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

Percentage Accurate: 95.5% → 99.5%

Time: 10.7s

Alternatives: 15

Speedup: 0.7×

• 28.2% 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: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot 3 \leq 10^{-61}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{-3} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (* t (/ (/ 0.3333333333333333 z) y)))))
   (if (<= (* z 3.0) -2e-10)
     t_1
     (if (<= (* z 3.0) 1e-61)
       (+ x (* (/ (- y (/ t y)) -3.0) (/ 1.0 z)))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t * ((0.3333333333333333 / z) / y));
	double tmp;
	if ((z * 3.0) <= -2e-10) {
		tmp = t_1;
	} else if ((z * 3.0) <= 1e-61) {
		tmp = x + (((y - (t / y)) / -3.0) * (1.0 / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (z * 3.0d0))) + (t * ((0.3333333333333333d0 / z) / y))
    if ((z * 3.0d0) <= (-2d-10)) then
        tmp = t_1
    else if ((z * 3.0d0) <= 1d-61) then
        tmp = x + (((y - (t / y)) / (-3.0d0)) * (1.0d0 / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t * ((0.3333333333333333 / z) / y));
	double tmp;
	if ((z * 3.0) <= -2e-10) {
		tmp = t_1;
	} else if ((z * 3.0) <= 1e-61) {
		tmp = x + (((y - (t / y)) / -3.0) * (1.0 / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (y / (z * 3.0))) + (t * ((0.3333333333333333 / z) / y))
	tmp = 0
	if (z * 3.0) <= -2e-10:
		tmp = t_1
	elif (z * 3.0) <= 1e-61:
		tmp = x + (((y - (t / y)) / -3.0) * (1.0 / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t * Float64(Float64(0.3333333333333333 / z) / y)))
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e-10)
		tmp = t_1;
	elseif (Float64(z * 3.0) <= 1e-61)
		tmp = Float64(x + Float64(Float64(Float64(y - Float64(t / y)) / -3.0) * Float64(1.0 / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (z * 3.0))) + (t * ((0.3333333333333333 / z) / y));
	tmp = 0.0;
	if ((z * 3.0) <= -2e-10)
		tmp = t_1;
	elseif ((z * 3.0) <= 1e-61)
		tmp = x + (((y - (t / y)) / -3.0) * (1.0 / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e-10], t$95$1, If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e-61], N[(x + N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / -3.0), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -2.00000000000000007e-10 or 1e-61 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.7%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. associate-/r* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval 99.7%

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

   4. Applied egg-rr 99.7%

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

   if -2.00000000000000007e-10 < (*.f64 z #s(literal 3 binary64)) < 1e-61

   1. Initial program 91.5%

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

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

   3. Simplified 99.7%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

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

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

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

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

      10. times-frac N/A

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

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

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

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

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

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

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

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

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

      15. metadata-eval N/A

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

      16. /-lowering-/.f64 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-10}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;z \cdot 3 \leq 10^{-61}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{-3} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))))
   (if (<= t_1 2e+307) t_1 (/ (* 0.3333333333333333 (- (/ t y) y)) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 2e+307) {
		tmp = t_1;
	} else {
		tmp = (0.3333333333333333 * ((t / y) - y)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    if (t_1 <= 2d+307) then
        tmp = t_1
    else
        tmp = (0.3333333333333333d0 * ((t / y) - y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 2e+307) {
		tmp = t_1;
	} else {
		tmp = (0.3333333333333333 * ((t / y) - y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	tmp = 0
	if t_1 <= 2e+307:
		tmp = t_1
	else:
		tmp = (0.3333333333333333 * ((t / y) - y)) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))))
	tmp = 0.0
	if (t_1 <= 2e+307)
		tmp = t_1;
	else
		tmp = Float64(Float64(0.3333333333333333 * Float64(Float64(t / y) - y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	tmp = 0.0;
	if (t_1 <= 2e+307)
		tmp = t_1;
	else
		tmp = (0.3333333333333333 * ((t / y) - y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+307], t$95$1, N[(N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 1.99999999999999997e307

   1. Initial program 98.0%

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

   if 1.99999999999999997e307 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))

   1. Initial program 84.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.9%

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

   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 0

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

      1. associate-*r/ N/A

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

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

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. cancel-sign-sub-inv N/A

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

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

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

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

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

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

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

      14. /-lowering-/.f64 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{-142}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (- (/ t y) y) (* z 3.0)))))
   (if (<= y -3.8e-159)
     t_1
     (if (<= y 1e-142) (+ x (/ (/ 0.3333333333333333 y) (/ z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((t / y) - y) / (z * 3.0));
	double tmp;
	if (y <= -3.8e-159) {
		tmp = t_1;
	} else if (y <= 1e-142) {
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((t / y) - y) / (z * 3.0d0))
    if (y <= (-3.8d-159)) then
        tmp = t_1
    else if (y <= 1d-142) then
        tmp = x + ((0.3333333333333333d0 / y) / (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((t / y) - y) / (z * 3.0));
	double tmp;
	if (y <= -3.8e-159) {
		tmp = t_1;
	} else if (y <= 1e-142) {
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((t / y) - y) / (z * 3.0))
	tmp = 0
	if y <= -3.8e-159:
		tmp = t_1
	elif y <= 1e-142:
		tmp = x + ((0.3333333333333333 / y) / (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)))
	tmp = 0.0
	if (y <= -3.8e-159)
		tmp = t_1;
	elseif (y <= 1e-142)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / y) / Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((t / y) - y) / (z * 3.0));
	tmp = 0.0;
	if (y <= -3.8e-159)
		tmp = t_1;
	elseif (y <= 1e-142)
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-159], t$95$1, If[LessEqual[y, 1e-142], N[(x + N[(N[(0.3333333333333333 / y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000001e-159 or 1e-142 < y

   1. Initial program 98.3%

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

      1. associate-+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%

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

   if -3.8000000000000001e-159 < y < 1e-142

   1. Initial program 88.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 88.3%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. div-inv N/A

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

      5. clear-num N/A

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

      6. associate-*l/ N/A

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

      7. div-inv N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-/r* N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

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

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 96.6%

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

   7. Applied egg-rr 96.6%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-159}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 10^{-142}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-144}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z)))))
   (if (<= y -4.6e-163)
     t_1
     (if (<= y 4.5e-144) (+ x (/ (/ 0.3333333333333333 y) (/ z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -4.6e-163) {
		tmp = t_1;
	} else if (y <= 4.5e-144) {
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
    if (y <= (-4.6d-163)) then
        tmp = t_1
    else if (y <= 4.5d-144) then
        tmp = x + ((0.3333333333333333d0 / y) / (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -4.6e-163) {
		tmp = t_1;
	} else if (y <= 4.5e-144) {
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -4.6e-163:
		tmp = t_1
	elif y <= 4.5e-144:
		tmp = x + ((0.3333333333333333 / y) / (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -4.6e-163)
		tmp = t_1;
	elseif (y <= 4.5e-144)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / y) / Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -4.6e-163)
		tmp = t_1;
	elseif (y <= 4.5e-144)
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e-163], t$95$1, If[LessEqual[y, 4.5e-144], N[(x + N[(N[(0.3333333333333333 / y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999999e-163 or 4.4999999999999998e-144 < y

   1. Initial program 98.3%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.7%

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

   3. Simplified 99.7%

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

   if -4.5999999999999999e-163 < y < 4.4999999999999998e-144

   1. Initial program 88.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 88.3%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. div-inv N/A

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

      5. clear-num N/A

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

      6. associate-*l/ N/A

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

      7. div-inv N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-/r* N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

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

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 96.6%

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

   7. Applied egg-rr 96.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-163}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-144}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+24}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.5e+35)
   (/ (/ y z) -3.0)
   (if (<= y 2.3e+24)
     (* 0.3333333333333333 (/ (/ t z) y))
     (if (<= y 7e+91) x (/ (/ y -3.0) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e+35) {
		tmp = (y / z) / -3.0;
	} else if (y <= 2.3e+24) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else if (y <= 7e+91) {
		tmp = x;
	} else {
		tmp = (y / -3.0) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.5d+35)) then
        tmp = (y / z) / (-3.0d0)
    else if (y <= 2.3d+24) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    else if (y <= 7d+91) then
        tmp = x
    else
        tmp = (y / (-3.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e+35) {
		tmp = (y / z) / -3.0;
	} else if (y <= 2.3e+24) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else if (y <= 7e+91) {
		tmp = x;
	} else {
		tmp = (y / -3.0) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.5e+35:
		tmp = (y / z) / -3.0
	elif y <= 2.3e+24:
		tmp = 0.3333333333333333 * ((t / z) / y)
	elif y <= 7e+91:
		tmp = x
	else:
		tmp = (y / -3.0) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.5e+35)
		tmp = Float64(Float64(y / z) / -3.0);
	elseif (y <= 2.3e+24)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	elseif (y <= 7e+91)
		tmp = x;
	else
		tmp = Float64(Float64(y / -3.0) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.5e+35)
		tmp = (y / z) / -3.0;
	elseif (y <= 2.3e+24)
		tmp = 0.3333333333333333 * ((t / z) / y);
	elseif (y <= 7e+91)
		tmp = x;
	else
		tmp = (y / -3.0) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.5e+35], N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[y, 2.3e+24], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+91], x, N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4999999999999997e35

   1. Initial program 99.7%

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

      1. associate-*l* N/A

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

      2. associate-/r* N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 93.0%

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 70.5%

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

   7. Simplified 70.5%

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

      1. associate-*l/ 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. div-inv N/A

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

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

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

      5. /-lowering-/.f64 70.5%

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

   9. Applied egg-rr 70.5%

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

   if -4.4999999999999997e35 < y < 2.2999999999999999e24

   1. Initial program 93.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

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

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. cancel-sign-sub-inv N/A

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

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

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

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

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

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

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

      14. /-lowering-/.f64 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in t around inf

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

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

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

      2. associate-/l/ N/A

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

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

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

      4. /-lowering-/.f64 67.0%

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

   10. Simplified 67.0%

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

   if 2.2999999999999999e24 < y < 7.00000000000000001e91

   1. Initial program 99.7%

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

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

   7. Simplified 58.0%

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

   if 7.00000000000000001e91 < y

   1. Initial program 97.9%

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

      1. associate-*l* N/A

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

      2. associate-/r* N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 94.1%

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

   4. Applied egg-rr 94.1%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 75.8%

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

   7. Simplified 75.8%

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

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

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. /-lowering-/.f64 75.9%

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

   9. Applied egg-rr 75.9%

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

Alternative 6: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (/ y z) -3.0))))
   (if (<= y -4.5e+40)
     t_1
     (if (<= y 4.4e+59) (+ x (/ (/ 0.3333333333333333 y) (/ z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / z) / -3.0);
	double tmp;
	if (y <= -4.5e+40) {
		tmp = t_1;
	} else if (y <= 4.4e+59) {
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / z) / (-3.0d0))
    if (y <= (-4.5d+40)) then
        tmp = t_1
    else if (y <= 4.4d+59) then
        tmp = x + ((0.3333333333333333d0 / y) / (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / z) / -3.0);
	double tmp;
	if (y <= -4.5e+40) {
		tmp = t_1;
	} else if (y <= 4.4e+59) {
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y / z) / -3.0)
	tmp = 0
	if y <= -4.5e+40:
		tmp = t_1
	elif y <= 4.4e+59:
		tmp = x + ((0.3333333333333333 / y) / (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y / z) / -3.0))
	tmp = 0.0
	if (y <= -4.5e+40)
		tmp = t_1;
	elseif (y <= 4.4e+59)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / y) / Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y / z) / -3.0);
	tmp = 0.0;
	if (y <= -4.5e+40)
		tmp = t_1;
	elseif (y <= 4.4e+59)
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+40], t$95$1, If[LessEqual[y, 4.4e+59], N[(x + N[(N[(0.3333333333333333 / y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.50000000000000032e40 or 4.3999999999999999e59 < y

   1. Initial program 98.8%

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

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

   3. Simplified 99.7%

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

   5. 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 97.8%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

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

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

      8. distribute-neg-frac2 N/A

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

      9. associate-/r* N/A

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

      10. distribute-neg-frac2 N/A

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

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

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

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

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

      13. metadata-eval 98.0%

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

   9. Applied egg-rr 98.0%

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

   if -4.50000000000000032e40 < y < 4.3999999999999999e59

   1. Initial program 93.7%

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

   3. Taylor expanded in 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 84.9%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. div-inv N/A

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

      5. clear-num N/A

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

      6. associate-*l/ N/A

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

      7. div-inv N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-/r* N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

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

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 89.0%

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

   7. Applied egg-rr 89.0%

      \[\leadsto x + \color{blue}{\frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (/ y z) -3.0))))
   (if (<= y -1.4e+38)
     t_1
     (if (<= y 4.4e+59) (+ x (/ t (* y (* z 3.0)))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / z) / -3.0);
	double tmp;
	if (y <= -1.4e+38) {
		tmp = t_1;
	} else if (y <= 4.4e+59) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / z) / (-3.0d0))
    if (y <= (-1.4d+38)) then
        tmp = t_1
    else if (y <= 4.4d+59) then
        tmp = x + (t / (y * (z * 3.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / z) / -3.0);
	double tmp;
	if (y <= -1.4e+38) {
		tmp = t_1;
	} else if (y <= 4.4e+59) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y / z) / -3.0)
	tmp = 0
	if y <= -1.4e+38:
		tmp = t_1
	elif y <= 4.4e+59:
		tmp = x + (t / (y * (z * 3.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y / z) / -3.0))
	tmp = 0.0
	if (y <= -1.4e+38)
		tmp = t_1;
	elseif (y <= 4.4e+59)
		tmp = Float64(x + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y / z) / -3.0);
	tmp = 0.0;
	if (y <= -1.4e+38)
		tmp = t_1;
	elseif (y <= 4.4e+59)
		tmp = x + (t / (y * (z * 3.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+38], t$95$1, If[LessEqual[y, 4.4e+59], N[(x + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e38 or 4.3999999999999999e59 < y

   1. Initial program 98.8%

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

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

   3. Simplified 99.7%

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

   5. 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 97.8%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

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

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

      8. distribute-neg-frac2 N/A

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

      9. associate-/r* N/A

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

      10. distribute-neg-frac2 N/A

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

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

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

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

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

      13. metadata-eval 98.0%

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

   9. Applied egg-rr 98.0%

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

   if -1.4e38 < y < 4.3999999999999999e59

   1. Initial program 93.7%

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

   3. Taylor expanded in 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 84.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -1.86 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (/ y z) -3.0))))
   (if (<= y -1.86e-56)
     t_1
     (if (<= y 6e-99) (/ (* t (/ 0.3333333333333333 z)) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / z) / -3.0);
	double tmp;
	if (y <= -1.86e-56) {
		tmp = t_1;
	} else if (y <= 6e-99) {
		tmp = (t * (0.3333333333333333 / z)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / z) / (-3.0d0))
    if (y <= (-1.86d-56)) then
        tmp = t_1
    else if (y <= 6d-99) then
        tmp = (t * (0.3333333333333333d0 / z)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / z) / -3.0);
	double tmp;
	if (y <= -1.86e-56) {
		tmp = t_1;
	} else if (y <= 6e-99) {
		tmp = (t * (0.3333333333333333 / z)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y / z) / -3.0)
	tmp = 0
	if y <= -1.86e-56:
		tmp = t_1
	elif y <= 6e-99:
		tmp = (t * (0.3333333333333333 / z)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y / z) / -3.0))
	tmp = 0.0
	if (y <= -1.86e-56)
		tmp = t_1;
	elseif (y <= 6e-99)
		tmp = Float64(Float64(t * Float64(0.3333333333333333 / z)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y / z) / -3.0);
	tmp = 0.0;
	if (y <= -1.86e-56)
		tmp = t_1;
	elseif (y <= 6e-99)
		tmp = (t * (0.3333333333333333 / z)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.86e-56], t$95$1, If[LessEqual[y, 6e-99], N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85999999999999997e-56 or 6.00000000000000012e-99 < y

   1. Initial program 99.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.7%

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

   3. Simplified 99.7%

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

   5. 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 86.0%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

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

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

      8. distribute-neg-frac2 N/A

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

      9. associate-/r* N/A

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

      10. distribute-neg-frac2 N/A

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

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

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

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

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

      13. metadata-eval 86.1%

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

   9. Applied egg-rr 86.1%

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

   if -1.85999999999999997e-56 < y < 6.00000000000000012e-99

   1. Initial program 90.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in y around 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 72.8%

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

   7. Simplified 72.8%

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

      1. times-frac N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

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

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

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

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

      6. /-lowering-/.f64 79.6%

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

   9. Applied egg-rr 79.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.86 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-99}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (/ y z) -3.0))))
   (if (<= y -3.2e-64)
     t_1
     (if (<= y 2.1e-99) (* 0.3333333333333333 (/ (/ t z) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / z) / -3.0);
	double tmp;
	if (y <= -3.2e-64) {
		tmp = t_1;
	} else if (y <= 2.1e-99) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / z) / (-3.0d0))
    if (y <= (-3.2d-64)) then
        tmp = t_1
    else if (y <= 2.1d-99) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / z) / -3.0);
	double tmp;
	if (y <= -3.2e-64) {
		tmp = t_1;
	} else if (y <= 2.1e-99) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y / z) / -3.0)
	tmp = 0
	if y <= -3.2e-64:
		tmp = t_1
	elif y <= 2.1e-99:
		tmp = 0.3333333333333333 * ((t / z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y / z) / -3.0))
	tmp = 0.0
	if (y <= -3.2e-64)
		tmp = t_1;
	elseif (y <= 2.1e-99)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y / z) / -3.0);
	tmp = 0.0;
	if (y <= -3.2e-64)
		tmp = t_1;
	elseif (y <= 2.1e-99)
		tmp = 0.3333333333333333 * ((t / z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e-64], t$95$1, If[LessEqual[y, 2.1e-99], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999975e-64 or 2.09999999999999984e-99 < y

   1. Initial program 99.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.7%

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

   3. Simplified 99.7%

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

   5. 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 86.0%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

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

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

      8. distribute-neg-frac2 N/A

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

      9. associate-/r* N/A

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

      10. distribute-neg-frac2 N/A

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

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

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

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

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

      13. metadata-eval 86.1%

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

   9. Applied egg-rr 86.1%

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

   if -3.19999999999999975e-64 < y < 2.09999999999999984e-99

   1. Initial program 90.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

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

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. cancel-sign-sub-inv N/A

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

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

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

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

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

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

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

      14. /-lowering-/.f64 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in t around inf

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

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

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

      2. associate-/l/ N/A

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

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

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

      4. /-lowering-/.f64 79.6%

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

   10. Simplified 79.6%

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

Alternative 10: 78.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-100}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -3.2e-61)
     t_1
     (if (<= y 4e-100) (* 0.3333333333333333 (/ (/ t z) 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 <= -3.2e-61) {
		tmp = t_1;
	} else if (y <= 4e-100) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((-0.3333333333333333d0) / z))
    if (y <= (-3.2d-61)) then
        tmp = t_1
    else if (y <= 4d-100) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -3.2e-61) {
		tmp = t_1;
	} else if (y <= 4e-100) {
		tmp = 0.3333333333333333 * ((t / z) / 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 <= -3.2e-61:
		tmp = t_1
	elif y <= 4e-100:
		tmp = 0.3333333333333333 * ((t / z) / 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 <= -3.2e-61)
		tmp = t_1;
	elseif (y <= 4e-100)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / 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 <= -3.2e-61)
		tmp = t_1;
	elseif (y <= 4e-100)
		tmp = 0.3333333333333333 * ((t / z) / 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, -3.2e-61], t$95$1, If[LessEqual[y, 4e-100], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000001e-61 or 4.0000000000000001e-100 < y

   1. Initial program 99.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.7%

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

   3. Simplified 99.7%

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

   5. 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 86.0%

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

   if -3.2000000000000001e-61 < y < 4.0000000000000001e-100

   1. Initial program 90.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

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

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. cancel-sign-sub-inv N/A

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

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

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

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

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

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

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

      14. /-lowering-/.f64 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in t around inf

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

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

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

      2. associate-/l/ N/A

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

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

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

      4. /-lowering-/.f64 79.6%

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

   10. Simplified 79.6%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-100}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-69) x (if (<= z 3.5e+22) (/ (/ y -3.0) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-69) {
		tmp = x;
	} else if (z <= 3.5e+22) {
		tmp = (y / -3.0) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d-69)) then
        tmp = x
    else if (z <= 3.5d+22) then
        tmp = (y / (-3.0d0)) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-69) {
		tmp = x;
	} else if (z <= 3.5e+22) {
		tmp = (y / -3.0) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-69:
		tmp = x
	elif z <= 3.5e+22:
		tmp = (y / -3.0) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-69)
		tmp = x;
	elseif (z <= 3.5e+22)
		tmp = Float64(Float64(y / -3.0) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-69)
		tmp = x;
	elseif (z <= 3.5e+22)
		tmp = (y / -3.0) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-69], x, If[LessEqual[z, 3.5e+22], N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999999e-69 or 3.5e22 < z

   1. Initial program 99.0%

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

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 47.9%

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

   if -1.59999999999999999e-69 < z < 3.5e22

   1. Initial program 92.7%

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

      1. associate-*l* N/A

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

      2. associate-/r* N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 49.0%

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

   7. Simplified 49.0%

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

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

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. /-lowering-/.f64 49.0%

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

   9. Applied egg-rr 49.0%

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

Alternative 12: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-69) x (if (<= z 7.6e+23) (/ (* y -0.3333333333333333) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-69) {
		tmp = x;
	} else if (z <= 7.6e+23) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d-69)) then
        tmp = x
    else if (z <= 7.6d+23) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-69) {
		tmp = x;
	} else if (z <= 7.6e+23) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-69:
		tmp = x
	elif z <= 7.6e+23:
		tmp = (y * -0.3333333333333333) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-69)
		tmp = x;
	elseif (z <= 7.6e+23)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-69)
		tmp = x;
	elseif (z <= 7.6e+23)
		tmp = (y * -0.3333333333333333) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-69], x, If[LessEqual[z, 7.6e+23], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999999e-69 or 7.5999999999999995e23 < z

   1. Initial program 99.0%

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

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 47.9%

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

   if -1.59999999999999999e-69 < z < 7.5999999999999995e23

   1. Initial program 92.7%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 49.0%

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

   7. Simplified 49.0%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+23}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.15e-70)
   x
   (if (<= z 2.75e+23) (/ -0.3333333333333333 (/ z y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e-70) {
		tmp = x;
	} else if (z <= 2.75e+23) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.15d-70)) then
        tmp = x
    else if (z <= 2.75d+23) then
        tmp = (-0.3333333333333333d0) / (z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e-70) {
		tmp = x;
	} else if (z <= 2.75e+23) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.15e-70:
		tmp = x
	elif z <= 2.75e+23:
		tmp = -0.3333333333333333 / (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.15e-70)
		tmp = x;
	elseif (z <= 2.75e+23)
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.15e-70)
		tmp = x;
	elseif (z <= 2.75e+23)
		tmp = -0.3333333333333333 / (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.15e-70], x, If[LessEqual[z, 2.75e+23], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e-70 or 2.75000000000000002e23 < z

   1. Initial program 99.0%

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

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 47.9%

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

   if -1.15e-70 < z < 2.75000000000000002e23

   1. Initial program 92.7%

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

      1. associate-*l* N/A

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

      2. associate-/r* N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 49.0%

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

   7. Simplified 49.0%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

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

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

      5. /-lowering-/.f64 48.9%

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

   9. Applied egg-rr 48.9%

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

Alternative 14: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-69) x (if (<= z 3.35e+22) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-69) {
		tmp = x;
	} else if (z <= 3.35e+22) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d-69)) then
        tmp = x
    else if (z <= 3.35d+22) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-69) {
		tmp = x;
	} else if (z <= 3.35e+22) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-69:
		tmp = x
	elif z <= 3.35e+22:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-69)
		tmp = x;
	elseif (z <= 3.35e+22)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-69)
		tmp = x;
	elseif (z <= 3.35e+22)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-69], x, If[LessEqual[z, 3.35e+22], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999999e-69 or 3.3500000000000001e22 < z

   1. Initial program 99.0%

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

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 47.9%

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

   if -1.59999999999999999e-69 < z < 3.3500000000000001e22

   1. Initial program 92.7%

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

      1. associate-*l* N/A

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

      2. associate-/r* N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 49.0%

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

   7. Simplified 49.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 48.9%

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

   9. Applied egg-rr 48.9%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.9% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 95.7%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
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 95.3%

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

3. Simplified 95.3%

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

5. Taylor expanded in x around inf

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

7. Simplified 28.1%

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

Developer Target 1: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024158 
(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))))