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

Percentage Accurate: 95.9% → 97.6%

Time: 26.5s

Alternatives: 15

Speedup: 0.7×

• 27.4% 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: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 2 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 2e-43)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-43) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 2d-43) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-43) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 2e-43:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 2e-43)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 2e-43)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-43], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < 2.00000000000000015e-43

   1. Initial program 92.5%

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

      1. sub-neg 92.5%

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

      2. associate-+l+ 92.5%

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

      3. +-commutative 92.5%

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

      4. remove-double-neg 92.5%

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

      5. distribute-frac-neg 92.5%

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

      6. distribute-neg-in 92.5%

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

      7. remove-double-neg 92.5%

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

      8. sub-neg 92.5%

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

      9. neg-mul-1 92.5%

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

      10. times-frac 98.8%

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

      11. distribute-frac-neg 98.8%

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

      12. neg-mul-1 98.8%

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

      13. *-commutative 98.8%

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

      14. associate-/l* 98.8%

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

      15. *-commutative 98.8%

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

   3. Simplified 99.3%

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

      1. metadata-eval 99.3%

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

      2. associate-/r* 99.3%

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

      3. *-commutative 99.3%

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

      4. associate-*l/ 99.4%

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

      5. *-un-lft-identity 99.4%

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

   6. Applied egg-rr 99.4%

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

   if 2.00000000000000015e-43 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.8%

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

Alternative 2: 91.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e-27)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 3.3e-16) (+ x (/ (/ t (* z 3.0)) y)) (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-27) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 3.3e-16) {
		tmp = x + ((t / (z * 3.0)) / 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 <= (-1.8d-27)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 3.3d-16) then
        tmp = x + ((t / (z * 3.0d0)) / 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 <= -1.8e-27) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 3.3e-16) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e-27:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 3.3e-16:
		tmp = x + ((t / (z * 3.0)) / y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e-27)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 3.3e-16)
		tmp = Float64(x + Float64(Float64(t / Float64(z * 3.0)) / 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 <= -1.8e-27)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 3.3e-16)
		tmp = x + ((t / (z * 3.0)) / y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e-27], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-16], N[(x + N[(N[(t / N[(z * 3.0), $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 < -1.7999999999999999e-27

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 90.6%

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

   if -1.7999999999999999e-27 < y < 3.29999999999999988e-16

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-+l+ 90.1%

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

      3. +-commutative 90.1%

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

      4. remove-double-neg 90.1%

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

      5. distribute-frac-neg 90.1%

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

      6. distribute-neg-in 90.1%

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

      7. remove-double-neg 90.1%

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

      8. sub-neg 90.1%

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

      9. neg-mul-1 90.1%

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

      10. times-frac 94.7%

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

      11. distribute-frac-neg 94.7%

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

      12. neg-mul-1 94.7%

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

      13. *-commutative 94.7%

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

      14. associate-/l* 94.7%

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

      15. *-commutative 94.7%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. *-commutative 87.8%

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

      3. times-frac 91.8%

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

      4. *-commutative 91.8%

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

   7. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r/ 95.4%

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

   9. Applied egg-rr 95.4%

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

       1. *-commutative 95.4%

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

       2. metadata-eval 95.4%

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

       3. associate-/r* 95.4%

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

       4. *-commutative 95.4%

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

       5. un-div-inv 95.4%

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

   11. Applied egg-rr 95.4%

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

   if 3.29999999999999988e-16 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 96.9%

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

      1. metadata-eval 96.9%

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

      2. times-frac 97.0%

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

      3. *-un-lft-identity 97.0%

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

      4. *-commutative 97.0%

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

   5. Applied egg-rr 97.0%

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

Alternative 3: 91.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-27}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.95e-27)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 1.05e-18)
     (+ 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 <= -1.95e-27) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 1.05e-18) {
		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 <= (-1.95d-27)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 1.05d-18) 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 <= -1.95e-27) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 1.05e-18) {
		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 <= -1.95e-27:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 1.05e-18:
		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 <= -1.95e-27)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 1.05e-18)
		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 <= -1.95e-27)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 1.05e-18)
		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, -1.95e-27], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-18], 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 < -1.94999999999999986e-27

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 90.6%

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

   if -1.94999999999999986e-27 < y < 1.05e-18

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-+l+ 90.1%

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

      3. +-commutative 90.1%

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

      4. remove-double-neg 90.1%

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

      5. distribute-frac-neg 90.1%

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

      6. distribute-neg-in 90.1%

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

      7. remove-double-neg 90.1%

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

      8. sub-neg 90.1%

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

      9. neg-mul-1 90.1%

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

      10. times-frac 94.7%

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

      11. distribute-frac-neg 94.7%

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

      12. neg-mul-1 94.7%

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

      13. *-commutative 94.7%

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

      14. associate-/l* 94.7%

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

      15. *-commutative 94.7%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. *-commutative 87.8%

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

      3. times-frac 91.8%

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

      4. *-commutative 91.8%

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

   7. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r/ 95.4%

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

   9. Applied egg-rr 95.4%

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

   if 1.05e-18 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 96.9%

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

      1. metadata-eval 96.9%

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

      2. times-frac 97.0%

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

      3. *-un-lft-identity 97.0%

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

      4. *-commutative 97.0%

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

   5. Applied egg-rr 97.0%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-27}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-34}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.2e-34)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 1.45e-18)
     (+ x (* (/ t y) (/ 0.3333333333333333 z)))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.2e-34) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 1.45e-18) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} 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 <= (-9.2d-34)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 1.45d-18) then
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    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 <= -9.2e-34) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 1.45e-18) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.2e-34:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 1.45e-18:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.2e-34)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 1.45e-18)
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	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 <= -9.2e-34)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 1.45e-18)
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.2e-34], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-18], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.20000000000000045e-34

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 90.6%

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

   if -9.20000000000000045e-34 < y < 1.45e-18

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-+l+ 90.1%

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

      3. +-commutative 90.1%

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

      4. remove-double-neg 90.1%

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

      5. distribute-frac-neg 90.1%

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

      6. distribute-neg-in 90.1%

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

      7. remove-double-neg 90.1%

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

      8. sub-neg 90.1%

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

      9. neg-mul-1 90.1%

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

      10. times-frac 94.7%

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

      11. distribute-frac-neg 94.7%

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

      12. neg-mul-1 94.7%

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

      13. *-commutative 94.7%

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

      14. associate-/l* 94.7%

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

      15. *-commutative 94.7%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. *-commutative 87.8%

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

      3. times-frac 91.8%

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

      4. *-commutative 91.8%

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

   7. Simplified 91.8%

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

   if 1.45e-18 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 96.9%

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

      1. metadata-eval 96.9%

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

      2. times-frac 97.0%

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

      3. *-un-lft-identity 97.0%

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

      4. *-commutative 97.0%

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

   5. Applied egg-rr 97.0%

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

Alternative 5: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-27}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-17}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e-27)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 5.4e-17)
     (+ x (* 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 <= -2.4e-27) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 5.4e-17) {
		tmp = x + (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 <= (-2.4d-27)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 5.4d-17) then
        tmp = x + (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 <= -2.4e-27) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 5.4e-17) {
		tmp = x + (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 <= -2.4e-27:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 5.4e-17:
		tmp = x + (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 <= -2.4e-27)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 5.4e-17)
		tmp = Float64(x + 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 <= -2.4e-27)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 5.4e-17)
		tmp = x + (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, -2.4e-27], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-17], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000002e-27

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 90.6%

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

   if -2.40000000000000002e-27 < y < 5.4000000000000002e-17

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-+l+ 90.1%

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

      3. +-commutative 90.1%

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

      4. remove-double-neg 90.1%

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

      5. distribute-frac-neg 90.1%

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

      6. distribute-neg-in 90.1%

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

      7. remove-double-neg 90.1%

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

      8. sub-neg 90.1%

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

      9. neg-mul-1 90.1%

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

      10. times-frac 94.7%

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

      11. distribute-frac-neg 94.7%

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

      12. neg-mul-1 94.7%

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

      13. *-commutative 94.7%

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

      14. associate-/l* 94.7%

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

      15. *-commutative 94.7%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around inf 87.8%

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

   if 5.4000000000000002e-17 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 96.9%

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

      1. metadata-eval 96.9%

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

      2. times-frac 97.0%

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

      3. *-un-lft-identity 97.0%

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

      4. *-commutative 97.0%

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

   5. Applied egg-rr 97.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-27}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-17}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-132} \lor \neg \left(y \leq 7.5 \cdot 10^{-145}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.6e-132) (not (<= y 7.5e-145)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* 0.3333333333333333 (/ (/ t z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.6e-132) || !(y <= 7.5e-145)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = 0.3333333333333333 * ((t / 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 <= (-6.6d-132)) .or. (.not. (y <= 7.5d-145))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = 0.3333333333333333d0 * ((t / 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 <= -6.6e-132) || !(y <= 7.5e-145)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = 0.3333333333333333 * ((t / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.6e-132) or not (y <= 7.5e-145):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = 0.3333333333333333 * ((t / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.6e-132) || !(y <= 7.5e-145))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.6e-132) || ~((y <= 7.5e-145)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = 0.3333333333333333 * ((t / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.6e-132], N[Not[LessEqual[y, 7.5e-145]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5999999999999994e-132 or 7.4999999999999996e-145 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 83.1%

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

   if -6.5999999999999994e-132 < y < 7.4999999999999996e-145

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. associate-+l+ 86.8%

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

      3. +-commutative 86.8%

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

      4. remove-double-neg 86.8%

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

      5. distribute-frac-neg 86.8%

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

      6. distribute-neg-in 86.8%

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

      7. remove-double-neg 86.8%

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

      8. sub-neg 86.8%

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

      9. neg-mul-1 86.8%

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

      10. times-frac 92.9%

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

      11. distribute-frac-neg 92.9%

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

      12. neg-mul-1 92.9%

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

      13. *-commutative 92.9%

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

      14. associate-/l* 92.9%

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

      15. *-commutative 92.9%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around inf 86.8%

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

      1. associate-*r/ 86.8%

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

      2. *-commutative 86.8%

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

      3. times-frac 93.1%

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

      4. *-commutative 93.1%

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

   7. Simplified 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*r/ 97.5%

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

   9. Applied egg-rr 97.5%

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

       1. *-commutative 97.5%

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

       2. metadata-eval 97.5%

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

       3. associate-/r* 97.5%

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

       4. *-commutative 97.5%

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

       5. un-div-inv 97.6%

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

   11. Applied egg-rr 97.6%

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

   12. Taylor expanded in x around 0 69.2%

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

       1. *-commutative 69.2%

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

       2. associate-/r* 76.3%

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

   14. Simplified 76.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-132} \lor \neg \left(y \leq 7.5 \cdot 10^{-145}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-133} \lor \neg \left(y \leq 7.5 \cdot 10^{-145}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e-133) (not (<= y 7.5e-145)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ (/ t z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-133) || !(y <= 7.5e-145)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * ((t / z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.02d-133)) .or. (.not. (y <= 7.5d-145))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-133) || !(y <= 7.5e-145)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * ((t / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e-133) or not (y <= 7.5e-145):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * ((t / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e-133) || !(y <= 7.5e-145))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.02e-133) || ~((y <= 7.5e-145)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * ((t / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e-133], N[Not[LessEqual[y, 7.5e-145]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e-133 or 7.4999999999999996e-145 < y

   1. Initial program 98.2%

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

      1. sub-neg 98.2%

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

      2. associate-+l+ 98.2%

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

      3. +-commutative 98.2%

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

      4. remove-double-neg 98.2%

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

      5. distribute-frac-neg 98.2%

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

      6. distribute-neg-in 98.2%

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

      7. remove-double-neg 98.2%

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

      8. sub-neg 98.2%

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

      9. neg-mul-1 98.2%

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

      10. times-frac 98.8%

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

      11. distribute-frac-neg 98.8%

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

      12. neg-mul-1 98.8%

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

      13. *-commutative 98.8%

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

      14. associate-/l* 98.7%

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

      15. *-commutative 98.7%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 83.1%

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

      1. metadata-eval 83.1%

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

      2. distribute-lft-neg-in 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*l/ 83.1%

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

      5. associate-*r/ 83.1%

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

      6. distribute-rgt-neg-in 83.1%

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

      7. distribute-neg-frac 83.1%

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

      8. metadata-eval 83.1%

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

   7. Simplified 83.1%

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

   if -1.02e-133 < y < 7.4999999999999996e-145

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. associate-+l+ 86.8%

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

      3. +-commutative 86.8%

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

      4. remove-double-neg 86.8%

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

      5. distribute-frac-neg 86.8%

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

      6. distribute-neg-in 86.8%

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

      7. remove-double-neg 86.8%

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

      8. sub-neg 86.8%

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

      9. neg-mul-1 86.8%

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

      10. times-frac 92.9%

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

      11. distribute-frac-neg 92.9%

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

      12. neg-mul-1 92.9%

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

      13. *-commutative 92.9%

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

      14. associate-/l* 92.9%

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

      15. *-commutative 92.9%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around inf 86.8%

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

      1. associate-*r/ 86.8%

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

      2. *-commutative 86.8%

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

      3. times-frac 93.1%

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

      4. *-commutative 93.1%

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

   7. Simplified 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*r/ 97.5%

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

   9. Applied egg-rr 97.5%

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

       1. *-commutative 97.5%

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

       2. metadata-eval 97.5%

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

       3. associate-/r* 97.5%

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

       4. *-commutative 97.5%

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

       5. un-div-inv 97.6%

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

   11. Applied egg-rr 97.6%

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

   12. Taylor expanded in x around 0 69.2%

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

       1. *-commutative 69.2%

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

       2. associate-/r* 76.3%

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

   14. Simplified 76.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-133} \lor \neg \left(y \leq 7.5 \cdot 10^{-145}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-135}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-146}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e-135)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 4.8e-146)
     (* 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 <= -3.6e-135) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 4.8e-146) {
		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 <= (-3.6d-135)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 4.8d-146) 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 <= -3.6e-135) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 4.8e-146) {
		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 <= -3.6e-135:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 4.8e-146:
		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 <= -3.6e-135)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 4.8e-146)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / 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 <= -3.6e-135)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 4.8e-146)
		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, -3.6e-135], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-146], N[(0.3333333333333333 * N[(N[(t / z), $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 < -3.59999999999999978e-135

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0 83.1%

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

   if -3.59999999999999978e-135 < y < 4.8000000000000003e-146

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. associate-+l+ 86.8%

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

      3. +-commutative 86.8%

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

      4. remove-double-neg 86.8%

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

      5. distribute-frac-neg 86.8%

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

      6. distribute-neg-in 86.8%

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

      7. remove-double-neg 86.8%

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

      8. sub-neg 86.8%

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

      9. neg-mul-1 86.8%

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

      10. times-frac 92.9%

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

      11. distribute-frac-neg 92.9%

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

      12. neg-mul-1 92.9%

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

      13. *-commutative 92.9%

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

      14. associate-/l* 92.9%

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

      15. *-commutative 92.9%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around inf 86.8%

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

      1. associate-*r/ 86.8%

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

      2. *-commutative 86.8%

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

      3. times-frac 93.1%

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

      4. *-commutative 93.1%

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

   7. Simplified 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*r/ 97.5%

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

   9. Applied egg-rr 97.5%

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

       1. *-commutative 97.5%

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

       2. metadata-eval 97.5%

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

       3. associate-/r* 97.5%

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

       4. *-commutative 97.5%

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

       5. un-div-inv 97.6%

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

   11. Applied egg-rr 97.6%

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

   12. Taylor expanded in x around 0 69.2%

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

       1. *-commutative 69.2%

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

       2. associate-/r* 76.3%

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

   14. Simplified 76.3%

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

   if 4.8000000000000003e-146 < y

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0 83.1%

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

      1. metadata-eval 83.1%

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

      2. times-frac 83.2%

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

      3. *-un-lft-identity 83.2%

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

      4. *-commutative 83.2%

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

   5. Applied egg-rr 83.2%

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

Alternative 9: 62.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-18}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e-27)
   (* (/ y z) -0.3333333333333333)
   (if (<= y 1.15e-18) (* 0.3333333333333333 (/ (/ t z) y)) (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-27) {
		tmp = (y / z) * -0.3333333333333333;
	} else if (y <= 1.15e-18) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} 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) :: tmp
    if (y <= (-2.4d-27)) then
        tmp = (y / z) * (-0.3333333333333333d0)
    else if (y <= 1.15d-18) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    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 tmp;
	if (y <= -2.4e-27) {
		tmp = (y / z) * -0.3333333333333333;
	} else if (y <= 1.15e-18) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e-27:
		tmp = (y / z) * -0.3333333333333333
	elif y <= 1.15e-18:
		tmp = 0.3333333333333333 * ((t / z) / y)
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e-27)
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	elseif (y <= 1.15e-18)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e-27)
		tmp = (y / z) * -0.3333333333333333;
	elseif (y <= 1.15e-18)
		tmp = 0.3333333333333333 * ((t / z) / y);
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e-27], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], If[LessEqual[y, 1.15e-18], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000002e-27

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 90.6%

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

      1. metadata-eval 90.6%

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

      2. times-frac 90.6%

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

      3. *-un-lft-identity 90.6%

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

      4. *-commutative 90.6%

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

   5. Applied egg-rr 90.6%

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

      1. *-commutative 90.6%

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

      2. metadata-eval 90.6%

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

      3. distribute-lft-neg-in 90.6%

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

      4. distribute-neg-frac2 90.6%

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

      5. distribute-frac-neg 90.6%

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

      6. neg-mul-1 90.6%

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

      7. times-frac 90.6%

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

      8. metadata-eval 90.6%

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

      9. associate-/l* 90.6%

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

      10. *-commutative 90.6%

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

      11. associate-*r/ 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in x around 0 58.6%

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

   if -2.40000000000000002e-27 < y < 1.15e-18

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-+l+ 90.1%

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

      3. +-commutative 90.1%

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

      4. remove-double-neg 90.1%

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

      5. distribute-frac-neg 90.1%

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

      6. distribute-neg-in 90.1%

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

      7. remove-double-neg 90.1%

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

      8. sub-neg 90.1%

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

      9. neg-mul-1 90.1%

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

      10. times-frac 94.7%

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

      11. distribute-frac-neg 94.7%

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

      12. neg-mul-1 94.7%

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

      13. *-commutative 94.7%

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

      14. associate-/l* 94.7%

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

      15. *-commutative 94.7%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. *-commutative 87.8%

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

      3. times-frac 91.8%

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

      4. *-commutative 91.8%

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

   7. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r/ 95.4%

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

   9. Applied egg-rr 95.4%

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

       1. *-commutative 95.4%

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

       2. metadata-eval 95.4%

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

       3. associate-/r* 95.4%

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

       4. *-commutative 95.4%

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

       5. un-div-inv 95.4%

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

   11. Applied egg-rr 95.4%

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

   12. Taylor expanded in x around 0 60.9%

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

       1. *-commutative 60.9%

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

       2. associate-/r* 66.2%

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

   14. Simplified 66.2%

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

   if 1.15e-18 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 96.9%

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

      1. metadata-eval 96.9%

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

      2. times-frac 97.0%

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

      3. *-un-lft-identity 97.0%

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

      4. *-commutative 97.0%

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

   5. Applied egg-rr 97.0%

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

      1. *-commutative 97.0%

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

      2. metadata-eval 97.0%

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

      3. distribute-lft-neg-in 97.0%

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

      4. distribute-neg-frac2 97.0%

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

      5. distribute-frac-neg 97.0%

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

      6. neg-mul-1 97.0%

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

      7. times-frac 96.9%

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

      8. metadata-eval 96.9%

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

      9. associate-/l* 96.8%

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

      10. *-commutative 96.8%

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

      11. associate-*r/ 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in x around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*l/ 66.8%

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

      3. associate-*r/ 66.7%

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

      4. clear-num 66.7%

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

      5. un-div-inv 66.8%

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

      6. div-inv 67.0%

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

      7. metadata-eval 67.0%

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

   10. Applied egg-rr 67.0%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-18}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-15}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e-27)
   (* (/ y z) -0.3333333333333333)
   (if (<= y 1.6e-15) (* 0.3333333333333333 (/ t (* z y))) (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e-27) {
		tmp = (y / z) * -0.3333333333333333;
	} else if (y <= 1.6e-15) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} 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) :: tmp
    if (y <= (-2d-27)) then
        tmp = (y / z) * (-0.3333333333333333d0)
    else if (y <= 1.6d-15) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    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 tmp;
	if (y <= -2e-27) {
		tmp = (y / z) * -0.3333333333333333;
	} else if (y <= 1.6e-15) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e-27:
		tmp = (y / z) * -0.3333333333333333
	elif y <= 1.6e-15:
		tmp = 0.3333333333333333 * (t / (z * y))
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e-27)
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	elseif (y <= 1.6e-15)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2e-27)
		tmp = (y / z) * -0.3333333333333333;
	elseif (y <= 1.6e-15)
		tmp = 0.3333333333333333 * (t / (z * y));
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e-27], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], If[LessEqual[y, 1.6e-15], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0000000000000001e-27

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 90.6%

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

      1. metadata-eval 90.6%

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

      2. times-frac 90.6%

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

      3. *-un-lft-identity 90.6%

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

      4. *-commutative 90.6%

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

   5. Applied egg-rr 90.6%

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

      1. *-commutative 90.6%

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

      2. metadata-eval 90.6%

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

      3. distribute-lft-neg-in 90.6%

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

      4. distribute-neg-frac2 90.6%

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

      5. distribute-frac-neg 90.6%

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

      6. neg-mul-1 90.6%

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

      7. times-frac 90.6%

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

      8. metadata-eval 90.6%

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

      9. associate-/l* 90.6%

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

      10. *-commutative 90.6%

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

      11. associate-*r/ 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in x around 0 58.6%

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

   if -2.0000000000000001e-27 < y < 1.6e-15

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-+l+ 90.1%

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

      3. +-commutative 90.1%

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

      4. remove-double-neg 90.1%

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

      5. distribute-frac-neg 90.1%

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

      6. distribute-neg-in 90.1%

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

      7. remove-double-neg 90.1%

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

      8. sub-neg 90.1%

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

      9. neg-mul-1 90.1%

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

      10. times-frac 94.7%

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

      11. distribute-frac-neg 94.7%

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

      12. neg-mul-1 94.7%

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

      13. *-commutative 94.7%

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

      14. associate-/l* 94.7%

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

      15. *-commutative 94.7%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. *-commutative 87.8%

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

      3. times-frac 91.8%

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

      4. *-commutative 91.8%

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

   7. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r/ 95.4%

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

   9. Applied egg-rr 95.4%

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

       1. *-commutative 95.4%

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

       2. metadata-eval 95.4%

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

       3. associate-/r* 95.4%

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

       4. *-commutative 95.4%

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

       5. un-div-inv 95.4%

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

   11. Applied egg-rr 95.4%

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

   12. Taylor expanded in x around 0 60.9%

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

   if 1.6e-15 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 96.9%

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

      1. metadata-eval 96.9%

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

      2. times-frac 97.0%

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

      3. *-un-lft-identity 97.0%

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

      4. *-commutative 97.0%

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

   5. Applied egg-rr 97.0%

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

      1. *-commutative 97.0%

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

      2. metadata-eval 97.0%

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

      3. distribute-lft-neg-in 97.0%

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

      4. distribute-neg-frac2 97.0%

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

      5. distribute-frac-neg 97.0%

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

      6. neg-mul-1 97.0%

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

      7. times-frac 96.9%

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

      8. metadata-eval 96.9%

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

      9. associate-/l* 96.8%

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

      10. *-commutative 96.8%

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

      11. associate-*r/ 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in x around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*l/ 66.8%

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

      3. associate-*r/ 66.7%

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

      4. clear-num 66.7%

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

      5. un-div-inv 66.8%

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

      6. div-inv 67.0%

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

      7. metadata-eval 67.0%

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

   10. Applied egg-rr 67.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-15}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e-100) x (if (<= z 1.3e+24) (/ y (* z -3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-100) {
		tmp = x;
	} else if (z <= 1.3e+24) {
		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 <= (-4.8d-100)) then
        tmp = x
    else if (z <= 1.3d+24) 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 <= -4.8e-100) {
		tmp = x;
	} else if (z <= 1.3e+24) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e-100:
		tmp = x
	elif z <= 1.3e+24:
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e-100)
		tmp = x;
	elseif (z <= 1.3e+24)
		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 <= -4.8e-100)
		tmp = x;
	elseif (z <= 1.3e+24)
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e-100], x, If[LessEqual[z, 1.3e+24], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000005e-100 or 1.2999999999999999e24 < z

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. associate-+l+ 99.0%

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

      3. distribute-frac-neg 99.0%

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

      4. neg-mul-1 99.0%

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

      5. *-commutative 99.0%

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

      6. times-frac 99.0%

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

      7. fma-define 99.0%

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

      8. metadata-eval 99.0%

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

      9. associate-*l* 99.0%

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

      10. *-commutative 99.0%

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{z \cdot \left(y \cdot 3\right)}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 56.0%

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

   if -4.8000000000000005e-100 < z < 1.2999999999999999e24

   1. Initial program 90.2%

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

   3. Taylor expanded in t around 0 56.6%

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

      1. metadata-eval 56.6%

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

      2. times-frac 56.6%

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

      3. *-un-lft-identity 56.6%

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

      4. *-commutative 56.6%

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

   5. Applied egg-rr 56.6%

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

      1. *-commutative 56.6%

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

      2. metadata-eval 56.6%

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

      3. distribute-lft-neg-in 56.6%

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

      4. distribute-neg-frac2 56.6%

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

      5. distribute-frac-neg 56.6%

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

      6. neg-mul-1 56.6%

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

      7. times-frac 56.6%

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

      8. metadata-eval 56.6%

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

      9. associate-/l* 56.5%

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

      10. *-commutative 56.5%

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

      11. associate-*r/ 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in x around 0 49.3%

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

      1. *-commutative 49.3%

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

      2. associate-*l/ 49.3%

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

      3. associate-*r/ 49.3%

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

      4. clear-num 49.3%

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

      5. un-div-inv 49.3%

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

      6. div-inv 49.4%

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

      7. metadata-eval 49.4%

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

   10. Applied egg-rr 49.4%

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

Alternative 12: 46.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e-100) x (if (<= z 7e+22) (* (/ y z) -0.3333333333333333) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-100) {
		tmp = x;
	} else if (z <= 7e+22) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.8d-100)) then
        tmp = x
    else if (z <= 7d+22) then
        tmp = (y / z) * (-0.3333333333333333d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-100) {
		tmp = x;
	} else if (z <= 7e+22) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e-100:
		tmp = x
	elif z <= 7e+22:
		tmp = (y / z) * -0.3333333333333333
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e-100)
		tmp = x;
	elseif (z <= 7e+22)
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e-100)
		tmp = x;
	elseif (z <= 7e+22)
		tmp = (y / z) * -0.3333333333333333;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e-100], x, If[LessEqual[z, 7e+22], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000005e-100 or 7e22 < z

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. associate-+l+ 99.0%

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

      3. distribute-frac-neg 99.0%

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

      4. neg-mul-1 99.0%

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

      5. *-commutative 99.0%

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

      6. times-frac 99.0%

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

      7. fma-define 99.0%

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

      8. metadata-eval 99.0%

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

      9. associate-*l* 99.0%

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

      10. *-commutative 99.0%

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{z \cdot \left(y \cdot 3\right)}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 56.0%

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

   if -4.8000000000000005e-100 < z < 7e22

   1. Initial program 90.2%

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

   3. Taylor expanded in t around 0 56.6%

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

      1. metadata-eval 56.6%

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

      2. times-frac 56.6%

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

      3. *-un-lft-identity 56.6%

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

      4. *-commutative 56.6%

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

   5. Applied egg-rr 56.6%

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

      1. *-commutative 56.6%

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

      2. metadata-eval 56.6%

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

      3. distribute-lft-neg-in 56.6%

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

      4. distribute-neg-frac2 56.6%

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

      5. distribute-frac-neg 56.6%

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

      6. neg-mul-1 56.6%

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

      7. times-frac 56.6%

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

      8. metadata-eval 56.6%

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

      9. associate-/l* 56.5%

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

      10. *-commutative 56.5%

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

      11. associate-*r/ 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in x around 0 49.3%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 95.5% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. sub-neg 94.5%

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

   2. associate-+l+ 94.5%

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

   3. +-commutative 94.5%

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

   4. remove-double-neg 94.5%

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

   5. distribute-frac-neg 94.5%

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

   6. distribute-neg-in 94.5%

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

   7. remove-double-neg 94.5%

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

   8. sub-neg 94.5%

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

   9. neg-mul-1 94.5%

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

   10. times-frac 96.8%

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

   11. distribute-frac-neg 96.8%

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

   12. neg-mul-1 96.8%

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

   13. *-commutative 96.8%

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

   14. associate-/l* 96.8%

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

   15. *-commutative 96.8%

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

3. Simplified 97.2%

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

   1. metadata-eval 97.2%

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

   2. associate-/r* 97.2%

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

   3. *-commutative 97.2%

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

   4. associate-*l/ 97.2%

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

   5. *-un-lft-identity 97.2%

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

6. Applied egg-rr 97.2%

   \[\leadsto x + \color{blue}{\frac{\frac{t}{y} - y}{z \cdot 3}} \]
7. Add Preprocessing

Alternative 14: 95.5% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((t / y) - y) * (0.3333333333333333d0 / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. sub-neg 94.5%

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

   2. associate-+l+ 94.5%

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

   3. +-commutative 94.5%

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

   4. remove-double-neg 94.5%

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

   5. distribute-frac-neg 94.5%

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

   6. distribute-neg-in 94.5%

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

   7. remove-double-neg 94.5%

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

   8. sub-neg 94.5%

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

   9. neg-mul-1 94.5%

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

   10. times-frac 96.8%

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

   11. distribute-frac-neg 96.8%

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

   12. neg-mul-1 96.8%

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

   13. *-commutative 96.8%

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

   14. associate-/l* 96.8%

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

   15. *-commutative 96.8%

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

3. Simplified 97.2%

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

5. Final simplification 97.2%

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

Alternative 15: 30.8% 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 94.5%

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

   1. sub-neg 94.5%

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

   2. associate-+l+ 94.5%

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

   3. distribute-frac-neg 94.5%

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

   4. neg-mul-1 94.5%

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

   5. *-commutative 94.5%

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

   6. times-frac 94.4%

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

   7. fma-define 94.4%

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

   8. metadata-eval 94.4%

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

   9. associate-*l* 94.4%

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

   10. *-commutative 94.4%

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

3. Simplified 94.4%

   \[\leadsto \color{blue}{x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{z \cdot \left(y \cdot 3\right)}\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 32.2%

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

Developer Target 1: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024143 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y)))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))