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

Percentage Accurate: 95.8% → 96.0%

Time: 10.7s

Alternatives: 15

Speedup: 1.4×

• 27.9% 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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 1.4× speedup

Math

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

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(Float64(t / y) - y) / 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[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.9%

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

   1. associate-+l- N/A

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

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

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

   3. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. sub-div N/A

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

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

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

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

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

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

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

   9. *-lowering-*.f64 97.2%

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

4. Applied egg-rr 97.2%

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

   1. associate-/r* N/A

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

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

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

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

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

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

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

   5. /-lowering-/.f64 97.6%

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

6. Applied egg-rr 97.6%

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

7. Final simplification 97.6%

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

Alternative 2: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.4e+98)
   (/ (/ y z) -3.0)
   (if (<= y -2.9e-179)
     x
     (if (<= y 5.5e-43)
       (* t (/ (/ 0.3333333333333333 z) y))
       (if (<= y 2.25e+73) x (/ (/ y -3.0) z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.4e+98) {
		tmp = (y / z) / -3.0;
	} else if (y <= -2.9e-179) {
		tmp = x;
	} else if (y <= 5.5e-43) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} else if (y <= 2.25e+73) {
		tmp = x;
	} else {
		tmp = (y / -3.0) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.4d+98)) then
        tmp = (y / z) / (-3.0d0)
    else if (y <= (-2.9d-179)) then
        tmp = x
    else if (y <= 5.5d-43) then
        tmp = t * ((0.3333333333333333d0 / z) / y)
    else if (y <= 2.25d+73) then
        tmp = x
    else
        tmp = (y / (-3.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.4e+98) {
		tmp = (y / z) / -3.0;
	} else if (y <= -2.9e-179) {
		tmp = x;
	} else if (y <= 5.5e-43) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} else if (y <= 2.25e+73) {
		tmp = x;
	} else {
		tmp = (y / -3.0) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.4e+98:
		tmp = (y / z) / -3.0
	elif y <= -2.9e-179:
		tmp = x
	elif y <= 5.5e-43:
		tmp = t * ((0.3333333333333333 / z) / y)
	elif y <= 2.25e+73:
		tmp = x
	else:
		tmp = (y / -3.0) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.4e+98)
		tmp = Float64(Float64(y / z) / -3.0);
	elseif (y <= -2.9e-179)
		tmp = x;
	elseif (y <= 5.5e-43)
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / z) / y));
	elseif (y <= 2.25e+73)
		tmp = x;
	else
		tmp = Float64(Float64(y / -3.0) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.4e+98)
		tmp = (y / z) / -3.0;
	elseif (y <= -2.9e-179)
		tmp = x;
	elseif (y <= 5.5e-43)
		tmp = t * ((0.3333333333333333 / z) / y);
	elseif (y <= 2.25e+73)
		tmp = x;
	else
		tmp = (y / -3.0) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.4e+98], N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[y, -2.9e-179], x, If[LessEqual[y, 5.5e-43], N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+73], x, N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.3999999999999994e98

   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. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

      10. associate-/r* N/A

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

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

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

      12. /-lowering-/.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 89.2%

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

   7. Simplified 89.2%

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

      1. frac-2neg N/A

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

      2. distribute-frac-neg2 N/A

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

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

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. associate-*l/ N/A

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

      7. div-inv N/A

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

      8. distribute-neg-frac2 N/A

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

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

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

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

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

      11. metadata-eval 89.3%

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

   9. Applied egg-rr 89.3%

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

   if -9.3999999999999994e98 < y < -2.8999999999999999e-179 or 5.50000000000000013e-43 < y < 2.24999999999999992e73

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 57.9%

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

   if -2.8999999999999999e-179 < y < 5.50000000000000013e-43

   1. Initial program 92.6%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 69.3%

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

   7. Simplified 69.3%

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

      1. times-frac N/A

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

      2. metadata-eval N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. div-inv N/A

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

      6. associate-/l/ N/A

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

      7. associate-/r* N/A

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

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

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

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

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

      10. *-lowering-*.f64 75.5%

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

   9. Applied egg-rr 75.5%

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

       1. associate-/r* N/A

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

       2. clear-num N/A

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

       3. associate-/r/ N/A

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

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

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

       5. associate-/r* N/A

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

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

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

       7. *-commutative N/A

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

       8. associate-/r* N/A

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

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

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

       10. metadata-eval 69.1%

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

   11. Applied egg-rr 69.1%

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

   if 2.24999999999999992e73 < y

   1. Initial program 95.9%

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

      1. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

      10. associate-/r* N/A

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

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

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

      12. /-lowering-/.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 65.1%

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

   7. Simplified 65.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

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

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

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

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

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

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. div-inv N/A

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

      13. clear-num N/A

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

      14. /-lowering-/.f64 65.1%

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

   9. Applied egg-rr 65.1%

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

       1. *-commutative N/A

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

       2. associate-*r/ N/A

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

       3. metadata-eval N/A

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

       4. div-inv N/A

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

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

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

       6. /-lowering-/.f64 65.3%

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

   11. Applied egg-rr 65.3%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -8.8e+38)
     t_1
     (if (<= y 1.15e+62) (+ x (/ t (* y (* z 3.0)))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) / 3.0);
	double tmp;
	if (y <= -8.8e+38) {
		tmp = t_1;
	} else if (y <= 1.15e+62) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / z) / 3.0d0)
    if (y <= (-8.8d+38)) then
        tmp = t_1
    else if (y <= 1.15d+62) then
        tmp = x + (t / (y * (z * 3.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) / 3.0);
	double tmp;
	if (y <= -8.8e+38) {
		tmp = t_1;
	} else if (y <= 1.15e+62) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) / 3.0)
	tmp = 0
	if y <= -8.8e+38:
		tmp = t_1
	elif y <= 1.15e+62:
		tmp = x + (t / (y * (z * 3.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) / 3.0))
	tmp = 0.0
	if (y <= -8.8e+38)
		tmp = t_1;
	elseif (y <= 1.15e+62)
		tmp = Float64(x + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((y / z) / 3.0);
	tmp = 0.0;
	if (y <= -8.8e+38)
		tmp = t_1;
	elseif (y <= 1.15e+62)
		tmp = x + (t / (y * (z * 3.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.8e+38], t$95$1, If[LessEqual[y, 1.15e+62], N[(x + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.80000000000000026e38 or 1.14999999999999992e62 < y

   1. Initial program 98.1%

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

      1. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

      10. associate-/r* N/A

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

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

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

      12. /-lowering-/.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 97.3%

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

   if -8.80000000000000026e38 < y < 1.14999999999999992e62

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 89.7%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -3.1e-177) t_1 (if (<= y 1.3e-58) (/ (/ t (* z 3.0)) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) / 3.0);
	double tmp;
	if (y <= -3.1e-177) {
		tmp = t_1;
	} else if (y <= 1.3e-58) {
		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 / z) / 3.0d0)
    if (y <= (-3.1d-177)) then
        tmp = t_1
    else if (y <= 1.3d-58) 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 / z) / 3.0);
	double tmp;
	if (y <= -3.1e-177) {
		tmp = t_1;
	} else if (y <= 1.3e-58) {
		tmp = (t / (z * 3.0)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) / 3.0)
	tmp = 0
	if y <= -3.1e-177:
		tmp = t_1
	elif y <= 1.3e-58:
		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 / z) / 3.0))
	tmp = 0.0
	if (y <= -3.1e-177)
		tmp = t_1;
	elseif (y <= 1.3e-58)
		tmp = Float64(Float64(t / Float64(z * 3.0)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((y / z) / 3.0);
	tmp = 0.0;
	if (y <= -3.1e-177)
		tmp = t_1;
	elseif (y <= 1.3e-58)
		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 / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e-177], t$95$1, If[LessEqual[y, 1.3e-58], N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000018e-177 or 1.30000000000000003e-58 < y

   1. Initial program 97.7%

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

      1. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

      10. associate-/r* N/A

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

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

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

      12. /-lowering-/.f64 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 84.2%

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

   if -3.10000000000000018e-177 < y < 1.30000000000000003e-58

   1. Initial program 92.0%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 71.4%

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

   7. Simplified 71.4%

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

      1. times-frac N/A

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

      2. metadata-eval N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. div-inv N/A

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

      6. associate-/l/ N/A

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

      7. associate-/r* N/A

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

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

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

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

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

      10. *-lowering-*.f64 78.1%

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

   9. Applied egg-rr 78.1%

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

Alternative 5: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-53}:\\ \;\;\;\;\frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -2.25e-175)
     t_1
     (if (<= y 1.85e-53) (/ 0.3333333333333333 (* z (/ y t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) / 3.0);
	double tmp;
	if (y <= -2.25e-175) {
		tmp = t_1;
	} else if (y <= 1.85e-53) {
		tmp = 0.3333333333333333 / (z * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / z) / 3.0d0)
    if (y <= (-2.25d-175)) then
        tmp = t_1
    else if (y <= 1.85d-53) then
        tmp = 0.3333333333333333d0 / (z * (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) / 3.0);
	double tmp;
	if (y <= -2.25e-175) {
		tmp = t_1;
	} else if (y <= 1.85e-53) {
		tmp = 0.3333333333333333 / (z * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) / 3.0)
	tmp = 0
	if y <= -2.25e-175:
		tmp = t_1
	elif y <= 1.85e-53:
		tmp = 0.3333333333333333 / (z * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) / 3.0))
	tmp = 0.0
	if (y <= -2.25e-175)
		tmp = t_1;
	elseif (y <= 1.85e-53)
		tmp = Float64(0.3333333333333333 / Float64(z * Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((y / z) / 3.0);
	tmp = 0.0;
	if (y <= -2.25e-175)
		tmp = t_1;
	elseif (y <= 1.85e-53)
		tmp = 0.3333333333333333 / (z * (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e-175], t$95$1, If[LessEqual[y, 1.85e-53], N[(0.3333333333333333 / N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.24999999999999999e-175 or 1.84999999999999991e-53 < y

   1. Initial program 97.7%

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

      1. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

      10. associate-/r* N/A

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

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

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

      12. /-lowering-/.f64 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 84.2%

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

   if -2.24999999999999999e-175 < y < 1.84999999999999991e-53

   1. Initial program 92.0%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 71.4%

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

   7. Simplified 71.4%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. frac-times N/A

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

      4. metadata-eval N/A

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

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

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

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

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

      7. /-lowering-/.f64 75.8%

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

   9. Applied egg-rr 75.8%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-175}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-53}:\\ \;\;\;\;\frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y z) 3.0))))
   (if (<= y -2.3e-175)
     t_1
     (if (<= y 1.9e-58) (* t (/ (/ 0.3333333333333333 z) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) / 3.0);
	double tmp;
	if (y <= -2.3e-175) {
		tmp = t_1;
	} else if (y <= 1.9e-58) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / z) / 3.0d0)
    if (y <= (-2.3d-175)) then
        tmp = t_1
    else if (y <= 1.9d-58) then
        tmp = t * ((0.3333333333333333d0 / z) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) / 3.0);
	double tmp;
	if (y <= -2.3e-175) {
		tmp = t_1;
	} else if (y <= 1.9e-58) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) / 3.0)
	tmp = 0
	if y <= -2.3e-175:
		tmp = t_1
	elif y <= 1.9e-58:
		tmp = t * ((0.3333333333333333 / z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) / 3.0))
	tmp = 0.0
	if (y <= -2.3e-175)
		tmp = t_1;
	elseif (y <= 1.9e-58)
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((y / z) / 3.0);
	tmp = 0.0;
	if (y <= -2.3e-175)
		tmp = t_1;
	elseif (y <= 1.9e-58)
		tmp = t * ((0.3333333333333333 / z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e-175], t$95$1, If[LessEqual[y, 1.9e-58], N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e-175 or 1.8999999999999999e-58 < y

   1. Initial program 97.7%

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

      1. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

      10. associate-/r* N/A

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

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

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

      12. /-lowering-/.f64 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 84.2%

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

   if -2.3e-175 < y < 1.8999999999999999e-58

   1. Initial program 92.0%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 71.4%

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

   7. Simplified 71.4%

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

      1. times-frac N/A

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

      2. metadata-eval N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. div-inv N/A

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

      6. associate-/l/ N/A

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

      7. associate-/r* N/A

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

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

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

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

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

      10. *-lowering-*.f64 78.1%

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

   9. Applied egg-rr 78.1%

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

       1. associate-/r* N/A

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

       2. clear-num N/A

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

       3. associate-/r/ N/A

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

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

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

       5. associate-/r* N/A

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

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

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

       7. *-commutative N/A

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

       8. associate-/r* N/A

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

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

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

       10. metadata-eval 71.2%

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

   11. Applied egg-rr 71.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-175}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -1.05e-175)
     t_1
     (if (<= y 8.1e-56) (* t (/ (/ 0.3333333333333333 z) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -1.05e-175) {
		tmp = t_1;
	} else if (y <= 8.1e-56) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((-0.3333333333333333d0) / z))
    if (y <= (-1.05d-175)) then
        tmp = t_1
    else if (y <= 8.1d-56) then
        tmp = t * ((0.3333333333333333d0 / z) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -1.05e-175) {
		tmp = t_1;
	} else if (y <= 8.1e-56) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -1.05e-175:
		tmp = t_1
	elif y <= 8.1e-56:
		tmp = t * ((0.3333333333333333 / z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -1.05e-175)
		tmp = t_1;
	elseif (y <= 8.1e-56)
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -1.05e-175)
		tmp = t_1;
	elseif (y <= 8.1e-56)
		tmp = t * ((0.3333333333333333 / z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e-175], t$95$1, If[LessEqual[y, 8.1e-56], N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e-175 or 8.1000000000000003e-56 < y

   1. Initial program 97.7%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 84.1%

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

   if -1.05e-175 < y < 8.1000000000000003e-56

   1. Initial program 92.0%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 71.4%

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

   7. Simplified 71.4%

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

      1. times-frac N/A

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

      2. metadata-eval N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. div-inv N/A

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

      6. associate-/l/ N/A

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

      7. associate-/r* N/A

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

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

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

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

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

      10. *-lowering-*.f64 78.1%

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

   9. Applied egg-rr 78.1%

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

       1. associate-/r* N/A

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

       2. clear-num N/A

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

       3. associate-/r/ N/A

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

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

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

       5. associate-/r* N/A

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

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

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

       7. *-commutative N/A

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

       8. associate-/r* N/A

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

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

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

       10. metadata-eval 71.2%

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

   11. Applied egg-rr 71.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-175}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+103}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.45e+103) (/ (/ y z) -3.0) (if (<= y 4e+73) x (/ (/ y -3.0) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.45e+103) {
		tmp = (y / z) / -3.0;
	} else if (y <= 4e+73) {
		tmp = x;
	} else {
		tmp = (y / -3.0) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.45d+103)) then
        tmp = (y / z) / (-3.0d0)
    else if (y <= 4d+73) then
        tmp = x
    else
        tmp = (y / (-3.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.45e+103) {
		tmp = (y / z) / -3.0;
	} else if (y <= 4e+73) {
		tmp = x;
	} else {
		tmp = (y / -3.0) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.45e+103:
		tmp = (y / z) / -3.0
	elif y <= 4e+73:
		tmp = x
	else:
		tmp = (y / -3.0) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.45e+103)
		tmp = Float64(Float64(y / z) / -3.0);
	elseif (y <= 4e+73)
		tmp = x;
	else
		tmp = Float64(Float64(y / -3.0) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.45e+103)
		tmp = (y / z) / -3.0;
	elseif (y <= 4e+73)
		tmp = x;
	else
		tmp = (y / -3.0) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.45e+103], N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[y, 4e+73], x, N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4499999999999999e103

   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. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

      10. associate-/r* N/A

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

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

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

      12. /-lowering-/.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 89.2%

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

   7. Simplified 89.2%

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

      1. frac-2neg N/A

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

      2. distribute-frac-neg2 N/A

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

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

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. associate-*l/ N/A

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

      7. div-inv N/A

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

      8. distribute-neg-frac2 N/A

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

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

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

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

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

      11. metadata-eval 89.3%

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

   9. Applied egg-rr 89.3%

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

   if -3.4499999999999999e103 < y < 3.99999999999999993e73

   1. Initial program 94.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 38.9%

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

   if 3.99999999999999993e73 < y

   1. Initial program 95.9%

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

      1. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

      10. associate-/r* N/A

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

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

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

      12. /-lowering-/.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 65.1%

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

   7. Simplified 65.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

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

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

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

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

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

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. div-inv N/A

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

      13. clear-num N/A

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

      14. /-lowering-/.f64 65.1%

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

   9. Applied egg-rr 65.1%

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

       1. *-commutative N/A

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

       2. associate-*r/ N/A

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

       3. metadata-eval N/A

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

       4. div-inv N/A

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

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

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

       6. /-lowering-/.f64 65.3%

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

   11. Applied egg-rr 65.3%

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

Alternative 9: 48.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{-3}}{z}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ y -3.0) z)))
   (if (<= y -7e+100) t_1 (if (<= y 2.9e+74) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / -3.0) / z;
	double tmp;
	if (y <= -7e+100) {
		tmp = t_1;
	} else if (y <= 2.9e+74) {
		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 / (-3.0d0)) / z
    if (y <= (-7d+100)) then
        tmp = t_1
    else if (y <= 2.9d+74) 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 / -3.0) / z;
	double tmp;
	if (y <= -7e+100) {
		tmp = t_1;
	} else if (y <= 2.9e+74) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / -3.0) / z
	tmp = 0
	if y <= -7e+100:
		tmp = t_1
	elif y <= 2.9e+74:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / -3.0) / z)
	tmp = 0.0
	if (y <= -7e+100)
		tmp = t_1;
	elseif (y <= 2.9e+74)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / -3.0) / z;
	tmp = 0.0;
	if (y <= -7e+100)
		tmp = t_1;
	elseif (y <= 2.9e+74)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -7e+100], t$95$1, If[LessEqual[y, 2.9e+74], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999953e100 or 2.9000000000000002e74 < y

   1. Initial program 97.8%

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

      1. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

      10. associate-/r* N/A

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

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

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

      12. /-lowering-/.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 76.9%

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

   7. Simplified 76.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

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

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

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

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

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

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. div-inv N/A

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

      13. clear-num N/A

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

      14. /-lowering-/.f64 76.9%

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

   9. Applied egg-rr 76.9%

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

       1. *-commutative N/A

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

       2. associate-*r/ N/A

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

       3. metadata-eval N/A

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

       4. div-inv N/A

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

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

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

       6. /-lowering-/.f64 77.0%

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

   11. Applied egg-rr 77.0%

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

   if -6.99999999999999953e100 < y < 2.9000000000000002e74

   1. Initial program 94.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

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

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

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

      21. /-lowering-/.f64 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 38.9%

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

Alternative 10: 48.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -9.4 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y -0.3333333333333333) z)))
   (if (<= y -9.4e+98) t_1 (if (<= y 3e+73) 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 <= -9.4e+98) {
		tmp = t_1;
	} else if (y <= 3e+73) {
		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 <= (-9.4d+98)) then
        tmp = t_1
    else if (y <= 3d+73) 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 <= -9.4e+98) {
		tmp = t_1;
	} else if (y <= 3e+73) {
		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 <= -9.4e+98:
		tmp = t_1
	elif y <= 3e+73:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * -0.3333333333333333) / z)
	tmp = 0.0
	if (y <= -9.4e+98)
		tmp = t_1;
	elseif (y <= 3e+73)
		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 <= -9.4e+98)
		tmp = t_1;
	elseif (y <= 3e+73)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -9.4e+98], t$95$1, If[LessEqual[y, 3e+73], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.3999999999999994e98 or 3.00000000000000011e73 < y

   1. Initial program 97.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

      4. remove-double-neg N/A

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

      5. unsub-neg N/A

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

      6. neg-mul-1 N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. distribute-neg-frac N/A

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

      12. neg-mul-1 N/A

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

      13. times-frac N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. associate-/r* N/A

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

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

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

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 76.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{3}, y\right), z\right) \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

   if -9.3999999999999994e98 < y < 3.00000000000000011e73

   1. Initial program 94.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 96.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 38.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+98}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.16 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e+100)
   (* y (/ -0.3333333333333333 z))
   (if (<= y 2.16e+74) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e+100) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 2.16e+74) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.35d+100)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else if (y <= 2.16d+74) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e+100) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 2.16e+74) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e+100:
		tmp = y * (-0.3333333333333333 / z)
	elif y <= 2.16e+74:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e+100)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	elseif (y <= 2.16e+74)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e+100)
		tmp = y * (-0.3333333333333333 / z);
	elseif (y <= 2.16e+74)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e+100], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.16e+74], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.34999999999999999e100

   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. +-commutative N/A

         \[\leadsto \frac{t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \color{blue}{\frac{y}{z \cdot 3}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right), \color{blue}{\left(\frac{y}{z \cdot 3}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right), x\right), \left(\frac{\color{blue}{y}}{z \cdot 3}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{t}{y \cdot \left(z \cdot 3\right)}\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{\frac{t}{y}}{z \cdot 3}\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{t}{y}\right), \left(z \cdot 3\right)\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(z \cdot 3\right)\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      10. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \left(\frac{\frac{y}{z}}{\color{blue}{3}}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \mathsf{/.f64}\left(\left(\frac{y}{z}\right), \color{blue}{3}\right)\right) \]

      12. /-lowering-/.f64 99.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, z\right), 3\right)\right) \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(\frac{\frac{t}{y}}{z \cdot 3} + x\right) - \frac{\frac{y}{z}}{3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 89.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{-1}{3}}{z} \cdot \color{blue}{y} \]

      3. clear-num N/A

         \[\leadsto \frac{1}{\frac{z}{\frac{-1}{3}}} \cdot y \]

      4. div-inv N/A

         \[\leadsto \frac{1}{z \cdot \frac{1}{\frac{-1}{3}}} \cdot y \]

      5. metadata-eval N/A

         \[\leadsto \frac{1}{z \cdot -3} \cdot y \]

      6. metadata-eval N/A

         \[\leadsto \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)} \cdot y \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(z \cdot 3\right)} \cdot y \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right), \color{blue}{y}\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot -3}\right), y\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot \frac{1}{\frac{-1}{3}}}\right), y\right) \]

      12. div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{z}{\frac{-1}{3}}}\right), y\right) \]

      13. clear-num N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), y\right) \]

      14. /-lowering-/.f64 89.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), y\right) \]

   9. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333}{z} \cdot y} \]

   if -1.34999999999999999e100 < y < 2.1599999999999999e74

   1. Initial program 94.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 96.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 38.9%

      \[\leadsto \color{blue}{x} \]

   if 2.1599999999999999e74 < y

   1. Initial program 95.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \color{blue}{\frac{y}{z \cdot 3}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right), \color{blue}{\left(\frac{y}{z \cdot 3}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right), x\right), \left(\frac{\color{blue}{y}}{z \cdot 3}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{t}{y \cdot \left(z \cdot 3\right)}\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{\frac{t}{y}}{z \cdot 3}\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{t}{y}\right), \left(z \cdot 3\right)\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(z \cdot 3\right)\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      10. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \left(\frac{\frac{y}{z}}{\color{blue}{3}}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \mathsf{/.f64}\left(\left(\frac{y}{z}\right), \color{blue}{3}\right)\right) \]

      12. /-lowering-/.f64 99.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, z\right), 3\right)\right) \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(\frac{\frac{t}{y}}{z \cdot 3} + x\right) - \frac{\frac{y}{z}}{3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 65.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 65.1%

      \[\leadsto \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{-1}{3}}{z} \cdot \color{blue}{y} \]

      3. clear-num N/A

         \[\leadsto \frac{1}{\frac{z}{\frac{-1}{3}}} \cdot y \]

      4. div-inv N/A

         \[\leadsto \frac{1}{z \cdot \frac{1}{\frac{-1}{3}}} \cdot y \]

      5. metadata-eval N/A

         \[\leadsto \frac{1}{z \cdot -3} \cdot y \]

      6. metadata-eval N/A

         \[\leadsto \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)} \cdot y \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(z \cdot 3\right)} \cdot y \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right), \color{blue}{y}\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot -3}\right), y\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot \frac{1}{\frac{-1}{3}}}\right), y\right) \]

      12. div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{z}{\frac{-1}{3}}}\right), y\right) \]

      13. clear-num N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), y\right) \]

      14. /-lowering-/.f64 65.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), y\right) \]

   9. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333}{z} \cdot y} \]
   10. Step-by-step derivation

       1. associate-*l/ N/A

          \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

       2. associate-/l* N/A

          \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{y}{z}} \]

       3. clear-num N/A

          \[\leadsto \frac{-1}{3} \cdot \frac{1}{\color{blue}{\frac{z}{y}}} \]

       4. div-inv N/A

          \[\leadsto \frac{\frac{-1}{3}}{\color{blue}{\frac{z}{y}}} \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

       6. /-lowering-/.f64 65.1%

          \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   11. Applied egg-rr 65.1%

       \[\leadsto \color{blue}{\frac{-0.3333333333333333}{\frac{z}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.16 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ -0.3333333333333333 z))))
   (if (<= y -7.4e+102) t_1 (if (<= y 2.65e+73) 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 <= -7.4e+102) {
		tmp = t_1;
	} else if (y <= 2.65e+73) {
		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 <= (-7.4d+102)) then
        tmp = t_1
    else if (y <= 2.65d+73) 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 <= -7.4e+102) {
		tmp = t_1;
	} else if (y <= 2.65e+73) {
		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 <= -7.4e+102:
		tmp = t_1
	elif y <= 2.65e+73:
		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 <= -7.4e+102)
		tmp = t_1;
	elseif (y <= 2.65e+73)
		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 <= -7.4e+102)
		tmp = t_1;
	elseif (y <= 2.65e+73)
		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, -7.4e+102], t$95$1, If[LessEqual[y, 2.65e+73], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.40000000000000045e102 or 2.64999999999999998e73 < y

   1. Initial program 97.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \color{blue}{\frac{y}{z \cdot 3}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right), \color{blue}{\left(\frac{y}{z \cdot 3}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right), x\right), \left(\frac{\color{blue}{y}}{z \cdot 3}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{t}{y \cdot \left(z \cdot 3\right)}\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\frac{\frac{t}{y}}{z \cdot 3}\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{t}{y}\right), \left(z \cdot 3\right)\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(z \cdot 3\right)\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \left(\frac{y}{z \cdot 3}\right)\right) \]

      10. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \left(\frac{\frac{y}{z}}{\color{blue}{3}}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \mathsf{/.f64}\left(\left(\frac{y}{z}\right), \color{blue}{3}\right)\right) \]

      12. /-lowering-/.f64 99.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{*.f64}\left(z, 3\right)\right), x\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, z\right), 3\right)\right) \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(\frac{\frac{t}{y}}{z \cdot 3} + x\right) - \frac{\frac{y}{z}}{3}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{3} \cdot y}{\color{blue}{z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 76.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{-1}{3}}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{-1}{3}}{z} \cdot \color{blue}{y} \]

      3. clear-num N/A

         \[\leadsto \frac{1}{\frac{z}{\frac{-1}{3}}} \cdot y \]

      4. div-inv N/A

         \[\leadsto \frac{1}{z \cdot \frac{1}{\frac{-1}{3}}} \cdot y \]

      5. metadata-eval N/A

         \[\leadsto \frac{1}{z \cdot -3} \cdot y \]

      6. metadata-eval N/A

         \[\leadsto \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)} \cdot y \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(z \cdot 3\right)} \cdot y \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right), \color{blue}{y}\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot -3}\right), y\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot \frac{1}{\frac{-1}{3}}}\right), y\right) \]

      12. div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{z}{\frac{-1}{3}}}\right), y\right) \]

      13. clear-num N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), y\right) \]

      14. /-lowering-/.f64 76.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), y\right) \]

   9. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333}{z} \cdot y} \]

   if -7.40000000000000045e102 < y < 2.64999999999999998e73

   1. Initial program 94.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 96.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 38.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 95.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - \frac{t}{y}}{z} \cdot -0.3333333333333333 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* (/ (- y (/ t y)) z) -0.3333333333333333)))

C

double code(double x, double y, double z, double t) {
	return x + (((y - (t / y)) / z) * -0.3333333333333333);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((y - (t / y)) / z) * (-0.3333333333333333d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((y - (t / y)) / z) * -0.3333333333333333);
}

Python

def code(x, y, z, t):
	return x + (((y - (t / y)) / z) * -0.3333333333333333)

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(y - Float64(t / y)) / z) * -0.3333333333333333))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((y - (t / y)) / z) * -0.3333333333333333);
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.9%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

   2. associate-+l+ N/A

      \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

   4. remove-double-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

   5. unsub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   8. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   9. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   11. distribute-neg-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

   12. neg-mul-1 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

   13. times-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

   14. distribute-lft-out-- N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   17. associate-/r* N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   18. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   19. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   20. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

   21. /-lowering-/.f64 97.5%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

3. Simplified 97.5%

   \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

   3. div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

   6. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

   7. associate-*r/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

   8. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

   9. times-frac N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

   13. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

   14. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   15. /-lowering-/.f64 97.5%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

6. Applied egg-rr 97.5%

   \[\leadsto x + \color{blue}{\frac{y - \frac{t}{y}}{z} \cdot -0.3333333333333333} \]
7. Add Preprocessing

Alternative 14: 96.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - (t / y)) * (-0.3333333333333333 / z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - (t / y)) * (-0.3333333333333333 / z));
}

Python

def code(x, y, z, t):
	return x + ((y - (t / y)) * (-0.3333333333333333 / z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.9%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

   2. associate-+l+ N/A

      \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

   4. remove-double-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

   5. unsub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   8. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   9. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   11. distribute-neg-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

   12. neg-mul-1 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

   13. times-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

   14. distribute-lft-out-- N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   17. associate-/r* N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   18. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   19. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   20. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

   21. /-lowering-/.f64 97.5%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

3. Simplified 97.5%

   \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
4. Add Preprocessing

5. Final simplification 97.5%

   \[\leadsto x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z} \]
6. Add Preprocessing

Alternative 15: 30.6% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 95.9%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \left(x + \left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right)\right) + \frac{\color{blue}{t}}{\left(z \cdot 3\right) \cdot y} \]

   2. associate-+l+ N/A

      \[\leadsto x + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

   4. remove-double-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

   5. unsub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   8. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   9. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   11. distribute-neg-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

   12. neg-mul-1 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

   13. times-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

   14. distribute-lft-out-- N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   17. associate-/r* N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   18. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   19. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   20. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

   21. /-lowering-/.f64 97.5%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

3. Simplified 97.5%

   \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 33.7%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 96.2% 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 2024150 
(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))))