Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.0% → 98.3%

Time: 9.2s

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: 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: 98.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y - z \cdot t\\ t_2 := \frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+248}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z y) (* z t))) (t_2 (* (/ x z) (/ 2.0 (- y t)))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 1e+248) (/ (* 2.0 x) (* z (- y t))) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) - (z * t);
	double t_2 = (x / z) * (2.0 / (y - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+248) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * y) - (z * t);
	double t_2 = (x / z) * (2.0 / (y - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 1e+248) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) - (z * t)
	t_2 = (x / z) * (2.0 / (y - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 1e+248:
		tmp = (2.0 * x) / (z * (y - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) - Float64(z * t))
	t_2 = Float64(Float64(x / z) * Float64(2.0 / Float64(y - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+248)
		tmp = Float64(Float64(2.0 * x) / Float64(z * Float64(y - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) - (z * t);
	t_2 = (x / z) * (2.0 / (y - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 1e+248)
		tmp = (2.0 * x) / (z * (y - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+248], N[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -inf.0 or 1.00000000000000005e248 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 61.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-out-- N/A

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

      7. times-frac N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   if -inf.0 < (-.f64 (*.f64 y z) (*.f64 t z)) < 1.00000000000000005e248

   1. Initial program 97.1%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-rgt-out-- N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 97.7

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

   4. Applied rewrites 97.7%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;z \cdot y - z \cdot t \leq 10^{+248}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot y - z \cdot t \leq 10^{+248}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{y} \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- (* z y) (* z t)) 1e+248)
   (/ (* 2.0 x) (* z (- y t)))
   (* (/ 2.0 y) (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * y) - (z * t)) <= 1e+248) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = (2.0 / y) * (x / 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 * y) - (z * t)) <= 1d+248) then
        tmp = (2.0d0 * x) / (z * (y - t))
    else
        tmp = (2.0d0 / y) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * y) - (z * t)) <= 1e+248) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = (2.0 / y) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * y) - (z * t)) <= 1e+248:
		tmp = (2.0 * x) / (z * (y - t))
	else:
		tmp = (2.0 / y) * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * y) - Float64(z * t)) <= 1e+248)
		tmp = Float64(Float64(2.0 * x) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 / y) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * y) - (z * t)) <= 1e+248)
		tmp = (2.0 * x) / (z * (y - t));
	else
		tmp = (2.0 / y) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision], 1e+248], N[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < 1.00000000000000005e248

   1. Initial program 92.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-rgt-out-- N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 93.4

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

   4. Applied rewrites 93.4%

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

   if 1.00000000000000005e248 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 62.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-out-- N/A

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

      7. times-frac N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 84.0

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

   7. Applied rewrites 84.0%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y - z \cdot t \leq 10^{+248}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{y} \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x \leq 4 \cdot 10^{-31}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2 \cdot x}{y - t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* 2.0 x) 4e-31)
   (/ (* 2.0 x) (* z (- y t)))
   (/ (/ (* 2.0 x) (- y t)) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((2.0 * x) <= 4e-31) {
		tmp = (2.0 * x) / (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 ((2.0d0 * x) <= 4d-31) then
        tmp = (2.0d0 * x) / (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 ((2.0 * x) <= 4e-31) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = ((2.0 * x) / (y - t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (2.0 * x) <= 4e-31:
		tmp = (2.0 * x) / (z * (y - t))
	else:
		tmp = ((2.0 * x) / (y - t)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(2.0 * x) <= 4e-31)
		tmp = Float64(Float64(2.0 * x) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(Float64(Float64(2.0 * x) / Float64(y - t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((2.0 * x) <= 4e-31)
		tmp = (2.0 * x) / (z * (y - t));
	else
		tmp = ((2.0 * x) / (y - t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(2.0 * x), $MachinePrecision], 4e-31], N[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 * x), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < 4e-31

   1. Initial program 89.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-rgt-out-- N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 93.7

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

   4. Applied rewrites 93.7%

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

   if 4e-31 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 82.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-rgt-out-- N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x \leq 4 \cdot 10^{-31}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2 \cdot x}{y - t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2 \cdot x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 5.5e+76) (* (/ (/ 2.0 (- y t)) z) x) (/ (/ (* 2.0 x) z) (- y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.5e+76) {
		tmp = ((2.0 / (y - t)) / z) * x;
	} 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 <= 5.5d+76) then
        tmp = ((2.0d0 / (y - t)) / z) * x
    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 <= 5.5e+76) {
		tmp = ((2.0 / (y - t)) / z) * x;
	} else {
		tmp = ((2.0 * x) / z) / (y - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 5.5e+76:
		tmp = ((2.0 / (y - t)) / z) * x
	else:
		tmp = ((2.0 * x) / z) / (y - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5.5e+76)
		tmp = Float64(Float64(Float64(2.0 / Float64(y - t)) / z) * x);
	else
		tmp = Float64(Float64(Float64(2.0 * x) / z) / Float64(y - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 5.5e+76)
		tmp = ((2.0 / (y - t)) / z) * x;
	else
		tmp = ((2.0 * x) / z) / (y - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 5.5e+76], N[(N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(2.0 * x), $MachinePrecision] / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.5000000000000001e76

   1. Initial program 91.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. distribute-rgt-out-- N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 93.8

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

   4. Applied rewrites 93.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. associate-/r* N/A

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

      5. lift-/.f64 N/A

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

      6. lower-/.f64 93.8

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

   6. Applied rewrites 93.8%

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

   if 5.5000000000000001e76 < z

   1. Initial program 72.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \frac{x \cdot 2}{\color{blue}{\mathsf{fma}\left(z, y, \mathsf{neg}\left(t \cdot z\right)\right)}} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot 2}{\mathsf{fma}\left(z, y, \mathsf{neg}\left(\color{blue}{t \cdot z}\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{x \cdot 2}{\mathsf{fma}\left(z, y, \mathsf{neg}\left(\color{blue}{z \cdot t}\right)\right)} \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \frac{x \cdot 2}{\mathsf{fma}\left(z, y, \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot t}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot 2}{\mathsf{fma}\left(z, y, \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot t}\right)} \]

      10. lower-neg.f64 86.6

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

   4. Applied rewrites 86.6%

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

      1. lift-/.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. distribute-lft-neg-out N/A

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

      7. *-commutative N/A

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

      8. sub-neg N/A

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

      9. distribute-rgt-out-- N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower--.f64 95.3

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

   6. Applied rewrites 95.3%

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

Alternative 5: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{0.5 \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 5.5e+76) (* (/ (/ 2.0 (- y t)) z) x) (/ (/ x z) (* 0.5 (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.5e+76) {
		tmp = ((2.0 / (y - t)) / z) * x;
	} else {
		tmp = (x / z) / (0.5 * (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 <= 5.5d+76) then
        tmp = ((2.0d0 / (y - t)) / z) * x
    else
        tmp = (x / z) / (0.5d0 * (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 <= 5.5e+76) {
		tmp = ((2.0 / (y - t)) / z) * x;
	} else {
		tmp = (x / z) / (0.5 * (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 5.5e+76:
		tmp = ((2.0 / (y - t)) / z) * x
	else:
		tmp = (x / z) / (0.5 * (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5.5e+76)
		tmp = Float64(Float64(Float64(2.0 / Float64(y - t)) / z) * x);
	else
		tmp = Float64(Float64(x / z) / Float64(0.5 * Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 5.5e+76)
		tmp = ((2.0 / (y - t)) / z) * x;
	else
		tmp = (x / z) / (0.5 * (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 5.5e+76], N[(N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(0.5 * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.5000000000000001e76

   1. Initial program 91.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. distribute-rgt-out-- N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 93.8

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

   4. Applied rewrites 93.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. associate-/r* N/A

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

      5. lift-/.f64 N/A

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

      6. lower-/.f64 93.8

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

   6. Applied rewrites 93.8%

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

   if 5.5000000000000001e76 < z

   1. Initial program 72.3%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-out-- N/A

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

      7. lift-*.f64 N/A

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

      8. times-frac N/A

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

      9. associate-/r* N/A

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

      10. clear-num N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. div-inv N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

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

      16. metadata-eval N/A

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. metadata-eval N/A

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

      20. metadata-eval 95.3

          \[\leadsto \frac{\frac{x}{z}}{\left(y - t\right) \cdot \color{blue}{0.5}} \]

   4. Applied rewrites 95.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{\left(y - t\right) \cdot 0.5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{0.5 \cdot \left(y - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{y - t}\\ \mathbf{if}\;z \leq 5 \cdot 10^{+76}:\\ \;\;\;\;\frac{t\_1}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (- y t))))
   (if (<= z 5e+76) (* (/ t_1 z) x) (* (/ x z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (y - t);
	double tmp;
	if (z <= 5e+76) {
		tmp = (t_1 / z) * x;
	} else {
		tmp = (x / z) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (y - t)
    if (z <= 5d+76) then
        tmp = (t_1 / z) * x
    else
        tmp = (x / z) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (y - t);
	double tmp;
	if (z <= 5e+76) {
		tmp = (t_1 / z) * x;
	} else {
		tmp = (x / z) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (y - t)
	tmp = 0
	if z <= 5e+76:
		tmp = (t_1 / z) * x
	else:
		tmp = (x / z) * t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(y - t))
	tmp = 0.0
	if (z <= 5e+76)
		tmp = Float64(Float64(t_1 / z) * x);
	else
		tmp = Float64(Float64(x / z) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (y - t);
	tmp = 0.0;
	if (z <= 5e+76)
		tmp = (t_1 / z) * x;
	else
		tmp = (x / z) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 5e+76], N[(N[(t$95$1 / z), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 4.99999999999999991e76

   1. Initial program 91.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. distribute-rgt-out-- N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 93.8

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

   4. Applied rewrites 93.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. associate-/r* N/A

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

      5. lift-/.f64 N/A

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

      6. lower-/.f64 93.8

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

   6. Applied rewrites 93.8%

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

   if 4.99999999999999991e76 < z

   1. Initial program 72.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-out-- N/A

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

      7. times-frac N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 95.2

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

   4. Applied rewrites 95.2%

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

Alternative 7: 94.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{\frac{2}{z}}{y - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 5.5e+76) (* (/ (/ 2.0 z) (- y t)) x) (* (/ x z) (/ 2.0 (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.5e+76) {
		tmp = ((2.0 / z) / (y - t)) * x;
	} else {
		tmp = (x / z) * (2.0 / (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 <= 5.5d+76) then
        tmp = ((2.0d0 / z) / (y - t)) * x
    else
        tmp = (x / z) * (2.0d0 / (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 <= 5.5e+76) {
		tmp = ((2.0 / z) / (y - t)) * x;
	} else {
		tmp = (x / z) * (2.0 / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 5.5e+76:
		tmp = ((2.0 / z) / (y - t)) * x
	else:
		tmp = (x / z) * (2.0 / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5.5e+76)
		tmp = Float64(Float64(Float64(2.0 / z) / Float64(y - t)) * x);
	else
		tmp = Float64(Float64(x / z) * Float64(2.0 / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 5.5e+76)
		tmp = ((2.0 / z) / (y - t)) * x;
	else
		tmp = (x / z) * (2.0 / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 5.5e+76], N[(N[(N[(2.0 / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.5000000000000001e76

   1. Initial program 91.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. distribute-rgt-out-- N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 93.8

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

   4. Applied rewrites 93.8%

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

   if 5.5000000000000001e76 < z

   1. Initial program 72.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-out-- N/A

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

      7. times-frac N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 95.2

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

   4. Applied rewrites 95.2%

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

Alternative 8: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 \cdot x}{z \cdot y}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;\frac{2 \cdot x}{\left(-t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* 2.0 x) (* z y))))
   (if (<= y -8.5e-14) t_1 (if (<= y 1.3e-17) (/ (* 2.0 x) (* (- t) z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 * x) / (z * y);
	double tmp;
	if (y <= -8.5e-14) {
		tmp = t_1;
	} else if (y <= 1.3e-17) {
		tmp = (2.0 * x) / (-t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 * x) / (z * y)
    if (y <= (-8.5d-14)) then
        tmp = t_1
    else if (y <= 1.3d-17) then
        tmp = (2.0d0 * x) / (-t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 * x) / (z * y);
	double tmp;
	if (y <= -8.5e-14) {
		tmp = t_1;
	} else if (y <= 1.3e-17) {
		tmp = (2.0 * x) / (-t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 * x) / (z * y)
	tmp = 0
	if y <= -8.5e-14:
		tmp = t_1
	elif y <= 1.3e-17:
		tmp = (2.0 * x) / (-t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 * x) / Float64(z * y))
	tmp = 0.0
	if (y <= -8.5e-14)
		tmp = t_1;
	elseif (y <= 1.3e-17)
		tmp = Float64(Float64(2.0 * x) / Float64(Float64(-t) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 * x) / (z * y);
	tmp = 0.0;
	if (y <= -8.5e-14)
		tmp = t_1;
	elseif (y <= 1.3e-17)
		tmp = (2.0 * x) / (-t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * x), $MachinePrecision] / N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e-14], t$95$1, If[LessEqual[y, 1.3e-17], N[(N[(2.0 * x), $MachinePrecision] / N[((-t) * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.50000000000000038e-14 or 1.30000000000000002e-17 < y

   1. Initial program 85.7%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -8.50000000000000038e-14 < y < 1.30000000000000002e-17

   1. Initial program 90.2%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x \cdot 2}{\color{blue}{-1 \cdot \left(t \cdot z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 77.6

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

   5. Applied rewrites 77.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;\frac{2 \cdot x}{\left(-t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 \cdot x}{z \cdot y}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* 2.0 x) (* z y))))
   (if (<= y -8.5e-14) t_1 (if (<= y 1.3e-17) (* -2.0 (/ x (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 * x) / (z * y);
	double tmp;
	if (y <= -8.5e-14) {
		tmp = t_1;
	} else if (y <= 1.3e-17) {
		tmp = -2.0 * (x / (z * 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) :: tmp
    t_1 = (2.0d0 * x) / (z * y)
    if (y <= (-8.5d-14)) then
        tmp = t_1
    else if (y <= 1.3d-17) then
        tmp = (-2.0d0) * (x / (z * 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 = (2.0 * x) / (z * y);
	double tmp;
	if (y <= -8.5e-14) {
		tmp = t_1;
	} else if (y <= 1.3e-17) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 * x) / (z * y)
	tmp = 0
	if y <= -8.5e-14:
		tmp = t_1
	elif y <= 1.3e-17:
		tmp = -2.0 * (x / (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 * x) / Float64(z * y))
	tmp = 0.0
	if (y <= -8.5e-14)
		tmp = t_1;
	elseif (y <= 1.3e-17)
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 * x) / (z * y);
	tmp = 0.0;
	if (y <= -8.5e-14)
		tmp = t_1;
	elseif (y <= 1.3e-17)
		tmp = -2.0 * (x / (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * x), $MachinePrecision] / N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e-14], t$95$1, If[LessEqual[y, 1.3e-17], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.50000000000000038e-14 or 1.30000000000000002e-17 < y

   1. Initial program 85.7%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -8.50000000000000038e-14 < y < 1.30000000000000002e-17

   1. Initial program 90.2%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 77.6

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

   5. Applied rewrites 77.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot y} \cdot x\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 (* z y)) x)))
   (if (<= y -8.5e-14) t_1 (if (<= y 1.3e-17) (* -2.0 (/ x (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / (z * y)) * x;
	double tmp;
	if (y <= -8.5e-14) {
		tmp = t_1;
	} else if (y <= 1.3e-17) {
		tmp = -2.0 * (x / (z * 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) :: tmp
    t_1 = (2.0d0 / (z * y)) * x
    if (y <= (-8.5d-14)) then
        tmp = t_1
    else if (y <= 1.3d-17) then
        tmp = (-2.0d0) * (x / (z * 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 = (2.0 / (z * y)) * x;
	double tmp;
	if (y <= -8.5e-14) {
		tmp = t_1;
	} else if (y <= 1.3e-17) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / (z * y)) * x
	tmp = 0
	if y <= -8.5e-14:
		tmp = t_1
	elif y <= 1.3e-17:
		tmp = -2.0 * (x / (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / Float64(z * y)) * x)
	tmp = 0.0
	if (y <= -8.5e-14)
		tmp = t_1;
	elseif (y <= 1.3e-17)
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / (z * y)) * x;
	tmp = 0.0;
	if (y <= -8.5e-14)
		tmp = t_1;
	elseif (y <= 1.3e-17)
		tmp = -2.0 * (x / (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -8.5e-14], t$95$1, If[LessEqual[y, 1.3e-17], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.50000000000000038e-14 or 1.30000000000000002e-17 < y

   1. Initial program 85.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. distribute-rgt-out-- N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 92.9

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

   4. Applied rewrites 92.9%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 79.4

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

   7. Applied rewrites 79.4%

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

   if -8.50000000000000038e-14 < y < 1.30000000000000002e-17

   1. Initial program 90.2%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 77.6

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

   5. Applied rewrites 77.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{2}{z \cdot y} \cdot x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.1% accurate, 1.2× speedup

Math

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

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(Float64(2.0 * x) / Float64(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[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.8%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. distribute-rgt-out-- N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lower--.f64 91.5

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

4. Applied rewrites 91.5%

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

5. Final simplification 91.5%

   \[\leadsto \frac{2 \cdot x}{z \cdot \left(y - t\right)} \]
6. Add Preprocessing

Alternative 12: 53.2% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

   \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in t around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lower-*.f64 55.8

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

5. Applied rewrites 55.8%

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

6. Final simplification 55.8%

   \[\leadsto -2 \cdot \frac{x}{z \cdot t} \]
7. Add Preprocessing

Developer Target 1: 97.1% 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 2024248 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (* x 2) (- (* y z) (* t z))) -2559141628295061/10000000000000000000000000000) (* (/ x (* (- y t) z)) 2) (if (< (/ (* x 2) (- (* y z) (* t z))) 522513913665063/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (* (/ x z) 2) (- y t)) (* (/ x (* (- y t) z)) 2))))

  (/ (* x 2.0) (- (* y z) (* t z))))