 2.0 (- y t)))
   (if (<= z 1.05e-34)
     (/ (* x 2.0) (* z (- y t)))
     (/ (/ (* x -2.0) (- t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+46) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (z <= 1.05e-34) {
		tmp = (x * 2.0) / (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 <= (-1.5d+46)) then
        tmp = (x / z) * (2.0d0 / (y - t))
    else if (z <= 1.05d-34) then
        tmp = (x * 2.0d0) / (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 <= -1.5e+46) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (z <= 1.05e-34) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = ((x * -2.0) / (t - y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+46:
		tmp = (x / z) * (2.0 / (y - t))
	elif z <= 1.05e-34:
		tmp = (x * 2.0) / (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 <= -1.5e+46)
		tmp = Float64(Float64(x / z) * Float64(2.0 / Float64(y - t)));
	elseif (z <= 1.05e-34)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(Float64(Float64(x * -2.0) / Float64(t - y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.5e+46)
		tmp = (x / z) * (2.0 / (y - t));
	elseif (z <= 1.05e-34)
		tmp = (x * 2.0) / (z * (y - t));
	else
		tmp = ((x * -2.0) / (t - y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e+46], N[(N[(x / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-34], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -2.0), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000012e46

   1. Initial program 74.4%

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

      1. distribute-rgt-out-- 79.6%

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

   3. Simplified 79.6%

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

      1. times-frac 99.7%

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

   5. Applied egg-rr 99.7%

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

   if -1.50000000000000012e46 < z < 1.05e-34

   1. Initial program 93.6%

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

      1. distribute-rgt-out-- 95.4%

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

   3. Simplified 95.4%

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

   if 1.05e-34 < z

   1. Initial program 85.5%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. distribute-rgt-out-- 89.9%

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

      4. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l/ 89.9%

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

      3. associate-*l/ 89.9%

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

      4. times-frac 95.1%

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

      5. associate-*l/ 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. frac-2neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-*r/ 99.8%

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

      4. neg-sub0 99.8%

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

      5. sub-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate--r+ 99.8%

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

      8. add-sqr-sqrt 48.1%

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

      9. sqrt-unprod 78.6%

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

      10. sqr-neg 78.6%

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

      11. sqrt-unprod 34.7%

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

      12. add-sqr-sqrt 64.5%

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

      13. neg-sub0 64.5%

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

      14. add-sqr-sqrt 29.8%

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

      15. sqrt-unprod 73.8%

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

      16. sqr-neg 73.8%

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

      17. sqrt-unprod 51.5%

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

      18. add-sqr-sqrt 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t - y}}{z}\\ \end{array} \]

Alternative 6: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-54} \lor \neg \left(y \leq 180000000\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.8e-54) (not (<= y 180000000.0)))
   (* 2.0 (/ (/ x z) y))
   (* (/ x z) (/ -2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.8e-54) || !(y <= 180000000.0)) {
		tmp = 2.0 * ((x / z) / y);
	} else {
		tmp = (x / z) * (-2.0 / 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 ((y <= (-2.8d-54)) .or. (.not. (y <= 180000000.0d0))) then
        tmp = 2.0d0 * ((x / z) / y)
    else
        tmp = (x / z) * ((-2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.8e-54) || !(y <= 180000000.0)) {
		tmp = 2.0 * ((x / z) / y);
	} else {
		tmp = (x / z) * (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.8e-54) or not (y <= 180000000.0):
		tmp = 2.0 * ((x / z) / y)
	else:
		tmp = (x / z) * (-2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.8e-54) || !(y <= 180000000.0))
		tmp = Float64(2.0 * Float64(Float64(x / z) / y));
	else
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.8e-54) || ~((y <= 180000000.0)))
		tmp = 2.0 * ((x / z) / y);
	else
		tmp = (x / z) * (-2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.8e-54], N[Not[LessEqual[y, 180000000.0]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8000000000000002e-54 or 1.8e8 < y

   1. Initial program 84.6%

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

      1. associate-*l/ 84.6%

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

      2. *-commutative 84.6%

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

      3. distribute-rgt-out-- 89.4%

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

      4. associate-/l/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/r* 76.3%

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

   6. Simplified 76.3%

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

   if -2.8000000000000002e-54 < y < 1.8e8

   1. Initial program 88.9%

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

      1. distribute-rgt-out-- 90.7%

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

   3. Simplified 90.7%

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

      1. times-frac 94.6%

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

   5. Applied egg-rr 94.6%

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

   6. Taylor expanded in y around 0 74.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-54} \lor \neg \left(y \leq 180000000\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \]

Alternative 7: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -600000000000 \lor \neg \left(y \leq 45000\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -600000000000.0) (not (<= y 45000.0)))
   (* 2.0 (/ (/ x z) y))
   (/ (* -2.0 (/ x t)) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -600000000000.0) || !(y <= 45000.0)) {
		tmp = 2.0 * ((x / z) / 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 ((y <= (-600000000000.0d0)) .or. (.not. (y <= 45000.0d0))) then
        tmp = 2.0d0 * ((x / z) / 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 ((y <= -600000000000.0) || !(y <= 45000.0)) {
		tmp = 2.0 * ((x / z) / y);
	} else {
		tmp = (-2.0 * (x / t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -600000000000.0) or not (y <= 45000.0):
		tmp = 2.0 * ((x / z) / y)
	else:
		tmp = (-2.0 * (x / t)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -600000000000.0) || !(y <= 45000.0))
		tmp = Float64(2.0 * Float64(Float64(x / z) / 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 ((y <= -600000000000.0) || ~((y <= 45000.0)))
		tmp = 2.0 * ((x / z) / y);
	else
		tmp = (-2.0 * (x / t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -600000000000.0], N[Not[LessEqual[y, 45000.0]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e11 or 45000 < y

   1. Initial program 84.9%

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

      1. associate-*l/ 84.9%

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

      2. *-commutative 84.9%

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

      3. distribute-rgt-out-- 89.3%

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

      4. associate-/l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around inf 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-/r* 78.2%

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

   6. Simplified 78.2%

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

   if -6e11 < y < 45000

   1. Initial program 88.2%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

      3. distribute-rgt-out-- 90.7%

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

      4. associate-/l/ 95.3%

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

   3. Simplified 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-/l/ 90.7%

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

      3. associate-*l/ 90.7%

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

      4. times-frac 93.4%

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

      5. associate-*l/ 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in y around 0 76.2%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -600000000000 \lor \neg \left(y \leq 45000\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \frac{x}{t}}{z}\\ \end{array} \]

Alternative 8: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-13}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.5e-33)
   (* (/ x z) (/ -2.0 t))
   (if (<= t 6.5e-13) (* 2.0 (/ (/ x z) y)) (* -2.0 (/ x (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.5e-33) {
		tmp = (x / z) * (-2.0 / t);
	} else if (t <= 6.5e-13) {
		tmp = 2.0 * ((x / z) / y);
	} else {
		tmp = -2.0 * (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.5d-33)) then
        tmp = (x / z) * ((-2.0d0) / t)
    else if (t <= 6.5d-13) then
        tmp = 2.0d0 * ((x / z) / y)
    else
        tmp = (-2.0d0) * (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.5e-33) {
		tmp = (x / z) * (-2.0 / t);
	} else if (t <= 6.5e-13) {
		tmp = 2.0 * ((x / z) / y);
	} else {
		tmp = -2.0 * (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.5e-33:
		tmp = (x / z) * (-2.0 / t)
	elif t <= 6.5e-13:
		tmp = 2.0 * ((x / z) / y)
	else:
		tmp = -2.0 * (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.5e-33)
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	elseif (t <= 6.5e-13)
		tmp = Float64(2.0 * Float64(Float64(x / z) / y));
	else
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.5e-33)
		tmp = (x / z) * (-2.0 / t);
	elseif (t <= 6.5e-13)
		tmp = 2.0 * ((x / z) / y);
	else
		tmp = -2.0 * (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.5e-33], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-13], N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5e-33

   1. Initial program 82.9%

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

      1. distribute-rgt-out-- 90.1%

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

   3. Simplified 90.1%

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

      1. times-frac 88.9%

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

   5. Applied egg-rr 88.9%

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

   6. Taylor expanded in y around 0 71.7%

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

   if -5.5e-33 < t < 6.49999999999999957e-13

   1. Initial program 87.6%

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

      1. associate-*l/ 87.6%

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

      2. *-commutative 87.6%

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

      3. distribute-rgt-out-- 89.2%

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

      4. associate-/l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-/r* 79.8%

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

   6. Simplified 79.8%

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

   if 6.49999999999999957e-13 < t

   1. Initial program 88.3%

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

      1. associate-*l/ 88.3%

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

      2. *-commutative 88.3%

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

      3. distribute-rgt-out-- 91.2%

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

      4. associate-/l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around 0 72.2%

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

      1. *-commutative 72.2%

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

      2. *-commutative 72.2%

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

   6. Simplified 72.2%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-13}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 9: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -26500000:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq 680000:\\ \;\;\;\;\frac{-2 \cdot \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -26500000.0)
   (/ (* 2.0 (/ x y)) z)
   (if (<= y 680000.0) (/ (* -2.0 (/ x t)) z) (* 2.0 (/ (/ x z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -26500000.0) {
		tmp = (2.0 * (x / y)) / z;
	} else if (y <= 680000.0) {
		tmp = (-2.0 * (x / t)) / z;
	} 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 (y <= (-26500000.0d0)) then
        tmp = (2.0d0 * (x / y)) / z
    else if (y <= 680000.0d0) then
        tmp = ((-2.0d0) * (x / t)) / z
    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 (y <= -26500000.0) {
		tmp = (2.0 * (x / y)) / z;
	} else if (y <= 680000.0) {
		tmp = (-2.0 * (x / t)) / z;
	} else {
		tmp = 2.0 * ((x / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -26500000.0:
		tmp = (2.0 * (x / y)) / z
	elif y <= 680000.0:
		tmp = (-2.0 * (x / t)) / z
	else:
		tmp = 2.0 * ((x / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -26500000.0)
		tmp = Float64(Float64(2.0 * Float64(x / y)) / z);
	elseif (y <= 680000.0)
		tmp = Float64(Float64(-2.0 * Float64(x / t)) / z);
	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 (y <= -26500000.0)
		tmp = (2.0 * (x / y)) / z;
	elseif (y <= 680000.0)
		tmp = (-2.0 * (x / t)) / z;
	else
		tmp = 2.0 * ((x / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -26500000.0], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 680000.0], N[(N[(-2.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.65e7

   1. Initial program 81.7%

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

      1. associate-*l/ 81.7%

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

      2. *-commutative 81.7%

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

      3. distribute-rgt-out-- 87.7%

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

      4. associate-/l/ 93.7%

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

   3. Simplified 93.7%

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

      1. *-commutative 93.7%

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

      2. associate-/l/ 87.7%

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

      3. associate-*l/ 87.7%

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

      4. times-frac 89.4%

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

      5. associate-*l/ 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in y around inf 84.8%

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

   if -2.65e7 < y < 6.8e5

   1. Initial program 88.2%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

      3. distribute-rgt-out-- 90.7%

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

      4. associate-/l/ 95.3%

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

   3. Simplified 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-/l/ 90.7%

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

      3. associate-*l/ 90.7%

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

      4. times-frac 93.4%

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

      5. associate-*l/ 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in y around 0 76.2%

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

   if 6.8e5 < y

   1. Initial program 87.8%

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

      1. associate-*l/ 87.8%

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

      2. *-commutative 87.8%

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

      3. distribute-rgt-out-- 90.7%

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

      4. associate-/l/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in y around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-/r* 77.4%

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

   6. Simplified 77.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -26500000:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq 680000:\\ \;\;\;\;\frac{-2 \cdot \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 10: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15500000000:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq 2750000:\\ \;\;\;\;\frac{-2 \cdot \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -15500000000.0)
   (/ (* 2.0 (/ x y)) z)
   (if (<= y 2750000.0) (/ (* -2.0 (/ x t)) z) (/ (* x 2.0) (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -15500000000.0) {
		tmp = (2.0 * (x / y)) / z;
	} else if (y <= 2750000.0) {
		tmp = (-2.0 * (x / 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 (y <= (-15500000000.0d0)) then
        tmp = (2.0d0 * (x / y)) / z
    else if (y <= 2750000.0d0) then
        tmp = ((-2.0d0) * (x / 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 (y <= -15500000000.0) {
		tmp = (2.0 * (x / y)) / z;
	} else if (y <= 2750000.0) {
		tmp = (-2.0 * (x / t)) / z;
	} else {
		tmp = (x * 2.0) / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -15500000000.0:
		tmp = (2.0 * (x / y)) / z
	elif y <= 2750000.0:
		tmp = (-2.0 * (x / t)) / z
	else:
		tmp = (x * 2.0) / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -15500000000.0)
		tmp = Float64(Float64(2.0 * Float64(x / y)) / z);
	elseif (y <= 2750000.0)
		tmp = Float64(Float64(-2.0 * Float64(x / t)) / z);
	else
		tmp = Float64(Float64(x * 2.0) / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -15500000000.0)
		tmp = (2.0 * (x / y)) / z;
	elseif (y <= 2750000.0)
		tmp = (-2.0 * (x / t)) / z;
	else
		tmp = (x * 2.0) / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -15500000000.0], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2750000.0], N[(N[(-2.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e10

   1. Initial program 81.7%

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

      1. associate-*l/ 81.7%

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

      2. *-commutative 81.7%

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

      3. distribute-rgt-out-- 87.7%

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

      4. associate-/l/ 93.7%

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

   3. Simplified 93.7%

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

      1. *-commutative 93.7%

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

      2. associate-/l/ 87.7%

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

      3. associate-*l/ 87.7%

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

      4. times-frac 89.4%

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

      5. associate-*l/ 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in y around inf 84.8%

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

   if -1.55e10 < y < 2.75e6

   1. Initial program 88.2%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

      3. distribute-rgt-out-- 90.7%

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

      4. associate-/l/ 95.3%

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

   3. Simplified 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-/l/ 90.7%

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

      3. associate-*l/ 90.7%

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

      4. times-frac 93.4%

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

      5. associate-*l/ 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in y around 0 76.2%

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

   if 2.75e6 < y

   1. Initial program 87.8%

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

      1. distribute-rgt-out-- 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in y around inf 78.9%

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

      1. *-commutative 78.9%

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

   6. Simplified 78.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15500000000:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq 2750000:\\ \;\;\;\;\frac{-2 \cdot \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \end{array} \]

Alternative 11: 92.2% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

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

   1. associate-*l/ 86.5%

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

   2. *-commutative 86.5%

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

   3. distribute-rgt-out-- 90.0%

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

   4. associate-/l/ 92.7%

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

3. Simplified 92.7%

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

4. Final simplification 92.7%

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

Alternative 12: 54.5% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

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

   1. associate-*l/ 86.5%

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

   2. *-commutative 86.5%

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

   3. distribute-rgt-out-- 90.0%

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

   4. associate-/l/ 92.7%

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

3. Simplified 92.7%

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

4. Taylor expanded in y around inf 54.5%

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

   1. *-commutative 54.5%

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

   2. associate-/r* 57.6%

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

6. Simplified 57.6%

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

7. Final simplification 57.6%

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

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 2023301 
(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))))