Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Percentage Accurate: 95.7% → 96.3%

Time: 12.3s

Alternatives: 22

Speedup: 1.4×

• 28.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * 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 = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * 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 = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 10^{-179}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 1e-179)
   (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))
   (+ (- x (/ (/ y z) 3.0)) (/ t (* (* z 3.0) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 1e-179) {
		tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
	} else {
		tmp = (x - ((y / z) / 3.0)) + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 1d-179) then
        tmp = (x - (y / (z * 3.0d0))) + ((t / (z * 3.0d0)) / y)
    else
        tmp = (x - ((y / z) / 3.0d0)) + (t / ((z * 3.0d0) * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 1e-179) {
		tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
	} else {
		tmp = (x - ((y / z) / 3.0)) + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 1e-179:
		tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)
	else:
		tmp = (x - ((y / z) / 3.0)) + (t / ((z * 3.0) * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 1e-179)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y));
	else
		tmp = Float64(Float64(x - Float64(Float64(y / z) / 3.0)) + Float64(t / Float64(Float64(z * 3.0) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 1e-179)
		tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
	else
		tmp = (x - ((y / z) / 3.0)) + (t / ((z * 3.0) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e-179], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < 1e-179

   1. Initial program 94.9%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \left(\frac{\frac{t}{z \cdot 3}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\left(\frac{t}{z \cdot 3}\right), \color{blue}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \left(z \cdot 3\right)\right), y\right)\right) \]

      4. *-lowering-*.f64 99.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, 3\right)\right), y\right)\right) \]

   4. Applied egg-rr 99.2%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   if 1e-179 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.7%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{\frac{y}{z}}{3}\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 3\right), y\right)\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y}{z}\right), 3\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 3\right), y\right)\right)\right) \]

      3. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, z\right), 3\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 3\right), y\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

Alternative 2: 80.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{+47}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= (* z 3.0) -2e+142)
     t_1
     (if (<= (* z 3.0) 5e+47)
       (* (/ 0.3333333333333333 z) (- (/ t y) y))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -2e+142) {
		tmp = t_1;
	} else if ((z * 3.0) <= 5e+47) {
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	} 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 = x - (y / (z * 3.0d0))
    if ((z * 3.0d0) <= (-2d+142)) then
        tmp = t_1
    else if ((z * 3.0d0) <= 5d+47) then
        tmp = (0.3333333333333333d0 / z) * ((t / y) - y)
    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 / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -2e+142) {
		tmp = t_1;
	} else if ((z * 3.0) <= 5e+47) {
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if (z * 3.0) <= -2e+142:
		tmp = t_1
	elif (z * 3.0) <= 5e+47:
		tmp = (0.3333333333333333 / z) * ((t / y) - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e+142)
		tmp = t_1;
	elseif (Float64(z * 3.0) <= 5e+47)
		tmp = Float64(Float64(0.3333333333333333 / z) * Float64(Float64(t / y) - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if ((z * 3.0) <= -2e+142)
		tmp = t_1;
	elseif ((z * 3.0) <= 5e+47)
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+142], t$95$1, If[LessEqual[N[(z * 3.0), $MachinePrecision], 5e+47], N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -2.0000000000000001e142 or 5.00000000000000022e47 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.8%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 91.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 91.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(z, 3\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 79.9%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]

   if -2.0000000000000001e142 < (*.f64 z #s(literal 3 binary64)) < 5.00000000000000022e47

   1. Initial program 95.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{y \cdot z} - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{z \cdot y} - \frac{1}{3} \cdot \frac{y}{z} \]

      3. times-frac N/A

         \[\leadsto \frac{\frac{1}{3}}{z} \cdot \frac{t}{y} - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      4. metadata-eval N/A

         \[\leadsto \frac{\frac{1}{3} \cdot 1}{z} \cdot \frac{t}{y} - \frac{1}{3} \cdot \frac{y}{z} \]

      5. associate-*r/ N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{z}\right) \cdot \frac{t}{y} - \frac{1}{3} \cdot \frac{y}{z} \]

      6. associate-*r/ N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{z}\right) \cdot \frac{t}{y} - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      7. associate-*l/ N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{z}\right) \cdot \frac{t}{y} - \frac{\frac{1}{3}}{z} \cdot \color{blue}{y} \]

      8. metadata-eval N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{z}\right) \cdot \frac{t}{y} - \frac{\frac{1}{3} \cdot 1}{z} \cdot y \]

      9. associate-*r/ N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{z}\right) \cdot \frac{t}{y} - \left(\frac{1}{3} \cdot \frac{1}{z}\right) \cdot y \]

      10. distribute-lft-out-- N/A

          \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{z}\right) \cdot \color{blue}{\left(\frac{t}{y} - y\right)} \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{3} \cdot \frac{1}{z}\right), \color{blue}{\left(\frac{t}{y} - y\right)}\right) \]

      12. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{3} \cdot 1}{z}\right), \left(\color{blue}{\frac{t}{y}} - y\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{3}}{z}\right), \left(\frac{\color{blue}{t}}{y} - y\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{3}, z\right), \left(\color{blue}{\frac{t}{y}} - y\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{3}, z\right), \mathsf{\_.f64}\left(\left(\frac{t}{y}\right), \color{blue}{y}\right)\right) \]

      16. /-lowering-/.f64 88.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{3}, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, y\right), y\right)\right) \]

   5. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 96.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq 10^{-179}:\\ \;\;\;\;t\_1 + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= (* z 3.0) 1e-179)
     (+ t_1 (/ (/ t (* z 3.0)) y))
     (+ t_1 (/ t (* (* z 3.0) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= 1e-179) {
		tmp = t_1 + ((t / (z * 3.0)) / y);
	} else {
		tmp = t_1 + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if ((z * 3.0d0) <= 1d-179) then
        tmp = t_1 + ((t / (z * 3.0d0)) / y)
    else
        tmp = t_1 + (t / ((z * 3.0d0) * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= 1e-179) {
		tmp = t_1 + ((t / (z * 3.0)) / y);
	} else {
		tmp = t_1 + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if (z * 3.0) <= 1e-179:
		tmp = t_1 + ((t / (z * 3.0)) / y)
	else:
		tmp = t_1 + (t / ((z * 3.0) * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (Float64(z * 3.0) <= 1e-179)
		tmp = Float64(t_1 + Float64(Float64(t / Float64(z * 3.0)) / y));
	else
		tmp = Float64(t_1 + Float64(t / Float64(Float64(z * 3.0) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if ((z * 3.0) <= 1e-179)
		tmp = t_1 + ((t / (z * 3.0)) / y);
	else
		tmp = t_1 + (t / ((z * 3.0) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e-179], N[(t$95$1 + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < 1e-179

   1. Initial program 94.9%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \left(\frac{\frac{t}{z \cdot 3}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\left(\frac{t}{z \cdot 3}\right), \color{blue}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \left(z \cdot 3\right)\right), y\right)\right) \]

      4. *-lowering-*.f64 99.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, 3\right)\right), y\right)\right) \]

   4. Applied egg-rr 99.2%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   if 1e-179 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+48}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{3 \cdot \left(z \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.15e+48)
   (+ (- x (/ y (* z 3.0))) (/ t (* 3.0 (* z y))))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.15e+48) {
		tmp = (x - (y / (z * 3.0))) + (t / (3.0 * (z * y)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.15d+48)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (3.0d0 * (z * y)))
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.15e+48) {
		tmp = (x - (y / (z * 3.0))) + (t / (3.0 * (z * y)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.15e+48:
		tmp = (x - (y / (z * 3.0))) + (t / (3.0 * (z * y)))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.15e+48)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(3.0 * Float64(z * y))));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.15e+48)
		tmp = (x - (y / (z * 3.0))) + (t / (3.0 * (z * y)));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.15e+48], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(3.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e48

   1. Initial program 99.7%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(z \cdot \color{blue}{\left(3 \cdot y\right)}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(z \cdot \left(y \cdot \color{blue}{3}\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(\left(z \cdot y\right) \cdot \color{blue}{3}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\left(z \cdot y\right), \color{blue}{3}\right)\right)\right) \]

      5. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, y\right), 3\right)\right)\right) \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot y\right) \cdot 3}} \]

   if -1.15e48 < t

   1. Initial program 96.1%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 98.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+48}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{3 \cdot \left(z \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+47}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.4e+47)
   (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y)))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+47) {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.4d+47)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+47) {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.4e+47:
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.4e+47)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.4e+47)
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.4e+47], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.40000000000000019e47

   1. Initial program 99.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   if -2.40000000000000019e47 < t

   1. Initial program 96.1%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 98.8%

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

Alternative 6: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+59}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3e+59)
   (+ (- x (/ y (* z 3.0))) (* t (/ (/ 0.3333333333333333 z) y)))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e+59) {
		tmp = (x - (y / (z * 3.0))) + (t * ((0.3333333333333333 / z) / y));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	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 <= (-3d+59)) then
        tmp = (x - (y / (z * 3.0d0))) + (t * ((0.3333333333333333d0 / z) / y))
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e+59) {
		tmp = (x - (y / (z * 3.0))) + (t * ((0.3333333333333333 / z) / y));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3e+59:
		tmp = (x - (y / (z * 3.0))) + (t * ((0.3333333333333333 / z) / y))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3e+59)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t * Float64(Float64(0.3333333333333333 / z) / y)));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3e+59)
		tmp = (x - (y / (z * 3.0))) + (t * ((0.3333333333333333 / z) / y));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3e+59], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e59

   1. Initial program 99.7%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \left(\frac{1}{\color{blue}{\frac{\left(z \cdot 3\right) \cdot y}{t}}}\right)\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \left(\frac{1}{\left(z \cdot 3\right) \cdot y} \cdot \color{blue}{t}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{*.f64}\left(\left(\frac{1}{\left(z \cdot 3\right) \cdot y}\right), \color{blue}{t}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{*.f64}\left(\left(\frac{\frac{1}{z \cdot 3}}{y}\right), t\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{z \cdot 3}\right), y\right), t\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{3 \cdot z}\right), y\right), t\right)\right) \]

      7. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{\frac{1}{3}}{z}\right), y\right), t\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{3}\right), z\right), y\right), t\right)\right) \]

      9. metadata-eval 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\frac{1}{3}, z\right), y\right), t\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{0.3333333333333333}{z}}{y} \cdot t} \]

   if -3e59 < t

   1. Initial program 96.2%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 98.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+59}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0032:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= y -1.7e+16)
     t_1
     (if (<= y 0.0032) (+ x (/ (/ t (* z 3.0)) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if (y <= -1.7e+16) {
		tmp = t_1;
	} else if (y <= 0.0032) {
		tmp = x + ((t / (z * 3.0)) / y);
	} 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 = x - (y / (z * 3.0d0))
    if (y <= (-1.7d+16)) then
        tmp = t_1
    else if (y <= 0.0032d0) then
        tmp = x + ((t / (z * 3.0d0)) / y)
    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 / (z * 3.0));
	double tmp;
	if (y <= -1.7e+16) {
		tmp = t_1;
	} else if (y <= 0.0032) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if y <= -1.7e+16:
		tmp = t_1
	elif y <= 0.0032:
		tmp = x + ((t / (z * 3.0)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (y <= -1.7e+16)
		tmp = t_1;
	elseif (y <= 0.0032)
		tmp = Float64(x + Float64(Float64(t / Float64(z * 3.0)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if (y <= -1.7e+16)
		tmp = t_1;
	elseif (y <= 0.0032)
		tmp = x + ((t / (z * 3.0)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+16], t$95$1, If[LessEqual[y, 0.0032], N[(x + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e16 or 0.00320000000000000015 < y

   1. Initial program 99.7%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(z, 3\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 94.0%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]

   if -1.7e16 < y < 0.00320000000000000015

   1. Initial program 94.3%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \left(\frac{\frac{t}{z \cdot 3}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\left(\frac{t}{z \cdot 3}\right), \color{blue}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \left(z \cdot 3\right)\right), y\right)\right) \]

      4. *-lowering-*.f64 98.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, 3\right)\right), y\right)\right) \]

   4. Applied egg-rr 98.4%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, 3\right)\right), y\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 92.8%

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

Alternative 8: 90.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0115:\\ \;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= y -9.6e+14)
     t_1
     (if (<= y 0.0115) (+ x (/ t (* (* z 3.0) y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if (y <= -9.6e+14) {
		tmp = t_1;
	} else if (y <= 0.0115) {
		tmp = x + (t / ((z * 3.0) * y));
	} 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 = x - (y / (z * 3.0d0))
    if (y <= (-9.6d+14)) then
        tmp = t_1
    else if (y <= 0.0115d0) then
        tmp = x + (t / ((z * 3.0d0) * y))
    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 / (z * 3.0));
	double tmp;
	if (y <= -9.6e+14) {
		tmp = t_1;
	} else if (y <= 0.0115) {
		tmp = x + (t / ((z * 3.0) * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if y <= -9.6e+14:
		tmp = t_1
	elif y <= 0.0115:
		tmp = x + (t / ((z * 3.0) * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (y <= -9.6e+14)
		tmp = t_1;
	elseif (y <= 0.0115)
		tmp = Float64(x + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if (y <= -9.6e+14)
		tmp = t_1;
	elseif (y <= 0.0115)
		tmp = x + (t / ((z * 3.0) * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+14], t$95$1, If[LessEqual[y, 0.0115], N[(x + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6e14 or 0.0115 < y

   1. Initial program 99.7%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(z, 3\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 94.0%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]

   if -9.6e14 < y < 0.0115

   1. Initial program 94.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 3\right), y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 89.4%

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

Alternative 9: 79.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-81}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{\frac{t}{z}}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.55e-81)
   (- x (/ y (* z 3.0)))
   (if (<= y 1.1e-84)
     (/ (/ (/ t z) 3.0) y)
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 1.1e-84) {
		tmp = ((t / z) / 3.0) / y;
	} else {
		tmp = x + (y * (-0.3333333333333333 / 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 <= (-1.55d-81)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 1.1d-84) then
        tmp = ((t / z) / 3.0d0) / y
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 1.1e-84) {
		tmp = ((t / z) / 3.0) / y;
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.55e-81:
		tmp = x - (y / (z * 3.0))
	elif y <= 1.1e-84:
		tmp = ((t / z) / 3.0) / y
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.55e-81)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 1.1e-84)
		tmp = Float64(Float64(Float64(t / z) / 3.0) / y);
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.55e-81)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 1.1e-84)
		tmp = ((t / z) / 3.0) / y;
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.55e-81], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-84], N[(N[(N[(t / z), $MachinePrecision] / 3.0), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999994e-81

   1. Initial program 99.8%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(z, 3\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 79.3%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]

   if -1.54999999999999994e-81 < y < 1.0999999999999999e-84

   1. Initial program 92.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{1}{3} \cdot t}{z}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), z\right), y\right) \]

      6. *-lowering-*.f64 67.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, t\right), z\right), y\right) \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\frac{0.3333333333333333 \cdot t}{z}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{y} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{t}{z} \cdot \frac{1}{3}}{y} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\frac{t}{z} \cdot \frac{1}{3}}{y} \]

      4. div-inv N/A

         \[\leadsto \frac{\frac{\frac{t}{z}}{3}}{y} \]

      5. associate-/r* N/A

         \[\leadsto \frac{\frac{t}{z \cdot 3}}{y} \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{t}{z \cdot 3}\right), \color{blue}{y}\right) \]

      7. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{t}{z}}{3}\right), y\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{t}{z}\right), 3\right), y\right) \]

      9. /-lowering-/.f64 67.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, z\right), 3\right), y\right) \]

   7. Applied egg-rr 67.9%

      \[\leadsto \color{blue}{\frac{\frac{\frac{t}{z}}{3}}{y}} \]

   if 1.0999999999999999e-84 < y

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) + \color{blue}{\frac{x}{y}}\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \cdot y + \color{blue}{\frac{x}{y} \cdot y} \]

      4. associate-*r/ N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      5. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      6. distribute-neg-frac N/A

         \[\leadsto \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \cdot y + \frac{\color{blue}{x}}{y} \cdot y \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{-1}{3}}{z} \cdot y + \frac{x}{y} \cdot y \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      9. associate-*r/ N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      10. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot y} \]

      11. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot \frac{x}{y}\right) \cdot y \]

      12. associate-*r/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{-1 \cdot x}{y} \cdot y \]

      13. associate-*l/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{\left(-1 \cdot x\right) \cdot y}{\color{blue}{y}} \]

      14. associate-/l* N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot x\right) \cdot \color{blue}{\frac{y}{y}} \]

      15. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{y}}{y} \]

      16. *-inverses N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot 1 \]

      17. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x \cdot 1} \]

      18. *-rgt-identity N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + x \]

      19. +-commutative N/A

          \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{-1}{3} \cdot \frac{y}{z}\right)}\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{-1}{3} \cdot y}{\color{blue}{z}}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \frac{-1}{3}}{z}\right)\right) \]

      23. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

   5. Simplified 88.6%

      \[\leadsto \color{blue}{x + y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 79.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-81}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{t}{\frac{z}{0.3333333333333333}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e-81)
   (- x (/ y (* z 3.0)))
   (if (<= y 3.5e-84)
     (/ (/ t (/ z 0.3333333333333333)) y)
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 3.5e-84) {
		tmp = (t / (z / 0.3333333333333333)) / y;
	} else {
		tmp = x + (y * (-0.3333333333333333 / 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 <= (-1.7d-81)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 3.5d-84) then
        tmp = (t / (z / 0.3333333333333333d0)) / y
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 3.5e-84) {
		tmp = (t / (z / 0.3333333333333333)) / y;
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e-81:
		tmp = x - (y / (z * 3.0))
	elif y <= 3.5e-84:
		tmp = (t / (z / 0.3333333333333333)) / y
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e-81)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 3.5e-84)
		tmp = Float64(Float64(t / Float64(z / 0.3333333333333333)) / y);
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e-81)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 3.5e-84)
		tmp = (t / (z / 0.3333333333333333)) / y;
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e-81], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-84], N[(N[(t / N[(z / 0.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6999999999999999e-81

   1. Initial program 99.8%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(z, 3\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 79.3%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]

   if -1.6999999999999999e-81 < y < 3.5000000000000001e-84

   1. Initial program 92.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{1}{3} \cdot t}{z}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), z\right), y\right) \]

      6. *-lowering-*.f64 67.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, t\right), z\right), y\right) \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\frac{0.3333333333333333 \cdot t}{z}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{y \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{t \cdot \frac{1}{3}}{\color{blue}{y} \cdot z} \]

      3. times-frac N/A

         \[\leadsto \frac{t}{y} \cdot \color{blue}{\frac{\frac{1}{3}}{z}} \]

      4. metadata-eval N/A

         \[\leadsto \frac{t}{y} \cdot \frac{\frac{1}{3}}{z} \]

      5. associate-/r* N/A

         \[\leadsto \frac{t}{y} \cdot \frac{1}{\color{blue}{3 \cdot z}} \]

      6. *-commutative N/A

         \[\leadsto \frac{t}{y} \cdot \frac{1}{z \cdot \color{blue}{3}} \]

      7. div-inv N/A

         \[\leadsto \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}} \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\color{blue}{z} \cdot 3\right)\right) \]

      10. *-lowering-*.f64 64.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right) \]

   7. Applied egg-rr 64.4%

      \[\leadsto \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}} \]
   8. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{t}{z \cdot 3}}{\color{blue}{y}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{t}{z \cdot 3}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \left(z \cdot 3\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \left(z \cdot \frac{1}{\frac{1}{3}}\right)\right), y\right) \]

      6. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \left(\frac{z}{\frac{1}{3}}\right)\right), y\right) \]

      7. /-lowering-/.f64 67.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \mathsf{/.f64}\left(z, \frac{1}{3}\right)\right), y\right) \]

   9. Applied egg-rr 67.8%

      \[\leadsto \color{blue}{\frac{\frac{t}{\frac{z}{0.3333333333333333}}}{y}} \]

   if 3.5000000000000001e-84 < y

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) + \color{blue}{\frac{x}{y}}\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \cdot y + \color{blue}{\frac{x}{y} \cdot y} \]

      4. associate-*r/ N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      5. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      6. distribute-neg-frac N/A

         \[\leadsto \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \cdot y + \frac{\color{blue}{x}}{y} \cdot y \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{-1}{3}}{z} \cdot y + \frac{x}{y} \cdot y \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      9. associate-*r/ N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      10. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot y} \]

      11. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot \frac{x}{y}\right) \cdot y \]

      12. associate-*r/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{-1 \cdot x}{y} \cdot y \]

      13. associate-*l/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{\left(-1 \cdot x\right) \cdot y}{\color{blue}{y}} \]

      14. associate-/l* N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot x\right) \cdot \color{blue}{\frac{y}{y}} \]

      15. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{y}}{y} \]

      16. *-inverses N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot 1 \]

      17. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x \cdot 1} \]

      18. *-rgt-identity N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + x \]

      19. +-commutative N/A

          \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{-1}{3} \cdot \frac{y}{z}\right)}\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{-1}{3} \cdot y}{\color{blue}{z}}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \frac{-1}{3}}{z}\right)\right) \]

      23. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

   5. Simplified 88.6%

      \[\leadsto \color{blue}{x + y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-81}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.55e-81)
   (- x (/ y (* z 3.0)))
   (if (<= y 4.7e-84)
     (/ (/ t y) (* z 3.0))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 4.7e-84) {
		tmp = (t / y) / (z * 3.0);
	} else {
		tmp = x + (y * (-0.3333333333333333 / 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 <= (-1.55d-81)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 4.7d-84) then
        tmp = (t / y) / (z * 3.0d0)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 4.7e-84) {
		tmp = (t / y) / (z * 3.0);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.55e-81:
		tmp = x - (y / (z * 3.0))
	elif y <= 4.7e-84:
		tmp = (t / y) / (z * 3.0)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.55e-81)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 4.7e-84)
		tmp = Float64(Float64(t / y) / Float64(z * 3.0));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.55e-81)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 4.7e-84)
		tmp = (t / y) / (z * 3.0);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.55e-81], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e-84], N[(N[(t / y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999994e-81

   1. Initial program 99.8%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(z, 3\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 79.3%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]

   if -1.54999999999999994e-81 < y < 4.7e-84

   1. Initial program 92.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{1}{3} \cdot t}{z}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), z\right), y\right) \]

      6. *-lowering-*.f64 67.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, t\right), z\right), y\right) \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\frac{0.3333333333333333 \cdot t}{z}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{y \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{t \cdot \frac{1}{3}}{\color{blue}{y} \cdot z} \]

      3. times-frac N/A

         \[\leadsto \frac{t}{y} \cdot \color{blue}{\frac{\frac{1}{3}}{z}} \]

      4. metadata-eval N/A

         \[\leadsto \frac{t}{y} \cdot \frac{\frac{1}{3}}{z} \]

      5. associate-/r* N/A

         \[\leadsto \frac{t}{y} \cdot \frac{1}{\color{blue}{3 \cdot z}} \]

      6. *-commutative N/A

         \[\leadsto \frac{t}{y} \cdot \frac{1}{z \cdot \color{blue}{3}} \]

      7. div-inv N/A

         \[\leadsto \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}} \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\color{blue}{z} \cdot 3\right)\right) \]

      10. *-lowering-*.f64 64.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right) \]

   7. Applied egg-rr 64.4%

      \[\leadsto \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}} \]

   if 4.7e-84 < y

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) + \color{blue}{\frac{x}{y}}\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \cdot y + \color{blue}{\frac{x}{y} \cdot y} \]

      4. associate-*r/ N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      5. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      6. distribute-neg-frac N/A

         \[\leadsto \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \cdot y + \frac{\color{blue}{x}}{y} \cdot y \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{-1}{3}}{z} \cdot y + \frac{x}{y} \cdot y \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      9. associate-*r/ N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      10. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot y} \]

      11. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot \frac{x}{y}\right) \cdot y \]

      12. associate-*r/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{-1 \cdot x}{y} \cdot y \]

      13. associate-*l/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{\left(-1 \cdot x\right) \cdot y}{\color{blue}{y}} \]

      14. associate-/l* N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot x\right) \cdot \color{blue}{\frac{y}{y}} \]

      15. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{y}}{y} \]

      16. *-inverses N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot 1 \]

      17. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x \cdot 1} \]

      18. *-rgt-identity N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + x \]

      19. +-commutative N/A

          \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{-1}{3} \cdot \frac{y}{z}\right)}\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{-1}{3} \cdot y}{\color{blue}{z}}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \frac{-1}{3}}{z}\right)\right) \]

      23. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

   5. Simplified 88.6%

      \[\leadsto \color{blue}{x + y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-81}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e-81)
   (- x (/ y (* z 3.0)))
   (if (<= y 2.8e-84)
     (/ t (* z (* 3.0 y)))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 2.8e-84) {
		tmp = t / (z * (3.0 * y));
	} else {
		tmp = x + (y * (-0.3333333333333333 / 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 <= (-2.1d-81)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 2.8d-84) then
        tmp = t / (z * (3.0d0 * y))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 2.8e-84) {
		tmp = t / (z * (3.0 * y));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e-81:
		tmp = x - (y / (z * 3.0))
	elif y <= 2.8e-84:
		tmp = t / (z * (3.0 * y))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e-81)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 2.8e-84)
		tmp = Float64(t / Float64(z * Float64(3.0 * y)));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.1e-81)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 2.8e-84)
		tmp = t / (z * (3.0 * y));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e-81], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-84], N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0999999999999999e-81

   1. Initial program 99.8%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(z, 3\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 79.3%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]

   if -2.0999999999999999e-81 < y < 2.79999999999999982e-84

   1. Initial program 92.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{1}{3} \cdot t}{z}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), z\right), y\right) \]

      6. *-lowering-*.f64 67.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, t\right), z\right), y\right) \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\frac{0.3333333333333333 \cdot t}{z}}{y}} \]
   6. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{z \cdot y}} \]

      2. *-commutative N/A

         \[\leadsto \frac{t \cdot \frac{1}{3}}{\color{blue}{z} \cdot y} \]

      3. associate-/l* N/A

         \[\leadsto t \cdot \color{blue}{\frac{\frac{1}{3}}{z \cdot y}} \]

      4. metadata-eval N/A

         \[\leadsto t \cdot \frac{\frac{1}{3}}{\color{blue}{z} \cdot y} \]

      5. associate-/r* N/A

         \[\leadsto t \cdot \frac{1}{\color{blue}{3 \cdot \left(z \cdot y\right)}} \]

      6. *-commutative N/A

         \[\leadsto t \cdot \frac{1}{\left(z \cdot y\right) \cdot \color{blue}{3}} \]

      7. div-inv N/A

         \[\leadsto \frac{t}{\color{blue}{\left(z \cdot y\right) \cdot 3}} \]

      8. *-commutative N/A

         \[\leadsto \frac{t}{3 \cdot \color{blue}{\left(z \cdot y\right)}} \]

      9. associate-/r* N/A

         \[\leadsto \frac{\frac{t}{3}}{\color{blue}{z \cdot y}} \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{t}{3}\right), \color{blue}{\left(z \cdot y\right)}\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, 3\right), \left(\color{blue}{z} \cdot y\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, 3\right), \left(y \cdot \color{blue}{z}\right)\right) \]

      13. *-lowering-*.f64 63.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, 3\right), \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 63.7%

      \[\leadsto \color{blue}{\frac{\frac{t}{3}}{y \cdot z}} \]
   8. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{t}{3} \cdot \color{blue}{\frac{1}{y \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{t}{3} \cdot \frac{1}{z \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{t}{3} \cdot \frac{\frac{1}{z}}{\color{blue}{y}} \]

      4. times-frac N/A

         \[\leadsto \frac{t \cdot \frac{1}{z}}{\color{blue}{3 \cdot y}} \]

      5. *-commutative N/A

         \[\leadsto \frac{t \cdot \frac{1}{z}}{y \cdot \color{blue}{3}} \]

      6. div-inv N/A

         \[\leadsto \frac{\frac{t}{z}}{\color{blue}{y} \cdot 3} \]

      7. associate-/l/ N/A

         \[\leadsto \frac{t}{\color{blue}{\left(y \cdot 3\right) \cdot z}} \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\left(y \cdot 3\right) \cdot z\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot 3\right), \color{blue}{z}\right)\right) \]

      10. *-lowering-*.f64 63.9%

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, 3\right), z\right)\right) \]

   9. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{\frac{t}{\left(y \cdot 3\right) \cdot z}} \]

   if 2.79999999999999982e-84 < y

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) + \color{blue}{\frac{x}{y}}\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \cdot y + \color{blue}{\frac{x}{y} \cdot y} \]

      4. associate-*r/ N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      5. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      6. distribute-neg-frac N/A

         \[\leadsto \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \cdot y + \frac{\color{blue}{x}}{y} \cdot y \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{-1}{3}}{z} \cdot y + \frac{x}{y} \cdot y \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      9. associate-*r/ N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      10. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot y} \]

      11. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot \frac{x}{y}\right) \cdot y \]

      12. associate-*r/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{-1 \cdot x}{y} \cdot y \]

      13. associate-*l/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{\left(-1 \cdot x\right) \cdot y}{\color{blue}{y}} \]

      14. associate-/l* N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot x\right) \cdot \color{blue}{\frac{y}{y}} \]

      15. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{y}}{y} \]

      16. *-inverses N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot 1 \]

      17. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x \cdot 1} \]

      18. *-rgt-identity N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + x \]

      19. +-commutative N/A

          \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{-1}{3} \cdot \frac{y}{z}\right)}\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{-1}{3} \cdot y}{\color{blue}{z}}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \frac{-1}{3}}{z}\right)\right) \]

      23. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

   5. Simplified 88.6%

      \[\leadsto \color{blue}{x + y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-81}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-81}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.75e-81)
   (- x (/ y (* z 3.0)))
   (if (<= y 1.45e-84)
     (/ t (* (* z 3.0) y))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 1.45e-84) {
		tmp = t / ((z * 3.0) * y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / 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 <= (-1.75d-81)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 1.45d-84) then
        tmp = t / ((z * 3.0d0) * y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e-81) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 1.45e-84) {
		tmp = t / ((z * 3.0) * y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.75e-81:
		tmp = x - (y / (z * 3.0))
	elif y <= 1.45e-84:
		tmp = t / ((z * 3.0) * y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.75e-81)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 1.45e-84)
		tmp = Float64(t / Float64(Float64(z * 3.0) * y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.75e-81)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 1.45e-84)
		tmp = t / ((z * 3.0) * y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.75e-81], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-84], N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999993e-81

   1. Initial program 99.8%

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

      1. associate-+l- N/A

         \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(z, 3\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 79.3%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]

   if -1.74999999999999993e-81 < y < 1.4500000000000001e-84

   1. Initial program 92.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{1}{3} \cdot t}{z}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), z\right), y\right) \]

      6. *-lowering-*.f64 67.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, t\right), z\right), y\right) \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{\frac{0.3333333333333333 \cdot t}{z}}{y}} \]
   6. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{z \cdot y}} \]

      2. *-commutative N/A

         \[\leadsto \frac{t \cdot \frac{1}{3}}{\color{blue}{z} \cdot y} \]

      3. associate-/l* N/A

         \[\leadsto t \cdot \color{blue}{\frac{\frac{1}{3}}{z \cdot y}} \]

      4. metadata-eval N/A

         \[\leadsto t \cdot \frac{\frac{1}{3}}{\color{blue}{z} \cdot y} \]

      5. associate-/r* N/A

         \[\leadsto t \cdot \frac{1}{\color{blue}{3 \cdot \left(z \cdot y\right)}} \]

      6. *-commutative N/A

         \[\leadsto t \cdot \frac{1}{\left(z \cdot y\right) \cdot \color{blue}{3}} \]

      7. div-inv N/A

         \[\leadsto \frac{t}{\color{blue}{\left(z \cdot y\right) \cdot 3}} \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\left(z \cdot y\right) \cdot 3\right)}\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(t, \left(\left(y \cdot z\right) \cdot 3\right)\right) \]

      10. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(t, \left(y \cdot \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      12. *-lowering-*.f64 63.9%

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   7. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{\frac{t}{y \cdot \left(z \cdot 3\right)}} \]

   if 1.4500000000000001e-84 < y

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) + \color{blue}{\frac{x}{y}}\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \cdot y + \color{blue}{\frac{x}{y} \cdot y} \]

      4. associate-*r/ N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      5. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

      6. distribute-neg-frac N/A

         \[\leadsto \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \cdot y + \frac{\color{blue}{x}}{y} \cdot y \]

      7. metadata-eval N/A

         \[\leadsto \frac{\frac{-1}{3}}{z} \cdot y + \frac{x}{y} \cdot y \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      9. associate-*r/ N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

      10. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot y} \]

      11. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot \frac{x}{y}\right) \cdot y \]

      12. associate-*r/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{-1 \cdot x}{y} \cdot y \]

      13. associate-*l/ N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{\left(-1 \cdot x\right) \cdot y}{\color{blue}{y}} \]

      14. associate-/l* N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot x\right) \cdot \color{blue}{\frac{y}{y}} \]

      15. mul-1-neg N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{y}}{y} \]

      16. *-inverses N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot 1 \]

      17. cancel-sign-sub N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x \cdot 1} \]

      18. *-rgt-identity N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + x \]

      19. +-commutative N/A

          \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      20. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{-1}{3} \cdot \frac{y}{z}\right)}\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{-1}{3} \cdot y}{\color{blue}{z}}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \frac{-1}{3}}{z}\right)\right) \]

      23. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

   5. Simplified 88.6%

      \[\leadsto \color{blue}{x + y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-81}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+143}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 0.85:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+143)
   (/ (/ y -3.0) z)
   (if (<= y 0.85) x (/ (* y -0.3333333333333333) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+143) {
		tmp = (y / -3.0) / z;
	} else if (y <= 0.85) {
		tmp = x;
	} else {
		tmp = (y * -0.3333333333333333) / 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 <= (-2.8d+143)) then
        tmp = (y / (-3.0d0)) / z
    else if (y <= 0.85d0) then
        tmp = x
    else
        tmp = (y * (-0.3333333333333333d0)) / z
    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+143) {
		tmp = (y / -3.0) / z;
	} else if (y <= 0.85) {
		tmp = x;
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+143:
		tmp = (y / -3.0) / z
	elif y <= 0.85:
		tmp = x
	else:
		tmp = (y * -0.3333333333333333) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+143)
		tmp = Float64(Float64(y / -3.0) / z);
	elseif (y <= 0.85)
		tmp = x;
	else
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e+143)
		tmp = (y / -3.0) / z;
	elseif (y <= 0.85)
		tmp = x;
	else
		tmp = (y * -0.3333333333333333) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+143], N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 0.85], x, N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999998e143

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y \cdot \frac{-1}{3}}{z} \]

      3. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}} \]

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \]

      5. distribute-neg-frac N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{z}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\frac{-1}{3}}{z}\right)\right) \]

      13. /-lowering-/.f64 85.8%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{z}\right)\right) \]

   5. Simplified 85.8%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}} \]

      2. div-inv N/A

         \[\leadsto y \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}} \]

      3. metadata-eval N/A

         \[\leadsto y \cdot \frac{1}{z \cdot -3} \]

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)} \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)} \]

      6. associate-*r/ N/A

         \[\leadsto \frac{y \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}} \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \frac{y \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}} \]

      8. times-frac N/A

         \[\leadsto \frac{y}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}} \]

      9. metadata-eval N/A

         \[\leadsto \frac{y}{z} \cdot \frac{1}{-3} \]

      10. metadata-eval N/A

          \[\leadsto \frac{y}{z} \cdot \frac{-1}{3} \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\frac{-1}{3}}\right) \]

      12. /-lowering-/.f64 85.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-1}{3}\right) \]

   7. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]
   8. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \frac{y \cdot \frac{-1}{3}}{\color{blue}{z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), \color{blue}{z}\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)\right), z\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(y \cdot \frac{1}{3}\right)\right), z\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \frac{1}{3}\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \frac{1}{3}\right), z\right) \]

      7. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(y\right)}{3}\right), z\right) \]

      8. frac-2neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)}{\mathsf{neg}\left(3\right)}\right), z\right) \]

      9. remove-double-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{\mathsf{neg}\left(3\right)}\right), z\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(3\right)\right)\right), z\right) \]

      11. metadata-eval 86.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, -3\right), z\right) \]

   9. Applied egg-rr 86.1%

      \[\leadsto \color{blue}{\frac{\frac{y}{-3}}{z}} \]

   if -2.79999999999999998e143 < y < 0.849999999999999978

   1. Initial program 95.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 36.7%

      \[\leadsto \color{blue}{x} \]

   if 0.849999999999999978 < y

   1. Initial program 99.7%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \left(\frac{\frac{t}{z \cdot 3}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\left(\frac{t}{z \cdot 3}\right), \color{blue}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \left(z \cdot 3\right)\right), y\right)\right) \]

      4. *-lowering-*.f64 98.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, 3\right)\right), y\right)\right) \]

   4. Applied egg-rr 98.0%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 73.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 73.0%

      \[\leadsto \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 45.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.05:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y -0.3333333333333333) z)))
   (if (<= y -2.7e+143) t_1 (if (<= y 2.05) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * -0.3333333333333333) / z;
	double tmp;
	if (y <= -2.7e+143) {
		tmp = t_1;
	} else if (y <= 2.05) {
		tmp = x;
	} 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 = (y * (-0.3333333333333333d0)) / z
    if (y <= (-2.7d+143)) then
        tmp = t_1
    else if (y <= 2.05d0) then
        tmp = x
    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 = (y * -0.3333333333333333) / z;
	double tmp;
	if (y <= -2.7e+143) {
		tmp = t_1;
	} else if (y <= 2.05) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * -0.3333333333333333) / z
	tmp = 0
	if y <= -2.7e+143:
		tmp = t_1
	elif y <= 2.05:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * -0.3333333333333333) / z)
	tmp = 0.0
	if (y <= -2.7e+143)
		tmp = t_1;
	elseif (y <= 2.05)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * -0.3333333333333333) / z;
	tmp = 0.0;
	if (y <= -2.7e+143)
		tmp = t_1;
	elseif (y <= 2.05)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -2.7e+143], t$95$1, If[LessEqual[y, 2.05], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000002e143 or 2.0499999999999998 < y

   1. Initial program 99.8%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \left(\frac{\frac{t}{z \cdot 3}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\left(\frac{t}{z \cdot 3}\right), \color{blue}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \left(z \cdot 3\right)\right), y\right)\right) \]

      4. *-lowering-*.f64 97.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, 3\right)\right), y\right)\right) \]

   4. Applied egg-rr 97.6%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -2.7000000000000002e143 < y < 2.0499999999999998

   1. Initial program 95.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 36.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{elif}\;y \leq 1.25:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e+120)
   (* (/ y z) -0.3333333333333333)
   (if (<= y 1.25) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+120) {
		tmp = (y / z) * -0.3333333333333333;
	} else if (y <= 1.25) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (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 <= (-8d+120)) then
        tmp = (y / z) * (-0.3333333333333333d0)
    else if (y <= 1.25d0) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) / (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 <= -8e+120) {
		tmp = (y / z) * -0.3333333333333333;
	} else if (y <= 1.25) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e+120:
		tmp = (y / z) * -0.3333333333333333
	elif y <= 1.25:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e+120)
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	elseif (y <= 1.25)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8e+120)
		tmp = (y / z) * -0.3333333333333333;
	elseif (y <= 1.25)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e+120], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], If[LessEqual[y, 1.25], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9999999999999998e120

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y \cdot \frac{-1}{3}}{z} \]

      3. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}} \]

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \]

      5. distribute-neg-frac N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{z}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\frac{-1}{3}}{z}\right)\right) \]

      13. /-lowering-/.f64 84.1%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{z}\right)\right) \]

   5. Simplified 84.1%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}} \]

      2. div-inv N/A

         \[\leadsto y \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}} \]

      3. metadata-eval N/A

         \[\leadsto y \cdot \frac{1}{z \cdot -3} \]

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)} \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)} \]

      6. associate-*r/ N/A

         \[\leadsto \frac{y \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}} \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \frac{y \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}} \]

      8. times-frac N/A

         \[\leadsto \frac{y}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}} \]

      9. metadata-eval N/A

         \[\leadsto \frac{y}{z} \cdot \frac{1}{-3} \]

      10. metadata-eval N/A

          \[\leadsto \frac{y}{z} \cdot \frac{-1}{3} \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\frac{-1}{3}}\right) \]

      12. /-lowering-/.f64 84.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-1}{3}\right) \]

   7. Applied egg-rr 84.2%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

   if -7.9999999999999998e120 < y < 1.25

   1. Initial program 95.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 36.5%

      \[\leadsto \color{blue}{x} \]

   if 1.25 < y

   1. Initial program 99.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y \cdot \frac{-1}{3}}{z} \]

      3. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}} \]

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \]

      5. distribute-neg-frac N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{z}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\frac{-1}{3}}{z}\right)\right) \]

      13. /-lowering-/.f64 72.7%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{z}\right)\right) \]

   5. Simplified 72.7%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}} \]

      2. div-inv N/A

         \[\leadsto y \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}} \]

      3. metadata-eval N/A

         \[\leadsto y \cdot \frac{1}{z \cdot -3} \]

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)} \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)} \]

      6. associate-*r/ N/A

         \[\leadsto \frac{y \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}} \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \frac{y \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}} \]

      8. times-frac N/A

         \[\leadsto \frac{y}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}} \]

      9. metadata-eval N/A

         \[\leadsto \frac{y}{z} \cdot \frac{1}{-3} \]

      10. metadata-eval N/A

          \[\leadsto \frac{y}{z} \cdot \frac{-1}{3} \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\frac{-1}{3}}\right) \]

      12. /-lowering-/.f64 72.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-1}{3}\right) \]

   7. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      2. clear-num N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{1}{\color{blue}{\frac{z}{y}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{\frac{-1}{3}}{\color{blue}{\frac{z}{y}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      5. /-lowering-/.f64 72.8%

         \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333}{\frac{z}{y}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{if}\;y \leq -2 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.35:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y z) -0.3333333333333333)))
   (if (<= y -2e+120) t_1 (if (<= y 2.35) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * -0.3333333333333333;
	double tmp;
	if (y <= -2e+120) {
		tmp = t_1;
	} else if (y <= 2.35) {
		tmp = x;
	} 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 = (y / z) * (-0.3333333333333333d0)
    if (y <= (-2d+120)) then
        tmp = t_1
    else if (y <= 2.35d0) then
        tmp = x
    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 = (y / z) * -0.3333333333333333;
	double tmp;
	if (y <= -2e+120) {
		tmp = t_1;
	} else if (y <= 2.35) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) * -0.3333333333333333
	tmp = 0
	if y <= -2e+120:
		tmp = t_1
	elif y <= 2.35:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) * -0.3333333333333333)
	tmp = 0.0
	if (y <= -2e+120)
		tmp = t_1;
	elseif (y <= 2.35)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) * -0.3333333333333333;
	tmp = 0.0;
	if (y <= -2e+120)
		tmp = t_1;
	elseif (y <= 2.35)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]}, If[LessEqual[y, -2e+120], t$95$1, If[LessEqual[y, 2.35], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2e120 or 2.35000000000000009 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y \cdot \frac{-1}{3}}{z} \]

      3. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}} \]

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \]

      5. distribute-neg-frac N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{z}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\frac{-1}{3}}{z}\right)\right) \]

      13. /-lowering-/.f64 77.4%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{z}\right)\right) \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}} \]

      2. div-inv N/A

         \[\leadsto y \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}} \]

      3. metadata-eval N/A

         \[\leadsto y \cdot \frac{1}{z \cdot -3} \]

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)} \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)} \]

      6. associate-*r/ N/A

         \[\leadsto \frac{y \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}} \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \frac{y \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}} \]

      8. times-frac N/A

         \[\leadsto \frac{y}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}} \]

      9. metadata-eval N/A

         \[\leadsto \frac{y}{z} \cdot \frac{1}{-3} \]

      10. metadata-eval N/A

          \[\leadsto \frac{y}{z} \cdot \frac{-1}{3} \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\frac{-1}{3}}\right) \]

      12. /-lowering-/.f64 77.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-1}{3}\right) \]

   7. Applied egg-rr 77.5%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

   if -2e120 < y < 2.35000000000000009

   1. Initial program 95.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 36.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.56:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ -0.3333333333333333 z))))
   (if (<= y -2.35e+120) t_1 (if (<= y 1.56) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (-0.3333333333333333 / z);
	double tmp;
	if (y <= -2.35e+120) {
		tmp = t_1;
	} else if (y <= 1.56) {
		tmp = x;
	} 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 = y * ((-0.3333333333333333d0) / z)
    if (y <= (-2.35d+120)) then
        tmp = t_1
    else if (y <= 1.56d0) then
        tmp = x
    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 = y * (-0.3333333333333333 / z);
	double tmp;
	if (y <= -2.35e+120) {
		tmp = t_1;
	} else if (y <= 1.56) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (-0.3333333333333333 / z)
	tmp = 0
	if y <= -2.35e+120:
		tmp = t_1
	elif y <= 1.56:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-0.3333333333333333 / z))
	tmp = 0.0
	if (y <= -2.35e+120)
		tmp = t_1;
	elseif (y <= 1.56)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (-0.3333333333333333 / z);
	tmp = 0.0;
	if (y <= -2.35e+120)
		tmp = t_1;
	elseif (y <= 1.56)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.35e+120], t$95$1, If[LessEqual[y, 1.56], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.34999999999999997e120 or 1.5600000000000001 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y \cdot \frac{-1}{3}}{z} \]

      3. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}} \]

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \]

      5. distribute-neg-frac N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto y \cdot \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{z}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{\frac{-1}{3}}{z}\right)\right) \]

      13. /-lowering-/.f64 77.4%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{z}\right)\right) \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   if -2.34999999999999997e120 < y < 1.5600000000000001

   1. Initial program 95.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 36.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 95.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - \frac{t}{y}}{z \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- x (/ (- y (/ t y)) (* z 3.0))))

C

double code(double x, double y, double z, double t) {
	return x - ((y - (t / y)) / (z * 3.0));
}

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 - ((y - (t / y)) / (z * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - ((y - (t / y)) / (z * 3.0));
}

Python

def code(x, y, z, t):
	return x - ((y - (t / y)) / (z * 3.0))

Julia

function code(x, y, z, t)
	return Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - ((y - (t / y)) / (z * 3.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

   1. associate-+l- N/A

      \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   2. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

   4. associate-/r* N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

   5. sub-div N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

   9. *-lowering-*.f64 96.1%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

4. Applied egg-rr 96.1%

   \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]
5. Add Preprocessing

Alternative 20: 63.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{z \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- x (/ y (* z 3.0))))

C

double code(double x, double y, double z, double t) {
	return x - (y / (z * 3.0));
}

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 - (y / (z * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (y / (z * 3.0));
}

Python

def code(x, y, z, t):
	return x - (y / (z * 3.0))

Julia

function code(x, y, z, t)
	return Float64(x - Float64(y / Float64(z * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (y / (z * 3.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

   1. associate-+l- N/A

      \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   2. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

   4. associate-/r* N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

   5. sub-div N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

   9. *-lowering-*.f64 96.1%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

4. Applied egg-rr 96.1%

   \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

5. Taylor expanded in y around inf

   \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(z, 3\right)\right)\right) \]
6. Step-by-step derivation

7. Simplified 64.9%

   \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]
8. Add Preprocessing

Alternative 21: 63.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{-0.3333333333333333}{z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* y (/ -0.3333333333333333 z))))

C

double code(double x, double y, double z, double t) {
	return x + (y * (-0.3333333333333333 / 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 + (y * ((-0.3333333333333333d0) / z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (y * (-0.3333333333333333 / z));
}

Python

def code(x, y, z, t):
	return x + (y * (-0.3333333333333333 / z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(y * Float64(-0.3333333333333333 / z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (y * (-0.3333333333333333 / z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
4. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto y \cdot \left(\frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right)}\right) \]

   2. +-commutative N/A

      \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) + \color{blue}{\frac{x}{y}}\right) \]

   3. distribute-rgt-in N/A

      \[\leadsto \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{z}\right)\right) \cdot y + \color{blue}{\frac{x}{y} \cdot y} \]

   4. associate-*r/ N/A

      \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

   5. metadata-eval N/A

      \[\leadsto \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{z}\right)\right) \cdot y + \frac{x}{y} \cdot y \]

   6. distribute-neg-frac N/A

      \[\leadsto \frac{\mathsf{neg}\left(\frac{1}{3}\right)}{z} \cdot y + \frac{\color{blue}{x}}{y} \cdot y \]

   7. metadata-eval N/A

      \[\leadsto \frac{\frac{-1}{3}}{z} \cdot y + \frac{x}{y} \cdot y \]

   8. associate-*l/ N/A

      \[\leadsto \frac{\frac{-1}{3} \cdot y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

   9. associate-*r/ N/A

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{\frac{x}{y}} \cdot y \]

   10. cancel-sign-sub N/A

       \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot y} \]

   11. mul-1-neg N/A

       \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot \frac{x}{y}\right) \cdot y \]

   12. associate-*r/ N/A

       \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{-1 \cdot x}{y} \cdot y \]

   13. associate-*l/ N/A

       \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \frac{\left(-1 \cdot x\right) \cdot y}{\color{blue}{y}} \]

   14. associate-/l* N/A

       \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(-1 \cdot x\right) \cdot \color{blue}{\frac{y}{y}} \]

   15. mul-1-neg N/A

       \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot \frac{\color{blue}{y}}{y} \]

   16. *-inverses N/A

       \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(x\right)\right) \cdot 1 \]

   17. cancel-sign-sub N/A

       \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x \cdot 1} \]

   18. *-rgt-identity N/A

       \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + x \]

   19. +-commutative N/A

       \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

   20. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{-1}{3} \cdot \frac{y}{z}\right)}\right) \]

   21. associate-*r/ N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{-1}{3} \cdot y}{\color{blue}{z}}\right)\right) \]

   22. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \frac{-1}{3}}{z}\right)\right) \]

   23. associate-/l* N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

5. Simplified 64.9%

   \[\leadsto \color{blue}{x + y \cdot \frac{-0.3333333333333333}{z}} \]
6. Add Preprocessing

Alternative 22: 29.5% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 96.9%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 31.3%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / 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 = (x - (y / (z * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024192 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y)))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))