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

Percentage Accurate: 95.7% → 99.3%

Time: 14.6s

Alternatives: 22

Speedup: 1.0×

• 28.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+37} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-106}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{3 \cdot \left(z \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -4e+37) (not (<= (* z 3.0) 2e-106)))
   (+ (- x (/ y (* z 3.0))) (/ t (* 3.0 (* z y))))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -4e+37) || !((z * 3.0) <= 2e-106)) {
		tmp = (x - (y / (z * 3.0))) + (t / (3.0 * (z * y)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 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) :: tmp
    if (((z * 3.0d0) <= (-4d+37)) .or. (.not. ((z * 3.0d0) <= 2d-106))) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (3.0d0 * (z * y)))
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    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) <= -4e+37) || !((z * 3.0) <= 2e-106)) {
		tmp = (x - (y / (z * 3.0))) + (t / (3.0 * (z * y)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -4e+37) or not ((z * 3.0) <= 2e-106):
		tmp = (x - (y / (z * 3.0))) + (t / (3.0 * (z * y)))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -4e+37) || !(Float64(z * 3.0) <= 2e-106))
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(3.0 * Float64(z * y))));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -4e+37) || ~(((z * 3.0) <= 2e-106)))
		tmp = (x - (y / (z * 3.0))) + (t / (3.0 * (z * y)));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+37], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-106]], $MachinePrecision]], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(3.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -3.99999999999999982e37 or 1.99999999999999988e-106 < (*.f64 z 3)

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.9%

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

   if -3.99999999999999982e37 < (*.f64 z 3) < 1.99999999999999988e-106

   1. Initial program 84.4%

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

      1. associate-+l- 84.4%

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

      2. sub-neg 84.4%

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

      3. sub-neg 84.4%

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

      4. distribute-frac-neg 84.4%

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

      5. distribute-neg-in 84.4%

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

      6. distribute-frac-neg 84.4%

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

      7. sub-neg 84.4%

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

      8. neg-mul-1 84.4%

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

      9. associate-*l/ 84.4%

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

      10. neg-mul-1 84.4%

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

      11. times-frac 97.1%

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

      12. distribute-lft-out-- 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-rgt-in 97.1%

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

      3. div-inv 97.1%

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

      4. *-commutative 97.1%

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

      5. associate-*l* 97.1%

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

      6. div-inv 97.1%

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

      7. *-commutative 97.1%

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

      8. metadata-eval 97.1%

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

      9. metadata-eval 97.1%

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

      10. times-frac 97.1%

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

      11. metadata-eval 97.1%

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

      12. neg-mul-1 97.1%

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

      13. *-commutative 97.1%

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

      14. distribute-neg-frac 97.1%

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

      15. distribute-neg-frac 97.1%

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

      16. clear-num 97.1%

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

      17. div-inv 97.1%

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

      18. metadata-eval 97.1%

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

      19. metadata-eval 97.1%

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

      20. distribute-rgt-neg-in 97.1%

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

      21. times-frac 84.4%

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

      22. *-commutative 84.4%

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

      23. times-frac 92.0%

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

   5. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+37} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-106}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{3 \cdot \left(z \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]

Alternative 2: 97.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+37}:\\ \;\;\;\;x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \frac{\frac{t}{z}}{3 \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -4e+37)
   (+ x (+ (* -0.3333333333333333 (/ y z)) (/ (/ t z) (* 3.0 y))))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e+37) {
		tmp = x + ((-0.3333333333333333 * (y / z)) + ((t / z) / (3.0 * y)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 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) :: tmp
    if ((z * 3.0d0) <= (-4d+37)) then
        tmp = x + (((-0.3333333333333333d0) * (y / z)) + ((t / z) / (3.0d0 * y)))
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    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) <= -4e+37) {
		tmp = x + ((-0.3333333333333333 * (y / z)) + ((t / z) / (3.0 * y)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -4e+37:
		tmp = x + ((-0.3333333333333333 * (y / z)) + ((t / z) / (3.0 * y)))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -4e+37)
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 * Float64(y / z)) + Float64(Float64(t / z) / Float64(3.0 * y))));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -4e+37)
		tmp = x + ((-0.3333333333333333 * (y / z)) + ((t / z) / (3.0 * y)));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+37], N[(x + N[(N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t / z), $MachinePrecision] / N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -3.99999999999999982e37

   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. remove-double-neg 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-frac-neg 99.8%

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

      6. associate-+r- 99.8%

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

      7. sub-neg 99.8%

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

      8. neg-mul-1 99.8%

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

      9. *-commutative 99.8%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. distribute-frac-neg 99.6%

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

      13. remove-double-neg 99.6%

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

      14. associate-*l* 99.6%

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

      15. *-commutative 99.6%

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

      16. associate-/r* 98.0%

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

   3. Simplified 98.0%

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

   if -3.99999999999999982e37 < (*.f64 z 3)

   1. Initial program 91.1%

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

      1. associate-+l- 91.1%

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

      2. sub-neg 91.1%

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

      3. sub-neg 91.1%

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

      4. distribute-frac-neg 91.1%

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

      5. distribute-neg-in 91.1%

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

      6. distribute-frac-neg 91.1%

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

      7. sub-neg 91.1%

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

      8. neg-mul-1 91.1%

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

      9. associate-*l/ 91.1%

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

      10. neg-mul-1 91.1%

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

      11. times-frac 95.9%

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

      12. distribute-lft-out-- 97.4%

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

      13. *-commutative 97.4%

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

      14. associate-/r* 97.4%

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

      15. metadata-eval 97.4%

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

   3. Simplified 97.4%

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

      1. sub-neg 97.4%

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

      2. distribute-rgt-in 95.9%

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

      3. div-inv 95.9%

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

      4. *-commutative 95.9%

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

      5. associate-*l* 95.9%

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

      6. div-inv 95.9%

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

      7. *-commutative 95.9%

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

      8. metadata-eval 95.9%

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

      9. metadata-eval 95.9%

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

      10. times-frac 96.0%

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

      11. metadata-eval 96.0%

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

      12. neg-mul-1 96.0%

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

      13. *-commutative 96.0%

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

      14. distribute-neg-frac 96.0%

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

      15. distribute-neg-frac 96.0%

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

      16. clear-num 95.9%

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

      17. div-inv 96.0%

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

      18. metadata-eval 96.0%

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

      19. metadata-eval 96.0%

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

      20. distribute-rgt-neg-in 96.0%

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

      21. times-frac 91.1%

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

      22. *-commutative 91.1%

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

      23. times-frac 94.5%

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

   5. Applied egg-rr 97.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+37}:\\ \;\;\;\;x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \frac{\frac{t}{z}}{3 \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]

Alternative 3: 81.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+40} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{+96}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -2e+40) (not (<= (* z 3.0) 2e+96)))
   (- x (/ y (* z 3.0)))
   (* -0.3333333333333333 (/ (- y (/ t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+40) || !((z * 3.0) <= 2e+96)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / 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) <= (-2d+40)) .or. (.not. ((z * 3.0d0) <= 2d+96))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (-0.3333333333333333d0) * ((y - (t / 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) <= -2e+40) || !((z * 3.0) <= 2e+96)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -2e+40) or not ((z * 3.0) <= 2e+96):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -2e+40) || !(Float64(z * 3.0) <= 2e+96))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -2e+40) || ~(((z * 3.0) <= 2e+96)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+40], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+96]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -2.00000000000000006e40 or 2.0000000000000001e96 < (*.f64 z 3)

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 77.7%

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

      1. *-commutative 77.7%

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

      2. metadata-eval 77.7%

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

      3. div-inv 77.7%

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

      4. associate-/r* 77.8%

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

   4. Applied egg-rr 77.8%

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

   if -2.00000000000000006e40 < (*.f64 z 3) < 2.0000000000000001e96

   1. Initial program 88.7%

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

      1. associate-+l- 88.7%

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

      2. sub-neg 88.7%

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

      3. sub-neg 88.7%

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

      4. distribute-frac-neg 88.7%

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

      5. distribute-neg-in 88.7%

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

      6. distribute-frac-neg 88.7%

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

      7. sub-neg 88.7%

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

      8. neg-mul-1 88.7%

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

      9. associate-*l/ 88.6%

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

      10. neg-mul-1 88.6%

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

      11. times-frac 97.2%

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

      12. distribute-lft-out-- 99.1%

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

      13. *-commutative 99.1%

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

      14. associate-/r* 99.1%

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

      15. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

      1. sub-neg 99.1%

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

      2. distribute-rgt-in 97.2%

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

      3. div-inv 97.2%

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

      4. *-commutative 97.2%

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

      5. associate-*l* 97.2%

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

      6. div-inv 97.2%

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

      7. *-commutative 97.2%

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

      8. metadata-eval 97.2%

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

      9. metadata-eval 97.2%

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

      10. times-frac 97.3%

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

      11. metadata-eval 97.3%

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

      12. neg-mul-1 97.3%

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

      13. *-commutative 97.3%

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

      14. distribute-neg-frac 97.3%

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

      15. distribute-neg-frac 97.3%

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

      16. clear-num 97.2%

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

      17. div-inv 97.3%

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

      18. metadata-eval 97.3%

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

      19. metadata-eval 97.3%

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

      20. distribute-rgt-neg-in 97.3%

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

      21. times-frac 88.7%

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

      22. *-commutative 88.7%

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

      23. times-frac 94.1%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in x around 0 91.9%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+40} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{+96}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \]

Alternative 4: 82.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+37} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{+65}\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -4e+37) (not (<= (* z 3.0) 2e+65)))
   (+ x (* 0.3333333333333333 (/ t (* z y))))
   (* -0.3333333333333333 (/ (- y (/ t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -4e+37) || !((z * 3.0) <= 2e+65)) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / 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) <= (-4d+37)) .or. (.not. ((z * 3.0d0) <= 2d+65))) then
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    else
        tmp = (-0.3333333333333333d0) * ((y - (t / 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) <= -4e+37) || !((z * 3.0) <= 2e+65)) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -4e+37) or not ((z * 3.0) <= 2e+65):
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	else:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -4e+37) || !(Float64(z * 3.0) <= 2e+65))
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	else
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -4e+37) || ~(((z * 3.0) <= 2e+65)))
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	else
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+37], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+65]], $MachinePrecision]], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -3.99999999999999982e37 or 2e65 < (*.f64 z 3)

   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. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. distribute-frac-neg 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. distribute-frac-neg 99.8%

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

      7. sub-neg 99.8%

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

      8. neg-mul-1 99.8%

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

      9. associate-*l/ 99.7%

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

      10. neg-mul-1 99.7%

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

      11. times-frac 88.1%

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

      12. distribute-lft-out-- 88.1%

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

      13. *-commutative 88.1%

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

      14. associate-/r* 88.1%

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

      15. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in y around 0 85.4%

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

   if -3.99999999999999982e37 < (*.f64 z 3) < 2e65

   1. Initial program 87.6%

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

      1. associate-+l- 87.6%

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

      2. sub-neg 87.6%

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

      3. sub-neg 87.6%

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

      4. distribute-frac-neg 87.6%

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

      5. distribute-neg-in 87.6%

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

      6. distribute-frac-neg 87.6%

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

      7. sub-neg 87.6%

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

      8. neg-mul-1 87.6%

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

      9. associate-*l/ 87.6%

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

      10. neg-mul-1 87.6%

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

      11. times-frac 97.6%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-rgt-in 97.6%

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

      3. div-inv 97.6%

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

      4. *-commutative 97.6%

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

      5. associate-*l* 97.6%

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

      6. div-inv 97.6%

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

      7. *-commutative 97.6%

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

      8. metadata-eval 97.6%

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

      9. metadata-eval 97.6%

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

      10. times-frac 97.6%

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

      11. metadata-eval 97.6%

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

      12. neg-mul-1 97.6%

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

      13. *-commutative 97.6%

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

      14. distribute-neg-frac 97.6%

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

      15. distribute-neg-frac 97.6%

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

      16. clear-num 97.6%

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

      17. div-inv 97.7%

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

      18. metadata-eval 97.7%

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

      19. metadata-eval 97.7%

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

      20. distribute-rgt-neg-in 97.7%

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

      21. times-frac 87.6%

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

      22. *-commutative 87.6%

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

      23. times-frac 93.6%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 93.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+37} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{+65}\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \]

Alternative 5: 59.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* z y)))))
   (if (<= y -2.15e-15)
     (/ (/ y z) -3.0)
     (if (<= y 1.9e-205)
       t_1
       (if (<= y 4.1e-188)
         x
         (if (<= y 1.15e-122) t_1 (if (<= y 6.8e+99) x (/ y (* z -3.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double tmp;
	if (y <= -2.15e-15) {
		tmp = (y / z) / -3.0;
	} else if (y <= 1.9e-205) {
		tmp = t_1;
	} else if (y <= 4.1e-188) {
		tmp = x;
	} else if (y <= 1.15e-122) {
		tmp = t_1;
	} else if (y <= 6.8e+99) {
		tmp = x;
	} else {
		tmp = y / (z * -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 = 0.3333333333333333d0 * (t / (z * y))
    if (y <= (-2.15d-15)) then
        tmp = (y / z) / (-3.0d0)
    else if (y <= 1.9d-205) then
        tmp = t_1
    else if (y <= 4.1d-188) then
        tmp = x
    else if (y <= 1.15d-122) then
        tmp = t_1
    else if (y <= 6.8d+99) then
        tmp = x
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double tmp;
	if (y <= -2.15e-15) {
		tmp = (y / z) / -3.0;
	} else if (y <= 1.9e-205) {
		tmp = t_1;
	} else if (y <= 4.1e-188) {
		tmp = x;
	} else if (y <= 1.15e-122) {
		tmp = t_1;
	} else if (y <= 6.8e+99) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (z * y))
	tmp = 0
	if y <= -2.15e-15:
		tmp = (y / z) / -3.0
	elif y <= 1.9e-205:
		tmp = t_1
	elif y <= 4.1e-188:
		tmp = x
	elif y <= 1.15e-122:
		tmp = t_1
	elif y <= 6.8e+99:
		tmp = x
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(z * y)))
	tmp = 0.0
	if (y <= -2.15e-15)
		tmp = Float64(Float64(y / z) / -3.0);
	elseif (y <= 1.9e-205)
		tmp = t_1;
	elseif (y <= 4.1e-188)
		tmp = x;
	elseif (y <= 1.15e-122)
		tmp = t_1;
	elseif (y <= 6.8e+99)
		tmp = x;
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (z * y));
	tmp = 0.0;
	if (y <= -2.15e-15)
		tmp = (y / z) / -3.0;
	elseif (y <= 1.9e-205)
		tmp = t_1;
	elseif (y <= 4.1e-188)
		tmp = x;
	elseif (y <= 1.15e-122)
		tmp = t_1;
	elseif (y <= 6.8e+99)
		tmp = x;
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e-15], N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[y, 1.9e-205], t$95$1, If[LessEqual[y, 4.1e-188], x, If[LessEqual[y, 1.15e-122], t$95$1, If[LessEqual[y, 6.8e+99], x, N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1499999999999998e-15

   1. Initial program 96.6%

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

      1. associate-+l- 96.6%

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

      2. sub-neg 96.6%

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

      3. sub-neg 96.6%

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

      4. distribute-frac-neg 96.6%

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

      5. distribute-neg-in 96.6%

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

      6. distribute-frac-neg 96.6%

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

      7. sub-neg 96.6%

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

      8. neg-mul-1 96.6%

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

      9. associate-*l/ 96.5%

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

      10. neg-mul-1 96.5%

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

      11. times-frac 96.5%

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

      12. distribute-lft-out-- 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.8%

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

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-rgt-in 96.5%

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

      3. div-inv 96.5%

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

      4. *-commutative 96.5%

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

      5. associate-*l* 96.4%

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

      6. div-inv 96.5%

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

      7. *-commutative 96.5%

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

      8. metadata-eval 96.5%

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

      9. metadata-eval 96.5%

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

      10. times-frac 96.6%

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

      11. metadata-eval 96.6%

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

      12. neg-mul-1 96.6%

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

      13. *-commutative 96.6%

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

      14. distribute-neg-frac 96.6%

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

      15. distribute-neg-frac 96.6%

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

      16. clear-num 96.6%

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

      17. div-inv 96.6%

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

      18. metadata-eval 96.6%

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

      19. metadata-eval 96.6%

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

      20. distribute-rgt-neg-in 96.6%

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

      21. times-frac 96.6%

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

      22. *-commutative 96.6%

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

      23. times-frac 91.9%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 82.2%

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

   7. Taylor expanded in y around inf 72.1%

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

      1. associate-*r/ 72.1%

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

      2. *-commutative 72.1%

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

      3. associate-*r/ 72.2%

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

   9. Simplified 72.2%

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

       1. associate-*r/ 72.1%

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

       2. associate-/l* 72.1%

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

       3. div-inv 72.2%

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

       4. associate-/r* 72.2%

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

       5. metadata-eval 72.2%

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

   11. Applied egg-rr 72.2%

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

   if -2.1499999999999998e-15 < y < 1.89999999999999996e-205 or 4.09999999999999982e-188 < y < 1.15000000000000003e-122

   1. Initial program 86.2%

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

      1. associate-+l- 86.2%

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

      2. sub-neg 86.2%

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

      3. sub-neg 86.2%

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

      4. distribute-frac-neg 86.2%

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

      5. distribute-neg-in 86.2%

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

      6. distribute-frac-neg 86.2%

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

      7. sub-neg 86.2%

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

      8. neg-mul-1 86.2%

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

      9. associate-*l/ 86.2%

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

      10. neg-mul-1 86.2%

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

      11. times-frac 88.1%

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

      12. distribute-lft-out-- 88.1%

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

      13. *-commutative 88.1%

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

      14. associate-/r* 88.1%

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

      15. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

      1. sub-neg 88.1%

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

      2. distribute-rgt-in 88.1%

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

      3. div-inv 88.1%

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

      4. *-commutative 88.1%

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

      5. associate-*l* 88.1%

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

      6. div-inv 88.1%

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

      7. *-commutative 88.1%

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

      8. metadata-eval 88.1%

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

      9. metadata-eval 88.1%

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

      10. times-frac 88.1%

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

      11. metadata-eval 88.1%

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

      12. neg-mul-1 88.1%

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

      13. *-commutative 88.1%

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

      14. distribute-neg-frac 88.1%

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

      15. distribute-neg-frac 88.1%

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

      16. clear-num 88.1%

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

      17. div-inv 88.1%

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

      18. metadata-eval 88.1%

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

      19. metadata-eval 88.1%

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

      20. distribute-rgt-neg-in 88.1%

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

      21. times-frac 86.2%

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

      22. *-commutative 86.2%

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

      23. times-frac 96.7%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in y around 0 66.3%

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

   if 1.89999999999999996e-205 < y < 4.09999999999999982e-188 or 1.15000000000000003e-122 < y < 6.79999999999999968e99

   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. associate-+l- 97.3%

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

      2. sub-neg 97.3%

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

      3. sub-neg 97.3%

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

      4. distribute-frac-neg 97.3%

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

      5. distribute-neg-in 97.3%

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

      6. distribute-frac-neg 97.3%

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

      7. sub-neg 97.3%

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

      8. neg-mul-1 97.3%

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

      9. associate-*l/ 97.3%

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

      10. neg-mul-1 97.3%

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

      11. times-frac 96.5%

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

      12. distribute-lft-out-- 96.5%

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

      13. *-commutative 96.5%

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

      14. associate-/r* 96.5%

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

      15. metadata-eval 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in x around inf 59.9%

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

   if 6.79999999999999968e99 < 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. associate-+l- 97.4%

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

      2. sub-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. distribute-frac-neg 97.4%

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

      5. distribute-neg-in 97.4%

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

      6. distribute-frac-neg 97.4%

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

      7. sub-neg 97.4%

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

      8. neg-mul-1 97.4%

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

      9. associate-*l/ 97.2%

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

      10. neg-mul-1 97.2%

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

      11. times-frac 97.2%

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

      12. distribute-lft-out-- 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.8%

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

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-rgt-in 97.2%

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

      3. div-inv 97.1%

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

      4. *-commutative 97.1%

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

      5. associate-*l* 97.1%

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

      6. div-inv 97.2%

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

      7. *-commutative 97.2%

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

      8. metadata-eval 97.2%

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

      9. metadata-eval 97.2%

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

      10. times-frac 97.4%

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

      11. metadata-eval 97.4%

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

      12. neg-mul-1 97.4%

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

      13. *-commutative 97.4%

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

      14. distribute-neg-frac 97.4%

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

      15. distribute-neg-frac 97.4%

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

      16. clear-num 97.4%

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

      17. div-inv 97.4%

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

      18. metadata-eval 97.4%

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

      19. metadata-eval 97.4%

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

      20. distribute-rgt-neg-in 97.4%

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

      21. times-frac 97.4%

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

      22. *-commutative 97.4%

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

      23. times-frac 90.0%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 81.2%

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

   7. Taylor expanded in y around inf 78.8%

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

      1. associate-*r/ 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r/ 79.0%

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

   9. Simplified 79.0%

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

       1. associate-*r/ 78.9%

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

       2. associate-/l* 78.9%

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

       3. div-inv 79.0%

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

       4. metadata-eval 79.0%

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

   11. Applied egg-rr 79.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-122}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 6: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ t_2 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* z y))))
        (t_2 (- x (* (/ y z) 0.3333333333333333))))
   (if (<= y -2.3e-18)
     t_2
     (if (<= y 1.9e-205)
       t_1
       (if (<= y 3.1e-188) x (if (<= y 7.8e-122) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double t_2 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -2.3e-18) {
		tmp = t_2;
	} else if (y <= 1.9e-205) {
		tmp = t_1;
	} else if (y <= 3.1e-188) {
		tmp = x;
	} else if (y <= 7.8e-122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (z * y))
    t_2 = x - ((y / z) * 0.3333333333333333d0)
    if (y <= (-2.3d-18)) then
        tmp = t_2
    else if (y <= 1.9d-205) then
        tmp = t_1
    else if (y <= 3.1d-188) then
        tmp = x
    else if (y <= 7.8d-122) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double t_2 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -2.3e-18) {
		tmp = t_2;
	} else if (y <= 1.9e-205) {
		tmp = t_1;
	} else if (y <= 3.1e-188) {
		tmp = x;
	} else if (y <= 7.8e-122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (z * y))
	t_2 = x - ((y / z) * 0.3333333333333333)
	tmp = 0
	if y <= -2.3e-18:
		tmp = t_2
	elif y <= 1.9e-205:
		tmp = t_1
	elif y <= 3.1e-188:
		tmp = x
	elif y <= 7.8e-122:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(z * y)))
	t_2 = Float64(x - Float64(Float64(y / z) * 0.3333333333333333))
	tmp = 0.0
	if (y <= -2.3e-18)
		tmp = t_2;
	elseif (y <= 1.9e-205)
		tmp = t_1;
	elseif (y <= 3.1e-188)
		tmp = x;
	elseif (y <= 7.8e-122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (z * y));
	t_2 = x - ((y / z) * 0.3333333333333333);
	tmp = 0.0;
	if (y <= -2.3e-18)
		tmp = t_2;
	elseif (y <= 1.9e-205)
		tmp = t_1;
	elseif (y <= 3.1e-188)
		tmp = x;
	elseif (y <= 7.8e-122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e-18], t$95$2, If[LessEqual[y, 1.9e-205], t$95$1, If[LessEqual[y, 3.1e-188], x, If[LessEqual[y, 7.8e-122], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3000000000000001e-18 or 7.79999999999999979e-122 < y

   1. Initial program 96.9%

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

   2. Taylor expanded in t around 0 86.4%

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

   if -2.3000000000000001e-18 < y < 1.89999999999999996e-205 or 3.1000000000000002e-188 < y < 7.79999999999999979e-122

   1. Initial program 86.2%

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

      1. associate-+l- 86.2%

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

      2. sub-neg 86.2%

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

      3. sub-neg 86.2%

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

      4. distribute-frac-neg 86.2%

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

      5. distribute-neg-in 86.2%

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

      6. distribute-frac-neg 86.2%

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

      7. sub-neg 86.2%

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

      8. neg-mul-1 86.2%

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

      9. associate-*l/ 86.2%

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

      10. neg-mul-1 86.2%

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

      11. times-frac 88.1%

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

      12. distribute-lft-out-- 88.1%

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

      13. *-commutative 88.1%

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

      14. associate-/r* 88.1%

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

      15. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

      1. sub-neg 88.1%

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

      2. distribute-rgt-in 88.1%

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

      3. div-inv 88.1%

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

      4. *-commutative 88.1%

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

      5. associate-*l* 88.1%

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

      6. div-inv 88.1%

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

      7. *-commutative 88.1%

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

      8. metadata-eval 88.1%

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

      9. metadata-eval 88.1%

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

      10. times-frac 88.1%

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

      11. metadata-eval 88.1%

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

      12. neg-mul-1 88.1%

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

      13. *-commutative 88.1%

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

      14. distribute-neg-frac 88.1%

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

      15. distribute-neg-frac 88.1%

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

      16. clear-num 88.1%

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

      17. div-inv 88.1%

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

      18. metadata-eval 88.1%

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

      19. metadata-eval 88.1%

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

      20. distribute-rgt-neg-in 88.1%

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

      21. times-frac 86.2%

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

      22. *-commutative 86.2%

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

      23. times-frac 96.7%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in y around 0 66.3%

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

   if 1.89999999999999996e-205 < y < 3.1000000000000002e-188

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. neg-mul-1 100.0%

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

      9. associate-*l/ 100.0%

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

      10. neg-mul-1 100.0%

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

      11. times-frac 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-/r* 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-122}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \end{array} \]

Alternative 7: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ t_2 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* z y)))) (t_2 (- x (/ y (* z 3.0)))))
   (if (<= y -2.8e-18)
     t_2
     (if (<= y 1.82e-205)
       t_1
       (if (<= y 3e-188) x (if (<= y 5e-122) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double t_2 = x - (y / (z * 3.0));
	double tmp;
	if (y <= -2.8e-18) {
		tmp = t_2;
	} else if (y <= 1.82e-205) {
		tmp = t_1;
	} else if (y <= 3e-188) {
		tmp = x;
	} else if (y <= 5e-122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (z * y))
    t_2 = x - (y / (z * 3.0d0))
    if (y <= (-2.8d-18)) then
        tmp = t_2
    else if (y <= 1.82d-205) then
        tmp = t_1
    else if (y <= 3d-188) then
        tmp = x
    else if (y <= 5d-122) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double t_2 = x - (y / (z * 3.0));
	double tmp;
	if (y <= -2.8e-18) {
		tmp = t_2;
	} else if (y <= 1.82e-205) {
		tmp = t_1;
	} else if (y <= 3e-188) {
		tmp = x;
	} else if (y <= 5e-122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (z * y))
	t_2 = x - (y / (z * 3.0))
	tmp = 0
	if y <= -2.8e-18:
		tmp = t_2
	elif y <= 1.82e-205:
		tmp = t_1
	elif y <= 3e-188:
		tmp = x
	elif y <= 5e-122:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(z * y)))
	t_2 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (y <= -2.8e-18)
		tmp = t_2;
	elseif (y <= 1.82e-205)
		tmp = t_1;
	elseif (y <= 3e-188)
		tmp = x;
	elseif (y <= 5e-122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (z * y));
	t_2 = x - (y / (z * 3.0));
	tmp = 0.0;
	if (y <= -2.8e-18)
		tmp = t_2;
	elseif (y <= 1.82e-205)
		tmp = t_1;
	elseif (y <= 3e-188)
		tmp = x;
	elseif (y <= 5e-122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e-18], t$95$2, If[LessEqual[y, 1.82e-205], t$95$1, If[LessEqual[y, 3e-188], x, If[LessEqual[y, 5e-122], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.80000000000000012e-18 or 4.9999999999999999e-122 < y

   1. Initial program 96.9%

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

   2. Taylor expanded in t around 0 86.4%

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

      1. *-commutative 86.4%

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

      2. metadata-eval 86.4%

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

      3. div-inv 86.4%

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

      4. associate-/r* 86.5%

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

   4. Applied egg-rr 86.5%

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

   if -2.80000000000000012e-18 < y < 1.81999999999999992e-205 or 3.00000000000000017e-188 < y < 4.9999999999999999e-122

   1. Initial program 86.2%

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

      1. associate-+l- 86.2%

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

      2. sub-neg 86.2%

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

      3. sub-neg 86.2%

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

      4. distribute-frac-neg 86.2%

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

      5. distribute-neg-in 86.2%

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

      6. distribute-frac-neg 86.2%

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

      7. sub-neg 86.2%

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

      8. neg-mul-1 86.2%

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

      9. associate-*l/ 86.2%

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

      10. neg-mul-1 86.2%

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

      11. times-frac 88.1%

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

      12. distribute-lft-out-- 88.1%

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

      13. *-commutative 88.1%

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

      14. associate-/r* 88.1%

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

      15. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

      1. sub-neg 88.1%

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

      2. distribute-rgt-in 88.1%

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

      3. div-inv 88.1%

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

      4. *-commutative 88.1%

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

      5. associate-*l* 88.1%

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

      6. div-inv 88.1%

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

      7. *-commutative 88.1%

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

      8. metadata-eval 88.1%

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

      9. metadata-eval 88.1%

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

      10. times-frac 88.1%

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

      11. metadata-eval 88.1%

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

      12. neg-mul-1 88.1%

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

      13. *-commutative 88.1%

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

      14. distribute-neg-frac 88.1%

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

      15. distribute-neg-frac 88.1%

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

      16. clear-num 88.1%

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

      17. div-inv 88.1%

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

      18. metadata-eval 88.1%

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

      19. metadata-eval 88.1%

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

      20. distribute-rgt-neg-in 88.1%

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

      21. times-frac 86.2%

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

      22. *-commutative 86.2%

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

      23. times-frac 96.7%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in y around 0 66.3%

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

   if 1.81999999999999992e-205 < y < 3.00000000000000017e-188

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. neg-mul-1 100.0%

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

      9. associate-*l/ 100.0%

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

      10. neg-mul-1 100.0%

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

      11. times-frac 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-/r* 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{-205}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-122}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 8: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* z y)))))
   (if (<= y -3.4e-18)
     (- x (/ (/ y 3.0) z))
     (if (<= y 9.4e-206)
       t_1
       (if (<= y 9.6e-188)
         x
         (if (<= y 2.55e-127) t_1 (- x (/ y (* z 3.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double tmp;
	if (y <= -3.4e-18) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 9.4e-206) {
		tmp = t_1;
	} else if (y <= 9.6e-188) {
		tmp = x;
	} else if (y <= 2.55e-127) {
		tmp = t_1;
	} else {
		tmp = x - (y / (z * 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 = 0.3333333333333333d0 * (t / (z * y))
    if (y <= (-3.4d-18)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 9.4d-206) then
        tmp = t_1
    else if (y <= 9.6d-188) then
        tmp = x
    else if (y <= 2.55d-127) then
        tmp = t_1
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double tmp;
	if (y <= -3.4e-18) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 9.4e-206) {
		tmp = t_1;
	} else if (y <= 9.6e-188) {
		tmp = x;
	} else if (y <= 2.55e-127) {
		tmp = t_1;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (z * y))
	tmp = 0
	if y <= -3.4e-18:
		tmp = x - ((y / 3.0) / z)
	elif y <= 9.4e-206:
		tmp = t_1
	elif y <= 9.6e-188:
		tmp = x
	elif y <= 2.55e-127:
		tmp = t_1
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(z * y)))
	tmp = 0.0
	if (y <= -3.4e-18)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 9.4e-206)
		tmp = t_1;
	elseif (y <= 9.6e-188)
		tmp = x;
	elseif (y <= 2.55e-127)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (z * y));
	tmp = 0.0;
	if (y <= -3.4e-18)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 9.4e-206)
		tmp = t_1;
	elseif (y <= 9.6e-188)
		tmp = x;
	elseif (y <= 2.55e-127)
		tmp = t_1;
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e-18], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.4e-206], t$95$1, If[LessEqual[y, 9.6e-188], x, If[LessEqual[y, 2.55e-127], t$95$1, N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.40000000000000001e-18

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 89.6%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

      3. metadata-eval 89.6%

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

      4. div-inv 89.7%

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

   4. Applied egg-rr 89.7%

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

   if -3.40000000000000001e-18 < y < 9.3999999999999997e-206 or 9.6e-188 < y < 2.55000000000000009e-127

   1. Initial program 86.2%

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

      1. associate-+l- 86.2%

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

      2. sub-neg 86.2%

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

      3. sub-neg 86.2%

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

      4. distribute-frac-neg 86.2%

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

      5. distribute-neg-in 86.2%

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

      6. distribute-frac-neg 86.2%

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

      7. sub-neg 86.2%

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

      8. neg-mul-1 86.2%

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

      9. associate-*l/ 86.2%

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

      10. neg-mul-1 86.2%

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

      11. times-frac 88.1%

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

      12. distribute-lft-out-- 88.1%

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

      13. *-commutative 88.1%

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

      14. associate-/r* 88.1%

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

      15. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

      1. sub-neg 88.1%

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

      2. distribute-rgt-in 88.1%

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

      3. div-inv 88.1%

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

      4. *-commutative 88.1%

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

      5. associate-*l* 88.1%

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

      6. div-inv 88.1%

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

      7. *-commutative 88.1%

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

      8. metadata-eval 88.1%

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

      9. metadata-eval 88.1%

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

      10. times-frac 88.1%

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

      11. metadata-eval 88.1%

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

      12. neg-mul-1 88.1%

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

      13. *-commutative 88.1%

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

      14. distribute-neg-frac 88.1%

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

      15. distribute-neg-frac 88.1%

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

      16. clear-num 88.1%

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

      17. div-inv 88.1%

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

      18. metadata-eval 88.1%

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

      19. metadata-eval 88.1%

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

      20. distribute-rgt-neg-in 88.1%

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

      21. times-frac 86.2%

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

      22. *-commutative 86.2%

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

      23. times-frac 96.7%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in y around 0 66.3%

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

   if 9.3999999999999997e-206 < y < 9.6e-188

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. neg-mul-1 100.0%

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

      9. associate-*l/ 100.0%

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

      10. neg-mul-1 100.0%

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

      11. times-frac 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-/r* 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   if 2.55000000000000009e-127 < y

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 84.2%

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

      1. *-commutative 84.2%

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

      2. metadata-eval 84.2%

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

      3. div-inv 84.2%

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

      4. associate-/r* 84.4%

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

   4. Applied egg-rr 84.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-206}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-127}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 9: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-92}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-211}:\\ \;\;\;\;\frac{\frac{t}{y} \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-128}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e-92)
   (- x (/ (/ y 3.0) z))
   (if (<= y 2.5e-211)
     (/ (* (/ t y) 0.3333333333333333) z)
     (if (<= y 3e-188)
       (- x (* (/ y z) 0.3333333333333333))
       (if (<= y 4.3e-128)
         (* 0.3333333333333333 (/ t (* z y)))
         (- x (/ y (* z 3.0))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-92) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 2.5e-211) {
		tmp = ((t / y) * 0.3333333333333333) / z;
	} else if (y <= 3e-188) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 4.3e-128) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = x - (y / (z * 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) :: tmp
    if (y <= (-4.8d-92)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 2.5d-211) then
        tmp = ((t / y) * 0.3333333333333333d0) / z
    else if (y <= 3d-188) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 4.3d-128) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-92) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 2.5e-211) {
		tmp = ((t / y) * 0.3333333333333333) / z;
	} else if (y <= 3e-188) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 4.3e-128) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e-92:
		tmp = x - ((y / 3.0) / z)
	elif y <= 2.5e-211:
		tmp = ((t / y) * 0.3333333333333333) / z
	elif y <= 3e-188:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 4.3e-128:
		tmp = 0.3333333333333333 * (t / (z * y))
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e-92)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 2.5e-211)
		tmp = Float64(Float64(Float64(t / y) * 0.3333333333333333) / z);
	elseif (y <= 3e-188)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 4.3e-128)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e-92)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 2.5e-211)
		tmp = ((t / y) * 0.3333333333333333) / z;
	elseif (y <= 3e-188)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 4.3e-128)
		tmp = 0.3333333333333333 * (t / (z * y));
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e-92], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-211], N[(N[(N[(t / y), $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 3e-188], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e-128], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.8000000000000002e-92

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 81.6%

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

      1. associate-*r/ 81.6%

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

      2. *-commutative 81.6%

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

      3. metadata-eval 81.6%

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

      4. div-inv 81.7%

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

   4. Applied egg-rr 81.7%

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

   if -4.8000000000000002e-92 < y < 2.5000000000000001e-211

   1. Initial program 84.6%

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

      1. associate-+l- 84.6%

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

      2. sub-neg 84.6%

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

      3. sub-neg 84.6%

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

      4. distribute-frac-neg 84.6%

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

      5. distribute-neg-in 84.6%

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

      6. distribute-frac-neg 84.6%

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

      7. sub-neg 84.6%

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

      8. neg-mul-1 84.6%

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

      9. associate-*l/ 84.6%

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

      10. neg-mul-1 84.6%

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

      11. times-frac 89.4%

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

      12. distribute-lft-out-- 89.4%

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

      13. *-commutative 89.4%

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

      14. associate-/r* 89.4%

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

      15. metadata-eval 89.4%

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

   3. Simplified 89.4%

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

      1. sub-neg 89.4%

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

      2. distribute-rgt-in 89.4%

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

      3. div-inv 89.4%

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

      4. *-commutative 89.4%

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

      5. associate-*l* 89.4%

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

      6. div-inv 89.4%

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

      7. *-commutative 89.4%

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

      8. metadata-eval 89.4%

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

      9. metadata-eval 89.4%

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

      10. times-frac 89.4%

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

      11. metadata-eval 89.4%

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

      12. neg-mul-1 89.4%

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

      13. *-commutative 89.4%

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

      14. distribute-neg-frac 89.4%

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

      15. distribute-neg-frac 89.4%

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

      16. clear-num 89.4%

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

      17. div-inv 89.4%

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

      18. metadata-eval 89.4%

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

      19. metadata-eval 89.4%

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

      20. distribute-rgt-neg-in 89.4%

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

      21. times-frac 84.6%

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

      22. *-commutative 84.6%

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

      23. times-frac 95.1%

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

   5. Applied egg-rr 89.5%

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

   6. Taylor expanded in y around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-*r/ 66.6%

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

   8. Simplified 66.6%

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

      1. associate-/r* 66.6%

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

      2. associate-*r/ 73.6%

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

   10. Applied egg-rr 73.6%

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

   11. Taylor expanded in t around 0 73.7%

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

   if 2.5000000000000001e-211 < y < 3.00000000000000017e-188

   1. Initial program 78.9%

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

   2. Taylor expanded in t around 0 75.4%

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

   if 3.00000000000000017e-188 < y < 4.29999999999999994e-128

   1. Initial program 88.0%

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

      1. associate-+l- 88.0%

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

      2. sub-neg 88.0%

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

      3. sub-neg 88.0%

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

      4. distribute-frac-neg 88.0%

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

      5. distribute-neg-in 88.0%

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

      6. distribute-frac-neg 88.0%

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

      7. sub-neg 88.0%

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

      8. neg-mul-1 88.0%

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

      9. associate-*l/ 88.0%

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

      10. neg-mul-1 88.0%

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

      11. times-frac 82.1%

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

      12. distribute-lft-out-- 82.1%

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

      13. *-commutative 82.1%

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

      14. associate-/r* 82.1%

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

      15. metadata-eval 82.1%

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

   3. Simplified 82.1%

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

      1. sub-neg 82.1%

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

      2. distribute-rgt-in 82.1%

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

      3. div-inv 82.1%

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

      4. *-commutative 82.1%

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

      5. associate-*l* 82.1%

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

      6. div-inv 82.1%

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

      7. *-commutative 82.1%

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

      8. metadata-eval 82.1%

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

      9. metadata-eval 82.1%

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

      10. times-frac 82.1%

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

      11. metadata-eval 82.1%

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

      12. neg-mul-1 82.1%

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

      13. *-commutative 82.1%

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

      14. distribute-neg-frac 82.1%

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

      15. distribute-neg-frac 82.1%

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

      16. clear-num 82.0%

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

      17. div-inv 82.1%

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

      18. metadata-eval 82.1%

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

      19. metadata-eval 82.1%

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

      20. distribute-rgt-neg-in 82.1%

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

      21. times-frac 88.0%

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

      22. *-commutative 88.0%

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

      23. times-frac 99.6%

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

   5. Applied egg-rr 82.2%

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

   6. Taylor expanded in y around 0 81.8%

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

   if 4.29999999999999994e-128 < y

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 84.2%

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

      1. *-commutative 84.2%

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

      2. metadata-eval 84.2%

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

      3. div-inv 84.2%

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

      4. associate-/r* 84.4%

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

   4. Applied egg-rr 84.4%

      \[\leadsto x - \color{blue}{\frac{y}{z \cdot 3}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-92}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-211}:\\ \;\;\;\;\frac{\frac{t}{y} \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-128}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 10: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* t (/ 0.3333333333333333 z)) y)))
   (if (<= y -2.4e-18)
     (- x (/ (/ y 3.0) z))
     (if (<= y 1.9e-205)
       t_1
       (if (<= y 3e-188) x (if (<= y 1.2e-112) t_1 (- x (/ y (* z 3.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * (0.3333333333333333 / z)) / y;
	double tmp;
	if (y <= -2.4e-18) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 1.9e-205) {
		tmp = t_1;
	} else if (y <= 3e-188) {
		tmp = x;
	} else if (y <= 1.2e-112) {
		tmp = t_1;
	} else {
		tmp = x - (y / (z * 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 = (t * (0.3333333333333333d0 / z)) / y
    if (y <= (-2.4d-18)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 1.9d-205) then
        tmp = t_1
    else if (y <= 3d-188) then
        tmp = x
    else if (y <= 1.2d-112) then
        tmp = t_1
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * (0.3333333333333333 / z)) / y;
	double tmp;
	if (y <= -2.4e-18) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 1.9e-205) {
		tmp = t_1;
	} else if (y <= 3e-188) {
		tmp = x;
	} else if (y <= 1.2e-112) {
		tmp = t_1;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * (0.3333333333333333 / z)) / y
	tmp = 0
	if y <= -2.4e-18:
		tmp = x - ((y / 3.0) / z)
	elif y <= 1.9e-205:
		tmp = t_1
	elif y <= 3e-188:
		tmp = x
	elif y <= 1.2e-112:
		tmp = t_1
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * Float64(0.3333333333333333 / z)) / y)
	tmp = 0.0
	if (y <= -2.4e-18)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 1.9e-205)
		tmp = t_1;
	elseif (y <= 3e-188)
		tmp = x;
	elseif (y <= 1.2e-112)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * (0.3333333333333333 / z)) / y;
	tmp = 0.0;
	if (y <= -2.4e-18)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 1.9e-205)
		tmp = t_1;
	elseif (y <= 3e-188)
		tmp = x;
	elseif (y <= 1.2e-112)
		tmp = t_1;
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.4e-18], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-205], t$95$1, If[LessEqual[y, 3e-188], x, If[LessEqual[y, 1.2e-112], t$95$1, N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.39999999999999994e-18

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 89.6%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

      3. metadata-eval 89.6%

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

      4. div-inv 89.7%

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

   4. Applied egg-rr 89.7%

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

   if -2.39999999999999994e-18 < y < 1.89999999999999996e-205 or 3.00000000000000017e-188 < y < 1.2e-112

   1. Initial program 86.0%

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

      1. associate-+l- 86.0%

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

      2. sub-neg 86.0%

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

      3. sub-neg 86.0%

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

      4. distribute-frac-neg 86.0%

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

      5. distribute-neg-in 86.0%

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

      6. distribute-frac-neg 86.0%

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

      7. sub-neg 86.0%

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

      8. neg-mul-1 86.0%

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

      9. associate-*l/ 86.0%

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

      10. neg-mul-1 86.0%

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

      11. times-frac 88.4%

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

      12. distribute-lft-out-- 88.4%

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

      13. *-commutative 88.4%

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

      14. associate-/r* 88.4%

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

      15. metadata-eval 88.4%

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

   3. Simplified 88.4%

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

      1. sub-neg 88.4%

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

      2. distribute-rgt-in 88.4%

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

      3. div-inv 88.4%

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

      4. *-commutative 88.4%

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

      5. associate-*l* 88.4%

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

      6. div-inv 88.4%

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

      7. *-commutative 88.4%

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

      8. metadata-eval 88.4%

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

      9. metadata-eval 88.4%

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

      10. times-frac 88.4%

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

      11. metadata-eval 88.4%

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

      12. neg-mul-1 88.4%

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

      13. *-commutative 88.4%

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

      14. distribute-neg-frac 88.4%

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

      15. distribute-neg-frac 88.4%

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

      16. clear-num 88.3%

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

      17. div-inv 88.4%

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

      18. metadata-eval 88.4%

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

      19. metadata-eval 88.4%

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

      20. distribute-rgt-neg-in 88.4%

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

      21. times-frac 86.0%

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

      22. *-commutative 86.0%

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

      23. times-frac 96.8%

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

   5. Applied egg-rr 88.5%

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

   6. Taylor expanded in y around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. *-commutative 65.5%

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

      3. associate-*r/ 64.4%

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

   8. Simplified 64.4%

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

      1. associate-*r/ 65.5%

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

      2. associate-/l/ 73.9%

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

      3. associate-*r/ 73.9%

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

   10. Applied egg-rr 73.9%

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

   if 1.89999999999999996e-205 < y < 3.00000000000000017e-188

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. neg-mul-1 100.0%

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

      9. associate-*l/ 100.0%

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

      10. neg-mul-1 100.0%

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

      11. times-frac 100.0%

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

      12. distribute-lft-out-- 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-/r* 100.0%

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

      15. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   if 1.2e-112 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in t around 0 85.0%

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

      1. *-commutative 85.0%

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

      2. metadata-eval 85.0%

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

      3. div-inv 85.0%

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

      4. associate-/r* 85.1%

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

   4. Applied egg-rr 85.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-112}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 11: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;\frac{\frac{t}{z}}{3 \cdot y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-112}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-18)
   (- x (/ (/ y 3.0) z))
   (if (<= y 1.9e-205)
     (/ (/ t z) (* 3.0 y))
     (if (<= y 3e-188)
       x
       (if (<= y 1.02e-112)
         (/ (* t (/ 0.3333333333333333 z)) y)
         (- x (/ y (* z 3.0))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-18) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 1.9e-205) {
		tmp = (t / z) / (3.0 * y);
	} else if (y <= 3e-188) {
		tmp = x;
	} else if (y <= 1.02e-112) {
		tmp = (t * (0.3333333333333333 / z)) / y;
	} else {
		tmp = x - (y / (z * 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) :: tmp
    if (y <= (-3.4d-18)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 1.9d-205) then
        tmp = (t / z) / (3.0d0 * y)
    else if (y <= 3d-188) then
        tmp = x
    else if (y <= 1.02d-112) then
        tmp = (t * (0.3333333333333333d0 / z)) / y
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-18) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 1.9e-205) {
		tmp = (t / z) / (3.0 * y);
	} else if (y <= 3e-188) {
		tmp = x;
	} else if (y <= 1.02e-112) {
		tmp = (t * (0.3333333333333333 / z)) / y;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-18:
		tmp = x - ((y / 3.0) / z)
	elif y <= 1.9e-205:
		tmp = (t / z) / (3.0 * y)
	elif y <= 3e-188:
		tmp = x
	elif y <= 1.02e-112:
		tmp = (t * (0.3333333333333333 / z)) / y
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-18)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 1.9e-205)
		tmp = Float64(Float64(t / z) / Float64(3.0 * y));
	elseif (y <= 3e-188)
		tmp = x;
	elseif (y <= 1.02e-112)
		tmp = Float64(Float64(t * Float64(0.3333333333333333 / z)) / y);
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-18)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 1.9e-205)
		tmp = (t / z) / (3.0 * y);
	elseif (y <= 3e-188)
		tmp = x;
	elseif (y <= 1.02e-112)
		tmp = (t * (0.3333333333333333 / z)) / y;
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-18], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-205], N[(N[(t / z), $MachinePrecision] / N[(3.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-188], x, If[LessEqual[y, 1.02e-112], N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.40000000000000001e-18

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 89.6%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

      3. metadata-eval 89.6%

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

      4. div-inv 89.7%

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

   4. Applied egg-rr 89.7%

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

   if -3.40000000000000001e-18 < y < 1.89999999999999996e-205

   1. Initial program 85.9%

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

      1. associate-+l- 85.9%

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

      2. sub-neg 85.9%

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

      3. sub-neg 85.9%

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

      4. distribute-frac-neg 85.9%

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

      5. distribute-neg-in 85.9%

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

      6. distribute-frac-neg 85.9%

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

      7. sub-neg 85.9%

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

      8. neg-mul-1 85.9%

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

      9. associate-*l/ 85.9%

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

      10. neg-mul-1 85.9%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 89.3%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 89.3%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 89.3%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 89.3%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 89.3%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg 89.3%

         \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)} \]

      2. distribute-rgt-in 89.3%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right)} \]

      3. div-inv 89.3%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      4. *-commutative 89.3%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      5. associate-*l* 89.3%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right) \cdot -0.3333333333333333} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      6. div-inv 89.3%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z}} \cdot -0.3333333333333333 + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      7. *-commutative 89.3%

         \[\leadsto x + \left(\color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      8. metadata-eval 89.3%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{3}} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      9. metadata-eval 89.3%

         \[\leadsto x + \left(\frac{\color{blue}{-1}}{3} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      10. times-frac 89.3%

          \[\leadsto x + \left(\color{blue}{\frac{\left(-1\right) \cdot y}{3 \cdot z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      11. metadata-eval 89.3%

          \[\leadsto x + \left(\frac{\color{blue}{-1} \cdot y}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      12. neg-mul-1 89.3%

          \[\leadsto x + \left(\frac{\color{blue}{-y}}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      13. *-commutative 89.3%

          \[\leadsto x + \left(\frac{-y}{\color{blue}{z \cdot 3}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      14. distribute-neg-frac 89.3%

          \[\leadsto x + \left(\color{blue}{\left(-\frac{y}{z \cdot 3}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      15. distribute-neg-frac 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{y}} \cdot \frac{-0.3333333333333333}{z}\right) \]

      16. clear-num 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}}\right) \]

      17. div-inv 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}\right) \]

      18. metadata-eval 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      19. metadata-eval 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{\left(-3\right)}}\right) \]

      20. distribute-rgt-neg-in 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{-z \cdot 3}}\right) \]

      21. times-frac 85.9%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\left(-t\right) \cdot 1}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      22. *-commutative 85.9%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{\left(-t\right) \cdot 1}{\color{blue}{\left(-z \cdot 3\right) \cdot y}}\right) \]

      23. times-frac 96.1%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{-z \cdot 3} \cdot \frac{1}{y}}\right) \]

   5. Applied egg-rr 89.4%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 63.3%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 63.3%

         \[\leadsto \color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}} \]

      2. *-commutative 63.3%

         \[\leadsto \frac{\color{blue}{t \cdot 0.3333333333333333}}{y \cdot z} \]

      3. associate-*r/ 62.4%

         \[\leadsto \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}} \]

   8. Simplified 62.4%

      \[\leadsto \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 63.3%

         \[\leadsto \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      2. *-commutative 63.3%

         \[\leadsto \frac{t \cdot 0.3333333333333333}{\color{blue}{z \cdot y}} \]

      3. times-frac 70.5%

         \[\leadsto \color{blue}{\frac{t}{z} \cdot \frac{0.3333333333333333}{y}} \]

      4. clear-num 70.5%

         \[\leadsto \frac{t}{z} \cdot \color{blue}{\frac{1}{\frac{y}{0.3333333333333333}}} \]

      5. un-div-inv 70.5%

         \[\leadsto \color{blue}{\frac{\frac{t}{z}}{\frac{y}{0.3333333333333333}}} \]

      6. div-inv 70.5%

         \[\leadsto \frac{\frac{t}{z}}{\color{blue}{y \cdot \frac{1}{0.3333333333333333}}} \]

      7. metadata-eval 70.5%

         \[\leadsto \frac{\frac{t}{z}}{y \cdot \color{blue}{3}} \]

   10. Applied egg-rr 70.5%

       \[\leadsto \color{blue}{\frac{\frac{t}{z}}{y \cdot 3}} \]

   if 1.89999999999999996e-205 < y < 3.00000000000000017e-188

   1. Initial program 100.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 100.0%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 100.0%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 100.0%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 100.0%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 100.0%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 100.0%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 100.0%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 100.0%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 100.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 100.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 100.0%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 100.0%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 100.0%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 3.00000000000000017e-188 < y < 1.01999999999999996e-112

   1. Initial program 86.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 86.7%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 86.7%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 86.7%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 86.7%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 86.7%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 86.7%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 86.7%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 86.7%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 86.7%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 86.7%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 84.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 84.0%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 84.0%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 84.0%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 84.0%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg 84.0%

         \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)} \]

      2. distribute-rgt-in 84.0%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right)} \]

      3. div-inv 84.0%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      4. *-commutative 84.0%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      5. associate-*l* 84.0%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right) \cdot -0.3333333333333333} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      6. div-inv 84.0%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z}} \cdot -0.3333333333333333 + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      7. *-commutative 84.0%

         \[\leadsto x + \left(\color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      8. metadata-eval 84.0%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{3}} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      9. metadata-eval 84.0%

         \[\leadsto x + \left(\frac{\color{blue}{-1}}{3} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      10. times-frac 84.0%

          \[\leadsto x + \left(\color{blue}{\frac{\left(-1\right) \cdot y}{3 \cdot z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      11. metadata-eval 84.0%

          \[\leadsto x + \left(\frac{\color{blue}{-1} \cdot y}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      12. neg-mul-1 84.0%

          \[\leadsto x + \left(\frac{\color{blue}{-y}}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      13. *-commutative 84.0%

          \[\leadsto x + \left(\frac{-y}{\color{blue}{z \cdot 3}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      14. distribute-neg-frac 84.0%

          \[\leadsto x + \left(\color{blue}{\left(-\frac{y}{z \cdot 3}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      15. distribute-neg-frac 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{y}} \cdot \frac{-0.3333333333333333}{z}\right) \]

      16. clear-num 83.9%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}}\right) \]

      17. div-inv 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}\right) \]

      18. metadata-eval 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      19. metadata-eval 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{\left(-3\right)}}\right) \]

      20. distribute-rgt-neg-in 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{-z \cdot 3}}\right) \]

      21. times-frac 86.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\left(-t\right) \cdot 1}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      22. *-commutative 86.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{\left(-t\right) \cdot 1}{\color{blue}{\left(-z \cdot 3\right) \cdot y}}\right) \]

      23. times-frac 99.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{-z \cdot 3} \cdot \frac{1}{y}}\right) \]

   5. Applied egg-rr 84.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 75.5%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 75.5%

         \[\leadsto \color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}} \]

      2. *-commutative 75.5%

         \[\leadsto \frac{\color{blue}{t \cdot 0.3333333333333333}}{y \cdot z} \]

      3. associate-*r/ 73.5%

         \[\leadsto \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}} \]

   8. Simplified 73.5%

      \[\leadsto \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 75.5%

         \[\leadsto \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      2. associate-/l/ 89.1%

         \[\leadsto \color{blue}{\frac{\frac{t \cdot 0.3333333333333333}{z}}{y}} \]

      3. associate-*r/ 89.2%

         \[\leadsto \frac{\color{blue}{t \cdot \frac{0.3333333333333333}{z}}}{y} \]

   10. Applied egg-rr 89.2%

       \[\leadsto \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   if 1.01999999999999996e-112 < y

   1. Initial program 97.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 85.0%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 85.0%

         \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]

      2. metadata-eval 85.0%

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      3. div-inv 85.0%

         \[\leadsto x - \color{blue}{\frac{\frac{y}{z}}{3}} \]

      4. associate-/r* 85.1%

         \[\leadsto x - \color{blue}{\frac{y}{z \cdot 3}} \]

   4. Applied egg-rr 85.1%

      \[\leadsto x - \color{blue}{\frac{y}{z \cdot 3}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;\frac{\frac{t}{z}}{3 \cdot y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-112}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 12: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot \frac{t}{z}}{-y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-112}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3e-18)
   (- x (/ (/ y 3.0) z))
   (if (<= y 1.9e-205)
     (/ (* -0.3333333333333333 (/ t z)) (- y))
     (if (<= y 3e-188)
       x
       (if (<= y 1.2e-112)
         (/ (* t (/ 0.3333333333333333 z)) y)
         (- x (/ y (* z 3.0))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-18) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 1.9e-205) {
		tmp = (-0.3333333333333333 * (t / z)) / -y;
	} else if (y <= 3e-188) {
		tmp = x;
	} else if (y <= 1.2e-112) {
		tmp = (t * (0.3333333333333333 / z)) / y;
	} else {
		tmp = x - (y / (z * 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) :: tmp
    if (y <= (-2.3d-18)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 1.9d-205) then
        tmp = ((-0.3333333333333333d0) * (t / z)) / -y
    else if (y <= 3d-188) then
        tmp = x
    else if (y <= 1.2d-112) then
        tmp = (t * (0.3333333333333333d0 / z)) / y
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-18) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 1.9e-205) {
		tmp = (-0.3333333333333333 * (t / z)) / -y;
	} else if (y <= 3e-188) {
		tmp = x;
	} else if (y <= 1.2e-112) {
		tmp = (t * (0.3333333333333333 / z)) / y;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.3e-18:
		tmp = x - ((y / 3.0) / z)
	elif y <= 1.9e-205:
		tmp = (-0.3333333333333333 * (t / z)) / -y
	elif y <= 3e-188:
		tmp = x
	elif y <= 1.2e-112:
		tmp = (t * (0.3333333333333333 / z)) / y
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3e-18)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 1.9e-205)
		tmp = Float64(Float64(-0.3333333333333333 * Float64(t / z)) / Float64(-y));
	elseif (y <= 3e-188)
		tmp = x;
	elseif (y <= 1.2e-112)
		tmp = Float64(Float64(t * Float64(0.3333333333333333 / z)) / y);
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.3e-18)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 1.9e-205)
		tmp = (-0.3333333333333333 * (t / z)) / -y;
	elseif (y <= 3e-188)
		tmp = x;
	elseif (y <= 1.2e-112)
		tmp = (t * (0.3333333333333333 / z)) / y;
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.3e-18], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-205], N[(N[(-0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 3e-188], x, If[LessEqual[y, 1.2e-112], N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.3000000000000001e-18

   1. Initial program 96.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 89.6%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 89.6%

         \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 89.6%

         \[\leadsto x - \frac{\color{blue}{y \cdot 0.3333333333333333}}{z} \]

      3. metadata-eval 89.6%

         \[\leadsto x - \frac{y \cdot \color{blue}{\frac{1}{3}}}{z} \]

      4. div-inv 89.7%

         \[\leadsto x - \frac{\color{blue}{\frac{y}{3}}}{z} \]

   4. Applied egg-rr 89.7%

      \[\leadsto x - \color{blue}{\frac{\frac{y}{3}}{z}} \]

   if -2.3000000000000001e-18 < y < 1.89999999999999996e-205

   1. Initial program 85.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 85.9%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 85.9%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 85.9%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 85.9%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 85.9%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 85.9%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 85.9%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 85.9%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 85.9%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 85.9%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 89.3%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 89.3%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 89.3%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 89.3%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 89.3%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg 89.3%

         \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)} \]

      2. distribute-rgt-in 89.3%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right)} \]

      3. div-inv 89.3%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      4. *-commutative 89.3%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      5. associate-*l* 89.3%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right) \cdot -0.3333333333333333} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      6. div-inv 89.3%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z}} \cdot -0.3333333333333333 + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      7. *-commutative 89.3%

         \[\leadsto x + \left(\color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      8. metadata-eval 89.3%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{3}} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      9. metadata-eval 89.3%

         \[\leadsto x + \left(\frac{\color{blue}{-1}}{3} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      10. times-frac 89.3%

          \[\leadsto x + \left(\color{blue}{\frac{\left(-1\right) \cdot y}{3 \cdot z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      11. metadata-eval 89.3%

          \[\leadsto x + \left(\frac{\color{blue}{-1} \cdot y}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      12. neg-mul-1 89.3%

          \[\leadsto x + \left(\frac{\color{blue}{-y}}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      13. *-commutative 89.3%

          \[\leadsto x + \left(\frac{-y}{\color{blue}{z \cdot 3}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      14. distribute-neg-frac 89.3%

          \[\leadsto x + \left(\color{blue}{\left(-\frac{y}{z \cdot 3}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      15. distribute-neg-frac 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{y}} \cdot \frac{-0.3333333333333333}{z}\right) \]

      16. clear-num 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}}\right) \]

      17. div-inv 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}\right) \]

      18. metadata-eval 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      19. metadata-eval 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{\left(-3\right)}}\right) \]

      20. distribute-rgt-neg-in 89.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{-z \cdot 3}}\right) \]

      21. times-frac 85.9%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\left(-t\right) \cdot 1}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      22. *-commutative 85.9%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{\left(-t\right) \cdot 1}{\color{blue}{\left(-z \cdot 3\right) \cdot y}}\right) \]

      23. times-frac 96.1%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{-z \cdot 3} \cdot \frac{1}{y}}\right) \]

   5. Applied egg-rr 89.4%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 63.3%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 63.3%

         \[\leadsto \color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}} \]

      2. *-commutative 63.3%

         \[\leadsto \frac{\color{blue}{t \cdot 0.3333333333333333}}{y \cdot z} \]

      3. associate-*r/ 62.4%

         \[\leadsto \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}} \]

   8. Simplified 62.4%

      \[\leadsto \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 63.3%

         \[\leadsto \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      2. associate-/l/ 70.5%

         \[\leadsto \color{blue}{\frac{\frac{t \cdot 0.3333333333333333}{z}}{y}} \]

      3. associate-*r/ 70.5%

         \[\leadsto \frac{\color{blue}{t \cdot \frac{0.3333333333333333}{z}}}{y} \]

      4. frac-2neg 70.5%

         \[\leadsto \color{blue}{\frac{-t \cdot \frac{0.3333333333333333}{z}}{-y}} \]

      5. neg-mul-1 70.5%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(t \cdot \frac{0.3333333333333333}{z}\right)}}{-y} \]

      6. metadata-eval 70.5%

         \[\leadsto \frac{\color{blue}{\left(-1\right)} \cdot \left(t \cdot \frac{0.3333333333333333}{z}\right)}{-y} \]

      7. *-commutative 70.5%

         \[\leadsto \frac{\left(-1\right) \cdot \color{blue}{\left(\frac{0.3333333333333333}{z} \cdot t\right)}}{-y} \]

      8. div-inv 70.5%

         \[\leadsto \frac{\left(-1\right) \cdot \left(\color{blue}{\left(0.3333333333333333 \cdot \frac{1}{z}\right)} \cdot t\right)}{-y} \]

      9. associate-*l* 70.5%

         \[\leadsto \frac{\left(-1\right) \cdot \color{blue}{\left(0.3333333333333333 \cdot \left(\frac{1}{z} \cdot t\right)\right)}}{-y} \]

      10. *-commutative 70.5%

          \[\leadsto \frac{\left(-1\right) \cdot \left(0.3333333333333333 \cdot \color{blue}{\left(t \cdot \frac{1}{z}\right)}\right)}{-y} \]

      11. div-inv 70.6%

          \[\leadsto \frac{\left(-1\right) \cdot \left(0.3333333333333333 \cdot \color{blue}{\frac{t}{z}}\right)}{-y} \]

      12. associate-*r* 70.6%

          \[\leadsto \frac{\color{blue}{\left(\left(-1\right) \cdot 0.3333333333333333\right) \cdot \frac{t}{z}}}{-y} \]

      13. metadata-eval 70.6%

          \[\leadsto \frac{\left(\color{blue}{-1} \cdot 0.3333333333333333\right) \cdot \frac{t}{z}}{-y} \]

      14. metadata-eval 70.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} \cdot \frac{t}{z}}{-y} \]

   10. Applied egg-rr 70.6%

       \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot \frac{t}{z}}{-y}} \]

   if 1.89999999999999996e-205 < y < 3.00000000000000017e-188

   1. Initial program 100.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 100.0%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 100.0%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 100.0%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 100.0%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 100.0%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 100.0%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 100.0%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 100.0%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 100.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 100.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 100.0%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 100.0%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 100.0%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 3.00000000000000017e-188 < y < 1.2e-112

   1. Initial program 86.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 86.7%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 86.7%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 86.7%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 86.7%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 86.7%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 86.7%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 86.7%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 86.7%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 86.7%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 86.7%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 84.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 84.0%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 84.0%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 84.0%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 84.0%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg 84.0%

         \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)} \]

      2. distribute-rgt-in 84.0%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right)} \]

      3. div-inv 84.0%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      4. *-commutative 84.0%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      5. associate-*l* 84.0%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right) \cdot -0.3333333333333333} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      6. div-inv 84.0%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z}} \cdot -0.3333333333333333 + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      7. *-commutative 84.0%

         \[\leadsto x + \left(\color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      8. metadata-eval 84.0%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{3}} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      9. metadata-eval 84.0%

         \[\leadsto x + \left(\frac{\color{blue}{-1}}{3} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      10. times-frac 84.0%

          \[\leadsto x + \left(\color{blue}{\frac{\left(-1\right) \cdot y}{3 \cdot z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      11. metadata-eval 84.0%

          \[\leadsto x + \left(\frac{\color{blue}{-1} \cdot y}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      12. neg-mul-1 84.0%

          \[\leadsto x + \left(\frac{\color{blue}{-y}}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      13. *-commutative 84.0%

          \[\leadsto x + \left(\frac{-y}{\color{blue}{z \cdot 3}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      14. distribute-neg-frac 84.0%

          \[\leadsto x + \left(\color{blue}{\left(-\frac{y}{z \cdot 3}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      15. distribute-neg-frac 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{y}} \cdot \frac{-0.3333333333333333}{z}\right) \]

      16. clear-num 83.9%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}}\right) \]

      17. div-inv 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}\right) \]

      18. metadata-eval 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      19. metadata-eval 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{\left(-3\right)}}\right) \]

      20. distribute-rgt-neg-in 84.0%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{-z \cdot 3}}\right) \]

      21. times-frac 86.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\left(-t\right) \cdot 1}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      22. *-commutative 86.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{\left(-t\right) \cdot 1}{\color{blue}{\left(-z \cdot 3\right) \cdot y}}\right) \]

      23. times-frac 99.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{-z \cdot 3} \cdot \frac{1}{y}}\right) \]

   5. Applied egg-rr 84.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 75.5%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 75.5%

         \[\leadsto \color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}} \]

      2. *-commutative 75.5%

         \[\leadsto \frac{\color{blue}{t \cdot 0.3333333333333333}}{y \cdot z} \]

      3. associate-*r/ 73.5%

         \[\leadsto \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}} \]

   8. Simplified 73.5%

      \[\leadsto \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 75.5%

         \[\leadsto \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      2. associate-/l/ 89.1%

         \[\leadsto \color{blue}{\frac{\frac{t \cdot 0.3333333333333333}{z}}{y}} \]

      3. associate-*r/ 89.2%

         \[\leadsto \frac{\color{blue}{t \cdot \frac{0.3333333333333333}{z}}}{y} \]

   10. Applied egg-rr 89.2%

       \[\leadsto \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   if 1.2e-112 < y

   1. Initial program 97.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 85.0%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 85.0%

         \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]

      2. metadata-eval 85.0%

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      3. div-inv 85.0%

         \[\leadsto x - \color{blue}{\frac{\frac{y}{z}}{3}} \]

      4. associate-/r* 85.1%

         \[\leadsto x - \color{blue}{\frac{y}{z \cdot 3}} \]

   4. Applied egg-rr 85.1%

      \[\leadsto x - \color{blue}{\frac{y}{z \cdot 3}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-205}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot \frac{t}{z}}{-y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-112}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 13: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-194} \lor \neg \left(y \leq 2.2 \cdot 10^{-64}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.3e-194) (not (<= y 2.2e-64)))
   (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z)))
   (+ x (/ (* t (/ 0.3333333333333333 z)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-194) || !(y <= 2.2e-64)) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.3d-194)) .or. (.not. (y <= 2.2d-64))) then
        tmp = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
    else
        tmp = x + ((t * (0.3333333333333333d0 / z)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-194) || !(y <= 2.2e-64)) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.3e-194) or not (y <= 2.2e-64):
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z))
	else:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.3e-194) || !(y <= 2.2e-64))
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.3e-194) || ~((y <= 2.2e-64)))
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	else
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.3e-194], N[Not[LessEqual[y, 2.2e-64]], $MachinePrecision]], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.30000000000000006e-194 or 2.2e-64 < y

   1. Initial program 96.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 96.4%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 96.4%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 96.4%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 96.4%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 96.4%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 96.4%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 96.4%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 96.4%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 96.4%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 96.4%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 96.9%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 98.6%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 98.6%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 98.6%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 98.6%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 98.6%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   if -4.30000000000000006e-194 < y < 2.2e-64

   1. Initial program 85.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 85.8%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 85.8%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 85.8%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 85.8%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 85.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 85.8%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 85.8%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 85.8%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 85.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 85.8%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 86.4%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 86.4%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 86.4%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 86.4%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 86.4%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in y around 0 84.4%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 84.4%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. associate-*l/ 84.4%

         \[\leadsto x + \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      3. times-frac 85.2%

         \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   6. Simplified 85.2%

      \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]
   7. Step-by-step derivation

      1. associate-*l/ 96.4%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   8. Applied egg-rr 96.4%

      \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-194} \lor \neg \left(y \leq 2.2 \cdot 10^{-64}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 14: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-211} \lor \neg \left(y \leq 2.1 \cdot 10^{-62}\right):\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.6e-211) (not (<= y 2.1e-62)))
   (- x (/ (- y (/ t y)) (* z 3.0)))
   (+ x (/ (/ 1.0 y) (/ (* z 3.0) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.6e-211) || !(y <= 2.1e-62)) {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	} else {
		tmp = x + ((1.0 / y) / ((z * 3.0) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.6d-211)) .or. (.not. (y <= 2.1d-62))) then
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    else
        tmp = x + ((1.0d0 / y) / ((z * 3.0d0) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.6e-211) || !(y <= 2.1e-62)) {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	} else {
		tmp = x + ((1.0 / y) / ((z * 3.0) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.6e-211) or not (y <= 2.1e-62):
		tmp = x - ((y - (t / y)) / (z * 3.0))
	else:
		tmp = x + ((1.0 / y) / ((z * 3.0) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.6e-211) || !(y <= 2.1e-62))
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(1.0 / y) / Float64(Float64(z * 3.0) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.6e-211) || ~((y <= 2.1e-62)))
		tmp = x - ((y - (t / y)) / (z * 3.0));
	else
		tmp = x + ((1.0 / y) / ((z * 3.0) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.6e-211], N[Not[LessEqual[y, 2.1e-62]], $MachinePrecision]], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / y), $MachinePrecision] / N[(N[(z * 3.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5999999999999996e-211 or 2.0999999999999999e-62 < y

   1. Initial program 95.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 95.6%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 95.6%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 95.6%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 95.6%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 95.6%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 95.6%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 95.6%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 95.6%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 95.5%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 95.5%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 97.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 98.7%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 98.7%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 98.7%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 98.7%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg 98.7%

         \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)} \]

      2. distribute-rgt-in 97.0%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right)} \]

      3. div-inv 96.9%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      4. *-commutative 96.9%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      5. associate-*l* 96.9%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right) \cdot -0.3333333333333333} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      6. div-inv 97.0%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z}} \cdot -0.3333333333333333 + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      7. *-commutative 97.0%

         \[\leadsto x + \left(\color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      8. metadata-eval 97.0%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{3}} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      9. metadata-eval 97.0%

         \[\leadsto x + \left(\frac{\color{blue}{-1}}{3} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      10. times-frac 97.1%

          \[\leadsto x + \left(\color{blue}{\frac{\left(-1\right) \cdot y}{3 \cdot z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      11. metadata-eval 97.1%

          \[\leadsto x + \left(\frac{\color{blue}{-1} \cdot y}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      12. neg-mul-1 97.1%

          \[\leadsto x + \left(\frac{\color{blue}{-y}}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      13. *-commutative 97.1%

          \[\leadsto x + \left(\frac{-y}{\color{blue}{z \cdot 3}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      14. distribute-neg-frac 97.1%

          \[\leadsto x + \left(\color{blue}{\left(-\frac{y}{z \cdot 3}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      15. distribute-neg-frac 97.1%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{y}} \cdot \frac{-0.3333333333333333}{z}\right) \]

      16. clear-num 97.1%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}}\right) \]

      17. div-inv 97.1%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}\right) \]

      18. metadata-eval 97.1%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      19. metadata-eval 97.1%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{\left(-3\right)}}\right) \]

      20. distribute-rgt-neg-in 97.1%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{-z \cdot 3}}\right) \]

      21. times-frac 95.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\left(-t\right) \cdot 1}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      22. *-commutative 95.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{\left(-t\right) \cdot 1}{\color{blue}{\left(-z \cdot 3\right) \cdot y}}\right) \]

      23. times-frac 94.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{-z \cdot 3} \cdot \frac{1}{y}}\right) \]

   5. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   if -5.5999999999999996e-211 < y < 2.0999999999999999e-62

   1. Initial program 87.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 87.0%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 87.0%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 87.0%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 87.0%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 87.0%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 87.0%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 87.0%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 87.0%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 87.0%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 87.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 85.4%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 85.4%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 85.4%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 85.3%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 85.3%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in y around 0 85.5%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 85.5%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. associate-*l/ 85.5%

         \[\leadsto x + \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      3. times-frac 84.1%

         \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   6. Simplified 84.1%

      \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 84.1%

         \[\leadsto x + \color{blue}{\frac{\frac{t}{y} \cdot 0.3333333333333333}{z}} \]

      2. associate-/l* 84.1%

         \[\leadsto x + \color{blue}{\frac{\frac{t}{y}}{\frac{z}{0.3333333333333333}}} \]

      3. div-inv 84.1%

         \[\leadsto x + \frac{\color{blue}{t \cdot \frac{1}{y}}}{\frac{z}{0.3333333333333333}} \]

      4. *-commutative 84.1%

         \[\leadsto x + \frac{\color{blue}{\frac{1}{y} \cdot t}}{\frac{z}{0.3333333333333333}} \]

      5. div-inv 84.2%

         \[\leadsto x + \frac{\frac{1}{y} \cdot t}{\color{blue}{z \cdot \frac{1}{0.3333333333333333}}} \]

      6. metadata-eval 84.2%

         \[\leadsto x + \frac{\frac{1}{y} \cdot t}{z \cdot \color{blue}{3}} \]

      7. associate-/l* 96.2%

         \[\leadsto x + \color{blue}{\frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}} \]

   8. Applied egg-rr 96.2%

      \[\leadsto x + \color{blue}{\frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-211} \lor \neg \left(y \leq 2.1 \cdot 10^{-62}\right):\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}\\ \end{array} \]

Alternative 15: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-167}:\\ \;\;\;\;x + \frac{t_1 \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + t_1 \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- y (/ t y))))
   (if (<= y -5e-167)
     (+ x (/ (* t_1 -0.3333333333333333) z))
     (if (<= y 3.8e-64)
       (+ x (/ (* t (/ 0.3333333333333333 z)) y))
       (+ x (* t_1 (/ -0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -5e-167) {
		tmp = x + ((t_1 * -0.3333333333333333) / z);
	} else if (y <= 3.8e-64) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (t / y)
    if (y <= (-5d-167)) then
        tmp = x + ((t_1 * (-0.3333333333333333d0)) / z)
    else if (y <= 3.8d-64) then
        tmp = x + ((t * (0.3333333333333333d0 / z)) / y)
    else
        tmp = x + (t_1 * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -5e-167) {
		tmp = x + ((t_1 * -0.3333333333333333) / z);
	} else if (y <= 3.8e-64) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y - (t / y)
	tmp = 0
	if y <= -5e-167:
		tmp = x + ((t_1 * -0.3333333333333333) / z)
	elif y <= 3.8e-64:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	else:
		tmp = x + (t_1 * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y - Float64(t / y))
	tmp = 0.0
	if (y <= -5e-167)
		tmp = Float64(x + Float64(Float64(t_1 * -0.3333333333333333) / z));
	elseif (y <= 3.8e-64)
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	else
		tmp = Float64(x + Float64(t_1 * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y - (t / y);
	tmp = 0.0;
	if (y <= -5e-167)
		tmp = x + ((t_1 * -0.3333333333333333) / z);
	elseif (y <= 3.8e-64)
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	else
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-167], N[(x + N[(N[(t$95$1 * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-64], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000002e-167

   1. Initial program 96.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 96.6%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 96.6%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 96.6%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 96.6%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 96.6%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 96.6%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 96.6%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 96.6%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 96.6%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 96.6%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 95.5%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 97.6%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 97.6%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 97.6%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 97.6%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. associate-*l/ 97.7%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot \left(y - \frac{t}{y}\right)}{z}} \]

   5. Applied egg-rr 97.7%

      \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot \left(y - \frac{t}{y}\right)}{z}} \]

   if -5.0000000000000002e-167 < y < 3.8000000000000002e-64

   1. Initial program 85.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 85.2%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 85.2%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 85.2%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 85.2%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 85.2%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 85.2%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 85.2%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 85.2%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 85.2%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 85.2%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 86.9%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 86.9%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 86.9%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 86.8%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 86.8%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in y around 0 83.9%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 83.9%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. associate-*l/ 83.8%

         \[\leadsto x + \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      3. times-frac 85.7%

         \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   6. Simplified 85.7%

      \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]
   7. Step-by-step derivation

      1. associate-*l/ 96.5%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   8. Applied egg-rr 96.5%

      \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   if 3.8000000000000002e-64 < y

   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. associate-+l- 97.3%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 97.3%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 97.3%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 97.3%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 97.3%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 97.3%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 97.3%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 97.3%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 97.2%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 97.2%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 98.5%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 99.8%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 99.8%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 99.8%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 99.8%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-167}:\\ \;\;\;\;x + \frac{\left(y - \frac{t}{y}\right) \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 16: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-202}:\\ \;\;\;\;x + \frac{t_1 \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t_1 \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- y (/ t y))))
   (if (<= y -2.5e-202)
     (+ x (/ (* t_1 -0.3333333333333333) z))
     (if (<= y 2.95e-64)
       (+ x (/ (/ 1.0 y) (/ (* z 3.0) t)))
       (+ x (* t_1 (/ -0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -2.5e-202) {
		tmp = x + ((t_1 * -0.3333333333333333) / z);
	} else if (y <= 2.95e-64) {
		tmp = x + ((1.0 / y) / ((z * 3.0) / t));
	} else {
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (t / y)
    if (y <= (-2.5d-202)) then
        tmp = x + ((t_1 * (-0.3333333333333333d0)) / z)
    else if (y <= 2.95d-64) then
        tmp = x + ((1.0d0 / y) / ((z * 3.0d0) / t))
    else
        tmp = x + (t_1 * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -2.5e-202) {
		tmp = x + ((t_1 * -0.3333333333333333) / z);
	} else if (y <= 2.95e-64) {
		tmp = x + ((1.0 / y) / ((z * 3.0) / t));
	} else {
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y - (t / y)
	tmp = 0
	if y <= -2.5e-202:
		tmp = x + ((t_1 * -0.3333333333333333) / z)
	elif y <= 2.95e-64:
		tmp = x + ((1.0 / y) / ((z * 3.0) / t))
	else:
		tmp = x + (t_1 * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y - Float64(t / y))
	tmp = 0.0
	if (y <= -2.5e-202)
		tmp = Float64(x + Float64(Float64(t_1 * -0.3333333333333333) / z));
	elseif (y <= 2.95e-64)
		tmp = Float64(x + Float64(Float64(1.0 / y) / Float64(Float64(z * 3.0) / t)));
	else
		tmp = Float64(x + Float64(t_1 * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y - (t / y);
	tmp = 0.0;
	if (y <= -2.5e-202)
		tmp = x + ((t_1 * -0.3333333333333333) / z);
	elseif (y <= 2.95e-64)
		tmp = x + ((1.0 / y) / ((z * 3.0) / t));
	else
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-202], N[(x + N[(N[(t$95$1 * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e-64], N[(x + N[(N[(1.0 / y), $MachinePrecision] / N[(N[(z * 3.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999986e-202

   1. Initial program 94.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 94.9%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 94.9%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 94.9%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 94.9%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 94.9%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 94.9%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 94.9%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 94.9%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 94.9%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 94.9%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 95.7%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 97.8%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 97.8%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 97.8%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 97.8%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 97.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. associate-*l/ 97.9%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot \left(y - \frac{t}{y}\right)}{z}} \]

   5. Applied egg-rr 97.9%

      \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot \left(y - \frac{t}{y}\right)}{z}} \]

   if -2.49999999999999986e-202 < y < 2.94999999999999997e-64

   1. Initial program 86.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 86.3%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 86.3%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 86.3%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 86.3%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 86.3%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 86.3%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 86.3%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 86.3%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 86.3%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 86.3%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 85.7%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 85.7%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 85.7%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 85.7%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 85.7%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in y around 0 84.8%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 84.8%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. associate-*l/ 84.8%

         \[\leadsto x + \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      3. times-frac 84.5%

         \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   6. Simplified 84.5%

      \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 84.5%

         \[\leadsto x + \color{blue}{\frac{\frac{t}{y} \cdot 0.3333333333333333}{z}} \]

      2. associate-/l* 84.5%

         \[\leadsto x + \color{blue}{\frac{\frac{t}{y}}{\frac{z}{0.3333333333333333}}} \]

      3. div-inv 84.5%

         \[\leadsto x + \frac{\color{blue}{t \cdot \frac{1}{y}}}{\frac{z}{0.3333333333333333}} \]

      4. *-commutative 84.5%

         \[\leadsto x + \frac{\color{blue}{\frac{1}{y} \cdot t}}{\frac{z}{0.3333333333333333}} \]

      5. div-inv 84.6%

         \[\leadsto x + \frac{\frac{1}{y} \cdot t}{\color{blue}{z \cdot \frac{1}{0.3333333333333333}}} \]

      6. metadata-eval 84.6%

         \[\leadsto x + \frac{\frac{1}{y} \cdot t}{z \cdot \color{blue}{3}} \]

      7. associate-/l* 96.2%

         \[\leadsto x + \color{blue}{\frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}} \]

   8. Applied egg-rr 96.2%

      \[\leadsto x + \color{blue}{\frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}} \]

   if 2.94999999999999997e-64 < y

   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. associate-+l- 97.3%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 97.3%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 97.3%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 97.3%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 97.3%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 97.3%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 97.3%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 97.3%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 97.2%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 97.2%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 98.5%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 99.8%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 99.8%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 99.8%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 99.8%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-202}:\\ \;\;\;\;x + \frac{\left(y - \frac{t}{y}\right) \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 17: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-156}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{-3} \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq 10^{-63}:\\ \;\;\;\;x + \frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3e-156)
   (+ x (* (/ (- (/ t y) y) -3.0) (/ -1.0 z)))
   (if (<= y 1e-63)
     (+ x (/ (/ 1.0 y) (/ (* z 3.0) t)))
     (- x (/ (- y (/ t y)) (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-156) {
		tmp = x + ((((t / y) - y) / -3.0) * (-1.0 / z));
	} else if (y <= 1e-63) {
		tmp = x + ((1.0 / y) / ((z * 3.0) / t));
	} else {
		tmp = x - ((y - (t / y)) / (z * 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) :: tmp
    if (y <= (-2.3d-156)) then
        tmp = x + ((((t / y) - y) / (-3.0d0)) * ((-1.0d0) / z))
    else if (y <= 1d-63) then
        tmp = x + ((1.0d0 / y) / ((z * 3.0d0) / t))
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-156) {
		tmp = x + ((((t / y) - y) / -3.0) * (-1.0 / z));
	} else if (y <= 1e-63) {
		tmp = x + ((1.0 / y) / ((z * 3.0) / t));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.3e-156:
		tmp = x + ((((t / y) - y) / -3.0) * (-1.0 / z))
	elif y <= 1e-63:
		tmp = x + ((1.0 / y) / ((z * 3.0) / t))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3e-156)
		tmp = Float64(x + Float64(Float64(Float64(Float64(t / y) - y) / -3.0) * Float64(-1.0 / z)));
	elseif (y <= 1e-63)
		tmp = Float64(x + Float64(Float64(1.0 / y) / Float64(Float64(z * 3.0) / t)));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.3e-156)
		tmp = x + ((((t / y) - y) / -3.0) * (-1.0 / z));
	elseif (y <= 1e-63)
		tmp = x + ((1.0 / y) / ((z * 3.0) / t));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.3e-156], N[(x + N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / -3.0), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-63], N[(x + N[(N[(1.0 / y), $MachinePrecision] / N[(N[(z * 3.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e-156

   1. Initial program 96.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. remove-double-neg 96.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      2. distribute-frac-neg 96.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) \]

      3. sub-neg 96.6%

         \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y}} \]

      4. sub-neg 96.6%

         \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} - \frac{-t}{\left(z \cdot 3\right) \cdot y} \]

      5. distribute-frac-neg 96.6%

         \[\leadsto \left(x + \color{blue}{\frac{-y}{z \cdot 3}}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y} \]

      6. associate-+r- 96.6%

         \[\leadsto \color{blue}{x + \left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      7. sub-neg 96.6%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      8. neg-mul-1 96.6%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      9. *-commutative 96.6%

         \[\leadsto x + \left(\frac{-1 \cdot y}{\color{blue}{3 \cdot z}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      10. times-frac 96.5%

          \[\leadsto x + \left(\color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      11. metadata-eval 96.5%

          \[\leadsto x + \left(\color{blue}{-0.3333333333333333} \cdot \frac{y}{z} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      12. distribute-frac-neg 96.5%

          \[\leadsto x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \left(-\color{blue}{\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right)\right) \]

      13. remove-double-neg 96.5%

          \[\leadsto x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right) \]

      14. associate-*l* 96.5%

          \[\leadsto x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}}\right) \]

      15. *-commutative 96.5%

          \[\leadsto x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}}\right) \]

      16. associate-/r* 93.1%

          \[\leadsto x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \color{blue}{\frac{\frac{t}{z}}{y \cdot 3}}\right) \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \frac{\frac{t}{z}}{y \cdot 3}\right)} \]
   4. Step-by-step derivation

      1. *-commutative 93.1%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z} \cdot -0.3333333333333333} + \frac{\frac{t}{z}}{y \cdot 3}\right) \]

      2. div-inv 93.0%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right)} \cdot -0.3333333333333333 + \frac{\frac{t}{z}}{y \cdot 3}\right) \]

      3. associate-*l* 93.1%

         \[\leadsto x + \left(\color{blue}{y \cdot \left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \frac{\frac{t}{z}}{y \cdot 3}\right) \]

      4. *-commutative 93.1%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \frac{\frac{t}{z}}{y \cdot 3}\right) \]

      5. div-inv 93.1%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{-0.3333333333333333}{z}} + \frac{\frac{t}{z}}{y \cdot 3}\right) \]

      6. div-inv 93.2%

         \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \frac{\color{blue}{t \cdot \frac{1}{z}}}{y \cdot 3}\right) \]

      7. times-frac 95.4%

         \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \color{blue}{\frac{t}{y} \cdot \frac{\frac{1}{z}}{3}}\right) \]

      8. associate-/r* 95.3%

         \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \frac{t}{y} \cdot \color{blue}{\frac{1}{z \cdot 3}}\right) \]

      9. frac-2neg 95.3%

         \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \color{blue}{\frac{-t}{-y}} \cdot \frac{1}{z \cdot 3}\right) \]

      10. times-frac 96.5%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \color{blue}{\frac{\left(-t\right) \cdot 1}{\left(-y\right) \cdot \left(z \cdot 3\right)}}\right) \]

      11. distribute-lft-neg-in 96.5%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \frac{\left(-t\right) \cdot 1}{\color{blue}{-y \cdot \left(z \cdot 3\right)}}\right) \]

      12. distribute-rgt-neg-in 96.5%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \frac{\left(-t\right) \cdot 1}{\color{blue}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      13. times-frac 95.3%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \color{blue}{\frac{-t}{y} \cdot \frac{1}{-z \cdot 3}}\right) \]

      14. distribute-neg-frac 95.3%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \color{blue}{\left(-\frac{t}{y}\right)} \cdot \frac{1}{-z \cdot 3}\right) \]

      15. distribute-rgt-neg-in 95.3%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{1}{\color{blue}{z \cdot \left(-3\right)}}\right) \]

      16. metadata-eval 95.3%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      17. metadata-eval 95.3%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{-0.3333333333333333}}}\right) \]

      18. div-inv 95.3%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{-0.3333333333333333}}}\right) \]

      19. clear-num 95.3%

          \[\leadsto x + \left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \color{blue}{\frac{-0.3333333333333333}{z}}\right) \]

      20. distribute-rgt-in 97.6%

          \[\leadsto x + \color{blue}{\frac{-0.3333333333333333}{z} \cdot \left(y + \left(-\frac{t}{y}\right)\right)} \]

      21. sub-neg 97.6%

          \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y - \frac{t}{y}\right)} \]

   5. Applied egg-rr 97.7%

      \[\leadsto x + \color{blue}{\frac{y - \frac{t}{y}}{-3} \cdot \frac{1}{z}} \]

   if -2.3e-156 < y < 1.00000000000000007e-63

   1. Initial program 85.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 85.7%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 85.7%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 85.7%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 85.7%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 85.7%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 85.7%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 85.7%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 85.7%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 85.7%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 85.7%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 87.3%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 87.3%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 87.3%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 87.3%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 87.3%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in y around 0 84.4%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 84.4%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. associate-*l/ 84.3%

         \[\leadsto x + \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      3. times-frac 86.2%

         \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   6. Simplified 86.2%

      \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 86.2%

         \[\leadsto x + \color{blue}{\frac{\frac{t}{y} \cdot 0.3333333333333333}{z}} \]

      2. associate-/l* 86.2%

         \[\leadsto x + \color{blue}{\frac{\frac{t}{y}}{\frac{z}{0.3333333333333333}}} \]

      3. div-inv 86.1%

         \[\leadsto x + \frac{\color{blue}{t \cdot \frac{1}{y}}}{\frac{z}{0.3333333333333333}} \]

      4. *-commutative 86.1%

         \[\leadsto x + \frac{\color{blue}{\frac{1}{y} \cdot t}}{\frac{z}{0.3333333333333333}} \]

      5. div-inv 86.2%

         \[\leadsto x + \frac{\frac{1}{y} \cdot t}{\color{blue}{z \cdot \frac{1}{0.3333333333333333}}} \]

      6. metadata-eval 86.2%

         \[\leadsto x + \frac{\frac{1}{y} \cdot t}{z \cdot \color{blue}{3}} \]

      7. associate-/l* 96.6%

         \[\leadsto x + \color{blue}{\frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}} \]

   8. Applied egg-rr 96.6%

      \[\leadsto x + \color{blue}{\frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}} \]

   if 1.00000000000000007e-63 < y

   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. associate-+l- 97.3%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 97.3%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 97.3%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 97.3%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 97.3%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 97.3%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 97.3%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 97.3%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 97.2%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 97.2%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 98.5%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 99.8%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 99.8%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 99.8%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 99.8%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)} \]

      2. distribute-rgt-in 98.5%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right)} \]

      3. div-inv 98.4%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      4. *-commutative 98.4%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      5. associate-*l* 98.4%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right) \cdot -0.3333333333333333} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      6. div-inv 98.4%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z}} \cdot -0.3333333333333333 + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      7. *-commutative 98.4%

         \[\leadsto x + \left(\color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      8. metadata-eval 98.4%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{3}} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      9. metadata-eval 98.4%

         \[\leadsto x + \left(\frac{\color{blue}{-1}}{3} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      10. times-frac 98.6%

          \[\leadsto x + \left(\color{blue}{\frac{\left(-1\right) \cdot y}{3 \cdot z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      11. metadata-eval 98.6%

          \[\leadsto x + \left(\frac{\color{blue}{-1} \cdot y}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      12. neg-mul-1 98.6%

          \[\leadsto x + \left(\frac{\color{blue}{-y}}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      13. *-commutative 98.6%

          \[\leadsto x + \left(\frac{-y}{\color{blue}{z \cdot 3}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      14. distribute-neg-frac 98.6%

          \[\leadsto x + \left(\color{blue}{\left(-\frac{y}{z \cdot 3}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      15. distribute-neg-frac 98.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{y}} \cdot \frac{-0.3333333333333333}{z}\right) \]

      16. clear-num 98.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}}\right) \]

      17. div-inv 98.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}\right) \]

      18. metadata-eval 98.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      19. metadata-eval 98.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{\left(-3\right)}}\right) \]

      20. distribute-rgt-neg-in 98.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{-z \cdot 3}}\right) \]

      21. times-frac 97.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\left(-t\right) \cdot 1}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      22. *-commutative 97.3%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{\left(-t\right) \cdot 1}{\color{blue}{\left(-z \cdot 3\right) \cdot y}}\right) \]

      23. times-frac 94.9%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{-z \cdot 3} \cdot \frac{1}{y}}\right) \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-156}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{-3} \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq 10^{-63}:\\ \;\;\;\;x + \frac{\frac{1}{y}}{\frac{z \cdot 3}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]

Alternative 18: 47.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -5e+34) x (if (<= (* z 3.0) 2e+65) (/ y (* z -3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -5e+34) {
		tmp = x;
	} else if ((z * 3.0) <= 2e+65) {
		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) <= (-5d+34)) then
        tmp = x
    else if ((z * 3.0d0) <= 2d+65) 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) <= -5e+34) {
		tmp = x;
	} else if ((z * 3.0) <= 2e+65) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -5e+34:
		tmp = x
	elif (z * 3.0) <= 2e+65:
		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) <= -5e+34)
		tmp = x;
	elseif (Float64(z * 3.0) <= 2e+65)
		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) <= -5e+34)
		tmp = x;
	elseif ((z * 3.0) <= 2e+65)
		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], -5e+34], x, If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+65], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -4.9999999999999998e34 or 2e65 < (*.f64 z 3)

   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. associate-+l- 99.8%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 99.8%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 99.8%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 99.8%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 99.8%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 99.8%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 88.2%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 88.2%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 88.2%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 88.2%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 88.2%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 59.0%

      \[\leadsto \color{blue}{x} \]

   if -4.9999999999999998e34 < (*.f64 z 3) < 2e65

   1. Initial program 87.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 87.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 87.5%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 87.5%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 87.5%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 87.5%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 87.5%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 87.5%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 87.5%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 87.5%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 87.5%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 97.6%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 99.7%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 99.7%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 99.7%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg 99.7%

         \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)} \]

      2. distribute-rgt-in 97.6%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right)} \]

      3. div-inv 97.6%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      4. *-commutative 97.6%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      5. associate-*l* 97.6%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right) \cdot -0.3333333333333333} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      6. div-inv 97.6%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z}} \cdot -0.3333333333333333 + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      7. *-commutative 97.6%

         \[\leadsto x + \left(\color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      8. metadata-eval 97.6%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{3}} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      9. metadata-eval 97.6%

         \[\leadsto x + \left(\frac{\color{blue}{-1}}{3} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      10. times-frac 97.6%

          \[\leadsto x + \left(\color{blue}{\frac{\left(-1\right) \cdot y}{3 \cdot z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      11. metadata-eval 97.6%

          \[\leadsto x + \left(\frac{\color{blue}{-1} \cdot y}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      12. neg-mul-1 97.6%

          \[\leadsto x + \left(\frac{\color{blue}{-y}}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      13. *-commutative 97.6%

          \[\leadsto x + \left(\frac{-y}{\color{blue}{z \cdot 3}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      14. distribute-neg-frac 97.6%

          \[\leadsto x + \left(\color{blue}{\left(-\frac{y}{z \cdot 3}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      15. distribute-neg-frac 97.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{y}} \cdot \frac{-0.3333333333333333}{z}\right) \]

      16. clear-num 97.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}}\right) \]

      17. div-inv 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}\right) \]

      18. metadata-eval 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      19. metadata-eval 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{\left(-3\right)}}\right) \]

      20. distribute-rgt-neg-in 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{-z \cdot 3}}\right) \]

      21. times-frac 87.5%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\left(-t\right) \cdot 1}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      22. *-commutative 87.5%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{\left(-t\right) \cdot 1}{\color{blue}{\left(-z \cdot 3\right) \cdot y}}\right) \]

      23. times-frac 93.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{-z \cdot 3} \cdot \frac{1}{y}}\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in x around 0 93.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   7. Taylor expanded in y around inf 50.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 50.7%

         \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 50.7%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

      3. associate-*r/ 50.7%

         \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   9. Simplified 50.7%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
   10. Step-by-step derivation

       1. associate-*r/ 50.7%

          \[\leadsto \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

       2. associate-/l* 50.7%

          \[\leadsto \color{blue}{\frac{y}{\frac{z}{-0.3333333333333333}}} \]

       3. div-inv 50.7%

          \[\leadsto \frac{y}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}} \]

       4. metadata-eval 50.7%

          \[\leadsto \frac{y}{z \cdot \color{blue}{-3}} \]

   11. Applied egg-rr 50.7%

       \[\leadsto \color{blue}{\frac{y}{z \cdot -3}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 35000000:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e-15)
   (- x (/ (/ y 3.0) z))
   (if (<= y 35000000.0)
     (+ x (/ (* t (/ 0.3333333333333333 z)) y))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-15) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 35000000.0) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x - (y / (z * 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) :: tmp
    if (y <= (-1.2d-15)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 35000000.0d0) then
        tmp = x + ((t * (0.3333333333333333d0 / z)) / y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-15) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 35000000.0) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e-15:
		tmp = x - ((y / 3.0) / z)
	elif y <= 35000000.0:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e-15)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 35000000.0)
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e-15)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 35000000.0)
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e-15], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 35000000.0], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999997e-15

   1. Initial program 96.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 89.6%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 89.6%

         \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 89.6%

         \[\leadsto x - \frac{\color{blue}{y \cdot 0.3333333333333333}}{z} \]

      3. metadata-eval 89.6%

         \[\leadsto x - \frac{y \cdot \color{blue}{\frac{1}{3}}}{z} \]

      4. div-inv 89.7%

         \[\leadsto x - \frac{\color{blue}{\frac{y}{3}}}{z} \]

   4. Applied egg-rr 89.7%

      \[\leadsto x - \color{blue}{\frac{\frac{y}{3}}{z}} \]

   if -1.19999999999999997e-15 < y < 3.5e7

   1. Initial program 89.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 89.0%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 89.0%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 89.0%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 89.0%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 89.0%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 89.0%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 89.0%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 89.0%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 89.0%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 89.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 90.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 90.0%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 90.0%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 90.0%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 90.0%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in y around 0 85.5%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 85.5%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. associate-*l/ 85.5%

         \[\leadsto x + \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      3. times-frac 86.7%

         \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   6. Simplified 86.7%

      \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]
   7. Step-by-step derivation

      1. associate-*l/ 94.3%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   8. Applied egg-rr 94.3%

      \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   if 3.5e7 < y

   1. Initial program 98.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 91.7%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 91.7%

         \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]

      2. metadata-eval 91.7%

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      3. div-inv 91.7%

         \[\leadsto x - \color{blue}{\frac{\frac{y}{z}}{3}} \]

      4. associate-/r* 91.9%

         \[\leadsto x - \color{blue}{\frac{y}{z \cdot 3}} \]

   4. Applied egg-rr 91.9%

      \[\leadsto x - \color{blue}{\frac{y}{z \cdot 3}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 35000000:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 20: 47.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.05 \cdot 10^{+64}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.4e+34) x (if (<= z 5.05e+64) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e+34) {
		tmp = x;
	} else if (z <= 5.05e+64) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.4d+34)) then
        tmp = x
    else if (z <= 5.05d+64) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e+34) {
		tmp = x;
	} else if (z <= 5.05e+64) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.4e+34:
		tmp = x
	elif z <= 5.05e+64:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.4e+34)
		tmp = x;
	elseif (z <= 5.05e+64)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.4e+34)
		tmp = x;
	elseif (z <= 5.05e+64)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.4e+34], x, If[LessEqual[z, 5.05e+64], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000004e34 or 5.0499999999999998e64 < z

   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. associate-+l- 99.8%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 99.8%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 99.8%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 99.8%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 99.8%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 99.8%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 88.2%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 88.2%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 88.2%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 88.2%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 88.2%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 59.0%

      \[\leadsto \color{blue}{x} \]

   if -1.40000000000000004e34 < z < 5.0499999999999998e64

   1. Initial program 87.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 87.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 87.5%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 87.5%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 87.5%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 87.5%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 87.5%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 87.5%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 87.5%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 87.5%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 87.5%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 97.6%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 99.7%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 99.7%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 99.7%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg 99.7%

         \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)} \]

      2. distribute-rgt-in 97.6%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right)} \]

      3. div-inv 97.6%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      4. *-commutative 97.6%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      5. associate-*l* 97.6%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right) \cdot -0.3333333333333333} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      6. div-inv 97.6%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z}} \cdot -0.3333333333333333 + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      7. *-commutative 97.6%

         \[\leadsto x + \left(\color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      8. metadata-eval 97.6%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{3}} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      9. metadata-eval 97.6%

         \[\leadsto x + \left(\frac{\color{blue}{-1}}{3} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      10. times-frac 97.6%

          \[\leadsto x + \left(\color{blue}{\frac{\left(-1\right) \cdot y}{3 \cdot z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      11. metadata-eval 97.6%

          \[\leadsto x + \left(\frac{\color{blue}{-1} \cdot y}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      12. neg-mul-1 97.6%

          \[\leadsto x + \left(\frac{\color{blue}{-y}}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      13. *-commutative 97.6%

          \[\leadsto x + \left(\frac{-y}{\color{blue}{z \cdot 3}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      14. distribute-neg-frac 97.6%

          \[\leadsto x + \left(\color{blue}{\left(-\frac{y}{z \cdot 3}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      15. distribute-neg-frac 97.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{y}} \cdot \frac{-0.3333333333333333}{z}\right) \]

      16. clear-num 97.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}}\right) \]

      17. div-inv 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}\right) \]

      18. metadata-eval 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      19. metadata-eval 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{\left(-3\right)}}\right) \]

      20. distribute-rgt-neg-in 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{-z \cdot 3}}\right) \]

      21. times-frac 87.5%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\left(-t\right) \cdot 1}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      22. *-commutative 87.5%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{\left(-t\right) \cdot 1}{\color{blue}{\left(-z \cdot 3\right) \cdot y}}\right) \]

      23. times-frac 93.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{-z \cdot 3} \cdot \frac{1}{y}}\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around inf 50.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.05 \cdot 10^{+64}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 47.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.01 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.34 \cdot 10^{+69}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.01e+34)
   x
   (if (<= z 1.34e+69) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.01e+34) {
		tmp = x;
	} else if (z <= 1.34e+69) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.01d+34)) then
        tmp = x
    else if (z <= 1.34d+69) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.01e+34) {
		tmp = x;
	} else if (z <= 1.34e+69) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.01e+34:
		tmp = x
	elif z <= 1.34e+69:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.01e+34)
		tmp = x;
	elseif (z <= 1.34e+69)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.01e+34)
		tmp = x;
	elseif (z <= 1.34e+69)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.01e+34], x, If[LessEqual[z, 1.34e+69], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.01e34 or 1.3399999999999999e69 < z

   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. associate-+l- 99.8%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 99.8%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 99.8%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 99.8%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 99.8%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 99.8%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 88.2%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 88.2%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 88.2%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 88.2%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 88.2%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 59.0%

      \[\leadsto \color{blue}{x} \]

   if -1.01e34 < z < 1.3399999999999999e69

   1. Initial program 87.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-+l- 87.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      2. sub-neg 87.5%

         \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      3. sub-neg 87.5%

         \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 87.5%

         \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. distribute-neg-in 87.5%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

      6. distribute-frac-neg 87.5%

         \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

      7. sub-neg 87.5%

         \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      8. neg-mul-1 87.5%

         \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. associate-*l/ 87.5%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. neg-mul-1 87.5%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      11. times-frac 97.6%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      12. distribute-lft-out-- 99.7%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      13. *-commutative 99.7%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. associate-/r* 99.7%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      15. metadata-eval 99.7%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg 99.7%

         \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)} \]

      2. distribute-rgt-in 97.6%

         \[\leadsto x + \color{blue}{\left(y \cdot \frac{-0.3333333333333333}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right)} \]

      3. div-inv 97.6%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{1}{z}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      4. *-commutative 97.6%

         \[\leadsto x + \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot -0.3333333333333333\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      5. associate-*l* 97.6%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot \frac{1}{z}\right) \cdot -0.3333333333333333} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      6. div-inv 97.6%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z}} \cdot -0.3333333333333333 + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      7. *-commutative 97.6%

         \[\leadsto x + \left(\color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      8. metadata-eval 97.6%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{3}} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      9. metadata-eval 97.6%

         \[\leadsto x + \left(\frac{\color{blue}{-1}}{3} \cdot \frac{y}{z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      10. times-frac 97.6%

          \[\leadsto x + \left(\color{blue}{\frac{\left(-1\right) \cdot y}{3 \cdot z}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      11. metadata-eval 97.6%

          \[\leadsto x + \left(\frac{\color{blue}{-1} \cdot y}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      12. neg-mul-1 97.6%

          \[\leadsto x + \left(\frac{\color{blue}{-y}}{3 \cdot z} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      13. *-commutative 97.6%

          \[\leadsto x + \left(\frac{-y}{\color{blue}{z \cdot 3}} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      14. distribute-neg-frac 97.6%

          \[\leadsto x + \left(\color{blue}{\left(-\frac{y}{z \cdot 3}\right)} + \left(-\frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\right) \]

      15. distribute-neg-frac 97.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{y}} \cdot \frac{-0.3333333333333333}{z}\right) \]

      16. clear-num 97.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}}\right) \]

      17. div-inv 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}\right) \]

      18. metadata-eval 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{-3}}\right) \]

      19. metadata-eval 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{z \cdot \color{blue}{\left(-3\right)}}\right) \]

      20. distribute-rgt-neg-in 97.7%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{-t}{y} \cdot \frac{1}{\color{blue}{-z \cdot 3}}\right) \]

      21. times-frac 87.5%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\left(-t\right) \cdot 1}{y \cdot \left(-z \cdot 3\right)}}\right) \]

      22. *-commutative 87.5%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{\left(-t\right) \cdot 1}{\color{blue}{\left(-z \cdot 3\right) \cdot y}}\right) \]

      23. times-frac 93.6%

          \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-t}{-z \cdot 3} \cdot \frac{1}{y}}\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in x around 0 93.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   7. Taylor expanded in y around inf 50.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 50.7%

         \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 50.7%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

      3. associate-*r/ 50.7%

         \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   9. Simplified 50.7%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.01 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.34 \cdot 10^{+69}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 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 92.9%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. associate-+l- 92.9%

      \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   2. sub-neg 92.9%

      \[\leadsto \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

   3. sub-neg 92.9%

      \[\leadsto x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

   4. distribute-frac-neg 92.9%

      \[\leadsto x + \left(-\left(\frac{y}{z \cdot 3} + \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

   5. distribute-neg-in 92.9%

      \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]

   6. distribute-frac-neg 92.9%

      \[\leadsto x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\frac{-t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]

   7. sub-neg 92.9%

      \[\leadsto x + \color{blue}{\left(\frac{-y}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   8. neg-mul-1 92.9%

      \[\leadsto x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

   9. associate-*l/ 92.9%

      \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

   10. neg-mul-1 92.9%

       \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

   11. times-frac 93.5%

       \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

   12. distribute-lft-out-- 94.6%

       \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

   13. *-commutative 94.6%

       \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

   14. associate-/r* 94.6%

       \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

   15. metadata-eval 94.6%

       \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

3. Simplified 94.6%

   \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

4. Taylor expanded in x around inf 29.9%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 29.9%

   \[\leadsto x \]

Developer target: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))