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

Percentage Accurate: 95.7% → 99.0%

Time: 13.2s

Alternatives: 18

Speedup: 1.4×

• 28.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;t\_1 + \frac{t}{3 \cdot \left(z \cdot y\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 10^{-124}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{3} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= (* z 3.0) -1e+31)
     (+ t_1 (/ t (* 3.0 (* z y))))
     (if (<= (* z 3.0) 1e-124)
       (+ x (* (/ (- (/ t y) y) 3.0) (/ 1.0 z)))
       (+ t_1 (* t (/ (/ 0.3333333333333333 z) y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -1e+31) {
		tmp = t_1 + (t / (3.0 * (z * y)));
	} else if ((z * 3.0) <= 1e-124) {
		tmp = x + ((((t / y) - y) / 3.0) * (1.0 / z));
	} else {
		tmp = t_1 + (t * ((0.3333333333333333 / z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if ((z * 3.0d0) <= (-1d+31)) then
        tmp = t_1 + (t / (3.0d0 * (z * y)))
    else if ((z * 3.0d0) <= 1d-124) then
        tmp = x + ((((t / y) - y) / 3.0d0) * (1.0d0 / z))
    else
        tmp = t_1 + (t * ((0.3333333333333333d0 / z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -1e+31) {
		tmp = t_1 + (t / (3.0 * (z * y)));
	} else if ((z * 3.0) <= 1e-124) {
		tmp = x + ((((t / y) - y) / 3.0) * (1.0 / z));
	} else {
		tmp = t_1 + (t * ((0.3333333333333333 / z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if (z * 3.0) <= -1e+31:
		tmp = t_1 + (t / (3.0 * (z * y)))
	elif (z * 3.0) <= 1e-124:
		tmp = x + ((((t / y) - y) / 3.0) * (1.0 / z))
	else:
		tmp = t_1 + (t * ((0.3333333333333333 / z) / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e+31)
		tmp = Float64(t_1 + Float64(t / Float64(3.0 * Float64(z * y))));
	elseif (Float64(z * 3.0) <= 1e-124)
		tmp = Float64(x + Float64(Float64(Float64(Float64(t / y) - y) / 3.0) * Float64(1.0 / z)));
	else
		tmp = Float64(t_1 + Float64(t * Float64(Float64(0.3333333333333333 / z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if ((z * 3.0) <= -1e+31)
		tmp = t_1 + (t / (3.0 * (z * y)));
	elseif ((z * 3.0) <= 1e-124)
		tmp = x + ((((t / y) - y) / 3.0) * (1.0 / z));
	else
		tmp = t_1 + (t * ((0.3333333333333333 / z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e+31], N[(t$95$1 + N[(t / N[(3.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e-124], N[(x + N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / 3.0), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -9.9999999999999996e30

   1. Initial program 99.8%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 99.8%

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

   4. Applied egg-rr 99.8%

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

   if -9.9999999999999996e30 < (*.f64 z #s(literal 3 binary64)) < 9.99999999999999933e-125

   1. Initial program 90.5%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. associate-*r/ N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

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

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

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

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 N/A

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

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

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

      19. /-lowering-/.f64 99.7%

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

   5. Simplified 99.7%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. times-frac N/A

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

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

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

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

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

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

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

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

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

      12. /-lowering-/.f64 99.8%

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

   7. Applied egg-rr 99.8%

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

   if 9.99999999999999933e-125 < (*.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. /-lowering-/.f64 N/A

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

      9. metadata-eval 99.8%

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

   4. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{3 \cdot \left(z \cdot y\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 10^{-124}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{3} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot 3 \leq 10^{-124}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{3} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) -1e+31)
     t_1
     (if (<= (* z 3.0) 1e-124)
       (+ x (* (/ (- (/ t y) 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) <= -1e+31) {
		tmp = t_1;
	} else if ((z * 3.0) <= 1e-124) {
		tmp = x + ((((t / y) - 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) <= (-1d+31)) then
        tmp = t_1
    else if ((z * 3.0d0) <= 1d-124) then
        tmp = x + ((((t / y) - 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) <= -1e+31) {
		tmp = t_1;
	} else if ((z * 3.0) <= 1e-124) {
		tmp = x + ((((t / y) - 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) <= -1e+31:
		tmp = t_1
	elif (z * 3.0) <= 1e-124:
		tmp = x + ((((t / y) - 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) <= -1e+31)
		tmp = t_1;
	elseif (Float64(z * 3.0) <= 1e-124)
		tmp = Float64(x + Float64(Float64(Float64(Float64(t / y) - 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) <= -1e+31)
		tmp = t_1;
	elseif ((z * 3.0) <= 1e-124)
		tmp = x + ((((t / y) - 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], -1e+31], t$95$1, If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e-124], N[(x + N[(N[(N[(N[(t / y), $MachinePrecision] - y), $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)) < -9.9999999999999996e30 or 9.99999999999999933e-125 < (*.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. /-lowering-/.f64 N/A

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

      9. metadata-eval 99.8%

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

   4. Applied egg-rr 99.8%

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

   if -9.9999999999999996e30 < (*.f64 z #s(literal 3 binary64)) < 9.99999999999999933e-125

   1. Initial program 90.5%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. associate-*r/ N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

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

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

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

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 N/A

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

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

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

      19. /-lowering-/.f64 99.7%

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

   5. Simplified 99.7%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. times-frac N/A

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

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

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

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

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

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

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

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

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

      12. /-lowering-/.f64 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;z \cdot 3 \leq 10^{-124}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{3} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y -0.3333333333333333) z))))
   (if (<= y -2.5e-55)
     t_1
     (if (<= y 2.4e+64) (+ x (/ t (* (* z 3.0) y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * -0.3333333333333333) / z);
	double tmp;
	if (y <= -2.5e-55) {
		tmp = t_1;
	} else if (y <= 2.4e+64) {
		tmp = x + (t / ((z * 3.0) * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * (-0.3333333333333333d0)) / z)
    if (y <= (-2.5d-55)) then
        tmp = t_1
    else if (y <= 2.4d+64) then
        tmp = x + (t / ((z * 3.0d0) * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * -0.3333333333333333) / z);
	double tmp;
	if (y <= -2.5e-55) {
		tmp = t_1;
	} else if (y <= 2.4e+64) {
		tmp = x + (t / ((z * 3.0) * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * -0.3333333333333333) / z)
	tmp = 0
	if y <= -2.5e-55:
		tmp = t_1
	elif y <= 2.4e+64:
		tmp = x + (t / ((z * 3.0) * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * -0.3333333333333333) / z))
	tmp = 0.0
	if (y <= -2.5e-55)
		tmp = t_1;
	elseif (y <= 2.4e+64)
		tmp = Float64(x + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * -0.3333333333333333) / z);
	tmp = 0.0;
	if (y <= -2.5e-55)
		tmp = t_1;
	elseif (y <= 2.4e+64)
		tmp = x + (t / ((z * 3.0) * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-55], t$95$1, If[LessEqual[y, 2.4e+64], N[(x + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5000000000000001e-55 or 2.39999999999999999e64 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. associate-*r/ N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

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

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

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

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 N/A

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

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

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

      19. /-lowering-/.f64 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 95.0%

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

   8. Simplified 95.0%

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

   if -2.5000000000000001e-55 < y < 2.39999999999999999e64

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 90.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+153}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y -0.3333333333333333) z))))
   (if (<= z -1.4e-69)
     t_1
     (if (<= z 1.55e+153) (* (- (/ t y) y) (/ 0.3333333333333333 z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * -0.3333333333333333) / z);
	double tmp;
	if (z <= -1.4e-69) {
		tmp = t_1;
	} else if (z <= 1.55e+153) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * (-0.3333333333333333d0)) / z)
    if (z <= (-1.4d-69)) then
        tmp = t_1
    else if (z <= 1.55d+153) then
        tmp = ((t / y) - y) * (0.3333333333333333d0 / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * -0.3333333333333333) / z);
	double tmp;
	if (z <= -1.4e-69) {
		tmp = t_1;
	} else if (z <= 1.55e+153) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * -0.3333333333333333) / z)
	tmp = 0
	if z <= -1.4e-69:
		tmp = t_1
	elif z <= 1.55e+153:
		tmp = ((t / y) - y) * (0.3333333333333333 / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * -0.3333333333333333) / z))
	tmp = 0.0
	if (z <= -1.4e-69)
		tmp = t_1;
	elseif (z <= 1.55e+153)
		tmp = Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * -0.3333333333333333) / z);
	tmp = 0.0;
	if (z <= -1.4e-69)
		tmp = t_1;
	elseif (z <= 1.55e+153)
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-69], t$95$1, If[LessEqual[z, 1.55e+153], N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3999999999999999e-69 or 1.55e153 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. associate-*r/ N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

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

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

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

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 N/A

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

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

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

      19. /-lowering-/.f64 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 78.6%

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

   8. Simplified 78.6%

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

   if -1.3999999999999999e-69 < z < 1.55e153

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. associate-*r/ N/A

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

      7. associate-*l/ N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

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

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

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

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

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

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

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

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

      16. /-lowering-/.f64 90.4%

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

   5. Simplified 90.4%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+153}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{\frac{t}{z}}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y -0.3333333333333333) z))))
   (if (<= y -1.85e-57) t_1 (if (<= y 2.95e+48) (/ (/ (/ t z) 3.0) 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 <= -1.85e-57) {
		tmp = t_1;
	} else if (y <= 2.95e+48) {
		tmp = ((t / z) / 3.0) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * (-0.3333333333333333d0)) / z)
    if (y <= (-1.85d-57)) then
        tmp = t_1
    else if (y <= 2.95d+48) then
        tmp = ((t / z) / 3.0d0) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * -0.3333333333333333) / z);
	double tmp;
	if (y <= -1.85e-57) {
		tmp = t_1;
	} else if (y <= 2.95e+48) {
		tmp = ((t / z) / 3.0) / 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 <= -1.85e-57:
		tmp = t_1
	elif y <= 2.95e+48:
		tmp = ((t / z) / 3.0) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * -0.3333333333333333) / z))
	tmp = 0.0
	if (y <= -1.85e-57)
		tmp = t_1;
	elseif (y <= 2.95e+48)
		tmp = Float64(Float64(Float64(t / z) / 3.0) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * -0.3333333333333333) / z);
	tmp = 0.0;
	if (y <= -1.85e-57)
		tmp = t_1;
	elseif (y <= 2.95e+48)
		tmp = ((t / z) / 3.0) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e-57], t$95$1, If[LessEqual[y, 2.95e+48], N[(N[(N[(t / z), $MachinePrecision] / 3.0), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e-57 or 2.95000000000000025e48 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. associate-*r/ N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

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

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

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

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 N/A

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

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

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

      19. /-lowering-/.f64 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 94.3%

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

   8. Simplified 94.3%

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

   if -1.85e-57 < y < 2.95000000000000025e48

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-lowering-*.f64 64.3%

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

   5. Simplified 64.3%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. clear-num N/A

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

      6. associate-/r* N/A

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

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

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

      8. /-lowering-/.f64 64.4%

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

   7. Applied egg-rr 64.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{\frac{t}{z}}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+48}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y -0.3333333333333333) z))))
   (if (<= y -2.4e-57)
     t_1
     (if (<= y 2.95e+48) (* (/ t z) (/ 0.3333333333333333 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * -0.3333333333333333) / z);
	double tmp;
	if (y <= -2.4e-57) {
		tmp = t_1;
	} else if (y <= 2.95e+48) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * (-0.3333333333333333d0)) / z)
    if (y <= (-2.4d-57)) then
        tmp = t_1
    else if (y <= 2.95d+48) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * -0.3333333333333333) / z);
	double tmp;
	if (y <= -2.4e-57) {
		tmp = t_1;
	} else if (y <= 2.95e+48) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * -0.3333333333333333) / z)
	tmp = 0
	if y <= -2.4e-57:
		tmp = t_1
	elif y <= 2.95e+48:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * -0.3333333333333333) / z))
	tmp = 0.0
	if (y <= -2.4e-57)
		tmp = t_1;
	elseif (y <= 2.95e+48)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * -0.3333333333333333) / z);
	tmp = 0.0;
	if (y <= -2.4e-57)
		tmp = t_1;
	elseif (y <= 2.95e+48)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e-57], t$95$1, If[LessEqual[y, 2.95e+48], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.40000000000000006e-57 or 2.95000000000000025e48 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. associate-*r/ N/A

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

      10. associate-*l/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

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

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

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

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 N/A

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

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

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

      19. /-lowering-/.f64 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 94.3%

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

   8. Simplified 94.3%

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

   if -2.40000000000000006e-57 < y < 2.95000000000000025e48

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-lowering-*.f64 64.3%

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

   5. Simplified 64.3%

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

      1. associate-/l/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

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

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

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

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

      7. /-lowering-/.f64 64.4%

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

   7. Applied egg-rr 64.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+48}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+48}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -2.5e-58)
     t_1
     (if (<= y 2.95e+48) (* (/ t z) (/ 0.3333333333333333 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -2.5e-58) {
		tmp = t_1;
	} else if (y <= 2.95e+48) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((-0.3333333333333333d0) / z))
    if (y <= (-2.5d-58)) then
        tmp = t_1
    else if (y <= 2.95d+48) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -2.5e-58) {
		tmp = t_1;
	} else if (y <= 2.95e+48) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -2.5e-58:
		tmp = t_1
	elif y <= 2.95e+48:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -2.5e-58)
		tmp = t_1;
	elseif (y <= 2.95e+48)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -2.5e-58)
		tmp = t_1;
	elseif (y <= 2.95e+48)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-58], t$95$1, If[LessEqual[y, 2.95e+48], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999989e-58 or 2.95000000000000025e48 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-frac N/A

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

      7. metadata-eval N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. cancel-sign-sub N/A

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

      11. mul-1-neg N/A

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

      12. associate-*r/ N/A

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

      13. associate-*l/ N/A

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

      14. associate-/l* N/A

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

      15. mul-1-neg N/A

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

      16. *-inverses N/A

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

      17. cancel-sign-sub N/A

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

      18. *-rgt-identity N/A

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

      19. +-commutative N/A

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

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

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

      21. associate-*r/ N/A

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

      22. *-commutative N/A

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

      23. associate-/l* N/A

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

   5. Simplified 94.3%

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

   if -2.49999999999999989e-58 < y < 2.95000000000000025e48

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-lowering-*.f64 64.3%

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

   5. Simplified 64.3%

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

      1. associate-/l/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

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

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

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

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

      7. /-lowering-/.f64 64.4%

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

   7. Applied egg-rr 64.4%

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

Alternative 8: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -0.0015:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ y z) -3.0)))
   (if (<= y -0.0015)
     t_1
     (if (<= y 3e+53) (* (/ t z) (/ 0.3333333333333333 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) / -3.0;
	double tmp;
	if (y <= -0.0015) {
		tmp = t_1;
	} else if (y <= 3e+53) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) / (-3.0d0)
    if (y <= (-0.0015d0)) then
        tmp = t_1
    else if (y <= 3d+53) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) / -3.0;
	double tmp;
	if (y <= -0.0015) {
		tmp = t_1;
	} else if (y <= 3e+53) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) / -3.0
	tmp = 0
	if y <= -0.0015:
		tmp = t_1
	elif y <= 3e+53:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) / -3.0)
	tmp = 0.0
	if (y <= -0.0015)
		tmp = t_1;
	elseif (y <= 3e+53)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) / -3.0;
	tmp = 0.0;
	if (y <= -0.0015)
		tmp = t_1;
	elseif (y <= 3e+53)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]}, If[LessEqual[y, -0.0015], t$95$1, If[LessEqual[y, 3e+53], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0015 or 2.99999999999999998e53 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 77.2%

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

   5. Simplified 77.2%

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

      1. associate-*r/ N/A

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

      2. /-rgt-identity N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. times-frac N/A

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

      6. metadata-eval N/A

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

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

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

      8. /-lowering-/.f64 77.2%

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

   7. Applied egg-rr 77.2%

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

      1. metadata-eval N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

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

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

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

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

      6. metadata-eval 77.3%

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

   9. Applied egg-rr 77.3%

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

   if -0.0015 < y < 2.99999999999999998e53

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-lowering-*.f64 61.2%

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

   5. Simplified 61.2%

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

      1. associate-/l/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

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

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

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

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

      7. /-lowering-/.f64 61.2%

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

   7. Applied egg-rr 61.2%

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

Alternative 9: 61.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -0.0002:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \frac{0.3333333333333333}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ y z) -3.0)))
   (if (<= y -0.0002)
     t_1
     (if (<= y 2.3e+64) (* t (/ 0.3333333333333333 (* z y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) / -3.0;
	double tmp;
	if (y <= -0.0002) {
		tmp = t_1;
	} else if (y <= 2.3e+64) {
		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 = (y / z) / (-3.0d0)
    if (y <= (-0.0002d0)) then
        tmp = t_1
    else if (y <= 2.3d+64) 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 = (y / z) / -3.0;
	double tmp;
	if (y <= -0.0002) {
		tmp = t_1;
	} else if (y <= 2.3e+64) {
		tmp = t * (0.3333333333333333 / (z * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) / -3.0
	tmp = 0
	if y <= -0.0002:
		tmp = t_1
	elif y <= 2.3e+64:
		tmp = t * (0.3333333333333333 / (z * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) / -3.0)
	tmp = 0.0
	if (y <= -0.0002)
		tmp = t_1;
	elseif (y <= 2.3e+64)
		tmp = Float64(t * Float64(0.3333333333333333 / Float64(z * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) / -3.0;
	tmp = 0.0;
	if (y <= -0.0002)
		tmp = t_1;
	elseif (y <= 2.3e+64)
		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[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]}, If[LessEqual[y, -0.0002], t$95$1, If[LessEqual[y, 2.3e+64], N[(t * N[(0.3333333333333333 / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0000000000000001e-4 or 2.3e64 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 77.6%

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

   5. Simplified 77.6%

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

      1. associate-*r/ N/A

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

      2. /-rgt-identity N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. times-frac N/A

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

      6. metadata-eval N/A

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

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

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

      8. /-lowering-/.f64 77.6%

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

   7. Applied egg-rr 77.6%

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

      1. metadata-eval N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

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

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

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

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

      6. metadata-eval 77.8%

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

   9. Applied egg-rr 77.8%

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

   if -2.0000000000000001e-4 < y < 2.3e64

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-lowering-*.f64 60.3%

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

   5. Simplified 60.3%

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

      1. associate-*l/ N/A

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

      2. associate-*l/ N/A

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

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

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

      4. associate-/l/ N/A

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

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

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

      6. *-lowering-*.f64 56.0%

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

   7. Applied egg-rr 56.0%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0002:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \frac{0.3333333333333333}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ y z) -3.0)))
   (if (<= y -7.8e+23) t_1 (if (<= y 1.9e+89) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) / -3.0;
	double tmp;
	if (y <= -7.8e+23) {
		tmp = t_1;
	} else if (y <= 1.9e+89) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) / (-3.0d0)
    if (y <= (-7.8d+23)) then
        tmp = t_1
    else if (y <= 1.9d+89) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) / -3.0;
	double tmp;
	if (y <= -7.8e+23) {
		tmp = t_1;
	} else if (y <= 1.9e+89) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) / -3.0
	tmp = 0
	if y <= -7.8e+23:
		tmp = t_1
	elif y <= 1.9e+89:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) / -3.0)
	tmp = 0.0
	if (y <= -7.8e+23)
		tmp = t_1;
	elseif (y <= 1.9e+89)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) / -3.0;
	tmp = 0.0;
	if (y <= -7.8e+23)
		tmp = t_1;
	elseif (y <= 1.9e+89)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]}, If[LessEqual[y, -7.8e+23], t$95$1, If[LessEqual[y, 1.9e+89], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.8000000000000001e23 or 1.90000000000000012e89 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 80.5%

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

   5. Simplified 80.5%

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

      1. associate-*r/ N/A

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

      2. /-rgt-identity N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. times-frac N/A

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

      6. metadata-eval N/A

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

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

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

      8. /-lowering-/.f64 80.5%

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

   7. Applied egg-rr 80.5%

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

      1. metadata-eval N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

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

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

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

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

      6. metadata-eval 80.7%

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

   9. Applied egg-rr 80.7%

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

   if -7.8000000000000001e23 < y < 1.90000000000000012e89

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 36.7%

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

Alternative 11: 47.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{-0.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e+41)
   (/ (* y -0.3333333333333333) z)
   (if (<= y 5.8e+88) x (/ y (/ z -0.3333333333333333)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e+41) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 5.8e+88) {
		tmp = x;
	} else {
		tmp = y / (z / -0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.4d+41)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= 5.8d+88) then
        tmp = x
    else
        tmp = y / (z / (-0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e+41) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 5.8e+88) {
		tmp = x;
	} else {
		tmp = y / (z / -0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e+41:
		tmp = (y * -0.3333333333333333) / z
	elif y <= 5.8e+88:
		tmp = x
	else:
		tmp = y / (z / -0.3333333333333333)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e+41)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= 5.8e+88)
		tmp = x;
	else
		tmp = Float64(y / Float64(z / -0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e+41)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= 5.8e+88)
		tmp = x;
	else
		tmp = y / (z / -0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e+41], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 5.8e+88], x, N[(y / N[(z / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000002e41

   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. *-commutative N/A

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

      2. associate-/r* N/A

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

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

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

      4. /-lowering-/.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 79.4%

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

   7. Simplified 79.4%

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

   if -2.4000000000000002e41 < y < 5.7999999999999999e88

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 37.1%

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

   if 5.7999999999999999e88 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 84.7%

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

   5. Simplified 84.7%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 84.8%

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

   7. Applied egg-rr 84.8%

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

Alternative 12: 47.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{-0.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e+42)
   (* y (/ -0.3333333333333333 z))
   (if (<= y 2.3e+93) x (/ y (/ z -0.3333333333333333)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+42) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 2.3e+93) {
		tmp = x;
	} else {
		tmp = y / (z / -0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d+42)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else if (y <= 2.3d+93) then
        tmp = x
    else
        tmp = y / (z / (-0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+42) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 2.3e+93) {
		tmp = x;
	} else {
		tmp = y / (z / -0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e+42:
		tmp = y * (-0.3333333333333333 / z)
	elif y <= 2.3e+93:
		tmp = x
	else:
		tmp = y / (z / -0.3333333333333333)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e+42)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	elseif (y <= 2.3e+93)
		tmp = x;
	else
		tmp = Float64(y / Float64(z / -0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e+42)
		tmp = y * (-0.3333333333333333 / z);
	elseif (y <= 2.3e+93)
		tmp = x;
	else
		tmp = y / (z / -0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e+42], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+93], x, N[(y / N[(z / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000003e42

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 79.3%

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

   5. Simplified 79.3%

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

   if -2.50000000000000003e42 < y < 2.3000000000000002e93

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 37.1%

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

   if 2.3000000000000002e93 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 84.7%

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

   5. Simplified 84.7%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 84.8%

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

   7. Applied egg-rr 84.8%

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

Alternative 13: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e+43)
   (* y (/ -0.3333333333333333 z))
   (if (<= y 6.6e+94) x (* -0.3333333333333333 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+43) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 6.6e+94) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.3d+43)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else if (y <= 6.6d+94) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+43) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 6.6e+94) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e+43:
		tmp = y * (-0.3333333333333333 / z)
	elif y <= 6.6e+94:
		tmp = x
	else:
		tmp = -0.3333333333333333 * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e+43)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	elseif (y <= 6.6e+94)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e+43)
		tmp = y * (-0.3333333333333333 / z);
	elseif (y <= 6.6e+94)
		tmp = x;
	else
		tmp = -0.3333333333333333 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e+43], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+94], x, N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3000000000000001e43

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 79.3%

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

   5. Simplified 79.3%

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

   if -1.3000000000000001e43 < y < 6.6e94

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 37.1%

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

   if 6.6e94 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 84.7%

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

   5. Simplified 84.7%

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

      1. associate-*r/ N/A

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

      2. /-rgt-identity N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. times-frac N/A

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

      6. metadata-eval N/A

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

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

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

      8. /-lowering-/.f64 84.8%

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

   7. Applied egg-rr 84.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ -0.3333333333333333 z))))
   (if (<= y -2.6e+40) t_1 (if (<= y 6.6e+40) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (-0.3333333333333333 / z);
	double tmp;
	if (y <= -2.6e+40) {
		tmp = t_1;
	} else if (y <= 6.6e+40) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((-0.3333333333333333d0) / z)
    if (y <= (-2.6d+40)) then
        tmp = t_1
    else if (y <= 6.6d+40) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (-0.3333333333333333 / z);
	double tmp;
	if (y <= -2.6e+40) {
		tmp = t_1;
	} else if (y <= 6.6e+40) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (-0.3333333333333333 / z)
	tmp = 0
	if y <= -2.6e+40:
		tmp = t_1
	elif y <= 6.6e+40:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-0.3333333333333333 / z))
	tmp = 0.0
	if (y <= -2.6e+40)
		tmp = t_1;
	elseif (y <= 6.6e+40)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (-0.3333333333333333 / z);
	tmp = 0.0;
	if (y <= -2.6e+40)
		tmp = t_1;
	elseif (y <= 6.6e+40)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+40], t$95$1, If[LessEqual[y, 6.6e+40], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6000000000000001e40 or 6.5999999999999997e40 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 77.7%

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

   5. Simplified 77.7%

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

   if -2.6000000000000001e40 < y < 6.5999999999999997e40

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 37.0%

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

Alternative 15: 95.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \frac{\frac{t}{y} - y}{3} \cdot \frac{1}{z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* (/ (- (/ t y) y) 3.0) (/ 1.0 z))))

C

double code(double x, double y, double z, double t) {
	return x + ((((t / y) - y) / 3.0) * (1.0 / z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((((t / y) - y) / 3.0d0) * (1.0d0 / z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((((t / y) - y) / 3.0) * (1.0 / z));
}

Python

def code(x, y, z, t):
	return x + ((((t / y) - y) / 3.0) * (1.0 / z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(Float64(t / y) - y) / 3.0) * Float64(1.0 / z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((((t / y) - y) / 3.0) * (1.0 / z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / 3.0), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.0%

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

3. Taylor expanded in x around 0

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

   1. associate--l+ N/A

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

   2. +-commutative N/A

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

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

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

   4. associate-*r/ N/A

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

   5. *-commutative N/A

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

   6. times-frac N/A

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

   7. metadata-eval N/A

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

   8. associate-*r/ N/A

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

   9. associate-*r/ N/A

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

   10. associate-*l/ N/A

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

   11. metadata-eval N/A

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

   12. associate-*r/ N/A

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

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

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

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

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

   15. associate-*r/ N/A

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

   16. metadata-eval N/A

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

   17. /-lowering-/.f64 N/A

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

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

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

   19. /-lowering-/.f64 94.2%

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

5. Simplified 94.2%

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

   1. *-commutative N/A

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

   2. metadata-eval N/A

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

   3. associate-/r* N/A

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

   4. *-commutative N/A

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

   5. associate-*r/ N/A

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

   6. *-commutative N/A

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

   7. times-frac N/A

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

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

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

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

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

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

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

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

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

   12. /-lowering-/.f64 94.3%

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

7. Applied egg-rr 94.3%

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

8. Final simplification 94.3%

   \[\leadsto x + \frac{\frac{t}{y} - y}{3} \cdot \frac{1}{z} \]
9. Add Preprocessing

Alternative 16: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

   1. associate-+l- N/A

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

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

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

   3. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. sub-div N/A

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

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

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

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

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

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

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

   9. *-lowering-*.f64 94.3%

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

4. Applied egg-rr 94.3%

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

5. Final simplification 94.3%

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

Alternative 17: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

3. Taylor expanded in x around 0

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

   1. associate--l+ N/A

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

   2. +-commutative N/A

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

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

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

   4. associate-*r/ N/A

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

   5. *-commutative N/A

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

   6. times-frac N/A

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

   7. metadata-eval N/A

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

   8. associate-*r/ N/A

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

   9. associate-*r/ N/A

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

   10. associate-*l/ N/A

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

   11. metadata-eval N/A

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

   12. associate-*r/ N/A

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

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

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

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

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

   15. associate-*r/ N/A

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

   16. metadata-eval N/A

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

   17. /-lowering-/.f64 N/A

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

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

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

   19. /-lowering-/.f64 94.2%

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

5. Simplified 94.2%

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

6. Final simplification 94.2%

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

Alternative 18: 30.0% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

3. Taylor expanded in x around inf

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

5. Simplified 28.1%

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

Developer Target 1: 96.5% 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 2024191 
(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))))