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

Percentage Accurate: 95.7% → 97.6%

Time: 11.4s

Alternatives: 20

Speedup: 0.7×

• 27.8% 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: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (/ (- (/ t y) y) z) 3.0))))
   (if (<= y -8.5e-52)
     t_1
     (if (<= y 4.8e-17) (+ x (/ (/ t (* z 3.0)) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((((t / y) - y) / z) / 3.0);
	double tmp;
	if (y <= -8.5e-52) {
		tmp = t_1;
	} else if (y <= 4.8e-17) {
		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 + ((((t / y) - y) / z) / 3.0d0)
    if (y <= (-8.5d-52)) then
        tmp = t_1
    else if (y <= 4.8d-17) 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 + ((((t / y) - y) / z) / 3.0);
	double tmp;
	if (y <= -8.5e-52) {
		tmp = t_1;
	} else if (y <= 4.8e-17) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((((t / y) - y) / z) / 3.0)
	tmp = 0
	if y <= -8.5e-52:
		tmp = t_1
	elif y <= 4.8e-17:
		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(Float64(Float64(Float64(t / y) - y) / z) / 3.0))
	tmp = 0.0
	if (y <= -8.5e-52)
		tmp = t_1;
	elseif (y <= 4.8e-17)
		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 + ((((t / y) - y) / z) / 3.0);
	tmp = 0.0;
	if (y <= -8.5e-52)
		tmp = t_1;
	elseif (y <= 4.8e-17)
		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[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e-52], t$95$1, If[LessEqual[y, 4.8e-17], 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 < -8.50000000000000006e-52 or 4.79999999999999973e-17 < y

   1. Initial program 97.8%

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

      1. associate-/r* N/A

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

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

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

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

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

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

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

      5. /-lowering-/.f64 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -8.50000000000000006e-52 < y < 4.79999999999999973e-17

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 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 90.7%

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

      1. associate-/r* N/A

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

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

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

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

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

      4. *-lowering-*.f64 97.2%

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

   7. Applied egg-rr 97.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{-3} \cdot \frac{-1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))))
   (if (<= t_1 1e+307) t_1 (+ x (* (/ (- (/ t y) y) -3.0) (/ -1.0 z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 1e+307) {
		tmp = t_1;
	} else {
		tmp = x + ((((t / y) - y) / -3.0) * (-1.0 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    if (t_1 <= 1d+307) then
        tmp = t_1
    else
        tmp = x + ((((t / y) - y) / (-3.0d0)) * ((-1.0d0) / z))
    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))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 1e+307) {
		tmp = t_1;
	} else {
		tmp = x + ((((t / y) - y) / -3.0) * (-1.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	tmp = 0
	if t_1 <= 1e+307:
		tmp = t_1
	else:
		tmp = x + ((((t / y) - y) / -3.0) * (-1.0 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))))
	tmp = 0.0
	if (t_1 <= 1e+307)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(Float64(Float64(t / y) - y) / -3.0) * Float64(-1.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	tmp = 0.0;
	if (t_1 <= 1e+307)
		tmp = t_1;
	else
		tmp = x + ((((t / y) - y) / -3.0) * (-1.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+307], t$95$1, N[(x + N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / -3.0), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 9.99999999999999986e306

   1. Initial program 98.1%

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

   if 9.99999999999999986e306 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))

   1. Initial program 82.3%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

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

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

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

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

      10. times-frac N/A

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 N/A

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

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

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

      15. metadata-eval N/A

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

      16. /-lowering-/.f64 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto x + \color{blue}{\frac{y - \frac{t}{y}}{-3} \cdot \frac{1}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 10^{+307}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{-3} \cdot \frac{-1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y} - y\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{t\_1}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{t\_1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ t y) y)))
   (if (<= y -2.6e-24)
     (+ x (/ t_1 (* z 3.0)))
     (if (<= y 1.8e-30)
       (+ x (/ (/ t (* z 3.0)) y))
       (- x (* -0.3333333333333333 (/ t_1 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -2.6e-24) {
		tmp = x + (t_1 / (z * 3.0));
	} else if (y <= 1.8e-30) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = x - (-0.3333333333333333 * (t_1 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t / y) - y
    if (y <= (-2.6d-24)) then
        tmp = x + (t_1 / (z * 3.0d0))
    else if (y <= 1.8d-30) then
        tmp = x + ((t / (z * 3.0d0)) / y)
    else
        tmp = x - ((-0.3333333333333333d0) * (t_1 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -2.6e-24) {
		tmp = x + (t_1 / (z * 3.0));
	} else if (y <= 1.8e-30) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = x - (-0.3333333333333333 * (t_1 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t / y) - y
	tmp = 0
	if y <= -2.6e-24:
		tmp = x + (t_1 / (z * 3.0))
	elif y <= 1.8e-30:
		tmp = x + ((t / (z * 3.0)) / y)
	else:
		tmp = x - (-0.3333333333333333 * (t_1 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / y) - y)
	tmp = 0.0
	if (y <= -2.6e-24)
		tmp = Float64(x + Float64(t_1 / Float64(z * 3.0)));
	elseif (y <= 1.8e-30)
		tmp = Float64(x + Float64(Float64(t / Float64(z * 3.0)) / y));
	else
		tmp = Float64(x - Float64(-0.3333333333333333 * Float64(t_1 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t / y) - y;
	tmp = 0.0;
	if (y <= -2.6e-24)
		tmp = x + (t_1 / (z * 3.0));
	elseif (y <= 1.8e-30)
		tmp = x + ((t / (z * 3.0)) / y);
	else
		tmp = x - (-0.3333333333333333 * (t_1 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[y, -2.6e-24], N[(x + N[(t$95$1 / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-30], N[(x + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(-0.3333333333333333 * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e-24

   1. Initial program 97.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -2.6e-24 < y < 1.8000000000000002e-30

   1. Initial program 92.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 90.9%

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

      1. associate-/r* N/A

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

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

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

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

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

      4. *-lowering-*.f64 97.2%

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

   7. Applied egg-rr 97.2%

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

   if 1.8000000000000002e-30 < y

   1. Initial program 98.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. times-frac N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

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

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

      13. /-lowering-/.f64 N/A

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

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

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

      15. /-lowering-/.f64 99.7%

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

   6. Applied egg-rr 99.7%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-52}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-35}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e-52)
   (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z)))
   (if (<= y 7e-35)
     (+ x (/ (/ t (* z 3.0)) y))
     (- x (* -0.3333333333333333 (/ (- (/ t y) y) z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e-52) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else if (y <= 7e-35) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = x - (-0.3333333333333333 * (((t / y) - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8d-52)) then
        tmp = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
    else if (y <= 7d-35) then
        tmp = x + ((t / (z * 3.0d0)) / y)
    else
        tmp = x - ((-0.3333333333333333d0) * (((t / y) - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e-52) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else if (y <= 7e-35) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = x - (-0.3333333333333333 * (((t / y) - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e-52:
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z))
	elif y <= 7e-35:
		tmp = x + ((t / (z * 3.0)) / y)
	else:
		tmp = x - (-0.3333333333333333 * (((t / y) - y) / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e-52)
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)));
	elseif (y <= 7e-35)
		tmp = Float64(x + Float64(Float64(t / Float64(z * 3.0)) / y));
	else
		tmp = Float64(x - Float64(-0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8e-52)
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	elseif (y <= 7e-35)
		tmp = x + ((t / (z * 3.0)) / y);
	else
		tmp = x - (-0.3333333333333333 * (((t / y) - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e-52], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-35], N[(x + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(-0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.0000000000000001e-52

   1. Initial program 97.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.8%

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

   3. Simplified 99.8%

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

   if -8.0000000000000001e-52 < y < 6.99999999999999992e-35

   1. Initial program 92.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 90.5%

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

      1. associate-/r* N/A

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

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

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

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

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

      4. *-lowering-*.f64 97.1%

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

   7. Applied egg-rr 97.1%

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

   if 6.99999999999999992e-35 < y

   1. Initial program 98.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. times-frac N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

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

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

      13. /-lowering-/.f64 N/A

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

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

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

      15. /-lowering-/.f64 99.7%

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

   6. Applied egg-rr 99.7%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-52}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-35}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -8 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z)))))
   (if (<= y -8e-52)
     t_1
     (if (<= y 2.65e-39) (+ x (/ (/ t (* z 3.0)) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -8e-52) {
		tmp = t_1;
	} else if (y <= 2.65e-39) {
		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 - (t / y)) * ((-0.3333333333333333d0) / z))
    if (y <= (-8d-52)) then
        tmp = t_1
    else if (y <= 2.65d-39) 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 - (t / y)) * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -8e-52) {
		tmp = t_1;
	} else if (y <= 2.65e-39) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -8e-52:
		tmp = t_1
	elif y <= 2.65e-39:
		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(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -8e-52)
		tmp = t_1;
	elseif (y <= 2.65e-39)
		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 - (t / y)) * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -8e-52)
		tmp = t_1;
	elseif (y <= 2.65e-39)
		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[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e-52], t$95$1, If[LessEqual[y, 2.65e-39], 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 < -8.0000000000000001e-52 or 2.65000000000000002e-39 < y

   1. Initial program 97.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.8%

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

   3. Simplified 99.8%

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

   if -8.0000000000000001e-52 < y < 2.65000000000000002e-39

   1. Initial program 92.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 90.5%

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

      1. associate-/r* N/A

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

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

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

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

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

      4. *-lowering-*.f64 97.1%

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

   7. Applied egg-rr 97.1%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-52}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -6.6e-24)
     t_1
     (if (<= y 1.1e+39) (+ 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 <= -6.6e-24) {
		tmp = t_1;
	} else if (y <= 1.1e+39) {
		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 <= (-6.6d-24)) then
        tmp = t_1
    else if (y <= 1.1d+39) 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 <= -6.6e-24) {
		tmp = t_1;
	} else if (y <= 1.1e+39) {
		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 <= -6.6e-24:
		tmp = t_1
	elif y <= 1.1e+39:
		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(Float64(y / z) / 3.0))
	tmp = 0.0
	if (y <= -6.6e-24)
		tmp = t_1;
	elseif (y <= 1.1e+39)
		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 <= -6.6e-24)
		tmp = t_1;
	elseif (y <= 1.1e+39)
		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[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e-24], t$95$1, If[LessEqual[y, 1.1e+39], 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 < -6.59999999999999968e-24 or 1.1000000000000001e39 < y

   1. Initial program 97.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 99.8%

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

   4. Applied egg-rr 99.8%

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

   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 93.0%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 93.1%

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

   9. Applied egg-rr 93.1%

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

   if -6.59999999999999968e-24 < y < 1.1000000000000001e39

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 88.8%

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

      1. associate-/r* N/A

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

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

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

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

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

      4. *-lowering-*.f64 93.7%

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

   7. Applied egg-rr 93.7%

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

Alternative 7: 92.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -6.6e-24)
     t_1
     (if (<= y 2.6e+39) (+ x (/ (/ t z) (* y 3.0))) 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 <= -6.6e-24) {
		tmp = t_1;
	} else if (y <= 2.6e+39) {
		tmp = x + ((t / z) / (y * 3.0));
	} 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 <= (-6.6d-24)) then
        tmp = t_1
    else if (y <= 2.6d+39) then
        tmp = x + ((t / z) / (y * 3.0d0))
    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 <= -6.6e-24) {
		tmp = t_1;
	} else if (y <= 2.6e+39) {
		tmp = x + ((t / z) / (y * 3.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) / 3.0)
	tmp = 0
	if y <= -6.6e-24:
		tmp = t_1
	elif y <= 2.6e+39:
		tmp = x + ((t / z) / (y * 3.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) / 3.0))
	tmp = 0.0
	if (y <= -6.6e-24)
		tmp = t_1;
	elseif (y <= 2.6e+39)
		tmp = Float64(x + Float64(Float64(t / z) / Float64(y * 3.0)));
	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 <= -6.6e-24)
		tmp = t_1;
	elseif (y <= 2.6e+39)
		tmp = x + ((t / z) / (y * 3.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e-24], t$95$1, If[LessEqual[y, 2.6e+39], N[(x + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.59999999999999968e-24 or 2.6e39 < y

   1. Initial program 97.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 99.8%

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

   4. Applied egg-rr 99.8%

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

   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 93.0%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 93.1%

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

   9. Applied egg-rr 93.1%

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

   if -6.59999999999999968e-24 < y < 2.6e39

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 88.8%

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

      1. associate-*l* N/A

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

      2. associate-/r* N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 93.7%

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

   7. Applied egg-rr 93.7%

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

Alternative 8: 89.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -4.2e-24)
     t_1
     (if (<= y 1.1e+39) (+ x (/ t (* y (* z 3.0)))) 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 <= -4.2e-24) {
		tmp = t_1;
	} else if (y <= 1.1e+39) {
		tmp = x + (t / (y * (z * 3.0)));
	} 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 <= (-4.2d-24)) then
        tmp = t_1
    else if (y <= 1.1d+39) then
        tmp = x + (t / (y * (z * 3.0d0)))
    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 <= -4.2e-24) {
		tmp = t_1;
	} else if (y <= 1.1e+39) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) / 3.0)
	tmp = 0
	if y <= -4.2e-24:
		tmp = t_1
	elif y <= 1.1e+39:
		tmp = x + (t / (y * (z * 3.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) / 3.0))
	tmp = 0.0
	if (y <= -4.2e-24)
		tmp = t_1;
	elseif (y <= 1.1e+39)
		tmp = Float64(x + Float64(t / Float64(y * Float64(z * 3.0))));
	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 <= -4.2e-24)
		tmp = t_1;
	elseif (y <= 1.1e+39)
		tmp = x + (t / (y * (z * 3.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e-24], t$95$1, If[LessEqual[y, 1.1e+39], N[(x + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999999e-24 or 1.1000000000000001e39 < y

   1. Initial program 97.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 99.8%

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

   4. Applied egg-rr 99.8%

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

   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 93.0%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 93.1%

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

   9. Applied egg-rr 93.1%

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

   if -4.1999999999999999e-24 < y < 1.1000000000000001e39

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 88.8%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-24}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{\frac{t}{3}}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -9e-51) t_1 (if (<= y 4.2e-87) (/ (/ (/ t 3.0) z) 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 <= -9e-51) {
		tmp = t_1;
	} else if (y <= 4.2e-87) {
		tmp = ((t / 3.0) / z) / 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 <= (-9d-51)) then
        tmp = t_1
    else if (y <= 4.2d-87) then
        tmp = ((t / 3.0d0) / z) / 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 <= -9e-51) {
		tmp = t_1;
	} else if (y <= 4.2e-87) {
		tmp = ((t / 3.0) / z) / 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 <= -9e-51:
		tmp = t_1
	elif y <= 4.2e-87:
		tmp = ((t / 3.0) / z) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) / 3.0))
	tmp = 0.0
	if (y <= -9e-51)
		tmp = t_1;
	elseif (y <= 4.2e-87)
		tmp = Float64(Float64(Float64(t / 3.0) / z) / 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 <= -9e-51)
		tmp = t_1;
	elseif (y <= 4.2e-87)
		tmp = ((t / 3.0) / z) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-51], t$95$1, If[LessEqual[y, 4.2e-87], N[(N[(N[(t / 3.0), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999948e-51 or 4.20000000000000014e-87 < y

   1. Initial program 97.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 98.0%

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

   4. Applied egg-rr 98.0%

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

   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 85.5%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 85.6%

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

   9. Applied egg-rr 85.6%

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

   if -8.99999999999999948e-51 < y < 4.20000000000000014e-87

   1. Initial program 91.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 88.7%

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

   4. Applied egg-rr 88.7%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. associate-*r/ N/A

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

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

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. /-lowering-/.f64 73.8%

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

   7. Simplified 73.8%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. div-inv N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

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

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

      9. /-lowering-/.f64 73.9%

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

   9. Applied egg-rr 73.9%

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

Alternative 10: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-89}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -5.6e-45)
     t_1
     (if (<= y 1.22e-89) (/ 0.3333333333333333 (* y (/ z t))) 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 <= -5.6e-45) {
		tmp = t_1;
	} else if (y <= 1.22e-89) {
		tmp = 0.3333333333333333 / (y * (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / z) / 3.0d0)
    if (y <= (-5.6d-45)) then
        tmp = t_1
    else if (y <= 1.22d-89) then
        tmp = 0.3333333333333333d0 / (y * (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) / 3.0);
	double tmp;
	if (y <= -5.6e-45) {
		tmp = t_1;
	} else if (y <= 1.22e-89) {
		tmp = 0.3333333333333333 / (y * (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) / 3.0)
	tmp = 0
	if y <= -5.6e-45:
		tmp = t_1
	elif y <= 1.22e-89:
		tmp = 0.3333333333333333 / (y * (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) / 3.0))
	tmp = 0.0
	if (y <= -5.6e-45)
		tmp = t_1;
	elseif (y <= 1.22e-89)
		tmp = Float64(0.3333333333333333 / Float64(y * Float64(z / t)));
	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 <= -5.6e-45)
		tmp = t_1;
	elseif (y <= 1.22e-89)
		tmp = 0.3333333333333333 / (y * (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e-45], t$95$1, If[LessEqual[y, 1.22e-89], N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6000000000000003e-45 or 1.22e-89 < y

   1. Initial program 97.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 98.0%

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

   4. Applied egg-rr 98.0%

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

   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 85.5%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 85.6%

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

   9. Applied egg-rr 85.6%

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

   if -5.6000000000000003e-45 < y < 1.22e-89

   1. Initial program 91.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 88.7%

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

   4. Applied egg-rr 88.7%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. associate-*r/ N/A

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

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

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. /-lowering-/.f64 73.8%

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

   7. Simplified 73.8%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. frac-times N/A

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

      4. metadata-eval N/A

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

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

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

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

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

      7. /-lowering-/.f64 66.0%

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

   9. Applied egg-rr 66.0%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

       3. associate-/r/ N/A

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

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

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

       5. /-lowering-/.f64 73.9%

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

   11. Applied egg-rr 73.9%

       \[\leadsto \frac{0.3333333333333333}{\color{blue}{\frac{z}{t} \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-45}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-89}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -1.3e-50)
     t_1
     (if (<= y 1.5e-87) (* 0.3333333333333333 (/ t (* y z))) 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 <= -1.3e-50) {
		tmp = t_1;
	} else if (y <= 1.5e-87) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / z) / 3.0d0)
    if (y <= (-1.3d-50)) then
        tmp = t_1
    else if (y <= 1.5d-87) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) / 3.0);
	double tmp;
	if (y <= -1.3e-50) {
		tmp = t_1;
	} else if (y <= 1.5e-87) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) / 3.0)
	tmp = 0
	if y <= -1.3e-50:
		tmp = t_1
	elif y <= 1.5e-87:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) / 3.0))
	tmp = 0.0
	if (y <= -1.3e-50)
		tmp = t_1;
	elseif (y <= 1.5e-87)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	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 <= -1.3e-50)
		tmp = t_1;
	elseif (y <= 1.5e-87)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e-50], t$95$1, If[LessEqual[y, 1.5e-87], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3000000000000001e-50 or 1.50000000000000008e-87 < y

   1. Initial program 97.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 98.0%

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

   4. Applied egg-rr 98.0%

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

   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 85.5%

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

      1. associate-/r* N/A

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

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

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

      3. /-lowering-/.f64 85.6%

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

   9. Applied egg-rr 85.6%

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

   if -1.3000000000000001e-50 < y < 1.50000000000000008e-87

   1. Initial program 91.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 88.7%

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

   4. Applied egg-rr 88.7%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. associate-*r/ N/A

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

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

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. /-lowering-/.f64 73.8%

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

   7. Simplified 73.8%

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

      1. associate-/l* N/A

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

      2. div-inv N/A

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

      3. associate-*l* N/A

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

      4. inv-pow N/A

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

      5. clear-num N/A

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

      6. inv-pow N/A

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

      7. pow-prod-down N/A

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

      8. inv-pow N/A

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

      9. associate-/l/ N/A

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

      10. clear-num N/A

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

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

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

      12. associate-/l/ N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-lowering-*.f64 66.0%

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

   9. Applied egg-rr 66.0%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{z \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-50}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-41}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e-41)
   (- x (/ y (* z 3.0)))
   (if (<= y 1.15e-87)
     (* 0.3333333333333333 (/ t (* y z)))
     (+ x (* -0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-41) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 1.15e-87) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (-0.3333333333333333 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.5d-41)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 1.15d-87) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = x + ((-0.3333333333333333d0) * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-41) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 1.15e-87) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (-0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e-41:
		tmp = x - (y / (z * 3.0))
	elif y <= 1.15e-87:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = x + (-0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e-41)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 1.15e-87)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e-41)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 1.15e-87)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = x + (-0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e-41], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-87], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000049e-41

   1. Initial program 97.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 99.9%

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

   4. Applied egg-rr 99.9%

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

   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 89.8%

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

   if -7.50000000000000049e-41 < y < 1.1500000000000001e-87

   1. Initial program 91.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 88.7%

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

   4. Applied egg-rr 88.7%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. associate-*r/ N/A

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

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

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. /-lowering-/.f64 73.8%

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

   7. Simplified 73.8%

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

      1. associate-/l* N/A

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

      2. div-inv N/A

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

      3. associate-*l* N/A

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

      4. inv-pow N/A

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

      5. clear-num N/A

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

      6. inv-pow N/A

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

      7. pow-prod-down N/A

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

      8. inv-pow N/A

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

      9. associate-/l/ N/A

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

      10. clear-num N/A

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

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

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

      12. associate-/l/ N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-lowering-*.f64 66.0%

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

   9. Applied egg-rr 66.0%

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

   if 1.1500000000000001e-87 < y

   1. Initial program 97.6%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 96.7%

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

   3. Simplified 96.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. times-frac N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

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

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

      13. /-lowering-/.f64 N/A

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

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

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

      15. /-lowering-/.f64 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\color{blue}{y}, z\right), \frac{-1}{3}\right)\right) \]
   8. Step-by-step derivation

   9. Simplified 82.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-41}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e-45)
   (+ x (* y (/ -0.3333333333333333 z)))
   (if (<= y 1.7e-87)
     (* 0.3333333333333333 (/ t (* y z)))
     (+ x (* -0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-45) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 1.7e-87) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (-0.3333333333333333 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.4d-45)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if (y <= 1.7d-87) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = x + ((-0.3333333333333333d0) * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-45) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 1.7e-87) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (-0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.4e-45:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif y <= 1.7e-87:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = x + (-0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.4e-45)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (y <= 1.7e-87)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.4e-45)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif (y <= 1.7e-87)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = x + (-0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.4e-45], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-87], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.39999999999999987e-45

   1. Initial program 97.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \color{blue}{y}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 89.7%

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

   if -4.39999999999999987e-45 < y < 1.6999999999999999e-87

   1. Initial program 91.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 88.7%

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

   4. Applied egg-rr 88.7%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. associate-*r/ N/A

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

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

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. /-lowering-/.f64 73.8%

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

   7. Simplified 73.8%

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

      1. associate-/l* N/A

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

      2. div-inv N/A

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

      3. associate-*l* N/A

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

      4. inv-pow N/A

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

      5. clear-num N/A

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

      6. inv-pow N/A

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

      7. pow-prod-down N/A

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

      8. inv-pow N/A

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

      9. associate-/l/ N/A

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

      10. clear-num N/A

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

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

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

      12. associate-/l/ N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-lowering-*.f64 66.0%

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

   9. Applied egg-rr 66.0%

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

   if 1.6999999999999999e-87 < y

   1. Initial program 97.6%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 96.7%

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

   3. Simplified 96.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. times-frac N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

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

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

      13. /-lowering-/.f64 N/A

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

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

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

      15. /-lowering-/.f64 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\color{blue}{y}, z\right), \frac{-1}{3}\right)\right) \]
   8. Step-by-step derivation

   9. Simplified 82.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -3.4e-48)
     t_1
     (if (<= y 2.85e-87) (* 0.3333333333333333 (/ t (* y z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -3.4e-48) {
		tmp = t_1;
	} else if (y <= 2.85e-87) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((-0.3333333333333333d0) / z))
    if (y <= (-3.4d-48)) then
        tmp = t_1
    else if (y <= 2.85d-87) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -3.4e-48) {
		tmp = t_1;
	} else if (y <= 2.85e-87) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -3.4e-48:
		tmp = t_1
	elif y <= 2.85e-87:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -3.4e-48)
		tmp = t_1;
	elseif (y <= 2.85e-87)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -3.4e-48)
		tmp = t_1;
	elseif (y <= 2.85e-87)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e-48], t$95$1, If[LessEqual[y, 2.85e-87], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000028e-48 or 2.85e-87 < y

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \color{blue}{y}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 85.5%

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

   if -3.40000000000000028e-48 < y < 2.85e-87

   1. Initial program 91.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 88.7%

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

   4. Applied egg-rr 88.7%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. associate-*r/ N/A

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

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

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. /-lowering-/.f64 73.8%

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

   7. Simplified 73.8%

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

      1. associate-/l* N/A

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

      2. div-inv N/A

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

      3. associate-*l* N/A

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

      4. inv-pow N/A

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

      5. clear-num N/A

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

      6. inv-pow N/A

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

      7. pow-prod-down N/A

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

      8. inv-pow N/A

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

      9. associate-/l/ N/A

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

      10. clear-num N/A

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

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

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

      12. associate-/l/ N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-lowering-*.f64 66.0%

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

   9. Applied egg-rr 66.0%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{z \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+39}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ y z) -3.0)))
   (if (<= y -6.6e-24)
     t_1
     (if (<= y 3.5e+39) (* 0.3333333333333333 (/ t (* y z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) / -3.0;
	double tmp;
	if (y <= -6.6e-24) {
		tmp = t_1;
	} else if (y <= 3.5e+39) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) / (-3.0d0)
    if (y <= (-6.6d-24)) then
        tmp = t_1
    else if (y <= 3.5d+39) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) / -3.0;
	double tmp;
	if (y <= -6.6e-24) {
		tmp = t_1;
	} else if (y <= 3.5e+39) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) / -3.0
	tmp = 0
	if y <= -6.6e-24:
		tmp = t_1
	elif y <= 3.5e+39:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) / -3.0)
	tmp = 0.0
	if (y <= -6.6e-24)
		tmp = t_1;
	elseif (y <= 3.5e+39)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) / -3.0;
	tmp = 0.0;
	if (y <= -6.6e-24)
		tmp = t_1;
	elseif (y <= 3.5e+39)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]}, If[LessEqual[y, -6.6e-24], t$95$1, If[LessEqual[y, 3.5e+39], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.59999999999999968e-24 or 3.5000000000000002e39 < y

   1. Initial program 97.6%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.8%

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

   3. Simplified 99.8%

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

   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. *-lowering-*.f64 68.9%

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

   7. Simplified 68.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 68.9%

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

   9. Applied egg-rr 68.9%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

       3. div-inv N/A

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

       4. associate-/r* N/A

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

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

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

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

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

       7. metadata-eval 69.0%

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

   11. Applied egg-rr 69.0%

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

   if -6.59999999999999968e-24 < y < 3.5000000000000002e39

   1. Initial program 93.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 89.3%

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

   4. Applied egg-rr 89.3%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. associate-*r/ N/A

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

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

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. /-lowering-/.f64 65.4%

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

   7. Simplified 65.4%

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

      1. associate-/l* N/A

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

      2. div-inv N/A

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

      3. associate-*l* N/A

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

      4. inv-pow N/A

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

      5. clear-num N/A

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

      6. inv-pow N/A

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

      7. pow-prod-down N/A

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

      8. inv-pow N/A

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

      9. associate-/l/ N/A

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

      10. clear-num N/A

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

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

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

      12. associate-/l/ N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-lowering-*.f64 60.4%

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

   9. Applied egg-rr 60.4%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{z \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+39}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+169}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2e+40) x (if (<= z 7e+169) (/ (/ y z) -3.0) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e+40) {
		tmp = x;
	} else if (z <= 7e+169) {
		tmp = (y / z) / -3.0;
	} else {
		tmp = x;
	}
	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 <= (-2d+40)) then
        tmp = x
    else if (z <= 7d+169) then
        tmp = (y / z) / (-3.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e+40) {
		tmp = x;
	} else if (z <= 7e+169) {
		tmp = (y / z) / -3.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2e+40:
		tmp = x
	elif z <= 7e+169:
		tmp = (y / z) / -3.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e+40)
		tmp = x;
	elseif (z <= 7e+169)
		tmp = Float64(Float64(y / z) / -3.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2e+40)
		tmp = x;
	elseif (z <= 7e+169)
		tmp = (y / z) / -3.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2e+40], x, If[LessEqual[z, 7e+169], N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000006e40 or 7.00000000000000038e169 < z

   1. Initial program 98.9%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 59.3%

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

   if -2.00000000000000006e40 < z < 7.00000000000000038e169

   1. Initial program 93.3%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

      18. /-lowering-/.f64 N/A

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 98.1%

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

   3. Simplified 98.1%

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

   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. *-lowering-*.f64 53.4%

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

   7. Simplified 53.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 53.4%

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

   9. Applied egg-rr 53.4%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

       3. div-inv N/A

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

       4. associate-/r* N/A

          \[\leadsto \frac{\frac{y}{z}}{\color{blue}{\frac{1}{\frac{-1}{3}}}} \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\left(\frac{1}{\frac{-1}{3}}\right)}\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, z\right), \left(\frac{\color{blue}{1}}{\frac{-1}{3}}\right)\right) \]

       7. metadata-eval 53.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, z\right), -3\right) \]

   11. Applied egg-rr 53.5%

       \[\leadsto \color{blue}{\frac{\frac{y}{z}}{-3}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 46.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+170}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+39) x (if (<= z 5.5e+170) (/ (* y -0.3333333333333333) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+39) {
		tmp = x;
	} else if (z <= 5.5e+170) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	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 <= (-1d+39)) then
        tmp = x
    else if (z <= 5.5d+170) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+39) {
		tmp = x;
	} else if (z <= 5.5e+170) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e+39:
		tmp = x
	elif z <= 5.5e+170:
		tmp = (y * -0.3333333333333333) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+39)
		tmp = x;
	elseif (z <= 5.5e+170)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e+39)
		tmp = x;
	elseif (z <= 5.5e+170)
		tmp = (y * -0.3333333333333333) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e+39], x, If[LessEqual[z, 5.5e+170], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999994e38 or 5.4999999999999999e170 < z

   1. Initial program 98.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 89.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 59.3%

      \[\leadsto \color{blue}{x} \]

   if -9.9999999999999994e38 < z < 5.4999999999999999e170

   1. Initial program 93.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 98.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   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. *-lowering-*.f64 53.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{3}, y\right), z\right) \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+170}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 46.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+169}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.04e+40)
   x
   (if (<= z 6.6e+169) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.04e+40) {
		tmp = x;
	} else if (z <= 6.6e+169) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.04d+40)) then
        tmp = x
    else if (z <= 6.6d+169) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.04e+40) {
		tmp = x;
	} else if (z <= 6.6e+169) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.04e+40:
		tmp = x
	elif z <= 6.6e+169:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.04e+40)
		tmp = x;
	elseif (z <= 6.6e+169)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.04e+40)
		tmp = x;
	elseif (z <= 6.6e+169)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.04e+40], x, If[LessEqual[z, 6.6e+169], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04e40 or 6.5999999999999994e169 < z

   1. Initial program 98.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 89.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 59.3%

      \[\leadsto \color{blue}{x} \]

   if -1.04e40 < z < 6.5999999999999994e169

   1. Initial program 93.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 98.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   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. *-lowering-*.f64 53.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{3}, y\right), z\right) \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y}{z} \cdot \color{blue}{\frac{-1}{3}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\frac{-1}{3}}\right) \]

      4. /-lowering-/.f64 53.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-1}{3}\right) \]

   9. Applied egg-rr 53.4%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+169}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 46.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.8e+39) x (if (<= z 6.6e+169) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e+39) {
		tmp = x;
	} else if (z <= 6.6e+169) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	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 <= (-7.8d+39)) then
        tmp = x
    else if (z <= 6.6d+169) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e+39) {
		tmp = x;
	} else if (z <= 6.6e+169) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.8e+39:
		tmp = x
	elif z <= 6.6e+169:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.8e+39)
		tmp = x;
	elseif (z <= 6.6e+169)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.8e+39)
		tmp = x;
	elseif (z <= 6.6e+169)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.8e+39], x, If[LessEqual[z, 6.6e+169], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000002e39 or 6.5999999999999994e169 < z

   1. Initial program 98.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 89.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 59.3%

      \[\leadsto \color{blue}{x} \]

   if -7.8000000000000002e39 < z < 6.5999999999999994e169

   1. Initial program 93.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 98.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   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. *-lowering-*.f64 53.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{3}, y\right), z\right) \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y \cdot \frac{-1}{3}}{z} \]

      2. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{\frac{-1}{3}}{z}\right)}\right) \]

      4. /-lowering-/.f64 53.4%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 53.4%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 30.5% 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 95.4%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

   2. associate-+l+ N/A

      \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

   4. remove-double-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

   5. unsub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   8. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   9. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   11. distribute-neg-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

   12. neg-mul-1 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

   13. times-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

   14. distribute-lft-out-- N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   17. associate-/r* N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   18. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   19. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   20. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

   21. /-lowering-/.f64 94.7%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

3. Simplified 94.7%

   \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 28.3%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 96.0% 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 2024138 
(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))))