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

Percentage Accurate: 95.9% → 97.5%

Time: 12.8s

Alternatives: 17

Speedup: 0.7×

• 28.3% 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: 97.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -0.5:\\ \;\;\;\;x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{3 \cdot \left(z \cdot y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -0.5)
   (+ x (fma -0.3333333333333333 (/ y z) (/ t (* 3.0 (* z y)))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -0.5) {
		tmp = x + fma(-0.3333333333333333, (y / z), (t / (3.0 * (z * y))));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -0.5)
		tmp = Float64(x + fma(-0.3333333333333333, Float64(y / z), Float64(t / Float64(3.0 * Float64(z * y)))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -0.5], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + N[(t / N[(3.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -0.5

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. sub-neg 98.1%

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

      3. remove-double-neg 98.1%

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

      4. distribute-neg-in 98.1%

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

      5. *-lft-identity 98.1%

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

      6. metadata-eval 98.1%

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

      7. times-frac 98.1%

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

      8. neg-mul-1 98.1%

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

      9. distribute-rgt-neg-out 98.1%

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

      10. associate-*r/ 98.1%

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

      11. neg-mul-1 98.1%

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

      12. distribute-neg-out 98.1%

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

      13. neg-mul-1 98.1%

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

      14. distribute-lft-neg-in 98.1%

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

      15. metadata-eval 98.1%

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

      16. *-lft-identity 98.1%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 99.7%

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

   if -0.5 < (*.f64 z 3)

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. *-commutative 95.5%

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

   3. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-*l* 95.5%

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

      3. associate-+l- 95.5%

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

      4. *-commutative 95.5%

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

      5. associate-/r* 97.4%

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

      6. sub-div 98.4%

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

   6. Applied egg-rr 98.4%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -0.5:\\ \;\;\;\;x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{3 \cdot \left(z \cdot y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+131} \lor \neg \left(z \cdot 3 \leq 10^{+128}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -1e+131) (not (<= (* z 3.0) 1e+128)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ (- (/ t y) y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -1e+131) || !((z * 3.0) <= 1e+128)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * 3.0d0) <= (-1d+131)) .or. (.not. ((z * 3.0d0) <= 1d+128))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * (((t / y) - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -1e+131) || !((z * 3.0) <= 1e+128)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -1e+131) or not ((z * 3.0) <= 1e+128):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -1e+131) || !(Float64(z * 3.0) <= 1e+128))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -1e+131) || ~(((z * 3.0) <= 1e+128)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -1e+131], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 1e+128]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -9.9999999999999991e130 or 1.0000000000000001e128 < (*.f64 z 3)

   1. Initial program 97.2%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around 0 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-*l/ 83.7%

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

      3. associate-*r/ 83.6%

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

   7. Simplified 83.6%

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

   if -9.9999999999999991e130 < (*.f64 z 3) < 1.0000000000000001e128

   1. Initial program 95.6%

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

      1. associate-*l* 95.6%

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

      2. *-commutative 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around 0 86.4%

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

      1. distribute-lft-out-- 86.4%

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

      2. *-un-lft-identity 86.4%

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

      3. times-frac 86.4%

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

      4. metadata-eval 86.4%

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

   7. Applied egg-rr 86.4%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+131} \lor \neg \left(z \cdot 3 \leq 10^{+128}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{-y}{z}}{3}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.0006:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ (- y) z) 3.0)))
   (if (<= y -4.4e+28)
     t_1
     (if (<= y -0.0006)
       x
       (if (<= y 4.6e-10) (* t (/ (/ 0.3333333333333333 z) y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-y / z) / 3.0;
	double tmp;
	if (y <= -4.4e+28) {
		tmp = t_1;
	} else if (y <= -0.0006) {
		tmp = x;
	} else if (y <= 4.6e-10) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-y / z) / 3.0d0
    if (y <= (-4.4d+28)) then
        tmp = t_1
    else if (y <= (-0.0006d0)) then
        tmp = x
    else if (y <= 4.6d-10) then
        tmp = t * ((0.3333333333333333d0 / z) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (-y / z) / 3.0;
	double tmp;
	if (y <= -4.4e+28) {
		tmp = t_1;
	} else if (y <= -0.0006) {
		tmp = x;
	} else if (y <= 4.6e-10) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-y / z) / 3.0
	tmp = 0
	if y <= -4.4e+28:
		tmp = t_1
	elif y <= -0.0006:
		tmp = x
	elif y <= 4.6e-10:
		tmp = t * ((0.3333333333333333 / z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-y) / z) / 3.0)
	tmp = 0.0
	if (y <= -4.4e+28)
		tmp = t_1;
	elseif (y <= -0.0006)
		tmp = x;
	elseif (y <= 4.6e-10)
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-y / z) / 3.0;
	tmp = 0.0;
	if (y <= -4.4e+28)
		tmp = t_1;
	elseif (y <= -0.0006)
		tmp = x;
	elseif (y <= 4.6e-10)
		tmp = t * ((0.3333333333333333 / z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-y) / z), $MachinePrecision] / 3.0), $MachinePrecision]}, If[LessEqual[y, -4.4e+28], t$95$1, If[LessEqual[y, -0.0006], x, If[LessEqual[y, 4.6e-10], N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.39999999999999973e28 or 4.60000000000000014e-10 < y

   1. Initial program 96.9%

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

      1. associate-*l* 96.9%

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

      2. *-commutative 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around 0 74.8%

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

   6. Taylor expanded in t around 0 68.2%

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

      1. *-commutative 68.2%

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

   8. Simplified 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*l/ 68.1%

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

   10. Applied egg-rr 68.1%

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

       1. *-commutative 68.1%

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

       2. div-inv 68.1%

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

       3. metadata-eval 68.1%

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

       4. distribute-lft-neg-in 68.1%

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

       5. div-inv 68.1%

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

       6. distribute-rgt-neg-in 68.1%

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

       7. metadata-eval 68.1%

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

       8. associate-/r* 67.4%

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

       9. *-commutative 67.4%

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

       10. div-inv 67.5%

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

       11. associate-/r* 68.3%

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

       12. distribute-neg-frac 68.3%

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

   12. Applied egg-rr 68.3%

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

   if -4.39999999999999973e28 < y < -5.99999999999999947e-4

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 69.8%

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

   if -5.99999999999999947e-4 < y < 4.60000000000000014e-10

   1. Initial program 94.8%

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

      1. associate-*l* 94.8%

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

      2. *-commutative 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around 0 72.4%

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

   6. Taylor expanded in t around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*r/ 67.7%

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

      3. div-inv 66.9%

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

      4. associate-*l* 68.4%

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

   8. Applied egg-rr 68.4%

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

      1. associate-*l/ 69.4%

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

      2. *-lft-identity 69.4%

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

   10. Simplified 69.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{-y}{z}}{3}\\ \mathbf{elif}\;y \leq -0.0006:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-y}{z}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{-y}{z}}{3}\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.00072:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ (- y) z) 3.0)))
   (if (<= y -4.7e+28)
     t_1
     (if (<= y -0.00072)
       x
       (if (<= y 4.2e-10) (* (/ t z) (/ 0.3333333333333333 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-y / z) / 3.0;
	double tmp;
	if (y <= -4.7e+28) {
		tmp = t_1;
	} else if (y <= -0.00072) {
		tmp = x;
	} else if (y <= 4.2e-10) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-y / z) / 3.0d0
    if (y <= (-4.7d+28)) then
        tmp = t_1
    else if (y <= (-0.00072d0)) then
        tmp = x
    else if (y <= 4.2d-10) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (-y / z) / 3.0;
	double tmp;
	if (y <= -4.7e+28) {
		tmp = t_1;
	} else if (y <= -0.00072) {
		tmp = x;
	} else if (y <= 4.2e-10) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-y / z) / 3.0
	tmp = 0
	if y <= -4.7e+28:
		tmp = t_1
	elif y <= -0.00072:
		tmp = x
	elif y <= 4.2e-10:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-y) / z) / 3.0)
	tmp = 0.0
	if (y <= -4.7e+28)
		tmp = t_1;
	elseif (y <= -0.00072)
		tmp = x;
	elseif (y <= 4.2e-10)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-y / z) / 3.0;
	tmp = 0.0;
	if (y <= -4.7e+28)
		tmp = t_1;
	elseif (y <= -0.00072)
		tmp = x;
	elseif (y <= 4.2e-10)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-y) / z), $MachinePrecision] / 3.0), $MachinePrecision]}, If[LessEqual[y, -4.7e+28], t$95$1, If[LessEqual[y, -0.00072], x, If[LessEqual[y, 4.2e-10], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.69999999999999965e28 or 4.2e-10 < y

   1. Initial program 96.9%

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

      1. associate-*l* 96.9%

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

      2. *-commutative 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around 0 74.8%

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

   6. Taylor expanded in t around 0 68.2%

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

      1. *-commutative 68.2%

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

   8. Simplified 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*l/ 68.1%

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

   10. Applied egg-rr 68.1%

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

       1. *-commutative 68.1%

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

       2. div-inv 68.1%

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

       3. metadata-eval 68.1%

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

       4. distribute-lft-neg-in 68.1%

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

       5. div-inv 68.1%

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

       6. distribute-rgt-neg-in 68.1%

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

       7. metadata-eval 68.1%

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

       8. associate-/r* 67.4%

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

       9. *-commutative 67.4%

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

       10. div-inv 67.5%

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

       11. associate-/r* 68.3%

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

       12. distribute-neg-frac 68.3%

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

   12. Applied egg-rr 68.3%

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

   if -4.69999999999999965e28 < y < -7.20000000000000045e-4

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 69.8%

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

   if -7.20000000000000045e-4 < y < 4.2e-10

   1. Initial program 94.8%

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

      1. associate-*l* 94.8%

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

      2. *-commutative 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around 0 72.4%

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

   6. Taylor expanded in t around inf 67.7%

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

      1. associate-*r/ 68.5%

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

      2. *-commutative 68.5%

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

      3. associate-/l/ 69.3%

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

      4. times-frac 72.6%

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

   8. Applied egg-rr 72.6%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{-y}{z}}{3}\\ \mathbf{elif}\;y \leq -0.00072:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-y}{z}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+14}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -4e+14)
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* 3.0 y))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e+14) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-4d+14)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (3.0d0 * y)))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e+14) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -4e+14:
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -4e+14)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(3.0 * y))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -4e+14)
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+14], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -4e14

   1. Initial program 98.1%

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

      1. associate-*l* 98.0%

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

      2. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   if -4e14 < (*.f64 z 3)

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. *-commutative 95.5%

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

   3. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-*l* 95.5%

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

      3. associate-+l- 95.5%

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

      4. *-commutative 95.5%

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

      5. associate-/r* 97.4%

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

      6. sub-div 98.4%

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

   6. Applied egg-rr 98.4%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+14}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+14}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -4e+14)
   (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y)))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e+14) {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-4d+14)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e+14) {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -4e+14:
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -4e+14)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -4e+14)
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+14], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -4e14

   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

   if -4e14 < (*.f64 z 3)

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. *-commutative 95.5%

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

   3. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-*l* 95.5%

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

      3. associate-+l- 95.5%

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

      4. *-commutative 95.5%

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

      5. associate-/r* 97.4%

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

      6. sub-div 98.4%

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

   6. Applied egg-rr 98.4%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+14}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 46.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+49}:\\ \;\;\;\;\frac{-y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -2e+120) x (if (<= (* z 3.0) 1e+49) (/ (- y) (* z 3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+120) {
		tmp = x;
	} else if ((z * 3.0) <= 1e+49) {
		tmp = -y / (z * 3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-2d+120)) then
        tmp = x
    else if ((z * 3.0d0) <= 1d+49) then
        tmp = -y / (z * 3.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+120) {
		tmp = x;
	} else if ((z * 3.0) <= 1e+49) {
		tmp = -y / (z * 3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -2e+120:
		tmp = x
	elif (z * 3.0) <= 1e+49:
		tmp = -y / (z * 3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e+120)
		tmp = x;
	elseif (Float64(z * 3.0) <= 1e+49)
		tmp = Float64(Float64(-y) / Float64(z * 3.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -2e+120)
		tmp = x;
	elseif ((z * 3.0) <= 1e+49)
		tmp = -y / (z * 3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+120], x, If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e+49], N[((-y) / N[(z * 3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -2e120 or 9.99999999999999946e48 < (*.f64 z 3)

   1. Initial program 97.7%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 55.0%

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

   if -2e120 < (*.f64 z 3) < 9.99999999999999946e48

   1. Initial program 95.1%

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

      1. associate-*l* 95.2%

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

      2. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 89.0%

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

   6. Taylor expanded in t around 0 46.6%

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

      1. *-commutative 46.6%

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

   8. Simplified 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*l/ 46.6%

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

   10. Applied egg-rr 46.6%

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

       1. *-commutative 46.6%

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

       2. div-inv 46.6%

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

       3. metadata-eval 46.6%

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

       4. distribute-lft-neg-in 46.6%

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

       5. div-inv 46.6%

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

       6. distribute-rgt-neg-in 46.6%

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

       7. metadata-eval 46.6%

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

       8. associate-/r* 46.6%

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

       9. *-commutative 46.6%

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

       10. div-inv 46.6%

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

       11. distribute-neg-frac 46.6%

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

   12. Applied egg-rr 46.6%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+49}:\\ \;\;\;\;\frac{-y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+49}:\\ \;\;\;\;\frac{\frac{-y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -2e+120) x (if (<= (* z 3.0) 1e+49) (/ (/ (- y) z) 3.0) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+120) {
		tmp = x;
	} else if ((z * 3.0) <= 1e+49) {
		tmp = (-y / z) / 3.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-2d+120)) then
        tmp = x
    else if ((z * 3.0d0) <= 1d+49) then
        tmp = (-y / z) / 3.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+120) {
		tmp = x;
	} else if ((z * 3.0) <= 1e+49) {
		tmp = (-y / z) / 3.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -2e+120:
		tmp = x
	elif (z * 3.0) <= 1e+49:
		tmp = (-y / z) / 3.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e+120)
		tmp = x;
	elseif (Float64(z * 3.0) <= 1e+49)
		tmp = Float64(Float64(Float64(-y) / z) / 3.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -2e+120)
		tmp = x;
	elseif ((z * 3.0) <= 1e+49)
		tmp = (-y / z) / 3.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+120], x, If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e+49], N[(N[((-y) / z), $MachinePrecision] / 3.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -2e120 or 9.99999999999999946e48 < (*.f64 z 3)

   1. Initial program 97.7%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 55.0%

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

   if -2e120 < (*.f64 z 3) < 9.99999999999999946e48

   1. Initial program 95.1%

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

      1. associate-*l* 95.2%

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

      2. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 89.0%

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

   6. Taylor expanded in t around 0 46.6%

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

      1. *-commutative 46.6%

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

   8. Simplified 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*l/ 46.6%

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

   10. Applied egg-rr 46.6%

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

       1. *-commutative 46.6%

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

       2. div-inv 46.6%

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

       3. metadata-eval 46.6%

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

       4. distribute-lft-neg-in 46.6%

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

       5. div-inv 46.6%

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

       6. distribute-rgt-neg-in 46.6%

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

       7. metadata-eval 46.6%

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

       8. associate-/r* 46.6%

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

       9. *-commutative 46.6%

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

       10. div-inv 46.6%

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

       11. associate-/r* 46.6%

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

       12. distribute-neg-frac 46.6%

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

   12. Applied egg-rr 46.6%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+49}:\\ \;\;\;\;\frac{\frac{-y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+49}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -2e+120)
   x
   (if (<= (* z 3.0) 1e+49) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+120) {
		tmp = x;
	} else if ((z * 3.0) <= 1e+49) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-2d+120)) then
        tmp = x
    else if ((z * 3.0d0) <= 1d+49) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+120) {
		tmp = x;
	} else if ((z * 3.0) <= 1e+49) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -2e+120:
		tmp = x
	elif (z * 3.0) <= 1e+49:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e+120)
		tmp = x;
	elseif (Float64(z * 3.0) <= 1e+49)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -2e+120)
		tmp = x;
	elseif ((z * 3.0) <= 1e+49)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+120], x, If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e+49], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -2e120 or 9.99999999999999946e48 < (*.f64 z 3)

   1. Initial program 97.7%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 55.0%

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

   if -2e120 < (*.f64 z 3) < 9.99999999999999946e48

   1. Initial program 95.1%

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

      1. associate-*l* 95.2%

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

      2. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 89.0%

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

   6. Taylor expanded in t around 0 46.6%

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

      1. *-commutative 46.6%

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

   8. Simplified 46.6%

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

      1. associate-/l* 46.6%

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

      2. associate-/r/ 46.6%

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

   10. Applied egg-rr 46.6%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+49}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.1e+28)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 4.6e-10)
     (+ 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 <= -3.1e+28) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 4.6e-10) {
		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 <= (-3.1d+28)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 4.6d-10) 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 <= -3.1e+28) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 4.6e-10) {
		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 <= -3.1e+28:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 4.6e-10:
		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 <= -3.1e+28)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 4.6e-10)
		tmp = Float64(x + 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 <= -3.1e+28)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 4.6e-10)
		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, -3.1e+28], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-10], N[(x + N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000001e28

   1. Initial program 96.7%

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

      1. associate-*l* 96.7%

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

      2. *-commutative 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 93.6%

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

   if -3.1000000000000001e28 < y < 4.60000000000000014e-10

   1. Initial program 95.1%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around inf 89.8%

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

      1. associate-*r/ 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-/r* 93.5%

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

      4. associate-*r/ 93.5%

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

      5. *-rgt-identity 93.5%

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

      6. associate-*r/ 92.8%

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

      7. associate-*l* 92.1%

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

      8. associate-*r/ 92.9%

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

      9. *-rgt-identity 92.9%

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

   7. Simplified 92.9%

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

   if 4.60000000000000014e-10 < y

   1. Initial program 97.1%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l/ 92.5%

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

      3. associate-*r/ 92.5%

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

   7. Simplified 92.5%

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

      1. clear-num 92.5%

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

      2. un-div-inv 92.5%

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

      3. div-inv 92.6%

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

      4. metadata-eval 92.6%

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

   9. Applied egg-rr 92.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+28)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 4.4e-10)
     (+ x (/ 0.3333333333333333 (/ y (/ t z))))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+28) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 4.4e-10) {
		tmp = x + (0.3333333333333333 / (y / (t / 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 <= (-1.7d+28)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 4.4d-10) then
        tmp = x + (0.3333333333333333d0 / (y / (t / 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 <= -1.7e+28) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 4.4e-10) {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+28:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 4.4e-10:
		tmp = x + (0.3333333333333333 / (y / (t / z)))
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+28)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 4.4e-10)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y / Float64(t / 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 <= -1.7e+28)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 4.4e-10)
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+28], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e-10], N[(x + N[(0.3333333333333333 / N[(y / N[(t / z), $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 < -1.7e28

   1. Initial program 96.7%

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

      1. associate-*l* 96.7%

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

      2. *-commutative 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 93.6%

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

   if -1.7e28 < y < 4.3999999999999998e-10

   1. Initial program 95.1%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around inf 89.8%

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

      1. associate-*r/ 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-/r* 93.5%

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

      4. associate-*r/ 93.5%

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

      5. *-rgt-identity 93.5%

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

      6. associate-*r/ 92.8%

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

      7. associate-*l* 92.1%

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

      8. associate-*r/ 92.9%

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

      9. *-rgt-identity 92.9%

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

   7. Simplified 92.9%

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

      1. clear-num 92.8%

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

      2. un-div-inv 93.5%

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

   9. Applied egg-rr 93.5%

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

   if 4.3999999999999998e-10 < y

   1. Initial program 97.1%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l/ 92.5%

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

      3. associate-*r/ 92.5%

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

   7. Simplified 92.5%

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

      1. clear-num 92.5%

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

      2. un-div-inv 92.5%

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

      3. div-inv 92.6%

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

      4. metadata-eval 92.6%

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

   9. Applied egg-rr 92.6%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-73} \lor \neg \left(y \leq 4 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e-73) (not (<= y 4e-10)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-73) || !(y <= 4e-10)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.15d-73)) .or. (.not. (y <= 4d-10))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-73) || !(y <= 4e-10)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e-73) or not (y <= 4e-10):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e-73) || !(y <= 4e-10))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.15e-73) || ~((y <= 4e-10)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e-73], N[Not[LessEqual[y, 4e-10]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999994e-73 or 4.00000000000000015e-10 < y

   1. Initial program 96.7%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*l/ 89.8%

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

      3. associate-*r/ 89.7%

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

   7. Simplified 89.7%

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

   if -1.14999999999999994e-73 < y < 4.00000000000000015e-10

   1. Initial program 95.1%

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

      1. associate-*l* 95.2%

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

      2. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 73.1%

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

   6. Taylor expanded in t around inf 70.6%

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

      1. associate-*r/ 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-/l/ 72.4%

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

      4. times-frac 76.1%

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

   8. Applied egg-rr 76.1%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-73} \lor \neg \left(y \leq 4 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-73}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-73)
   (+ x (* y (/ -0.3333333333333333 z)))
   (if (<= y 3.7e-10)
     (* (/ t z) (/ 0.3333333333333333 y))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-73) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 3.7e-10) {
		tmp = (t / z) * (0.3333333333333333 / 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 <= (-2.5d-73)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if (y <= 3.7d-10) then
        tmp = (t / z) * (0.3333333333333333d0 / 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 <= -2.5e-73) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 3.7e-10) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-73:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif y <= 3.7e-10:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-73)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (y <= 3.7e-10)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / 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 <= -2.5e-73)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif (y <= 3.7e-10)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-73], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-10], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999999e-73

   1. Initial program 96.3%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-*l/ 87.5%

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

      3. associate-*r/ 87.4%

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

   7. Simplified 87.4%

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

   if -2.4999999999999999e-73 < y < 3.70000000000000015e-10

   1. Initial program 95.1%

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

      1. associate-*l* 95.2%

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

      2. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 73.1%

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

   6. Taylor expanded in t around inf 70.6%

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

      1. associate-*r/ 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-/l/ 72.4%

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

      4. times-frac 76.1%

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

   8. Applied egg-rr 76.1%

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

   if 3.70000000000000015e-10 < y

   1. Initial program 97.1%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l/ 92.5%

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

      3. associate-*r/ 92.5%

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

   7. Simplified 92.5%

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

      1. clear-num 92.5%

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

      2. un-div-inv 92.5%

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

      3. div-inv 92.6%

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

      4. metadata-eval 92.6%

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

   9. Applied egg-rr 92.6%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-73}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 78.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e-75)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 3.7e-10)
     (* (/ t z) (/ 0.3333333333333333 y))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-75) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 3.7e-10) {
		tmp = (t / z) * (0.3333333333333333 / 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 <= (-1.65d-75)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 3.7d-10) then
        tmp = (t / z) * (0.3333333333333333d0 / 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 <= -1.65e-75) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 3.7e-10) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e-75:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 3.7e-10:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e-75)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 3.7e-10)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / 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 <= -1.65e-75)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 3.7e-10)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e-75], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-10], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e-75

   1. Initial program 96.3%

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

      1. associate-*l* 96.3%

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

      2. *-commutative 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0 87.5%

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

   if -1.65e-75 < y < 3.70000000000000015e-10

   1. Initial program 95.1%

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

      1. associate-*l* 95.2%

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

      2. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 73.1%

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

   6. Taylor expanded in t around inf 70.6%

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

      1. associate-*r/ 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-/l/ 72.4%

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

      4. times-frac 76.1%

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

   8. Applied egg-rr 76.1%

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

   if 3.70000000000000015e-10 < y

   1. Initial program 97.1%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l/ 92.5%

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

      3. associate-*r/ 92.5%

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

   7. Simplified 92.5%

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

      1. clear-num 92.5%

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

      2. un-div-inv 92.5%

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

      3. div-inv 92.6%

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

      4. metadata-eval 92.6%

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

   9. Applied egg-rr 92.6%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e+117) x (if (<= z 3.2e+50) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+117) {
		tmp = x;
	} else if (z <= 3.2e+50) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.8d+117)) then
        tmp = x
    else if (z <= 3.2d+50) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+117) {
		tmp = x;
	} else if (z <= 3.2e+50) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e+117:
		tmp = x
	elif z <= 3.2e+50:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e+117)
		tmp = x;
	elseif (z <= 3.2e+50)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e+117)
		tmp = x;
	elseif (z <= 3.2e+50)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e+117], x, If[LessEqual[z, 3.2e+50], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7999999999999998e117 or 3.19999999999999983e50 < z

   1. Initial program 97.7%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 55.0%

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

   if -4.7999999999999998e117 < z < 3.19999999999999983e50

   1. Initial program 95.1%

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

      1. associate-*l* 95.2%

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

      2. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 89.0%

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

   6. Taylor expanded in t around 0 46.6%

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

      1. *-commutative 46.6%

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

   8. Simplified 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*l/ 46.6%

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

   10. Applied egg-rr 46.6%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 95.4% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 17: 29.7% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Simplified 96.5%

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

5. Taylor expanded in x around inf 26.8%

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

6. Final simplification 26.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.0% 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 2024020 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

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