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

Percentage Accurate: 95.5% → 97.6%

Time: 11.2s

Alternatives: 14

Speedup: 1.4×

• 27.2% 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: 95.5% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -5e+75)
   (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y)))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -5e+75) {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-5d+75)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -5e+75) {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -5e+75:
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -5e+75)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -5e+75)
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -5e+75], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -5.0000000000000002e75

   1. Initial program 99.9%

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

   if -5.0000000000000002e75 < (*.f64 z #s(literal 3 binary64))

   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. 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 98.5%

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

   4. Applied egg-rr 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e+74)
   (/ (/ y -3.0) z)
   (if (<= y -1.15e-57)
     x
     (if (<= y 3.9e+15)
       (* (/ t z) (/ 0.3333333333333333 y))
       (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+74) {
		tmp = (y / -3.0) / z;
	} else if (y <= -1.15e-57) {
		tmp = x;
	} else if (y <= 3.9e+15) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.8d+74)) then
        tmp = (y / (-3.0d0)) / z
    else if (y <= (-1.15d-57)) then
        tmp = x
    else if (y <= 3.9d+15) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+74) {
		tmp = (y / -3.0) / z;
	} else if (y <= -1.15e-57) {
		tmp = x;
	} else if (y <= 3.9e+15) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e+74:
		tmp = (y / -3.0) / z
	elif y <= -1.15e-57:
		tmp = x
	elif y <= 3.9e+15:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e+74)
		tmp = Float64(Float64(y / -3.0) / z);
	elseif (y <= -1.15e-57)
		tmp = x;
	elseif (y <= 3.9e+15)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e+74)
		tmp = (y / -3.0) / z;
	elseif (y <= -1.15e-57)
		tmp = x;
	elseif (y <= 3.9e+15)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e+74], N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -1.15e-57], x, If[LessEqual[y, 3.9e+15], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.7999999999999998e74

   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. Taylor expanded in y around inf

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

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

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

      2. /-lowering-/.f64 81.4%

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

   7. Simplified 81.4%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. metadata-eval N/A

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

      4. div-inv N/A

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

      5. associate-/l/ N/A

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

      6. associate-/r* N/A

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

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

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

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

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

      9. metadata-eval 81.6%

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

   9. Applied egg-rr 81.6%

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

   if -6.7999999999999998e74 < y < -1.15e-57

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 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. Taylor expanded in x around inf

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

   7. Simplified 56.9%

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

   if -1.15e-57 < y < 3.9e15

   1. Initial program 88.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 92.7%

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

   3. Simplified 92.7%

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

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 58.9%

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

   7. Simplified 58.9%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 63.9%

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

   9. Applied egg-rr 63.9%

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

   if 3.9e15 < y

   1. Initial program 96.7%

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

      1. associate-+l- N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. sub-div N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 99.9%

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

   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

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

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

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

      2. /-lowering-/.f64 69.5%

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

   7. Simplified 69.5%

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

      1. metadata-eval N/A

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

      2. times-frac N/A

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

      3. neg-mul-1 N/A

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

      4. *-commutative N/A

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

      5. distribute-neg-frac N/A

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

      6. distribute-neg-frac2 N/A

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

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

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

      8. metadata-eval N/A

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

      9. div-inv N/A

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

      10. distribute-neg-frac2 N/A

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

      11. metadata-eval N/A

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

      12. /-lowering-/.f64 69.5%

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

   9. Applied egg-rr 69.5%

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

       1. div-inv N/A

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

       2. metadata-eval N/A

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

       3. *-lowering-*.f64 69.7%

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

   11. Applied egg-rr 69.7%

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

Alternative 3: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-21}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e-21)
   (- x (/ (/ y 3.0) z))
   (if (<= y 1.8e+14) (+ x (/ t (* (* z 3.0) y))) (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-21) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 1.8e+14) {
		tmp = x + (t / ((z * 3.0) * y));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.3d-21)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 1.8d+14) then
        tmp = x + (t / ((z * 3.0d0) * y))
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-21) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 1.8e+14) {
		tmp = x + (t / ((z * 3.0) * y));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e-21:
		tmp = x - ((y / 3.0) / z)
	elif y <= 1.8e+14:
		tmp = x + (t / ((z * 3.0) * y))
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e-21)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 1.8e+14)
		tmp = Float64(x + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e-21)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 1.8e+14)
		tmp = x + (t / ((z * 3.0) * y));
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e-21], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+14], N[(x + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000009e-21

   1. Initial program 98.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 94.4%

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

      1. associate-/l/ N/A

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

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

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

      3. /-lowering-/.f64 94.6%

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

   9. Applied egg-rr 94.6%

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

   if -1.30000000000000009e-21 < y < 1.8e14

   1. Initial program 88.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 87.7%

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

   if 1.8e14 < y

   1. Initial program 96.8%

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

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

   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 95.2%

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

Alternative 4: 78.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-59}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 28000:\\ \;\;\;\;\frac{\frac{t}{z}}{3 \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.1e-59)
   (- x (/ (/ y 3.0) z))
   (if (<= y 28000.0) (/ (/ t z) (* 3.0 y)) (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-59) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 28000.0) {
		tmp = (t / z) / (3.0 * y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.1d-59)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 28000.0d0) then
        tmp = (t / z) / (3.0d0 * y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-59) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 28000.0) {
		tmp = (t / z) / (3.0 * y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.1e-59:
		tmp = x - ((y / 3.0) / z)
	elif y <= 28000.0:
		tmp = (t / z) / (3.0 * y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.1e-59)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 28000.0)
		tmp = Float64(Float64(t / z) / Float64(3.0 * y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.1e-59)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 28000.0)
		tmp = (t / z) / (3.0 * y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.1e-59], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 28000.0], N[(N[(t / z), $MachinePrecision] / N[(3.0 * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0999999999999996e-59

   1. Initial program 98.5%

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

      1. associate-+l- N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. sub-div N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 93.5%

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

      1. associate-/l/ N/A

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

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

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

      3. /-lowering-/.f64 93.6%

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

   9. Applied egg-rr 93.6%

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

   if -4.0999999999999996e-59 < y < 28000

   1. Initial program 88.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 92.4%

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

   3. Simplified 92.4%

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

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 60.6%

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

   7. Simplified 60.6%

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

      1. times-frac N/A

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

      2. metadata-eval N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. div-inv N/A

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

      6. associate-/l/ N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. div-inv N/A

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

      11. /-lowering-/.f64 60.6%

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

   9. Applied egg-rr 60.6%

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

       1. associate-*l/ N/A

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

       2. div-inv N/A

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

       3. metadata-eval N/A

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

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

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 60.6%

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

   11. Applied egg-rr 60.6%

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

       3. associate-/r* N/A

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

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

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

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

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

       6. *-lowering-*.f64 65.7%

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

   13. Applied egg-rr 65.7%

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

   if 28000 < y

   1. Initial program 96.9%

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

      1. associate-+l- N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. sub-div N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 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 94.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-59}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 28000:\\ \;\;\;\;\frac{\frac{t}{z}}{3 \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-58}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.5e-58)
   (- x (/ (/ y 3.0) z))
   (if (<= y 31500.0)
     (* (/ t z) (/ 0.3333333333333333 y))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-58) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 31500.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.5d-58)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 31500.0d0) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-58) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 31500.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.5e-58:
		tmp = x - ((y / 3.0) / z)
	elif y <= 31500.0:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.5e-58)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 31500.0)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.5e-58)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 31500.0)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.5e-58], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 31500.0], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4999999999999999e-58

   1. Initial program 98.5%

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

      1. associate-+l- N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. sub-div N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 93.5%

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

      1. associate-/l/ N/A

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

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

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

      3. /-lowering-/.f64 93.6%

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

   9. Applied egg-rr 93.6%

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

   if -3.4999999999999999e-58 < y < 31500

   1. Initial program 88.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 92.4%

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

   3. Simplified 92.4%

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

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 60.6%

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

   7. Simplified 60.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 65.7%

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

   9. Applied egg-rr 65.7%

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

   if 31500 < y

   1. Initial program 96.9%

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

      1. associate-+l- N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. sub-div N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 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 94.0%

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

Alternative 6: 78.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 12200:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e-59)
   (+ x (* y (/ -0.3333333333333333 z)))
   (if (<= y 12200.0)
     (* (/ t z) (/ 0.3333333333333333 y))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-59) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 12200.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.35d-59)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if (y <= 12200.0d0) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-59) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 12200.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e-59:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif y <= 12200.0:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e-59)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (y <= 12200.0)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e-59)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif (y <= 12200.0)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e-59], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 12200.0], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3499999999999999e-59

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 93.6%

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

   if -1.3499999999999999e-59 < y < 12200

   1. Initial program 88.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 92.4%

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

   3. Simplified 92.4%

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

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 60.6%

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

   7. Simplified 60.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 65.7%

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

   9. Applied egg-rr 65.7%

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

   if 12200 < y

   1. Initial program 96.9%

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

      1. associate-+l- N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. sub-div N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 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 94.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 12200:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 12200:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -2.2e-57)
     t_1
     (if (<= y 12200.0) (* (/ t z) (/ 0.3333333333333333 y)) 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 <= -2.2e-57) {
		tmp = t_1;
	} else if (y <= 12200.0) {
		tmp = (t / z) * (0.3333333333333333 / 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 * ((-0.3333333333333333d0) / z))
    if (y <= (-2.2d-57)) then
        tmp = t_1
    else if (y <= 12200.0d0) then
        tmp = (t / z) * (0.3333333333333333d0 / 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 * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -2.2e-57) {
		tmp = t_1;
	} else if (y <= 12200.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -2.2e-57:
		tmp = t_1
	elif y <= 12200.0:
		tmp = (t / z) * (0.3333333333333333 / y)
	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 <= -2.2e-57)
		tmp = t_1;
	elseif (y <= 12200.0)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	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 <= -2.2e-57)
		tmp = t_1;
	elseif (y <= 12200.0)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e-57], t$95$1, If[LessEqual[y, 12200.0], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.19999999999999999e-57 or 12200 < 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

   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 93.7%

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

   if -2.19999999999999999e-57 < y < 12200

   1. Initial program 88.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 92.4%

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

   3. Simplified 92.4%

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

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 60.6%

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

   7. Simplified 60.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

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

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

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

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

      5. /-lowering-/.f64 65.7%

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

   9. Applied egg-rr 65.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-57}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 12200:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e+76) (/ (/ y -3.0) z) (if (<= y 1.65e+69) x (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e+76) {
		tmp = (y / -3.0) / z;
	} else if (y <= 1.65e+69) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.4d+76)) then
        tmp = (y / (-3.0d0)) / z
    else if (y <= 1.65d+69) then
        tmp = x
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e+76) {
		tmp = (y / -3.0) / z;
	} else if (y <= 1.65e+69) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e+76:
		tmp = (y / -3.0) / z
	elif y <= 1.65e+69:
		tmp = x
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e+76)
		tmp = Float64(Float64(y / -3.0) / z);
	elseif (y <= 1.65e+69)
		tmp = x;
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e+76)
		tmp = (y / -3.0) / z;
	elseif (y <= 1.65e+69)
		tmp = x;
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e+76], N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.65e+69], x, N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e76

   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. Taylor expanded in y around inf

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

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

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

      2. /-lowering-/.f64 81.4%

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

   7. Simplified 81.4%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. metadata-eval N/A

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

      4. div-inv N/A

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

      5. associate-/l/ N/A

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

      6. associate-/r* N/A

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

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

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

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

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

      9. metadata-eval 81.6%

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

   9. Applied egg-rr 81.6%

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

   if -2.4e76 < y < 1.6499999999999999e69

   1. Initial program 91.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 39.4%

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

   if 1.6499999999999999e69 < y

   1. Initial program 95.9%

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

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

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

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

      2. /-lowering-/.f64 75.7%

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

   7. Simplified 75.7%

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

      1. metadata-eval N/A

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

      2. times-frac N/A

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

      3. neg-mul-1 N/A

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

      4. *-commutative N/A

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

      5. distribute-neg-frac N/A

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

      6. distribute-neg-frac2 N/A

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

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

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

      8. metadata-eval N/A

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

      9. div-inv N/A

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

      10. distribute-neg-frac2 N/A

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

      11. metadata-eval N/A

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

      12. /-lowering-/.f64 75.7%

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

   9. Applied egg-rr 75.7%

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

       1. div-inv N/A

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

       2. metadata-eval N/A

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

       3. *-lowering-*.f64 75.8%

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

   11. Applied egg-rr 75.8%

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

Alternative 9: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e+74)
   (* y (/ -0.3333333333333333 z))
   (if (<= y 3.5e+69) x (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+74) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 3.5e+69) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7d+74)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else if (y <= 3.5d+69) then
        tmp = x
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+74) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 3.5e+69) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7e+74:
		tmp = y * (-0.3333333333333333 / z)
	elif y <= 3.5e+69:
		tmp = x
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e+74)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	elseif (y <= 3.5e+69)
		tmp = x;
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7e+74)
		tmp = y * (-0.3333333333333333 / z);
	elseif (y <= 3.5e+69)
		tmp = x;
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7e+74], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+69], x, N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.00000000000000029e74

   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. Taylor expanded in y around inf

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

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

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

      2. /-lowering-/.f64 81.4%

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

   7. Simplified 81.4%

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

      1. metadata-eval N/A

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

      2. times-frac N/A

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

      3. neg-mul-1 N/A

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

      4. *-commutative N/A

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

      5. frac-2neg N/A

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

      6. remove-double-neg N/A

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

      7. div-inv N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

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

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

      12. associate-/r* N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 81.5%

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

   9. Applied egg-rr 81.5%

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

   if -7.00000000000000029e74 < y < 3.49999999999999987e69

   1. Initial program 91.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 39.4%

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

   if 3.49999999999999987e69 < y

   1. Initial program 95.9%

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

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

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

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

      2. /-lowering-/.f64 75.7%

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

   7. Simplified 75.7%

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

      1. metadata-eval N/A

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

      2. times-frac N/A

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

      3. neg-mul-1 N/A

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

      4. *-commutative N/A

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

      5. distribute-neg-frac N/A

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

      6. distribute-neg-frac2 N/A

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

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

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

      8. metadata-eval N/A

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

      9. div-inv N/A

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

      10. distribute-neg-frac2 N/A

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

      11. metadata-eval N/A

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

      12. /-lowering-/.f64 75.7%

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

   9. Applied egg-rr 75.7%

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

       1. div-inv N/A

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

       2. metadata-eval N/A

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

       3. *-lowering-*.f64 75.8%

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

   11. Applied egg-rr 75.8%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e+77)
   (* y (/ -0.3333333333333333 z))
   (if (<= y 1.85e+71) x (* -0.3333333333333333 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e+77) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 1.85e+71) {
		tmp = x;
	} else {
		tmp = -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 <= (-1.35d+77)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else if (y <= 1.85d+71) then
        tmp = x
    else
        tmp = (-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 <= -1.35e+77) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 1.85e+71) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e+77:
		tmp = y * (-0.3333333333333333 / z)
	elif y <= 1.85e+71:
		tmp = x
	else:
		tmp = -0.3333333333333333 * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e+77)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	elseif (y <= 1.85e+71)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e+77)
		tmp = y * (-0.3333333333333333 / z);
	elseif (y <= 1.85e+71)
		tmp = x;
	else
		tmp = -0.3333333333333333 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e+77], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+71], x, N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3499999999999999e77

   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. Taylor expanded in y around inf

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

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

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

      2. /-lowering-/.f64 81.4%

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

   7. Simplified 81.4%

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

      1. metadata-eval N/A

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

      2. times-frac N/A

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

      3. neg-mul-1 N/A

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

      4. *-commutative N/A

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

      5. frac-2neg N/A

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

      6. remove-double-neg N/A

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

      7. div-inv N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

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

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

      12. associate-/r* N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 81.5%

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

   9. Applied egg-rr 81.5%

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

   if -1.3499999999999999e77 < y < 1.85e71

   1. Initial program 91.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 39.4%

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

   if 1.85e71 < y

   1. Initial program 95.9%

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

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

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

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

      2. /-lowering-/.f64 75.7%

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

   7. Simplified 75.7%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.3333333333333333 (/ y z))))
   (if (<= y -3.6e+77) t_1 (if (<= y 2.45e+70) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.3333333333333333 * (y / z);
	double tmp;
	if (y <= -3.6e+77) {
		tmp = t_1;
	} else if (y <= 2.45e+70) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-0.3333333333333333d0) * (y / z)
    if (y <= (-3.6d+77)) then
        tmp = t_1
    else if (y <= 2.45d+70) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.3333333333333333 * (y / z);
	double tmp;
	if (y <= -3.6e+77) {
		tmp = t_1;
	} else if (y <= 2.45e+70) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.3333333333333333 * (y / z)
	tmp = 0
	if y <= -3.6e+77:
		tmp = t_1
	elif y <= 2.45e+70:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.3333333333333333 * Float64(y / z))
	tmp = 0.0
	if (y <= -3.6e+77)
		tmp = t_1;
	elseif (y <= 2.45e+70)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.3333333333333333 * (y / z);
	tmp = 0.0;
	if (y <= -3.6e+77)
		tmp = t_1;
	elseif (y <= 2.45e+70)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+77], t$95$1, If[LessEqual[y, 2.45e+70], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999998e77 or 2.45000000000000014e70 < y

   1. Initial program 96.9%

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

      1. associate-+l- N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. sub-div N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 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

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

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

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

      2. /-lowering-/.f64 78.6%

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

   7. Simplified 78.6%

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

   if -3.5999999999999998e77 < y < 2.45000000000000014e70

   1. Initial program 91.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 39.4%

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

Alternative 12: 95.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((t / y) - y) / (z * 3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
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 96.6%

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

4. Applied egg-rr 96.6%

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

5. Final simplification 96.6%

   \[\leadsto x + \frac{\frac{t}{y} - y}{z \cdot 3} \]
6. Add Preprocessing

Alternative 13: 95.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - (t / y)) * (-0.3333333333333333 / z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - (t / y)) * (-0.3333333333333333 / z));
}

Python

def code(x, y, z, t):
	return x + ((y - (t / y)) * (-0.3333333333333333 / z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
end

Wolfram

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

Derivation

1. Initial program 93.6%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
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 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 14: 30.7% 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 93.6%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
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 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in x around inf

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

7. Simplified 31.2%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 95.9% 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 2024163 
(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))))