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

Percentage Accurate: 95.8% → 97.7%

Time: 10.9s

Alternatives: 15

Speedup: 0.7×

• 27.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-27} \lor \neg \left(y \leq 1.25 \cdot 10^{-107}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.1e-27) (not (<= y 1.25e-107)))
   (+ x (/ (- y (/ t y)) (* z -3.0)))
   (+ x (/ (/ t (* z 3.0)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-27) || !(y <= 1.25e-107)) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = x + ((t / (z * 3.0)) / 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 <= (-3.1d-27)) .or. (.not. (y <= 1.25d-107))) then
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    else
        tmp = x + ((t / (z * 3.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-27) || !(y <= 1.25e-107)) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = x + ((t / (z * 3.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.1e-27) or not (y <= 1.25e-107):
		tmp = x + ((y - (t / y)) / (z * -3.0))
	else:
		tmp = x + ((t / (z * 3.0)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.1e-27) || !(y <= 1.25e-107))
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / Float64(z * 3.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.1e-27) || ~((y <= 1.25e-107)))
		tmp = x + ((y - (t / y)) / (z * -3.0));
	else
		tmp = x + ((t / (z * 3.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.1e-27], N[Not[LessEqual[y, 1.25e-107]], $MachinePrecision]], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999998e-27 or 1.24999999999999993e-107 < y

   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. +-commutative 97.4%

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

      2. associate-+r- 97.4%

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

      3. +-commutative 97.4%

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

      4. associate--l+ 97.4%

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

      5. sub-neg 97.4%

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

      6. remove-double-neg 97.4%

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

      7. distribute-frac-neg 97.4%

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

      8. distribute-neg-in 97.4%

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

      9. remove-double-neg 97.4%

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

      10. sub-neg 97.4%

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

      11. neg-mul-1 97.4%

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

      12. times-frac 99.2%

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

      13. distribute-frac-neg 99.2%

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

      14. neg-mul-1 99.2%

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

      15. *-commutative 99.2%

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

      16. associate-/l* 99.1%

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

      17. *-commutative 99.1%

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

   3. Simplified 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 99.6%

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

      2. inv-pow 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

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

   8. Simplified 99.6%

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

      1. associate-*l/ 99.7%

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

      2. *-un-lft-identity 99.7%

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

      3. frac-2neg 99.7%

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

      4. div-inv 99.8%

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

      5. metadata-eval 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

   10. Applied egg-rr 99.8%

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

   if -3.0999999999999998e-27 < y < 1.24999999999999993e-107

   1. Initial program 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-+r- 88.3%

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

      3. +-commutative 88.3%

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

      4. associate--l+ 88.3%

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

      5. sub-neg 88.3%

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

      6. remove-double-neg 88.3%

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

      7. distribute-frac-neg 88.3%

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

      8. distribute-neg-in 88.3%

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

      9. remove-double-neg 88.3%

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

      10. sub-neg 88.3%

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

      11. neg-mul-1 88.3%

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

      12. times-frac 86.2%

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

      13. distribute-frac-neg 86.2%

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

      14. neg-mul-1 86.2%

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

      15. *-commutative 86.2%

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

      16. associate-/l* 86.2%

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

      17. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around inf 86.2%

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

      1. associate-*r/ 98.8%

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

      2. clear-num 98.8%

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

      3. associate-*l/ 98.9%

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

      4. *-un-lft-identity 98.9%

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

      5. div-inv 98.9%

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

      6. metadata-eval 98.9%

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

   7. Applied egg-rr 98.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-27} \lor \neg \left(y \leq 1.25 \cdot 10^{-107}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-69}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{-86}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -1e-69)
   (- x (* y (/ 0.3333333333333333 z)))
   (if (<= (* z 3.0) 2e-86)
     (* 0.3333333333333333 (/ (- (/ t y) y) z))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e-69) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if ((z * 3.0) <= 2e-86) {
		tmp = 0.3333333333333333 * (((t / y) - 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 ((z * 3.0d0) <= (-1d-69)) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else if ((z * 3.0d0) <= 2d-86) then
        tmp = 0.3333333333333333d0 * (((t / y) - 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 ((z * 3.0) <= -1e-69) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if ((z * 3.0) <= 2e-86) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -1e-69:
		tmp = x - (y * (0.3333333333333333 / z))
	elif (z * 3.0) <= 2e-86:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e-69)
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	elseif (Float64(z * 3.0) <= 2e-86)
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - 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 ((z * 3.0) <= -1e-69)
		tmp = x - (y * (0.3333333333333333 / z));
	elseif ((z * 3.0) <= 2e-86)
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e-69], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-86], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -9.9999999999999996e-70

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-+r- 97.5%

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

      3. +-commutative 97.5%

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

      4. associate--l+ 97.5%

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

      5. sub-neg 97.5%

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

      6. remove-double-neg 97.5%

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

      7. distribute-frac-neg 97.5%

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

      8. distribute-neg-in 97.5%

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

      9. remove-double-neg 97.5%

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

      10. sub-neg 97.5%

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

      11. neg-mul-1 97.5%

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

      12. times-frac 93.0%

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

      13. distribute-frac-neg 93.0%

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

      14. neg-mul-1 93.0%

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

      15. *-commutative 93.0%

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

      16. associate-/l* 92.9%

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

      17. *-commutative 92.9%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around 0 79.7%

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

      1. neg-mul-1 79.7%

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

   7. Simplified 79.7%

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

      1. add-cube-cbrt 78.7%

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

      2. fma-define 78.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{0.3333333333333333}{z} \cdot \left(-y\right)\right)} \]

      3. distribute-rgt-neg-out 78.7%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \color{blue}{-\frac{0.3333333333333333}{z} \cdot y}\right) \]

      4. add-sqr-sqrt 32.2%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

      5. sqrt-unprod 42.8%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

      6. sqr-neg 42.8%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

      7. sqrt-unprod 29.9%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

      8. add-sqr-sqrt 51.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(-y\right)}\right) \]

      9. fma-neg 51.4%

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

      10. *-commutative 51.4%

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

      11. add-cube-cbrt 52.3%

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

      12. add-sqr-sqrt 30.3%

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

      13. sqrt-unprod 43.4%

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

      14. sqr-neg 43.4%

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

      15. sqrt-unprod 32.7%

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

      16. add-sqr-sqrt 79.7%

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

   9. Applied egg-rr 79.7%

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

   if -9.9999999999999996e-70 < (*.f64 z #s(literal 3 binary64)) < 2.00000000000000017e-86

   1. Initial program 87.4%

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

      1. +-commutative 87.4%

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

      2. associate-+r- 87.4%

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

      3. sub-neg 87.4%

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

      4. associate-*l* 87.4%

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

      5. *-commutative 87.4%

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

      6. distribute-frac-neg2 87.4%

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

      7. distribute-rgt-neg-in 87.4%

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

      8. metadata-eval 87.4%

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

   3. Simplified 87.4%

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

      1. *-un-lft-identity 87.4%

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

      2. *-commutative 87.4%

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

      3. associate-*l* 87.4%

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

      4. *-commutative 87.4%

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

      5. times-frac 91.4%

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

      6. *-un-lft-identity 91.4%

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

      7. *-commutative 91.4%

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

      8. times-frac 91.3%

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

      9. metadata-eval 91.3%

         \[\leadsto \left(\frac{1}{y} \cdot \left(\color{blue}{0.3333333333333333} \cdot \frac{t}{z}\right) + x\right) + \frac{y}{z \cdot -3} \]

   6. Applied egg-rr 91.3%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 91.4%

         \[\leadsto \left(\color{blue}{\frac{1 \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)}{y}} + x\right) + \frac{y}{z \cdot -3} \]

      2. *-lft-identity 91.4%

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

      3. associate-*r/ 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in z around 0 95.2%

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

       1. +-commutative 95.2%

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

       2. metadata-eval 95.2%

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

       3. associate-*r* 95.2%

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

       4. neg-mul-1 95.2%

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

       5. distribute-lft-in 95.1%

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

       6. sub-neg 95.1%

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

       7. associate-*r/ 94.5%

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

   11. Simplified 94.5%

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

   if 2.00000000000000017e-86 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 72.2%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-69}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{-86}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-27} \lor \neg \left(y \leq 1.85 \cdot 10^{-107}\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.7e-27) (not (<= y 1.85e-107)))
   (+ x (* 0.3333333333333333 (/ (- (/ t y) y) z)))
   (+ x (/ (/ t (* z 3.0)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.7e-27) || !(y <= 1.85e-107)) {
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	} else {
		tmp = x + ((t / (z * 3.0)) / 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 <= (-4.7d-27)) .or. (.not. (y <= 1.85d-107))) then
        tmp = x + (0.3333333333333333d0 * (((t / y) - y) / z))
    else
        tmp = x + ((t / (z * 3.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.7e-27) || !(y <= 1.85e-107)) {
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	} else {
		tmp = x + ((t / (z * 3.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.7e-27) or not (y <= 1.85e-107):
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z))
	else:
		tmp = x + ((t / (z * 3.0)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.7e-27) || !(y <= 1.85e-107))
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(t / Float64(z * 3.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.7e-27) || ~((y <= 1.85e-107)))
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	else
		tmp = x + ((t / (z * 3.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.7e-27], N[Not[LessEqual[y, 1.85e-107]], $MachinePrecision]], N[(x + N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.70000000000000032e-27 or 1.8500000000000001e-107 < y

   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. +-commutative 97.4%

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

      2. associate-+r- 97.4%

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

      3. +-commutative 97.4%

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

      4. associate--l+ 97.4%

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

      5. sub-neg 97.4%

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

      6. remove-double-neg 97.4%

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

      7. distribute-frac-neg 97.4%

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

      8. distribute-neg-in 97.4%

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

      9. remove-double-neg 97.4%

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

      10. sub-neg 97.4%

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

      11. neg-mul-1 97.4%

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

      12. times-frac 99.2%

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

      13. distribute-frac-neg 99.2%

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

      14. neg-mul-1 99.2%

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

      15. *-commutative 99.2%

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

      16. associate-/l* 99.1%

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

      17. *-commutative 99.1%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.2%

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

   if -4.70000000000000032e-27 < y < 1.8500000000000001e-107

   1. Initial program 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-+r- 88.3%

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

      3. +-commutative 88.3%

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

      4. associate--l+ 88.3%

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

      5. sub-neg 88.3%

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

      6. remove-double-neg 88.3%

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

      7. distribute-frac-neg 88.3%

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

      8. distribute-neg-in 88.3%

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

      9. remove-double-neg 88.3%

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

      10. sub-neg 88.3%

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

      11. neg-mul-1 88.3%

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

      12. times-frac 86.2%

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

      13. distribute-frac-neg 86.2%

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

      14. neg-mul-1 86.2%

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

      15. *-commutative 86.2%

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

      16. associate-/l* 86.2%

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

      17. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around inf 86.2%

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

      1. associate-*r/ 98.8%

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

      2. clear-num 98.8%

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

      3. associate-*l/ 98.9%

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

      4. *-un-lft-identity 98.9%

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

      5. div-inv 98.9%

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

      6. metadata-eval 98.9%

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

   7. Applied egg-rr 98.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-27} \lor \neg \left(y \leq 1.85 \cdot 10^{-107}\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-27} \lor \neg \left(y \leq 1.6 \cdot 10^{-108}\right):\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.1e-27) (not (<= y 1.6e-108)))
   (+ x (* (- (/ t y) y) (/ 0.3333333333333333 z)))
   (+ x (/ (/ t (* z 3.0)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-27) || !(y <= 1.6e-108)) {
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
	} else {
		tmp = x + ((t / (z * 3.0)) / 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 <= (-3.1d-27)) .or. (.not. (y <= 1.6d-108))) then
        tmp = x + (((t / y) - y) * (0.3333333333333333d0 / z))
    else
        tmp = x + ((t / (z * 3.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-27) || !(y <= 1.6e-108)) {
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
	} else {
		tmp = x + ((t / (z * 3.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.1e-27) or not (y <= 1.6e-108):
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z))
	else:
		tmp = x + ((t / (z * 3.0)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.1e-27) || !(y <= 1.6e-108))
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(Float64(t / Float64(z * 3.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.1e-27) || ~((y <= 1.6e-108)))
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
	else
		tmp = x + ((t / (z * 3.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.1e-27], N[Not[LessEqual[y, 1.6e-108]], $MachinePrecision]], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999998e-27 or 1.6e-108 < y

   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. +-commutative 97.4%

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

      2. associate-+r- 97.4%

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

      3. +-commutative 97.4%

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

      4. associate--l+ 97.4%

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

      5. sub-neg 97.4%

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

      6. remove-double-neg 97.4%

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

      7. distribute-frac-neg 97.4%

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

      8. distribute-neg-in 97.4%

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

      9. remove-double-neg 97.4%

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

      10. sub-neg 97.4%

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

      11. neg-mul-1 97.4%

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

      12. times-frac 99.2%

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

      13. distribute-frac-neg 99.2%

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

      14. neg-mul-1 99.2%

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

      15. *-commutative 99.2%

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

      16. associate-/l* 99.1%

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

      17. *-commutative 99.1%

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

   3. Simplified 99.7%

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

   if -3.0999999999999998e-27 < y < 1.6e-108

   1. Initial program 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-+r- 88.3%

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

      3. +-commutative 88.3%

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

      4. associate--l+ 88.3%

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

      5. sub-neg 88.3%

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

      6. remove-double-neg 88.3%

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

      7. distribute-frac-neg 88.3%

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

      8. distribute-neg-in 88.3%

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

      9. remove-double-neg 88.3%

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

      10. sub-neg 88.3%

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

      11. neg-mul-1 88.3%

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

      12. times-frac 86.2%

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

      13. distribute-frac-neg 86.2%

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

      14. neg-mul-1 86.2%

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

      15. *-commutative 86.2%

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

      16. associate-/l* 86.2%

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

      17. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around inf 86.2%

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

      1. associate-*r/ 98.8%

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

      2. clear-num 98.8%

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

      3. associate-*l/ 98.9%

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

      4. *-un-lft-identity 98.9%

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

      5. div-inv 98.9%

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

      6. metadata-eval 98.9%

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

   7. Applied egg-rr 98.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-27} \lor \neg \left(y \leq 1.6 \cdot 10^{-108}\right):\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;t \leq 10^{-111}:\\ \;\;\;\;\left(\frac{\frac{t \cdot 0.3333333333333333}{z}}{y} + x\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z -3.0))))
   (if (<= t 1e-111)
     (+ (+ (/ (/ (* t 0.3333333333333333) z) y) x) t_1)
     (+ t_1 (+ x (/ t (* z (* y 3.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (t <= 1e-111) {
		tmp = ((((t * 0.3333333333333333) / z) / y) + x) + t_1;
	} else {
		tmp = t_1 + (x + (t / (z * (y * 3.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z * (-3.0d0))
    if (t <= 1d-111) then
        tmp = ((((t * 0.3333333333333333d0) / z) / y) + x) + t_1
    else
        tmp = t_1 + (x + (t / (z * (y * 3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (t <= 1e-111) {
		tmp = ((((t * 0.3333333333333333) / z) / y) + x) + t_1;
	} else {
		tmp = t_1 + (x + (t / (z * (y * 3.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * -3.0)
	tmp = 0
	if t <= 1e-111:
		tmp = ((((t * 0.3333333333333333) / z) / y) + x) + t_1
	else:
		tmp = t_1 + (x + (t / (z * (y * 3.0))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * -3.0))
	tmp = 0.0
	if (t <= 1e-111)
		tmp = Float64(Float64(Float64(Float64(Float64(t * 0.3333333333333333) / z) / y) + x) + t_1);
	else
		tmp = Float64(t_1 + Float64(x + Float64(t / Float64(z * Float64(y * 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * -3.0);
	tmp = 0.0;
	if (t <= 1e-111)
		tmp = ((((t * 0.3333333333333333) / z) / y) + x) + t_1;
	else
		tmp = t_1 + (x + (t / (z * (y * 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 1e-111], N[(N[(N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision] + x), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(x + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000009e-111

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-+r- 92.5%

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

      3. sub-neg 92.5%

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

      4. associate-*l* 92.5%

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

      5. *-commutative 92.5%

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

      6. distribute-frac-neg2 92.5%

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

      7. distribute-rgt-neg-in 92.5%

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

      8. metadata-eval 92.5%

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

   3. Simplified 92.5%

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

      1. *-un-lft-identity 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-*l* 92.5%

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

      4. *-commutative 92.5%

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

      5. times-frac 98.7%

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

      6. *-un-lft-identity 98.7%

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

      7. *-commutative 98.7%

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

      8. times-frac 98.7%

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

      9. metadata-eval 98.7%

         \[\leadsto \left(\frac{1}{y} \cdot \left(\color{blue}{0.3333333333333333} \cdot \frac{t}{z}\right) + x\right) + \frac{y}{z \cdot -3} \]

   6. Applied egg-rr 98.7%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 98.7%

         \[\leadsto \left(\color{blue}{\frac{1 \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)}{y}} + x\right) + \frac{y}{z \cdot -3} \]

      2. *-lft-identity 98.7%

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

      3. associate-*r/ 98.8%

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

   8. Simplified 98.8%

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

   if 1.00000000000000009e-111 < t

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. associate-+r- 97.3%

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

      3. sub-neg 97.3%

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

      4. associate-*l* 97.4%

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

      5. *-commutative 97.4%

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

      6. distribute-frac-neg2 97.4%

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

      7. distribute-rgt-neg-in 97.4%

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

      8. metadata-eval 97.4%

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

   3. Simplified 97.4%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-111}:\\ \;\;\;\;\left(\frac{\frac{t \cdot 0.3333333333333333}{z}}{y} + x\right) + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -10000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -10000000000.0)
   x
   (if (<= (* z 3.0) 5e+32) (/ y (* z -3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -10000000000.0) {
		tmp = x;
	} else if ((z * 3.0) <= 5e+32) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-10000000000.0d0)) then
        tmp = x
    else if ((z * 3.0d0) <= 5d+32) then
        tmp = y / (z * (-3.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -10000000000.0) {
		tmp = x;
	} else if ((z * 3.0) <= 5e+32) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -10000000000.0:
		tmp = x
	elif (z * 3.0) <= 5e+32:
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -10000000000.0)
		tmp = x;
	elseif (Float64(z * 3.0) <= 5e+32)
		tmp = Float64(y / Float64(z * -3.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -10000000000.0)
		tmp = x;
	elseif ((z * 3.0) <= 5e+32)
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -10000000000.0], x, If[LessEqual[N[(z * 3.0), $MachinePrecision], 5e+32], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -1e10 or 4.9999999999999997e32 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r- 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--l+ 99.0%

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

      5. sub-neg 99.0%

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

      6. remove-double-neg 99.0%

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

      7. distribute-frac-neg 99.0%

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

      8. distribute-neg-in 99.0%

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

      9. remove-double-neg 99.0%

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

      10. sub-neg 99.0%

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

      11. neg-mul-1 99.0%

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

      12. times-frac 88.9%

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

      13. distribute-frac-neg 88.9%

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

      14. neg-mul-1 88.9%

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

      15. *-commutative 88.9%

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

      16. associate-/l* 88.9%

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

      17. *-commutative 88.9%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around inf 57.6%

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

   if -1e10 < (*.f64 z #s(literal 3 binary64)) < 4.9999999999999997e32

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-+r- 89.4%

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

      3. sub-neg 89.4%

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

      4. associate-*l* 89.4%

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

      5. *-commutative 89.4%

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

      6. distribute-frac-neg2 89.4%

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

      7. distribute-rgt-neg-in 89.4%

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

      8. metadata-eval 89.4%

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

   3. Simplified 89.4%

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

      1. *-un-lft-identity 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-*l* 89.4%

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

      4. *-commutative 89.4%

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

      5. times-frac 92.5%

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

      6. *-un-lft-identity 92.5%

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

      7. *-commutative 92.5%

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

      8. times-frac 92.4%

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

      9. metadata-eval 92.4%

         \[\leadsto \left(\frac{1}{y} \cdot \left(\color{blue}{0.3333333333333333} \cdot \frac{t}{z}\right) + x\right) + \frac{y}{z \cdot -3} \]

   6. Applied egg-rr 92.4%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 92.5%

         \[\leadsto \left(\color{blue}{\frac{1 \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)}{y}} + x\right) + \frac{y}{z \cdot -3} \]

      2. *-lft-identity 92.5%

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

      3. associate-*r/ 92.6%

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

   8. Simplified 92.6%

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

   9. Taylor expanded in y around inf 46.2%

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

       1. metadata-eval 46.2%

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

       2. times-frac 46.8%

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

       3. *-un-lft-identity 46.8%

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

       4. *-commutative 46.8%

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

   11. Applied egg-rr 46.8%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -10000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+33}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e+33)
   (- x (* y (/ 0.3333333333333333 z)))
   (if (<= y 1.4e+16)
     (+ 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 <= -2e+33) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 1.4e+16) {
		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 <= (-2d+33)) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else if (y <= 1.4d+16) 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 <= -2e+33) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 1.4e+16) {
		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 <= -2e+33:
		tmp = x - (y * (0.3333333333333333 / z))
	elif y <= 1.4e+16:
		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 <= -2e+33)
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	elseif (y <= 1.4e+16)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	else
		tmp = Float64(x - Float64(Float64(0.3333333333333333 * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2e+33)
		tmp = x - (y * (0.3333333333333333 / z));
	elseif (y <= 1.4e+16)
		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, -2e+33], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+16], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e33

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-+r- 96.9%

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

      3. +-commutative 96.9%

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

      4. associate--l+ 96.9%

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

      5. sub-neg 96.9%

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

      6. remove-double-neg 96.9%

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

      7. distribute-frac-neg 96.9%

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

      8. distribute-neg-in 96.9%

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

      9. remove-double-neg 96.9%

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

      10. sub-neg 96.9%

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

      11. neg-mul-1 96.9%

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

      12. times-frac 98.3%

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

      13. distribute-frac-neg 98.3%

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

      14. neg-mul-1 98.3%

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

      15. *-commutative 98.3%

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

      16. associate-/l* 98.2%

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

      17. *-commutative 98.2%

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

   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 94.9%

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

      1. neg-mul-1 94.9%

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

   7. Simplified 94.9%

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

      1. add-cube-cbrt 94.2%

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

      2. fma-define 94.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{0.3333333333333333}{z} \cdot \left(-y\right)\right)} \]

      3. distribute-rgt-neg-out 94.2%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \color{blue}{-\frac{0.3333333333333333}{z} \cdot y}\right) \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

      5. sqrt-unprod 21.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

      6. sqr-neg 21.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

      7. sqrt-unprod 35.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

      8. add-sqr-sqrt 35.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(-y\right)}\right) \]

      9. fma-neg 35.6%

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

      10. *-commutative 35.6%

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

      11. add-cube-cbrt 36.1%

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

      12. add-sqr-sqrt 36.1%

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

      13. sqrt-unprod 21.7%

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

      14. sqr-neg 21.7%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 94.9%

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

   9. Applied egg-rr 94.9%

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

   if -1.9999999999999999e33 < y < 1.4e16

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-+r- 89.4%

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

      3. +-commutative 89.4%

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

      4. associate--l+ 89.4%

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

      5. sub-neg 89.4%

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

      6. remove-double-neg 89.4%

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

      7. distribute-frac-neg 89.4%

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

      8. distribute-neg-in 89.4%

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

      9. remove-double-neg 89.4%

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

      10. sub-neg 89.4%

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

      11. neg-mul-1 89.4%

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

      12. times-frac 89.2%

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

      13. distribute-frac-neg 89.2%

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

      14. neg-mul-1 89.2%

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

      15. *-commutative 89.2%

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

      16. associate-/l* 89.3%

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

      17. *-commutative 89.3%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf 86.7%

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

   if 1.4e16 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. remove-double-neg 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   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 88.1%

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

      1. metadata-eval 88.1%

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

      2. cancel-sign-sub-inv 88.1%

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

      3. associate-*r/ 89.3%

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

   7. Simplified 89.3%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+33}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+33}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+19}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.1e+33)
   (- x (* y (/ 0.3333333333333333 z)))
   (if (<= y 3.4e+19)
     (+ 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 <= -3.1e+33) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 3.4e+19) {
		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 <= (-3.1d+33)) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else if (y <= 3.4d+19) 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 <= -3.1e+33) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 3.4e+19) {
		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 <= -3.1e+33:
		tmp = x - (y * (0.3333333333333333 / z))
	elif y <= 3.4e+19:
		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 <= -3.1e+33)
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	elseif (y <= 3.4e+19)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(t / z) / y)));
	else
		tmp = Float64(x - Float64(Float64(0.3333333333333333 * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.1e+33)
		tmp = x - (y * (0.3333333333333333 / z));
	elseif (y <= 3.4e+19)
		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, -3.1e+33], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+19], N[(x + N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1e33

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-+r- 96.9%

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

      3. +-commutative 96.9%

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

      4. associate--l+ 96.9%

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

      5. sub-neg 96.9%

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

      6. remove-double-neg 96.9%

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

      7. distribute-frac-neg 96.9%

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

      8. distribute-neg-in 96.9%

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

      9. remove-double-neg 96.9%

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

      10. sub-neg 96.9%

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

      11. neg-mul-1 96.9%

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

      12. times-frac 98.3%

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

      13. distribute-frac-neg 98.3%

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

      14. neg-mul-1 98.3%

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

      15. *-commutative 98.3%

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

      16. associate-/l* 98.2%

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

      17. *-commutative 98.2%

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

   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 94.9%

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

      1. neg-mul-1 94.9%

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

   7. Simplified 94.9%

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

      1. add-cube-cbrt 94.2%

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

      2. fma-define 94.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{0.3333333333333333}{z} \cdot \left(-y\right)\right)} \]

      3. distribute-rgt-neg-out 94.2%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \color{blue}{-\frac{0.3333333333333333}{z} \cdot y}\right) \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

      5. sqrt-unprod 21.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

      6. sqr-neg 21.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

      7. sqrt-unprod 35.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

      8. add-sqr-sqrt 35.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(-y\right)}\right) \]

      9. fma-neg 35.6%

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

      10. *-commutative 35.6%

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

      11. add-cube-cbrt 36.1%

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

      12. add-sqr-sqrt 36.1%

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

      13. sqrt-unprod 21.7%

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

      14. sqr-neg 21.7%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 94.9%

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

   9. Applied egg-rr 94.9%

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

   if -3.1e33 < y < 3.4e19

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-+r- 89.4%

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

      3. +-commutative 89.4%

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

      4. associate--l+ 89.4%

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

      5. sub-neg 89.4%

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

      6. remove-double-neg 89.4%

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

      7. distribute-frac-neg 89.4%

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

      8. distribute-neg-in 89.4%

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

      9. remove-double-neg 89.4%

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

      10. sub-neg 89.4%

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

      11. neg-mul-1 89.4%

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

      12. times-frac 89.2%

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

      13. distribute-frac-neg 89.2%

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

      14. neg-mul-1 89.2%

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

      15. *-commutative 89.2%

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

      16. associate-/l* 89.3%

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

      17. *-commutative 89.3%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf 86.7%

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

      1. metadata-eval 86.7%

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

      2. *-commutative 86.7%

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

      3. times-frac 86.7%

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

      4. *-commutative 86.7%

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

      5. associate-*r* 86.7%

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

      6. *-commutative 86.7%

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

      7. times-frac 95.7%

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

      8. associate-*l/ 95.7%

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

      9. *-commutative 95.7%

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

      10. times-frac 95.6%

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

      11. metadata-eval 95.6%

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

   7. Simplified 95.6%

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

   if 3.4e19 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. remove-double-neg 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   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 88.1%

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

      1. metadata-eval 88.1%

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

      2. cancel-sign-sub-inv 88.1%

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

      3. associate-*r/ 89.3%

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

   7. Simplified 89.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+33}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+19}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e+33)
   (- x (* y (/ 0.3333333333333333 z)))
   (if (<= y 6.2e+19)
     (+ x (/ 0.3333333333333333 (* y (/ z t))))
     (- x (/ (* 0.3333333333333333 y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e+33) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 6.2e+19) {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	} 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 <= (-3.6d+33)) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else if (y <= 6.2d+19) then
        tmp = x + (0.3333333333333333d0 / (y * (z / t)))
    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 <= -3.6e+33) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 6.2e+19) {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	} else {
		tmp = x - ((0.3333333333333333 * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.6e+33:
		tmp = x - (y * (0.3333333333333333 / z))
	elif y <= 6.2e+19:
		tmp = x + (0.3333333333333333 / (y * (z / t)))
	else:
		tmp = x - ((0.3333333333333333 * y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.6e+33)
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	elseif (y <= 6.2e+19)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y * Float64(z / t))));
	else
		tmp = Float64(x - Float64(Float64(0.3333333333333333 * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.6e+33)
		tmp = x - (y * (0.3333333333333333 / z));
	elseif (y <= 6.2e+19)
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	else
		tmp = x - ((0.3333333333333333 * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.6e+33], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+19], N[(x + N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000003e33

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-+r- 96.9%

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

      3. +-commutative 96.9%

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

      4. associate--l+ 96.9%

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

      5. sub-neg 96.9%

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

      6. remove-double-neg 96.9%

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

      7. distribute-frac-neg 96.9%

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

      8. distribute-neg-in 96.9%

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

      9. remove-double-neg 96.9%

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

      10. sub-neg 96.9%

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

      11. neg-mul-1 96.9%

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

      12. times-frac 98.3%

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

      13. distribute-frac-neg 98.3%

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

      14. neg-mul-1 98.3%

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

      15. *-commutative 98.3%

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

      16. associate-/l* 98.2%

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

      17. *-commutative 98.2%

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

   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 94.9%

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

      1. neg-mul-1 94.9%

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

   7. Simplified 94.9%

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

      1. add-cube-cbrt 94.2%

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

      2. fma-define 94.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{0.3333333333333333}{z} \cdot \left(-y\right)\right)} \]

      3. distribute-rgt-neg-out 94.2%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \color{blue}{-\frac{0.3333333333333333}{z} \cdot y}\right) \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

      5. sqrt-unprod 21.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

      6. sqr-neg 21.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

      7. sqrt-unprod 35.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

      8. add-sqr-sqrt 35.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(-y\right)}\right) \]

      9. fma-neg 35.6%

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

      10. *-commutative 35.6%

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

      11. add-cube-cbrt 36.1%

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

      12. add-sqr-sqrt 36.1%

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

      13. sqrt-unprod 21.7%

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

      14. sqr-neg 21.7%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 94.9%

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

   9. Applied egg-rr 94.9%

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

   if -3.6000000000000003e33 < y < 6.2e19

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-+r- 89.4%

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

      3. +-commutative 89.4%

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

      4. associate--l+ 89.4%

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

      5. sub-neg 89.4%

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

      6. remove-double-neg 89.4%

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

      7. distribute-frac-neg 89.4%

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

      8. distribute-neg-in 89.4%

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

      9. remove-double-neg 89.4%

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

      10. sub-neg 89.4%

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

      11. neg-mul-1 89.4%

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

      12. times-frac 89.2%

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

      13. distribute-frac-neg 89.2%

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

      14. neg-mul-1 89.2%

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

      15. *-commutative 89.2%

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

      16. associate-/l* 89.3%

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

      17. *-commutative 89.3%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf 86.7%

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

      1. metadata-eval 86.7%

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

      2. *-commutative 86.7%

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

      3. times-frac 86.7%

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

      4. *-commutative 86.7%

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

      5. associate-*r* 86.7%

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

      6. *-commutative 86.7%

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

      7. times-frac 95.7%

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

      8. associate-*l/ 95.7%

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

      9. *-commutative 95.7%

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

      10. times-frac 95.6%

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

      11. metadata-eval 95.6%

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

   7. Simplified 95.6%

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

      1. associate-*r/ 95.6%

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

      2. metadata-eval 95.6%

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

      3. clear-num 95.6%

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

      4. inv-pow 95.6%

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

      5. unpow-prod-down 95.6%

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

      6. inv-pow 95.6%

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

      7. div-inv 95.6%

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

      8. associate-/r* 95.6%

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

      9. metadata-eval 95.6%

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

      10. frac-times 95.6%

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

      11. metadata-eval 95.6%

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

   9. Applied egg-rr 95.6%

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

   if 6.2e19 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. remove-double-neg 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   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 88.1%

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

      1. metadata-eval 88.1%

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

      2. cancel-sign-sub-inv 88.1%

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

      3. associate-*r/ 89.3%

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

   7. Simplified 89.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+32}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+32)
   (- x (* y (/ 0.3333333333333333 z)))
   (if (<= y 1.9e+20)
     (+ x (/ (/ t (* z 3.0)) y))
     (- x (/ (* 0.3333333333333333 y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+32) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 1.9e+20) {
		tmp = x + ((t / (z * 3.0)) / 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 <= (-1.7d+32)) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else if (y <= 1.9d+20) then
        tmp = x + ((t / (z * 3.0d0)) / 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 <= -1.7e+32) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 1.9e+20) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = x - ((0.3333333333333333 * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+32:
		tmp = x - (y * (0.3333333333333333 / z))
	elif y <= 1.9e+20:
		tmp = x + ((t / (z * 3.0)) / y)
	else:
		tmp = x - ((0.3333333333333333 * y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+32)
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	elseif (y <= 1.9e+20)
		tmp = Float64(x + Float64(Float64(t / Float64(z * 3.0)) / y));
	else
		tmp = Float64(x - Float64(Float64(0.3333333333333333 * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+32)
		tmp = x - (y * (0.3333333333333333 / z));
	elseif (y <= 1.9e+20)
		tmp = x + ((t / (z * 3.0)) / y);
	else
		tmp = x - ((0.3333333333333333 * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+32], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+20], N[(x + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999989e32

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-+r- 96.9%

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

      3. +-commutative 96.9%

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

      4. associate--l+ 96.9%

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

      5. sub-neg 96.9%

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

      6. remove-double-neg 96.9%

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

      7. distribute-frac-neg 96.9%

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

      8. distribute-neg-in 96.9%

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

      9. remove-double-neg 96.9%

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

      10. sub-neg 96.9%

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

      11. neg-mul-1 96.9%

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

      12. times-frac 98.3%

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

      13. distribute-frac-neg 98.3%

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

      14. neg-mul-1 98.3%

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

      15. *-commutative 98.3%

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

      16. associate-/l* 98.2%

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

      17. *-commutative 98.2%

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

   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 94.9%

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

      1. neg-mul-1 94.9%

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

   7. Simplified 94.9%

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

      1. add-cube-cbrt 94.2%

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

      2. fma-define 94.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{0.3333333333333333}{z} \cdot \left(-y\right)\right)} \]

      3. distribute-rgt-neg-out 94.2%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \color{blue}{-\frac{0.3333333333333333}{z} \cdot y}\right) \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

      5. sqrt-unprod 21.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

      6. sqr-neg 21.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

      7. sqrt-unprod 35.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

      8. add-sqr-sqrt 35.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(-y\right)}\right) \]

      9. fma-neg 35.6%

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

      10. *-commutative 35.6%

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

      11. add-cube-cbrt 36.1%

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

      12. add-sqr-sqrt 36.1%

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

      13. sqrt-unprod 21.7%

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

      14. sqr-neg 21.7%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 94.9%

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

   9. Applied egg-rr 94.9%

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

   if -1.69999999999999989e32 < y < 1.9e20

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-+r- 89.4%

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

      3. +-commutative 89.4%

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

      4. associate--l+ 89.4%

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

      5. sub-neg 89.4%

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

      6. remove-double-neg 89.4%

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

      7. distribute-frac-neg 89.4%

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

      8. distribute-neg-in 89.4%

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

      9. remove-double-neg 89.4%

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

      10. sub-neg 89.4%

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

      11. neg-mul-1 89.4%

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

      12. times-frac 89.2%

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

      13. distribute-frac-neg 89.2%

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

      14. neg-mul-1 89.2%

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

      15. *-commutative 89.2%

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

      16. associate-/l* 89.3%

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

      17. *-commutative 89.3%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf 85.8%

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

      1. associate-*r/ 95.6%

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

      2. clear-num 95.6%

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

      3. associate-*l/ 95.6%

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

      4. *-un-lft-identity 95.6%

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

      5. div-inv 95.7%

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

      6. metadata-eval 95.7%

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

   7. Applied egg-rr 95.7%

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

   if 1.9e20 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. remove-double-neg 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   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 88.1%

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

      1. metadata-eval 88.1%

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

      2. cancel-sign-sub-inv 88.1%

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

      3. associate-*r/ 89.3%

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

   7. Simplified 89.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+32}:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1950000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1950000.0)
   x
   (if (<= z 2.4e+32) (* (/ y z) -0.3333333333333333) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1950000.0) {
		tmp = x;
	} else if (z <= 2.4e+32) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1950000.0d0)) then
        tmp = x
    else if (z <= 2.4d+32) then
        tmp = (y / z) * (-0.3333333333333333d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1950000.0) {
		tmp = x;
	} else if (z <= 2.4e+32) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1950000.0:
		tmp = x
	elif z <= 2.4e+32:
		tmp = (y / z) * -0.3333333333333333
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1950000.0)
		tmp = x;
	elseif (z <= 2.4e+32)
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1950000.0)
		tmp = x;
	elseif (z <= 2.4e+32)
		tmp = (y / z) * -0.3333333333333333;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1950000.0], x, If[LessEqual[z, 2.4e+32], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e6 or 2.39999999999999991e32 < z

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r- 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--l+ 99.0%

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

      5. sub-neg 99.0%

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

      6. remove-double-neg 99.0%

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

      7. distribute-frac-neg 99.0%

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

      8. distribute-neg-in 99.0%

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

      9. remove-double-neg 99.0%

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

      10. sub-neg 99.0%

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

      11. neg-mul-1 99.0%

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

      12. times-frac 88.9%

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

      13. distribute-frac-neg 88.9%

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

      14. neg-mul-1 88.9%

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

      15. *-commutative 88.9%

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

      16. associate-/l* 88.9%

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

      17. *-commutative 88.9%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around inf 57.6%

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

   if -1.95e6 < z < 2.39999999999999991e32

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-+r- 89.4%

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

      3. sub-neg 89.4%

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

      4. associate-*l* 89.4%

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

      5. *-commutative 89.4%

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

      6. distribute-frac-neg2 89.4%

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

      7. distribute-rgt-neg-in 89.4%

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

      8. metadata-eval 89.4%

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

   3. Simplified 89.4%

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

      1. *-un-lft-identity 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-*l* 89.4%

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

      4. *-commutative 89.4%

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

      5. times-frac 92.5%

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

      6. *-un-lft-identity 92.5%

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

      7. *-commutative 92.5%

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

      8. times-frac 92.4%

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

      9. metadata-eval 92.4%

         \[\leadsto \left(\frac{1}{y} \cdot \left(\color{blue}{0.3333333333333333} \cdot \frac{t}{z}\right) + x\right) + \frac{y}{z \cdot -3} \]

   6. Applied egg-rr 92.4%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 92.5%

         \[\leadsto \left(\color{blue}{\frac{1 \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)}{y}} + x\right) + \frac{y}{z \cdot -3} \]

      2. *-lft-identity 92.5%

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

      3. associate-*r/ 92.6%

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

   8. Simplified 92.6%

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

   9. Taylor expanded in y around inf 46.2%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1950000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2300000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2300000000.0)
   x
   (if (<= z 1.4e+33) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2300000000.0) {
		tmp = x;
	} else if (z <= 1.4e+33) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2300000000.0d0)) then
        tmp = x
    else if (z <= 1.4d+33) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2300000000.0) {
		tmp = x;
	} else if (z <= 1.4e+33) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2300000000.0:
		tmp = x
	elif z <= 1.4e+33:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2300000000.0)
		tmp = x;
	elseif (z <= 1.4e+33)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2300000000.0)
		tmp = x;
	elseif (z <= 1.4e+33)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2300000000.0], x, If[LessEqual[z, 1.4e+33], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e9 or 1.4e33 < z

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r- 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--l+ 99.0%

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

      5. sub-neg 99.0%

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

      6. remove-double-neg 99.0%

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

      7. distribute-frac-neg 99.0%

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

      8. distribute-neg-in 99.0%

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

      9. remove-double-neg 99.0%

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

      10. sub-neg 99.0%

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

      11. neg-mul-1 99.0%

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

      12. times-frac 88.9%

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

      13. distribute-frac-neg 88.9%

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

      14. neg-mul-1 88.9%

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

      15. *-commutative 88.9%

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

      16. associate-/l* 88.9%

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

      17. *-commutative 88.9%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around inf 57.6%

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

   if -2.3e9 < z < 1.4e33

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-+r- 89.4%

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

      3. sub-neg 89.4%

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

      4. associate-*l* 89.4%

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

      5. *-commutative 89.4%

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

      6. distribute-frac-neg2 89.4%

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

      7. distribute-rgt-neg-in 89.4%

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

      8. metadata-eval 89.4%

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

   3. Simplified 89.4%

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

      1. *-un-lft-identity 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-*l* 89.4%

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

      4. *-commutative 89.4%

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

      5. times-frac 92.5%

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

      6. *-un-lft-identity 92.5%

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

      7. *-commutative 92.5%

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

      8. times-frac 92.4%

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

      9. metadata-eval 92.4%

         \[\leadsto \left(\frac{1}{y} \cdot \left(\color{blue}{0.3333333333333333} \cdot \frac{t}{z}\right) + x\right) + \frac{y}{z \cdot -3} \]

   6. Applied egg-rr 92.4%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 92.5%

         \[\leadsto \left(\color{blue}{\frac{1 \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)}{y}} + x\right) + \frac{y}{z \cdot -3} \]

      2. *-lft-identity 92.5%

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

      3. associate-*r/ 92.6%

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

   8. Simplified 92.6%

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

   9. Taylor expanded in y around inf 46.2%

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

       1. associate-*r/ 46.8%

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

       2. metadata-eval 46.8%

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

       3. associate-*r* 46.8%

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

       4. neg-mul-1 46.8%

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

       5. associate-*l/ 46.8%

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

       6. distribute-rgt-neg-out 46.8%

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

       7. *-commutative 46.8%

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

       8. distribute-rgt-neg-in 46.8%

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

       9. distribute-neg-frac 46.8%

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

       10. metadata-eval 46.8%

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

   11. Simplified 46.8%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2300000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.3% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

3. Taylor expanded in t around 0 65.6%

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

4. Final simplification 65.6%

   \[\leadsto x - 0.3333333333333333 \cdot \frac{y}{z} \]
5. Add Preprocessing

Alternative 14: 64.4% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. +-commutative 93.9%

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

   2. associate-+r- 93.9%

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

   3. +-commutative 93.9%

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

   4. associate--l+ 93.9%

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

   5. sub-neg 93.9%

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

   6. remove-double-neg 93.9%

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

   7. distribute-frac-neg 93.9%

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

   8. distribute-neg-in 93.9%

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

   9. remove-double-neg 93.9%

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

   10. sub-neg 93.9%

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

   11. neg-mul-1 93.9%

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

   12. times-frac 94.3%

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

   13. distribute-frac-neg 94.3%

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

   14. neg-mul-1 94.3%

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

   15. *-commutative 94.3%

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

   16. associate-/l* 94.2%

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

   17. *-commutative 94.2%

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

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 0 65.9%

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

   1. neg-mul-1 65.9%

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

7. Simplified 65.9%

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

   1. add-cube-cbrt 65.2%

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

   2. fma-define 65.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{0.3333333333333333}{z} \cdot \left(-y\right)\right)} \]

   3. distribute-rgt-neg-out 65.2%

      \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \color{blue}{-\frac{0.3333333333333333}{z} \cdot y}\right) \]

   4. add-sqr-sqrt 29.4%

      \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

   5. sqrt-unprod 40.0%

      \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

   6. sqr-neg 40.0%

      \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

   7. sqrt-unprod 19.4%

      \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

   8. add-sqr-sqrt 32.5%

      \[\leadsto \mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -\frac{0.3333333333333333}{z} \cdot \color{blue}{\left(-y\right)}\right) \]

   9. fma-neg 32.5%

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

   10. *-commutative 32.5%

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

   11. add-cube-cbrt 33.1%

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

   12. add-sqr-sqrt 19.7%

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

   13. sqrt-unprod 40.4%

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

   14. sqr-neg 40.4%

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

   15. sqrt-unprod 29.6%

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

   16. add-sqr-sqrt 65.9%

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

9. Applied egg-rr 65.9%

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

10. Final simplification 65.9%

    \[\leadsto x - y \cdot \frac{0.3333333333333333}{z} \]
11. Add Preprocessing

Alternative 15: 30.1% 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 93.9%

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

   1. +-commutative 93.9%

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

   2. associate-+r- 93.9%

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

   3. +-commutative 93.9%

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

   4. associate--l+ 93.9%

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

   5. sub-neg 93.9%

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

   6. remove-double-neg 93.9%

      \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   7. distribute-frac-neg 93.9%

      \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   8. distribute-neg-in 93.9%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

   9. remove-double-neg 93.9%

      \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

   10. sub-neg 93.9%

       \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

   11. neg-mul-1 93.9%

       \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   12. times-frac 94.3%

       \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   13. distribute-frac-neg 94.3%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

   14. neg-mul-1 94.3%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

   15. *-commutative 94.3%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

   16. associate-/l* 94.2%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

   17. *-commutative 94.2%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

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 x around inf 33.5%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 33.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 95.8% 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 2024059 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :alt
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))