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

Percentage Accurate: 96.2% → 98.1%

Time: 11.1s

Alternatives: 15

Speedup: 0.4×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% 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: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right) + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \left(\frac{1}{\frac{y}{t}} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0)))) 2e+301)
   (+ (+ x (/ t (* z (* y 3.0)))) (/ y (* z -3.0)))
   (+ x (* (/ 0.3333333333333333 z) (- (/ 1.0 (/ y t)) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))) <= 2e+301) {
		tmp = (x + (t / (z * (y * 3.0)))) + (y / (z * -3.0));
	} else {
		tmp = x + ((0.3333333333333333 / z) * ((1.0 / (y / t)) - 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 (((x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))) <= 2d+301) then
        tmp = (x + (t / (z * (y * 3.0d0)))) + (y / (z * (-3.0d0)))
    else
        tmp = x + ((0.3333333333333333d0 / z) * ((1.0d0 / (y / t)) - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))) <= 2e+301) {
		tmp = (x + (t / (z * (y * 3.0)))) + (y / (z * -3.0));
	} else {
		tmp = x + ((0.3333333333333333 / z) * ((1.0 / (y / t)) - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))) <= 2e+301:
		tmp = (x + (t / (z * (y * 3.0)))) + (y / (z * -3.0))
	else:
		tmp = x + ((0.3333333333333333 / z) * ((1.0 / (y / t)) - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0)))) <= 2e+301)
		tmp = Float64(Float64(x + Float64(t / Float64(z * Float64(y * 3.0)))) + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / z) * Float64(Float64(1.0 / Float64(y / t)) - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))) <= 2e+301)
		tmp = (x + (t / (z * (y * 3.0)))) + (y / (z * -3.0));
	else
		tmp = x + ((0.3333333333333333 / z) * ((1.0 / (y / t)) - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+301], N[(N[(x + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(N[(1.0 / N[(y / t), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 2.00000000000000011e301

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. associate-+r- 98.3%

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

      3. sub-neg 98.3%

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

      4. associate-*l* 98.3%

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

      5. *-commutative 98.3%

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

      6. distribute-frac-neg2 98.3%

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

      7. distribute-rgt-neg-in 98.3%

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

      8. metadata-eval 98.3%

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

   3. Simplified 98.3%

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

   if 2.00000000000000011e301 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))

   1. Initial program 77.2%

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

      1. sub-neg 77.2%

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

      2. associate-+l+ 77.2%

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

      3. +-commutative 77.2%

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

      4. remove-double-neg 77.2%

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

      5. distribute-frac-neg 77.2%

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

      6. distribute-neg-in 77.2%

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

      7. remove-double-neg 77.2%

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

      8. sub-neg 77.2%

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

      9. neg-mul-1 77.2%

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

      10. times-frac 90.8%

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

      11. distribute-frac-neg 90.8%

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

      12. neg-mul-1 90.8%

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

      13. *-commutative 90.8%

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

      14. associate-/l* 90.8%

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

      15. *-commutative 90.8%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

         \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]

      2. inv-pow 99.9%

         \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{{\left(\frac{y}{t}\right)}^{-1}} - y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{{\left(\frac{y}{t}\right)}^{-1}} - y\right) \]
   7. Step-by-step derivation

      1. unpow-1 99.9%

         \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]

   8. Simplified 99.9%

      \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right) + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \left(\frac{1}{\frac{y}{t}} - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e+36)
   (/ (* y -0.3333333333333333) z)
   (if (<= y -1.35e-102)
     x
     (if (<= y 1.4e-18)
       (* (/ t z) (/ 0.3333333333333333 y))
       (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+36) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -1.35e-102) {
		tmp = x;
	} else if (y <= 1.4e-18) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.5d+36)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= (-1.35d-102)) then
        tmp = x
    else if (y <= 1.4d-18) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+36) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -1.35e-102) {
		tmp = x;
	} else if (y <= 1.4e-18) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e+36:
		tmp = (y * -0.3333333333333333) / z
	elif y <= -1.35e-102:
		tmp = x
	elif y <= 1.4e-18:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+36)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= -1.35e-102)
		tmp = x;
	elseif (y <= 1.4e-18)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.5e+36)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= -1.35e-102)
		tmp = x;
	elseif (y <= 1.4e-18)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e+36], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -1.35e-102], x, If[LessEqual[y, 1.4e-18], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5e36

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 79.8%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. *-commutative 72.5%

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

   6. Simplified 72.5%

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

   if -1.5e36 < y < -1.35e-102

   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 97.4%

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

      2. associate-+l+ 97.4%

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

      3. +-commutative 97.4%

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

      4. remove-double-neg 97.4%

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

      5. distribute-frac-neg 97.4%

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

      6. distribute-neg-in 97.4%

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

      7. remove-double-neg 97.4%

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

      8. sub-neg 97.4%

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

      9. neg-mul-1 97.4%

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

      10. times-frac 99.9%

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

      11. distribute-frac-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. *-commutative 99.9%

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

      14. associate-/l* 99.9%

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

      15. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 62.8%

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

   if -1.35e-102 < y < 1.40000000000000006e-18

   1. Initial program 91.0%

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

   3. Taylor expanded in z around 0 64.9%

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

   4. Taylor expanded in t around inf 62.2%

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

      1. associate-*r/ 62.2%

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

   6. Simplified 62.2%

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

      1. associate-/l/ 63.7%

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

      2. *-commutative 63.7%

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

      3. times-frac 66.8%

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

   8. Applied egg-rr 66.8%

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

   if 1.40000000000000006e-18 < y

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 69.6%

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

   4. Taylor expanded in t around 0 59.7%

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

      1. *-commutative 59.7%

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

   6. Simplified 59.7%

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

      1. clear-num 59.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot -0.3333333333333333}}} \]

      2. inv-pow 59.8%

         \[\leadsto \color{blue}{{\left(\frac{z}{y \cdot -0.3333333333333333}\right)}^{-1}} \]

      3. *-un-lft-identity 59.8%

         \[\leadsto {\left(\frac{\color{blue}{1 \cdot z}}{y \cdot -0.3333333333333333}\right)}^{-1} \]

      4. *-commutative 59.8%

         \[\leadsto {\left(\frac{1 \cdot z}{\color{blue}{-0.3333333333333333 \cdot y}}\right)}^{-1} \]

      5. times-frac 59.8%

         \[\leadsto {\color{blue}{\left(\frac{1}{-0.3333333333333333} \cdot \frac{z}{y}\right)}}^{-1} \]

      6. metadata-eval 59.8%

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

   8. Applied egg-rr 59.8%

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

      1. unpow-1 59.8%

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

      2. associate-/r* 59.8%

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

      3. metadata-eval 59.8%

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

   10. Simplified 59.8%

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

       1. associate-/r/ 59.8%

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

   12. Applied egg-rr 59.8%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-18}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.02e+41)
   (/ (* y -0.3333333333333333) z)
   (if (<= y -8.1e-103)
     x
     (if (<= y 1.35e-18)
       (* (/ 0.3333333333333333 z) (/ t y))
       (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e+41) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -8.1e-103) {
		tmp = x;
	} else if (y <= 1.35e-18) {
		tmp = (0.3333333333333333 / z) * (t / y);
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.02d+41)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= (-8.1d-103)) then
        tmp = x
    else if (y <= 1.35d-18) then
        tmp = (0.3333333333333333d0 / z) * (t / y)
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e+41) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -8.1e-103) {
		tmp = x;
	} else if (y <= 1.35e-18) {
		tmp = (0.3333333333333333 / z) * (t / y);
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.02e+41:
		tmp = (y * -0.3333333333333333) / z
	elif y <= -8.1e-103:
		tmp = x
	elif y <= 1.35e-18:
		tmp = (0.3333333333333333 / z) * (t / y)
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.02e+41)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= -8.1e-103)
		tmp = x;
	elseif (y <= 1.35e-18)
		tmp = Float64(Float64(0.3333333333333333 / z) * Float64(t / y));
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.02e+41)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= -8.1e-103)
		tmp = x;
	elseif (y <= 1.35e-18)
		tmp = (0.3333333333333333 / z) * (t / y);
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.02e+41], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -8.1e-103], x, If[LessEqual[y, 1.35e-18], N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.01999999999999992e41

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 79.8%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. *-commutative 72.5%

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

   6. Simplified 72.5%

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

   if -1.01999999999999992e41 < y < -8.09999999999999979e-103

   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 97.4%

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

      2. associate-+l+ 97.4%

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

      3. +-commutative 97.4%

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

      4. remove-double-neg 97.4%

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

      5. distribute-frac-neg 97.4%

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

      6. distribute-neg-in 97.4%

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

      7. remove-double-neg 97.4%

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

      8. sub-neg 97.4%

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

      9. neg-mul-1 97.4%

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

      10. times-frac 99.9%

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

      11. distribute-frac-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. *-commutative 99.9%

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

      14. associate-/l* 99.9%

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

      15. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 62.8%

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

   if -8.09999999999999979e-103 < y < 1.34999999999999994e-18

   1. Initial program 91.0%

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

   3. Taylor expanded in z around 0 64.9%

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

   4. Taylor expanded in t around inf 62.2%

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

      1. associate-*r/ 62.2%

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

   6. Simplified 62.2%

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

      1. associate-/r* 63.7%

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

      2. *-commutative 63.7%

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

      3. times-frac 62.2%

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

   8. Applied egg-rr 62.2%

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

   if 1.34999999999999994e-18 < y

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 69.6%

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

   4. Taylor expanded in t around 0 59.7%

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

      1. *-commutative 59.7%

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

   6. Simplified 59.7%

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

      1. clear-num 59.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot -0.3333333333333333}}} \]

      2. inv-pow 59.8%

         \[\leadsto \color{blue}{{\left(\frac{z}{y \cdot -0.3333333333333333}\right)}^{-1}} \]

      3. *-un-lft-identity 59.8%

         \[\leadsto {\left(\frac{\color{blue}{1 \cdot z}}{y \cdot -0.3333333333333333}\right)}^{-1} \]

      4. *-commutative 59.8%

         \[\leadsto {\left(\frac{1 \cdot z}{\color{blue}{-0.3333333333333333 \cdot y}}\right)}^{-1} \]

      5. times-frac 59.8%

         \[\leadsto {\color{blue}{\left(\frac{1}{-0.3333333333333333} \cdot \frac{z}{y}\right)}}^{-1} \]

      6. metadata-eval 59.8%

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

   8. Applied egg-rr 59.8%

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

      1. unpow-1 59.8%

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

      2. associate-/r* 59.8%

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

      3. metadata-eval 59.8%

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

   10. Simplified 59.8%

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

       1. associate-/r/ 59.8%

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

   12. Applied egg-rr 59.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-18}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-19}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \left(\frac{1}{y} \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.6e+66)
   (- x (/ (* y 0.3333333333333333) z))
   (if (<= y 1.05e-19)
     (+ x (* 0.3333333333333333 (* (/ 1.0 y) (/ t z))))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+66) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 1.05e-19) {
		tmp = x + (0.3333333333333333 * ((1.0 / y) * (t / z)));
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.6d+66)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 1.05d-19) then
        tmp = x + (0.3333333333333333d0 * ((1.0d0 / y) * (t / z)))
    else
        tmp = x - (0.3333333333333333d0 * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+66) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 1.05e-19) {
		tmp = x + (0.3333333333333333 * ((1.0 / y) * (t / z)));
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.6e+66:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 1.05e-19:
		tmp = x + (0.3333333333333333 * ((1.0 / y) * (t / z)))
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.6e+66)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 1.05e-19)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(1.0 / y) * Float64(t / z))));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.6e+66)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 1.05e-19)
		tmp = x + (0.3333333333333333 * ((1.0 / y) * (t / z)));
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.6e+66], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-19], N[(x + N[(0.3333333333333333 * N[(N[(1.0 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.6000000000000004e66

   1. Initial program 95.5%

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

      1. sub-neg 95.5%

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

      2. associate-+l+ 95.5%

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

      3. +-commutative 95.5%

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

      4. remove-double-neg 95.5%

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

      5. distribute-frac-neg 95.5%

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

      6. distribute-neg-in 95.5%

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

      7. remove-double-neg 95.5%

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

      8. sub-neg 95.5%

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

      9. neg-mul-1 95.5%

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

      10. times-frac 95.5%

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

      11. distribute-frac-neg 95.5%

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

      12. neg-mul-1 95.5%

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

      13. *-commutative 95.5%

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

      14. associate-/l* 95.5%

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

      15. *-commutative 95.5%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 97.7%

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

      1. metadata-eval 97.7%

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

      2. cancel-sign-sub-inv 97.7%

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

      3. associate-*r/ 97.7%

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

   7. Simplified 97.7%

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

   if -7.6000000000000004e66 < y < 1.0499999999999999e-19

   1. Initial program 92.8%

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

      1. sub-neg 92.8%

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

      2. associate-+l+ 92.8%

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

      3. +-commutative 92.8%

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

      4. remove-double-neg 92.8%

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

      5. distribute-frac-neg 92.8%

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

      6. distribute-neg-in 92.8%

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

      7. remove-double-neg 92.8%

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

      8. sub-neg 92.8%

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

      9. neg-mul-1 92.8%

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

      10. times-frac 94.1%

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

      11. distribute-frac-neg 94.1%

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

      12. neg-mul-1 94.1%

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

      13. *-commutative 94.1%

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

      14. associate-/l* 94.1%

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

      15. *-commutative 94.1%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around inf 89.2%

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

      1. *-un-lft-identity 89.2%

         \[\leadsto x + 0.3333333333333333 \cdot \frac{\color{blue}{1 \cdot t}}{y \cdot z} \]

      2. times-frac 94.4%

         \[\leadsto x + 0.3333333333333333 \cdot \color{blue}{\left(\frac{1}{y} \cdot \frac{t}{z}\right)} \]

   7. Applied egg-rr 94.4%

      \[\leadsto x + 0.3333333333333333 \cdot \color{blue}{\left(\frac{1}{y} \cdot \frac{t}{z}\right)} \]

   if 1.0499999999999999e-19 < y

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0 90.0%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-19}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \left(\frac{1}{y} \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 10^{-18}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.6e+66)
   (- x (/ (* y 0.3333333333333333) z))
   (if (<= y 1e-18)
     (+ x (* 0.3333333333333333 (/ (/ t z) y)))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+66) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 1e-18) {
		tmp = x + (0.3333333333333333 * ((t / z) / y));
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.6d+66)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 1d-18) then
        tmp = x + (0.3333333333333333d0 * ((t / z) / y))
    else
        tmp = x - (0.3333333333333333d0 * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+66) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 1e-18) {
		tmp = x + (0.3333333333333333 * ((t / z) / y));
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.6e+66:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 1e-18:
		tmp = x + (0.3333333333333333 * ((t / z) / y))
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.6e+66)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 1e-18)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(t / z) / y)));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.6e+66)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 1e-18)
		tmp = x + (0.3333333333333333 * ((t / z) / y));
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.6e+66], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-18], N[(x + N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.6000000000000004e66

   1. Initial program 95.5%

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

      1. sub-neg 95.5%

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

      2. associate-+l+ 95.5%

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

      3. +-commutative 95.5%

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

      4. remove-double-neg 95.5%

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

      5. distribute-frac-neg 95.5%

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

      6. distribute-neg-in 95.5%

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

      7. remove-double-neg 95.5%

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

      8. sub-neg 95.5%

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

      9. neg-mul-1 95.5%

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

      10. times-frac 95.5%

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

      11. distribute-frac-neg 95.5%

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

      12. neg-mul-1 95.5%

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

      13. *-commutative 95.5%

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

      14. associate-/l* 95.5%

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

      15. *-commutative 95.5%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 97.7%

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

      1. metadata-eval 97.7%

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

      2. cancel-sign-sub-inv 97.7%

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

      3. associate-*r/ 97.7%

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

   7. Simplified 97.7%

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

   if -7.6000000000000004e66 < y < 1.0000000000000001e-18

   1. Initial program 92.8%

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

      1. sub-neg 92.8%

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

      2. associate-+l+ 92.8%

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

      3. +-commutative 92.8%

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

      4. remove-double-neg 92.8%

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

      5. distribute-frac-neg 92.8%

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

      6. distribute-neg-in 92.8%

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

      7. remove-double-neg 92.8%

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

      8. sub-neg 92.8%

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

      9. neg-mul-1 92.8%

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

      10. times-frac 94.1%

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

      11. distribute-frac-neg 94.1%

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

      12. neg-mul-1 94.1%

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

      13. *-commutative 94.1%

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

      14. associate-/l* 94.1%

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

      15. *-commutative 94.1%

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

   3. Simplified 94.2%

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

      1. clear-num 94.2%

         \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]

      2. inv-pow 94.2%

         \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{{\left(\frac{y}{t}\right)}^{-1}} - y\right) \]

   6. Applied egg-rr 94.2%

      \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{{\left(\frac{y}{t}\right)}^{-1}} - y\right) \]
   7. Step-by-step derivation

      1. unpow-1 94.2%

         \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]

   8. Simplified 94.2%

      \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]

   9. Taylor expanded in y around 0 89.2%

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

       1. *-commutative 89.2%

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

       2. associate-/r* 94.4%

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

   11. Simplified 94.4%

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

   if 1.0000000000000001e-18 < y

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0 90.0%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 10^{-18}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.6e+66)
   (- x (/ (* y 0.3333333333333333) z))
   (if (<= y 1.75e+31)
     (+ x (* 0.3333333333333333 (/ t (* y z))))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+66) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 1.75e+31) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.6d+66)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 1.75d+31) then
        tmp = x + (0.3333333333333333d0 * (t / (y * z)))
    else
        tmp = x - (0.3333333333333333d0 * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+66) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 1.75e+31) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.6e+66:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 1.75e+31:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.6e+66)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 1.75e+31)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.6e+66)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 1.75e+31)
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.6e+66], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+31], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.6000000000000004e66

   1. Initial program 95.5%

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

      1. sub-neg 95.5%

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

      2. associate-+l+ 95.5%

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

      3. +-commutative 95.5%

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

      4. remove-double-neg 95.5%

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

      5. distribute-frac-neg 95.5%

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

      6. distribute-neg-in 95.5%

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

      7. remove-double-neg 95.5%

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

      8. sub-neg 95.5%

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

      9. neg-mul-1 95.5%

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

      10. times-frac 95.5%

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

      11. distribute-frac-neg 95.5%

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

      12. neg-mul-1 95.5%

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

      13. *-commutative 95.5%

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

      14. associate-/l* 95.5%

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

      15. *-commutative 95.5%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 97.7%

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

      1. metadata-eval 97.7%

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

      2. cancel-sign-sub-inv 97.7%

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

      3. associate-*r/ 97.7%

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

   7. Simplified 97.7%

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

   if -7.6000000000000004e66 < y < 1.75e31

   1. Initial program 93.3%

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

      1. sub-neg 93.3%

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

      2. associate-+l+ 93.3%

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

      3. +-commutative 93.3%

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

      4. remove-double-neg 93.3%

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

      5. distribute-frac-neg 93.3%

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

      6. distribute-neg-in 93.3%

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

      7. remove-double-neg 93.3%

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

      8. sub-neg 93.3%

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

      9. neg-mul-1 93.3%

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

      10. times-frac 94.6%

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

      11. distribute-frac-neg 94.6%

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

      12. neg-mul-1 94.6%

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

      13. *-commutative 94.6%

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

      14. associate-/l* 94.6%

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

      15. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around inf 87.7%

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

   if 1.75e31 < y

   1. Initial program 93.2%

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

   3. Taylor expanded in t around 0 95.5%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-102} \lor \neg \left(y \leq 6.6 \cdot 10^{-37}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.25e-102) (not (<= y 6.6e-37)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.25e-102) || !(y <= 6.6e-37)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / 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 <= (-2.25d-102)) .or. (.not. (y <= 6.6d-37))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.25e-102) || !(y <= 6.6e-37)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.25e-102) or not (y <= 6.6e-37):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.25e-102) || !(y <= 6.6e-37))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.25e-102) || ~((y <= 6.6e-37)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.25e-102], N[Not[LessEqual[y, 6.6e-37]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25e-102 or 6.59999999999999964e-37 < 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. Taylor expanded in t around 0 84.9%

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

   if -2.25e-102 < y < 6.59999999999999964e-37

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 64.8%

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

   4. Taylor expanded in t around inf 63.0%

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

      1. associate-*r/ 62.9%

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

   6. Simplified 62.9%

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

      1. associate-/l/ 64.5%

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

      2. *-commutative 64.5%

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

      3. times-frac 67.6%

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

   8. Applied egg-rr 67.6%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-102} \lor \neg \left(y \leq 6.6 \cdot 10^{-37}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-104} \lor \neg \left(y \leq 2.6 \cdot 10^{-38}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e-104) (not (<= y 2.6e-38)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-104) || !(y <= 2.6e-38)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / 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 <= (-5.2d-104)) .or. (.not. (y <= 2.6d-38))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-104) || !(y <= 2.6e-38)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e-104) or not (y <= 2.6e-38):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.2e-104) || !(y <= 2.6e-38))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.2e-104) || ~((y <= 2.6e-38)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.2e-104], N[Not[LessEqual[y, 2.6e-38]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.20000000000000005e-104 or 2.60000000000000011e-38 < y

   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 95.9%

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

      2. associate-+l+ 95.9%

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

      3. +-commutative 95.9%

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

      4. remove-double-neg 95.9%

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

      5. distribute-frac-neg 95.9%

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

      6. distribute-neg-in 95.9%

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

      7. remove-double-neg 95.9%

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

      8. sub-neg 95.9%

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

      9. neg-mul-1 95.9%

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

      10. times-frac 96.5%

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

      11. distribute-frac-neg 96.5%

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

      12. neg-mul-1 96.5%

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

      13. *-commutative 96.5%

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

      14. associate-/l* 96.4%

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

      15. *-commutative 96.4%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

         \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]

      2. inv-pow 99.7%

         \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{{\left(\frac{y}{t}\right)}^{-1}} - y\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{{\left(\frac{y}{t}\right)}^{-1}} - y\right) \]
   7. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]

   8. Simplified 99.7%

      \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]
   9. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto x + \color{blue}{\frac{0.3333333333333333 \cdot \left(\frac{1}{\frac{y}{t}} - y\right)}{z}} \]

      2. clear-num 99.8%

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

      3. distribute-lft-out-- 99.8%

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

      4. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{0.3333333333333333 \cdot \frac{t}{y} - 0.3333333333333333 \cdot y}}} \]

      5. *-un-lft-identity 99.7%

         \[\leadsto x + \frac{1}{\frac{\color{blue}{1 \cdot z}}{0.3333333333333333 \cdot \frac{t}{y} - 0.3333333333333333 \cdot y}} \]

      6. distribute-lft-out-- 99.7%

         \[\leadsto x + \frac{1}{\frac{1 \cdot z}{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}} \]

      7. clear-num 99.7%

         \[\leadsto x + \frac{1}{\frac{1 \cdot z}{0.3333333333333333 \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right)}} \]

      8. times-frac 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{0.3333333333333333} \cdot \frac{z}{\frac{1}{\frac{y}{t}} - y}}} \]

      9. metadata-eval 99.8%

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

      10. clear-num 99.8%

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

   10. Applied egg-rr 99.8%

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

       1. associate-/r* 99.8%

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

       2. metadata-eval 99.8%

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

   12. Simplified 99.8%

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

   13. Taylor expanded in t around 0 84.9%

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

       1. associate-*r/ 84.9%

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

       2. *-commutative 84.9%

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

       3. associate-*r/ 84.8%

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

   15. Simplified 84.8%

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

   if -5.20000000000000005e-104 < y < 2.60000000000000011e-38

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 64.8%

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

   4. Taylor expanded in t around inf 63.0%

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

      1. associate-*r/ 62.9%

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

   6. Simplified 62.9%

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

      1. associate-/l/ 64.5%

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

      2. *-commutative 64.5%

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

      3. times-frac 67.6%

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

   8. Applied egg-rr 67.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-104} \lor \neg \left(y \leq 2.6 \cdot 10^{-38}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-103}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.22 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e-103)
   (- x (/ (* y 0.3333333333333333) z))
   (if (<= y 2.22e-38)
     (* (/ t z) (/ 0.3333333333333333 y))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e-103) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 2.22e-38) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.1d-103)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 2.22d-38) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = x - (0.3333333333333333d0 * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e-103) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 2.22e-38) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e-103:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 2.22e-38:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e-103)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 2.22e-38)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.1e-103)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 2.22e-38)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e-103], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.22e-38], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e-103

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. associate-+l+ 96.6%

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

      3. +-commutative 96.6%

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

      4. remove-double-neg 96.6%

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

      5. distribute-frac-neg 96.6%

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

      6. distribute-neg-in 96.6%

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

      7. remove-double-neg 96.6%

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

      8. sub-neg 96.6%

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

      9. neg-mul-1 96.6%

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

      10. times-frac 97.5%

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

      11. distribute-frac-neg 97.5%

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

      12. neg-mul-1 97.5%

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

      13. *-commutative 97.5%

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

      14. associate-/l* 97.5%

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

      15. *-commutative 97.5%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 82.2%

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

      1. metadata-eval 82.2%

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

      2. cancel-sign-sub-inv 82.2%

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

      3. associate-*r/ 82.3%

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

   7. Simplified 82.3%

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

   if -1.1e-103 < y < 2.21999999999999996e-38

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 64.8%

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

   4. Taylor expanded in t around inf 63.0%

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

      1. associate-*r/ 62.9%

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

   6. Simplified 62.9%

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

      1. associate-/l/ 64.5%

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

      2. *-commutative 64.5%

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

      3. times-frac 67.6%

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

   8. Applied egg-rr 67.6%

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

   if 2.21999999999999996e-38 < y

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 88.8%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-103}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.22 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.32 \cdot 10^{+36} \lor \neg \left(y \leq 7 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.32e+36) (not (<= y 7e+76)))
   (* y (/ -0.3333333333333333 z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.32e+36) || !(y <= 7e+76)) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.32d+36)) .or. (.not. (y <= 7d+76))) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.32e+36) || !(y <= 7e+76)) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.32e+36) or not (y <= 7e+76):
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.32e+36) || !(y <= 7e+76))
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.32e+36) || ~((y <= 7e+76)))
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.32e+36], N[Not[LessEqual[y, 7e+76]], $MachinePrecision]], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.31999999999999996e36 or 7.00000000000000001e76 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0 79.3%

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

   4. Taylor expanded in t around 0 74.0%

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

      1. *-commutative 74.0%

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

   6. Simplified 74.0%

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

      1. clear-num 73.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot -0.3333333333333333}}} \]

      2. inv-pow 73.9%

         \[\leadsto \color{blue}{{\left(\frac{z}{y \cdot -0.3333333333333333}\right)}^{-1}} \]

      3. *-un-lft-identity 73.9%

         \[\leadsto {\left(\frac{\color{blue}{1 \cdot z}}{y \cdot -0.3333333333333333}\right)}^{-1} \]

      4. *-commutative 73.9%

         \[\leadsto {\left(\frac{1 \cdot z}{\color{blue}{-0.3333333333333333 \cdot y}}\right)}^{-1} \]

      5. times-frac 74.0%

         \[\leadsto {\color{blue}{\left(\frac{1}{-0.3333333333333333} \cdot \frac{z}{y}\right)}}^{-1} \]

      6. metadata-eval 74.0%

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

   8. Applied egg-rr 74.0%

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

      1. unpow-1 74.0%

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

      2. associate-/r* 74.0%

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

      3. metadata-eval 74.0%

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

   10. Simplified 74.0%

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

       1. associate-/r/ 73.9%

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

   12. Applied egg-rr 73.9%

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

   if -2.31999999999999996e36 < y < 7.00000000000000001e76

   1. Initial program 92.8%

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

      1. sub-neg 92.8%

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

      2. associate-+l+ 92.8%

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

      3. +-commutative 92.8%

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

      4. remove-double-neg 92.8%

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

      5. distribute-frac-neg 92.8%

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

      6. distribute-neg-in 92.8%

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

      7. remove-double-neg 92.8%

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

      8. sub-neg 92.8%

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

      9. neg-mul-1 92.8%

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

      10. times-frac 94.0%

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

      11. distribute-frac-neg 94.0%

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

      12. neg-mul-1 94.0%

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

      13. *-commutative 94.0%

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

      14. associate-/l* 94.0%

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

      15. *-commutative 94.0%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in x around inf 39.3%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.32 \cdot 10^{+36} \lor \neg \left(y \leq 7 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.2e+40)
   (/ (* y -0.3333333333333333) z)
   (if (<= y 9e+71) x (* y (/ -0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e+40) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 9e+71) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / 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 <= (-8.2d+40)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= 9d+71) then
        tmp = x
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e+40) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 9e+71) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e+40:
		tmp = (y * -0.3333333333333333) / z
	elif y <= 9e+71:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e+40)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= 9e+71)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e+40)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= 9e+71)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.2e+40], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 9e+71], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2000000000000003e40

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 79.8%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. *-commutative 72.5%

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

   6. Simplified 72.5%

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

   if -8.2000000000000003e40 < y < 9.00000000000000087e71

   1. Initial program 92.8%

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

      1. sub-neg 92.8%

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

      2. associate-+l+ 92.8%

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

      3. +-commutative 92.8%

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

      4. remove-double-neg 92.8%

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

      5. distribute-frac-neg 92.8%

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

      6. distribute-neg-in 92.8%

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

      7. remove-double-neg 92.8%

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

      8. sub-neg 92.8%

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

      9. neg-mul-1 92.8%

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

      10. times-frac 94.0%

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

      11. distribute-frac-neg 94.0%

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

      12. neg-mul-1 94.0%

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

      13. *-commutative 94.0%

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

      14. associate-/l* 94.0%

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

      15. *-commutative 94.0%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in x around inf 39.3%

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

   if 9.00000000000000087e71 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 78.6%

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

   4. Taylor expanded in t around 0 76.1%

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

      1. *-commutative 76.1%

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

   6. Simplified 76.1%

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

      1. clear-num 76.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot -0.3333333333333333}}} \]

      2. inv-pow 76.1%

         \[\leadsto \color{blue}{{\left(\frac{z}{y \cdot -0.3333333333333333}\right)}^{-1}} \]

      3. *-un-lft-identity 76.1%

         \[\leadsto {\left(\frac{\color{blue}{1 \cdot z}}{y \cdot -0.3333333333333333}\right)}^{-1} \]

      4. *-commutative 76.1%

         \[\leadsto {\left(\frac{1 \cdot z}{\color{blue}{-0.3333333333333333 \cdot y}}\right)}^{-1} \]

      5. times-frac 76.3%

         \[\leadsto {\color{blue}{\left(\frac{1}{-0.3333333333333333} \cdot \frac{z}{y}\right)}}^{-1} \]

      6. metadata-eval 76.3%

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

   8. Applied egg-rr 76.3%

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

      1. unpow-1 76.3%

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

      2. associate-/r* 76.2%

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

      3. metadata-eval 76.2%

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

   10. Simplified 76.2%

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

       1. associate-/r/ 76.2%

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

   12. Applied egg-rr 76.2%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.1e+31)
   (/ -0.3333333333333333 (/ z y))
   (if (<= y 5.5e+71) x (* y (/ -0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.1e+31) {
		tmp = -0.3333333333333333 / (z / y);
	} else if (y <= 5.5e+71) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.1d+31)) then
        tmp = (-0.3333333333333333d0) / (z / y)
    else if (y <= 5.5d+71) then
        tmp = x
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.1e+31) {
		tmp = -0.3333333333333333 / (z / y);
	} else if (y <= 5.5e+71) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.1e+31:
		tmp = -0.3333333333333333 / (z / y)
	elif y <= 5.5e+71:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.1e+31)
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	elseif (y <= 5.5e+71)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.1e+31)
		tmp = -0.3333333333333333 / (z / y);
	elseif (y <= 5.5e+71)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.1e+31], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+71], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.09999999999999961e31

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 79.8%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. *-commutative 72.5%

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

   6. Simplified 72.5%

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

      1. clear-num 72.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot -0.3333333333333333}}} \]

      2. inv-pow 72.3%

         \[\leadsto \color{blue}{{\left(\frac{z}{y \cdot -0.3333333333333333}\right)}^{-1}} \]

      3. *-un-lft-identity 72.3%

         \[\leadsto {\left(\frac{\color{blue}{1 \cdot z}}{y \cdot -0.3333333333333333}\right)}^{-1} \]

      4. *-commutative 72.3%

         \[\leadsto {\left(\frac{1 \cdot z}{\color{blue}{-0.3333333333333333 \cdot y}}\right)}^{-1} \]

      5. times-frac 72.4%

         \[\leadsto {\color{blue}{\left(\frac{1}{-0.3333333333333333} \cdot \frac{z}{y}\right)}}^{-1} \]

      6. metadata-eval 72.4%

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

   8. Applied egg-rr 72.4%

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

      1. unpow-1 72.4%

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

      2. associate-/r* 72.4%

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

      3. metadata-eval 72.4%

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

   10. Simplified 72.4%

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

   if -7.09999999999999961e31 < y < 5.5e71

   1. Initial program 92.8%

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

      1. sub-neg 92.8%

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

      2. associate-+l+ 92.8%

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

      3. +-commutative 92.8%

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

      4. remove-double-neg 92.8%

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

      5. distribute-frac-neg 92.8%

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

      6. distribute-neg-in 92.8%

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

      7. remove-double-neg 92.8%

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

      8. sub-neg 92.8%

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

      9. neg-mul-1 92.8%

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

      10. times-frac 94.0%

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

      11. distribute-frac-neg 94.0%

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

      12. neg-mul-1 94.0%

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

      13. *-commutative 94.0%

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

      14. associate-/l* 94.0%

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

      15. *-commutative 94.0%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in x around inf 39.3%

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

   if 5.5e71 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 78.6%

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

   4. Taylor expanded in t around 0 76.1%

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

      1. *-commutative 76.1%

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

   6. Simplified 76.1%

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

      1. clear-num 76.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot -0.3333333333333333}}} \]

      2. inv-pow 76.1%

         \[\leadsto \color{blue}{{\left(\frac{z}{y \cdot -0.3333333333333333}\right)}^{-1}} \]

      3. *-un-lft-identity 76.1%

         \[\leadsto {\left(\frac{\color{blue}{1 \cdot z}}{y \cdot -0.3333333333333333}\right)}^{-1} \]

      4. *-commutative 76.1%

         \[\leadsto {\left(\frac{1 \cdot z}{\color{blue}{-0.3333333333333333 \cdot y}}\right)}^{-1} \]

      5. times-frac 76.3%

         \[\leadsto {\color{blue}{\left(\frac{1}{-0.3333333333333333} \cdot \frac{z}{y}\right)}}^{-1} \]

      6. metadata-eval 76.3%

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

   8. Applied egg-rr 76.3%

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

      1. unpow-1 76.3%

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

      2. associate-/r* 76.2%

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

      3. metadata-eval 76.2%

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

   10. Simplified 76.2%

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

       1. associate-/r/ 76.2%

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

   12. Applied egg-rr 76.2%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 95.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \frac{0.3333333333333333}{\frac{z}{\frac{t}{y} - y}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + (0.3333333333333333 / (z / ((t / y) - 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 + (0.3333333333333333d0 / (z / ((t / y) - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. sub-neg 93.7%

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

   2. associate-+l+ 93.7%

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

   3. +-commutative 93.7%

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

   4. remove-double-neg 93.7%

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

   5. distribute-frac-neg 93.7%

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

   6. distribute-neg-in 93.7%

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

   7. remove-double-neg 93.7%

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

   8. sub-neg 93.7%

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

   9. neg-mul-1 93.7%

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

   10. times-frac 94.5%

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

   11. distribute-frac-neg 94.5%

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

   12. neg-mul-1 94.5%

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

   13. *-commutative 94.5%

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

   14. associate-/l* 94.5%

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

   15. *-commutative 94.5%

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

3. Simplified 96.4%

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

   1. clear-num 96.4%

      \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]

   2. inv-pow 96.4%

      \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{{\left(\frac{y}{t}\right)}^{-1}} - y\right) \]

6. Applied egg-rr 96.4%

   \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{{\left(\frac{y}{t}\right)}^{-1}} - y\right) \]
7. Step-by-step derivation

   1. unpow-1 96.4%

      \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]

8. Simplified 96.4%

   \[\leadsto x + \frac{0.3333333333333333}{z} \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right) \]
9. Step-by-step derivation

   1. associate-*l/ 96.5%

      \[\leadsto x + \color{blue}{\frac{0.3333333333333333 \cdot \left(\frac{1}{\frac{y}{t}} - y\right)}{z}} \]

   2. clear-num 96.5%

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

   3. distribute-lft-out-- 96.5%

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

   4. clear-num 96.4%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{0.3333333333333333 \cdot \frac{t}{y} - 0.3333333333333333 \cdot y}}} \]

   5. *-un-lft-identity 96.4%

      \[\leadsto x + \frac{1}{\frac{\color{blue}{1 \cdot z}}{0.3333333333333333 \cdot \frac{t}{y} - 0.3333333333333333 \cdot y}} \]

   6. distribute-lft-out-- 96.4%

      \[\leadsto x + \frac{1}{\frac{1 \cdot z}{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}} \]

   7. clear-num 96.4%

      \[\leadsto x + \frac{1}{\frac{1 \cdot z}{0.3333333333333333 \cdot \left(\color{blue}{\frac{1}{\frac{y}{t}}} - y\right)}} \]

   8. times-frac 96.5%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{0.3333333333333333} \cdot \frac{z}{\frac{1}{\frac{y}{t}} - y}}} \]

   9. metadata-eval 96.5%

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

   10. clear-num 96.5%

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

10. Applied egg-rr 96.5%

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

    1. associate-/r* 96.4%

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

    2. metadata-eval 96.4%

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

12. Simplified 96.4%

    \[\leadsto x + \color{blue}{\frac{0.3333333333333333}{\frac{z}{\frac{t}{y} - y}}} \]
13. Add Preprocessing

Alternative 14: 95.4% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((0.3333333333333333 / z) * ((t / y) - 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 + ((0.3333333333333333d0 / z) * ((t / y) - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. sub-neg 93.7%

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

   2. associate-+l+ 93.7%

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

   3. +-commutative 93.7%

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

   4. remove-double-neg 93.7%

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

   5. distribute-frac-neg 93.7%

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

   6. distribute-neg-in 93.7%

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

   7. remove-double-neg 93.7%

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

   8. sub-neg 93.7%

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

   9. neg-mul-1 93.7%

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

   10. times-frac 94.5%

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

   11. distribute-frac-neg 94.5%

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

   12. neg-mul-1 94.5%

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

   13. *-commutative 94.5%

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

   14. associate-/l* 94.5%

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

   15. *-commutative 94.5%

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

3. Simplified 96.4%

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

Alternative 15: 30.7% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. sub-neg 93.7%

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

   2. associate-+l+ 93.7%

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

   3. +-commutative 93.7%

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

   4. remove-double-neg 93.7%

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

   5. distribute-frac-neg 93.7%

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

   6. distribute-neg-in 93.7%

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

   7. remove-double-neg 93.7%

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

   8. sub-neg 93.7%

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

   9. neg-mul-1 93.7%

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

   10. times-frac 94.5%

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

   11. distribute-frac-neg 94.5%

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

   12. neg-mul-1 94.5%

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

   13. *-commutative 94.5%

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

   14. associate-/l* 94.5%

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

   15. *-commutative 94.5%

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

3. Simplified 96.4%

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

5. Taylor expanded in x around inf 33.5%

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

Developer Target 1: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024137 
(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))))