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

Percentage Accurate: 95.6% → 97.3%

Time: 16.6s

Alternatives: 20

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: 95.6% 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: 97.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 20000000:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{3 \cdot \left(z \cdot y\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 20000000.0)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ x (fma -0.3333333333333333 (/ y z) (/ t (* 3.0 (* z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 20000000.0) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + fma(-0.3333333333333333, (y / z), (t / (3.0 * (z * y))));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 20000000.0)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(x + fma(-0.3333333333333333, Float64(y / z), Float64(t / Float64(3.0 * Float64(z * y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 20000000.0], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + N[(t / N[(3.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 2e7

   1. Initial program 93.3%

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

      1. associate-*l* 93.3%

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

      2. *-commutative 93.3%

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

   3. Simplified 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l* 93.3%

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

      3. associate-+l- 93.3%

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

      4. *-commutative 93.3%

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

      5. associate-/r* 96.7%

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

      6. sub-div 98.3%

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

   6. Applied egg-rr 98.3%

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

   if 2e7 < (*.f64 z 3)

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 20000000:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{3 \cdot \left(z \cdot y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-231}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.65:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 10^{+180}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15)
   (* -0.3333333333333333 (/ y z))
   (if (<= y -1.45e-231)
     (* 0.3333333333333333 (/ t (* z y)))
     (if (<= y 1.65)
       (* (/ t y) (/ 0.3333333333333333 z))
       (if (<= y 1.55e+136)
         (/ (/ y z) -3.0)
         (if (<= y 1e+180) x (/ y (* z -3.0))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= -1.45e-231) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 1.65) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else if (y <= 1.55e+136) {
		tmp = (y / z) / -3.0;
	} else if (y <= 1e+180) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.15d0)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= (-1.45d-231)) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else if (y <= 1.65d0) then
        tmp = (t / y) * (0.3333333333333333d0 / z)
    else if (y <= 1.55d+136) then
        tmp = (y / z) / (-3.0d0)
    else if (y <= 1d+180) then
        tmp = x
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= -1.45e-231) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 1.65) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else if (y <= 1.55e+136) {
		tmp = (y / z) / -3.0;
	} else if (y <= 1e+180) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= -1.45e-231:
		tmp = 0.3333333333333333 * (t / (z * y))
	elif y <= 1.65:
		tmp = (t / y) * (0.3333333333333333 / z)
	elif y <= 1.55e+136:
		tmp = (y / z) / -3.0
	elif y <= 1e+180:
		tmp = x
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= -1.45e-231)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	elseif (y <= 1.65)
		tmp = Float64(Float64(t / y) * Float64(0.3333333333333333 / z));
	elseif (y <= 1.55e+136)
		tmp = Float64(Float64(y / z) / -3.0);
	elseif (y <= 1e+180)
		tmp = x;
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= -1.45e-231)
		tmp = 0.3333333333333333 * (t / (z * y));
	elseif (y <= 1.65)
		tmp = (t / y) * (0.3333333333333333 / z);
	elseif (y <= 1.55e+136)
		tmp = (y / z) / -3.0;
	elseif (y <= 1e+180)
		tmp = x;
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-231], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65], N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+136], N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[y, 1e+180], x, N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.1499999999999999

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-*l* 97.9%

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

      3. associate-+l- 97.9%

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

      4. *-commutative 97.9%

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

      5. associate-/r* 97.9%

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

      6. sub-div 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 69.3%

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

   if -1.1499999999999999 < y < -1.45e-231

   1. Initial program 99.7%

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

      1. associate-*l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. associate-+l- 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/r* 87.9%

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

      6. sub-div 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in y around 0 75.8%

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

      1. *-commutative 75.8%

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

   9. Simplified 75.8%

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

   if -1.45e-231 < y < 1.6499999999999999

   1. Initial program 89.8%

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

      1. associate-*l* 89.8%

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

      2. *-commutative 89.8%

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

   3. Simplified 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 89.8%

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

      3. associate-+l- 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-/r* 93.8%

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

      6. sub-div 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. associate-*l/ 68.5%

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

      3. sub-neg 68.5%

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

      4. distribute-frac-neg 68.5%

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

      5. distribute-rgt-out 68.5%

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

      6. +-commutative 68.5%

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

      7. *-commutative 68.5%

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

      8. associate-*r/ 69.4%

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

      9. associate-*l/ 69.3%

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

      10. neg-mul-1 69.3%

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

      11. associate-*r* 69.3%

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

      12. metadata-eval 69.3%

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

      13. *-commutative 69.3%

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

      14. associate-/l/ 61.4%

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

      15. times-frac 68.5%

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

      16. *-commutative 68.5%

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

      17. metadata-eval 68.5%

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

      18. distribute-neg-frac 68.5%

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

      19. cancel-sign-sub-inv 68.5%

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

      20. *-commutative 68.5%

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

      21. distribute-lft-out-- 68.5%

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

   9. Simplified 68.5%

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

   10. Taylor expanded in t around inf 64.8%

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

   if 1.6499999999999999 < y < 1.54999999999999992e136

   1. Initial program 93.3%

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

      1. associate-*l* 93.3%

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

      2. *-commutative 93.3%

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

   3. Simplified 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l* 93.3%

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

      3. associate-+l- 93.3%

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

      4. *-commutative 93.3%

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

      5. associate-/r* 93.3%

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

      6. sub-div 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 59.9%

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

      1. associate-*r/ 59.9%

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

      2. *-commutative 59.9%

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

      3. clear-num 60.0%

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

      4. reciprocal-define 31.9%

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

      5. *-commutative 31.9%

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

      6. associate-/r* 31.9%

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

      7. div-inv 31.9%

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

      8. metadata-eval 31.9%

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

   9. Applied egg-rr 31.9%

      \[\leadsto \color{blue}{\mathsf{reciprocal}\left(\left(\frac{z \cdot -3}{y}\right)\right)} \]
   10. Step-by-step derivation

       1. reciprocal-undefine 59.9%

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

       2. clear-num 59.9%

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

       3. associate-/r* 59.9%

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

   11. Applied egg-rr 59.9%

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

   if 1.54999999999999992e136 < y < 1e180

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+l+ 99.9%

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

      3. remove-double-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. associate-*r/ 99.9%

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

      8. associate-*l/ 99.9%

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

      9. neg-mul-1 99.9%

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

      10. times-frac 99.9%

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

      11. distribute-lft-out-- 99.9%

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

      12. *-commutative 99.9%

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

      13. associate-/r* 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 67.7%

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

   if 1e180 < y

   1. Initial program 99.9%

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

      1. associate-*l* 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 99.9%

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

      3. associate-+l- 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 88.2%

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

      1. *-commutative 88.2%

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

      2. associate-/r/ 88.2%

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

      3. div-inv 88.4%

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

      4. metadata-eval 88.4%

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

   9. Applied egg-rr 88.4%

      \[\leadsto \color{blue}{\frac{y}{z \cdot -3}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-231}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.65:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 10^{+180}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -600:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 64:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+180}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -600.0)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 64.0)
     (* (/ t y) (/ 0.3333333333333333 z))
     (if (<= y 1.55e+136)
       (/ (/ y z) -3.0)
       (if (<= y 1.25e+180) x (/ y (* z -3.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -600.0) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 64.0) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else if (y <= 1.55e+136) {
		tmp = (y / z) / -3.0;
	} else if (y <= 1.25e+180) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-600.0d0)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 64.0d0) then
        tmp = (t / y) * (0.3333333333333333d0 / z)
    else if (y <= 1.55d+136) then
        tmp = (y / z) / (-3.0d0)
    else if (y <= 1.25d+180) then
        tmp = x
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -600.0) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 64.0) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else if (y <= 1.55e+136) {
		tmp = (y / z) / -3.0;
	} else if (y <= 1.25e+180) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -600.0:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 64.0:
		tmp = (t / y) * (0.3333333333333333 / z)
	elif y <= 1.55e+136:
		tmp = (y / z) / -3.0
	elif y <= 1.25e+180:
		tmp = x
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -600.0)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 64.0)
		tmp = Float64(Float64(t / y) * Float64(0.3333333333333333 / z));
	elseif (y <= 1.55e+136)
		tmp = Float64(Float64(y / z) / -3.0);
	elseif (y <= 1.25e+180)
		tmp = x;
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -600.0)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 64.0)
		tmp = (t / y) * (0.3333333333333333 / z);
	elseif (y <= 1.55e+136)
		tmp = (y / z) / -3.0;
	elseif (y <= 1.25e+180)
		tmp = x;
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -600.0], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 64.0], N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+136], N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[y, 1.25e+180], x, N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -600

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-*l* 97.9%

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

      3. associate-+l- 97.9%

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

      4. *-commutative 97.9%

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

      5. associate-/r* 97.9%

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

      6. sub-div 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 69.3%

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

   if -600 < y < 64

   1. Initial program 92.7%

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

      1. associate-*l* 92.8%

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

      2. *-commutative 92.8%

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

   3. Simplified 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l* 92.7%

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

      3. associate-+l- 92.7%

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

      4. *-commutative 92.7%

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

      5. associate-/r* 92.0%

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

      6. sub-div 92.0%

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in x around 0 68.6%

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

      1. associate-*r/ 68.5%

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

      2. associate-*l/ 68.5%

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

      3. sub-neg 68.5%

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

      4. distribute-frac-neg 68.5%

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

      5. distribute-rgt-out 68.6%

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

      6. +-commutative 68.6%

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

      7. *-commutative 68.6%

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

      8. associate-*r/ 72.6%

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

      9. associate-*l/ 72.7%

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

      10. neg-mul-1 72.7%

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

      11. associate-*r* 72.7%

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

      12. metadata-eval 72.7%

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

      13. *-commutative 72.7%

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

      14. associate-/l/ 67.2%

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

      15. times-frac 68.6%

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

      16. *-commutative 68.6%

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

      17. metadata-eval 68.6%

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

      18. distribute-neg-frac 68.6%

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

      19. cancel-sign-sub-inv 68.6%

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

      20. *-commutative 68.6%

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

      21. distribute-lft-out-- 68.5%

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

   9. Simplified 68.5%

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

   10. Taylor expanded in t around inf 64.5%

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

   if 64 < y < 1.54999999999999992e136

   1. Initial program 93.3%

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

      1. associate-*l* 93.3%

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

      2. *-commutative 93.3%

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

   3. Simplified 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l* 93.3%

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

      3. associate-+l- 93.3%

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

      4. *-commutative 93.3%

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

      5. associate-/r* 93.3%

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

      6. sub-div 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 59.9%

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

      1. associate-*r/ 59.9%

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

      2. *-commutative 59.9%

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

      3. clear-num 60.0%

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

      4. reciprocal-define 31.9%

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

      5. *-commutative 31.9%

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

      6. associate-/r* 31.9%

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

      7. div-inv 31.9%

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

      8. metadata-eval 31.9%

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

   9. Applied egg-rr 31.9%

      \[\leadsto \color{blue}{\mathsf{reciprocal}\left(\left(\frac{z \cdot -3}{y}\right)\right)} \]
   10. Step-by-step derivation

       1. reciprocal-undefine 59.9%

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

       2. clear-num 59.9%

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

       3. associate-/r* 59.9%

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

   11. Applied egg-rr 59.9%

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

   if 1.54999999999999992e136 < y < 1.2499999999999999e180

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+l+ 99.9%

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

      3. remove-double-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. associate-*r/ 99.9%

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

      8. associate-*l/ 99.9%

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

      9. neg-mul-1 99.9%

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

      10. times-frac 99.9%

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

      11. distribute-lft-out-- 99.9%

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

      12. *-commutative 99.9%

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

      13. associate-/r* 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 67.7%

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

   if 1.2499999999999999e180 < y

   1. Initial program 99.9%

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

      1. associate-*l* 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 99.9%

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

      3. associate-+l- 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 88.2%

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

      1. *-commutative 88.2%

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

      2. associate-/r/ 88.2%

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

      3. div-inv 88.4%

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

      4. metadata-eval 88.4%

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

   9. Applied egg-rr 88.4%

      \[\leadsto \color{blue}{\frac{y}{z \cdot -3}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -600:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 64:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+180}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+55}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -2e+25)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= (* z 3.0) 1e+55)
     (* (/ 0.3333333333333333 z) (- (/ t y) y))
     (- x (* (/ y z) 0.3333333333333333)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+25) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if ((z * 3.0) <= 1e+55) {
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	} else {
		tmp = x - ((y / z) * 0.3333333333333333);
	}
	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+25)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if ((z * 3.0d0) <= 1d+55) then
        tmp = (0.3333333333333333d0 / z) * ((t / y) - y)
    else
        tmp = x - ((y / z) * 0.3333333333333333d0)
    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+25) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if ((z * 3.0) <= 1e+55) {
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	} else {
		tmp = x - ((y / z) * 0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -2e+25:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif (z * 3.0) <= 1e+55:
		tmp = (0.3333333333333333 / z) * ((t / y) - y)
	else:
		tmp = x - ((y / z) * 0.3333333333333333)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e+25)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (Float64(z * 3.0) <= 1e+55)
		tmp = Float64(Float64(0.3333333333333333 / z) * Float64(Float64(t / y) - y));
	else
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -2e+25)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif ((z * 3.0) <= 1e+55)
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	else
		tmp = x - ((y / z) * 0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+25], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e+55], N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -2.00000000000000018e25

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-+l+ 99.8%

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

      3. remove-double-neg 99.8%

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

      4. distribute-frac-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. associate-*r/ 99.8%

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

      8. associate-*l/ 99.7%

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

      9. neg-mul-1 99.7%

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

      10. times-frac 94.0%

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

      11. distribute-lft-out-- 94.0%

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

      12. *-commutative 94.0%

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

      13. associate-/r* 94.0%

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

      14. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around inf 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*r/ 72.8%

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

   7. Applied egg-rr 72.8%

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

   if -2.00000000000000018e25 < (*.f64 z 3) < 1.00000000000000001e55

   1. Initial program 91.7%

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

      1. associate-*l* 91.7%

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

      2. *-commutative 91.7%

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

   3. Simplified 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l* 91.7%

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

      3. associate-+l- 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-/r* 97.2%

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

      6. sub-div 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in x around 0 90.3%

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

      1. associate-*r/ 90.2%

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

      2. associate-*l/ 90.3%

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

      3. sub-neg 90.3%

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

      4. distribute-frac-neg 90.3%

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

      5. distribute-rgt-out 88.3%

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

      6. +-commutative 88.3%

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

      7. *-commutative 88.3%

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

      8. associate-*r/ 86.9%

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

      9. associate-*l/ 86.9%

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

      10. neg-mul-1 86.9%

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

      11. associate-*r* 86.9%

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

      12. metadata-eval 86.9%

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

      13. *-commutative 86.9%

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

      14. associate-/l/ 82.8%

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

      15. times-frac 88.3%

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

      16. *-commutative 88.3%

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

      17. metadata-eval 88.3%

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

      18. distribute-neg-frac 88.3%

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

      19. cancel-sign-sub-inv 88.3%

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

      20. *-commutative 88.3%

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

      21. distribute-lft-out-- 90.3%

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

   9. Simplified 90.3%

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

   if 1.00000000000000001e55 < (*.f64 z 3)

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 78.0%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+55}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -0.04:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-231}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -0.04)
     t_1
     (if (<= y -2.4e-231)
       (* 0.3333333333333333 (/ t (* z y)))
       (if (<= y 2.5e-5) (* (/ t y) (/ 0.3333333333333333 z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -0.04) {
		tmp = t_1;
	} else if (y <= -2.4e-231) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 2.5e-5) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} 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 = x + (y * ((-0.3333333333333333d0) / z))
    if (y <= (-0.04d0)) then
        tmp = t_1
    else if (y <= (-2.4d-231)) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else if (y <= 2.5d-5) then
        tmp = (t / y) * (0.3333333333333333d0 / z)
    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 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -0.04) {
		tmp = t_1;
	} else if (y <= -2.4e-231) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 2.5e-5) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -0.04:
		tmp = t_1
	elif y <= -2.4e-231:
		tmp = 0.3333333333333333 * (t / (z * y))
	elif y <= 2.5e-5:
		tmp = (t / y) * (0.3333333333333333 / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -0.04)
		tmp = t_1;
	elseif (y <= -2.4e-231)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	elseif (y <= 2.5e-5)
		tmp = Float64(Float64(t / y) * Float64(0.3333333333333333 / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -0.04)
		tmp = t_1;
	elseif (y <= -2.4e-231)
		tmp = 0.3333333333333333 * (t / (z * y));
	elseif (y <= 2.5e-5)
		tmp = (t / y) * (0.3333333333333333 / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.04], t$95$1, If[LessEqual[y, -2.4e-231], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-5], N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0400000000000000008 or 2.50000000000000012e-5 < y

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. associate-+l+ 97.3%

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

      3. remove-double-neg 97.3%

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

      4. distribute-frac-neg 97.3%

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

      5. unsub-neg 97.3%

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

      6. neg-mul-1 97.3%

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

      7. associate-*r/ 97.3%

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

      8. associate-*l/ 97.2%

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

      9. neg-mul-1 97.2%

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

      10. times-frac 97.2%

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

      11. distribute-lft-out-- 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.4%

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

   if -0.0400000000000000008 < y < -2.39999999999999992e-231

   1. Initial program 99.7%

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

      1. associate-*l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. associate-+l- 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/r* 87.9%

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

      6. sub-div 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in y around 0 75.8%

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

      1. *-commutative 75.8%

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

   9. Simplified 75.8%

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

   if -2.39999999999999992e-231 < y < 2.50000000000000012e-5

   1. Initial program 89.8%

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

      1. associate-*l* 89.8%

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

      2. *-commutative 89.8%

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

   3. Simplified 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 89.8%

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

      3. associate-+l- 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-/r* 93.8%

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

      6. sub-div 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. associate-*l/ 68.5%

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

      3. sub-neg 68.5%

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

      4. distribute-frac-neg 68.5%

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

      5. distribute-rgt-out 68.5%

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

      6. +-commutative 68.5%

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

      7. *-commutative 68.5%

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

      8. associate-*r/ 69.4%

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

      9. associate-*l/ 69.3%

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

      10. neg-mul-1 69.3%

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

      11. associate-*r* 69.3%

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

      12. metadata-eval 69.3%

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

      13. *-commutative 69.3%

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

      14. associate-/l/ 61.4%

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

      15. times-frac 68.5%

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

      16. *-commutative 68.5%

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

      17. metadata-eval 68.5%

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

      18. distribute-neg-frac 68.5%

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

      19. cancel-sign-sub-inv 68.5%

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

      20. *-commutative 68.5%

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

      21. distribute-lft-out-- 68.5%

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

   9. Simplified 68.5%

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

   10. Taylor expanded in t around inf 64.8%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.04:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-231}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.25:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-230}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.25)
   (+ x (/ -0.3333333333333333 (/ z y)))
   (if (<= y -2.1e-230)
     (* 0.3333333333333333 (/ t (* z y)))
     (if (<= y 8.5e-12)
       (* (/ t y) (/ 0.3333333333333333 z))
       (+ x (* y (/ -0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.25) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= -2.1e-230) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 8.5e-12) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-0.25d0)) then
        tmp = x + ((-0.3333333333333333d0) / (z / y))
    else if (y <= (-2.1d-230)) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else if (y <= 8.5d-12) then
        tmp = (t / y) * (0.3333333333333333d0 / z)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.25) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= -2.1e-230) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 8.5e-12) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.25:
		tmp = x + (-0.3333333333333333 / (z / y))
	elif y <= -2.1e-230:
		tmp = 0.3333333333333333 * (t / (z * y))
	elif y <= 8.5e-12:
		tmp = (t / y) * (0.3333333333333333 / z)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.25)
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)));
	elseif (y <= -2.1e-230)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	elseif (y <= 8.5e-12)
		tmp = Float64(Float64(t / y) * Float64(0.3333333333333333 / z));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.25)
		tmp = x + (-0.3333333333333333 / (z / y));
	elseif (y <= -2.1e-230)
		tmp = 0.3333333333333333 * (t / (z * y));
	elseif (y <= 8.5e-12)
		tmp = (t / y) * (0.3333333333333333 / z);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.25], N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-230], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-12], N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.25

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. associate-+l+ 97.9%

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

      3. remove-double-neg 97.9%

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

      4. distribute-frac-neg 97.9%

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

      5. unsub-neg 97.9%

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

      6. neg-mul-1 97.9%

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

      7. associate-*r/ 97.9%

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

      8. associate-*l/ 97.7%

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

      9. neg-mul-1 97.7%

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

      10. times-frac 97.7%

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

      11. distribute-lft-out-- 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.9%

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

      1. associate-*l/ 95.0%

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

      2. associate-/l* 95.0%

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

   7. Applied egg-rr 95.0%

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

   if -0.25 < y < -2.0999999999999998e-230

   1. Initial program 99.7%

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

      1. associate-*l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. associate-+l- 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/r* 87.9%

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

      6. sub-div 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in y around 0 75.8%

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

      1. *-commutative 75.8%

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

   9. Simplified 75.8%

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

   if -2.0999999999999998e-230 < y < 8.4999999999999997e-12

   1. Initial program 89.8%

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

      1. associate-*l* 89.8%

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

      2. *-commutative 89.8%

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

   3. Simplified 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 89.8%

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

      3. associate-+l- 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-/r* 93.8%

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

      6. sub-div 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. associate-*l/ 68.5%

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

      3. sub-neg 68.5%

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

      4. distribute-frac-neg 68.5%

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

      5. distribute-rgt-out 68.5%

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

      6. +-commutative 68.5%

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

      7. *-commutative 68.5%

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

      8. associate-*r/ 69.4%

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

      9. associate-*l/ 69.3%

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

      10. neg-mul-1 69.3%

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

      11. associate-*r* 69.3%

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

      12. metadata-eval 69.3%

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

      13. *-commutative 69.3%

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

      14. associate-/l/ 61.4%

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

      15. times-frac 68.5%

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

      16. *-commutative 68.5%

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

      17. metadata-eval 68.5%

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

      18. distribute-neg-frac 68.5%

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

      19. cancel-sign-sub-inv 68.5%

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

      20. *-commutative 68.5%

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

      21. distribute-lft-out-- 68.5%

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

   9. Simplified 68.5%

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

   10. Taylor expanded in t around inf 64.8%

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

   if 8.4999999999999997e-12 < y

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. associate-+l+ 96.8%

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

      3. remove-double-neg 96.8%

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

      4. distribute-frac-neg 96.8%

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

      5. unsub-neg 96.8%

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

      6. neg-mul-1 96.8%

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

      7. associate-*r/ 96.8%

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

      8. associate-*l/ 96.8%

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

      9. neg-mul-1 96.8%

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

      10. times-frac 96.8%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.25:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-230}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.66:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-230}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.66)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y -1.35e-230)
     (* 0.3333333333333333 (/ t (* z y)))
     (if (<= y 8.6e-12)
       (* (/ t y) (/ 0.3333333333333333 z))
       (+ x (* y (/ -0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.66) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= -1.35e-230) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 8.6e-12) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.66d0)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= (-1.35d-230)) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else if (y <= 8.6d-12) then
        tmp = (t / y) * (0.3333333333333333d0 / z)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.66) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= -1.35e-230) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 8.6e-12) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.66:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= -1.35e-230:
		tmp = 0.3333333333333333 * (t / (z * y))
	elif y <= 8.6e-12:
		tmp = (t / y) * (0.3333333333333333 / z)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.66)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= -1.35e-230)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	elseif (y <= 8.6e-12)
		tmp = Float64(Float64(t / y) * Float64(0.3333333333333333 / z));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.66)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= -1.35e-230)
		tmp = 0.3333333333333333 * (t / (z * y));
	elseif (y <= 8.6e-12)
		tmp = (t / y) * (0.3333333333333333 / z);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.66], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-230], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-12], N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.65999999999999992

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. associate-+l+ 97.9%

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

      3. remove-double-neg 97.9%

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

      4. distribute-frac-neg 97.9%

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

      5. unsub-neg 97.9%

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

      6. neg-mul-1 97.9%

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

      7. associate-*r/ 97.9%

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

      8. associate-*l/ 97.7%

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

      9. neg-mul-1 97.7%

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

      10. times-frac 97.7%

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

      11. distribute-lft-out-- 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*r/ 95.0%

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

   7. Applied egg-rr 95.0%

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

   if -1.65999999999999992 < y < -1.35000000000000006e-230

   1. Initial program 99.7%

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

      1. associate-*l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. associate-+l- 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/r* 87.9%

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

      6. sub-div 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in y around 0 75.8%

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

      1. *-commutative 75.8%

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

   9. Simplified 75.8%

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

   if -1.35000000000000006e-230 < y < 8.59999999999999971e-12

   1. Initial program 89.8%

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

      1. associate-*l* 89.8%

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

      2. *-commutative 89.8%

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

   3. Simplified 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 89.8%

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

      3. associate-+l- 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-/r* 93.8%

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

      6. sub-div 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. associate-*l/ 68.5%

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

      3. sub-neg 68.5%

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

      4. distribute-frac-neg 68.5%

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

      5. distribute-rgt-out 68.5%

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

      6. +-commutative 68.5%

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

      7. *-commutative 68.5%

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

      8. associate-*r/ 69.4%

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

      9. associate-*l/ 69.3%

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

      10. neg-mul-1 69.3%

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

      11. associate-*r* 69.3%

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

      12. metadata-eval 69.3%

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

      13. *-commutative 69.3%

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

      14. associate-/l/ 61.4%

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

      15. times-frac 68.5%

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

      16. *-commutative 68.5%

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

      17. metadata-eval 68.5%

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

      18. distribute-neg-frac 68.5%

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

      19. cancel-sign-sub-inv 68.5%

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

      20. *-commutative 68.5%

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

      21. distribute-lft-out-- 68.5%

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

   9. Simplified 68.5%

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

   10. Taylor expanded in t around inf 64.8%

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

   if 8.59999999999999971e-12 < y

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. associate-+l+ 96.8%

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

      3. remove-double-neg 96.8%

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

      4. distribute-frac-neg 96.8%

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

      5. unsub-neg 96.8%

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

      6. neg-mul-1 96.8%

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

      7. associate-*r/ 96.8%

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

      8. associate-*l/ 96.8%

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

      9. neg-mul-1 96.8%

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

      10. times-frac 96.8%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.66:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-230}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.043:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-231}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.043)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y -5.2e-231)
     (* 0.3333333333333333 (/ t (* z y)))
     (if (<= y 8e-12)
       (* (/ t y) (/ 0.3333333333333333 z))
       (+ x (* y (/ -0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.043) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= -5.2e-231) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 8e-12) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-0.043d0)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= (-5.2d-231)) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else if (y <= 8d-12) then
        tmp = (t / y) * (0.3333333333333333d0 / z)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.043) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= -5.2e-231) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 8e-12) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.043:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= -5.2e-231:
		tmp = 0.3333333333333333 * (t / (z * y))
	elif y <= 8e-12:
		tmp = (t / y) * (0.3333333333333333 / z)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.043)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= -5.2e-231)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	elseif (y <= 8e-12)
		tmp = Float64(Float64(t / y) * Float64(0.3333333333333333 / z));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.043)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= -5.2e-231)
		tmp = 0.3333333333333333 * (t / (z * y));
	elseif (y <= 8e-12)
		tmp = (t / y) * (0.3333333333333333 / z);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.043], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e-231], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-12], N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.042999999999999997

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around 0 95.0%

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

   if -0.042999999999999997 < y < -5.20000000000000006e-231

   1. Initial program 99.7%

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

      1. associate-*l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. associate-+l- 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/r* 87.9%

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

      6. sub-div 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in y around 0 75.8%

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

      1. *-commutative 75.8%

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

   9. Simplified 75.8%

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

   if -5.20000000000000006e-231 < y < 7.99999999999999984e-12

   1. Initial program 89.8%

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

      1. associate-*l* 89.8%

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

      2. *-commutative 89.8%

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

   3. Simplified 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 89.8%

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

      3. associate-+l- 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-/r* 93.8%

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

      6. sub-div 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. associate-*l/ 68.5%

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

      3. sub-neg 68.5%

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

      4. distribute-frac-neg 68.5%

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

      5. distribute-rgt-out 68.5%

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

      6. +-commutative 68.5%

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

      7. *-commutative 68.5%

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

      8. associate-*r/ 69.4%

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

      9. associate-*l/ 69.3%

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

      10. neg-mul-1 69.3%

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

      11. associate-*r* 69.3%

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

      12. metadata-eval 69.3%

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

      13. *-commutative 69.3%

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

      14. associate-/l/ 61.4%

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

      15. times-frac 68.5%

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

      16. *-commutative 68.5%

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

      17. metadata-eval 68.5%

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

      18. distribute-neg-frac 68.5%

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

      19. cancel-sign-sub-inv 68.5%

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

      20. *-commutative 68.5%

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

      21. distribute-lft-out-- 68.5%

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

   9. Simplified 68.5%

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

   10. Taylor expanded in t around inf 64.8%

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

   if 7.99999999999999984e-12 < y

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. associate-+l+ 96.8%

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

      3. remove-double-neg 96.8%

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

      4. distribute-frac-neg 96.8%

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

      5. unsub-neg 96.8%

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

      6. neg-mul-1 96.8%

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

      7. associate-*r/ 96.8%

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

      8. associate-*l/ 96.8%

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

      9. neg-mul-1 96.8%

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

      10. times-frac 96.8%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.043:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-231}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 5000000000:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)} + \left(x - \frac{0.3333333333333333}{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 5000000000.0)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (/ t (* z (* 3.0 y))) (- x (/ 0.3333333333333333 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 5000000000.0) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (t / (z * (3.0 * y))) + (x - (0.3333333333333333 / (z / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 5000000000.0d0) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (t / (z * (3.0d0 * y))) + (x - (0.3333333333333333d0 / (z / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 5000000000.0) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (t / (z * (3.0 * y))) + (x - (0.3333333333333333 / (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 5000000000.0:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (t / (z * (3.0 * y))) + (x - (0.3333333333333333 / (z / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 5000000000.0)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(t / Float64(z * Float64(3.0 * y))) + Float64(x - Float64(0.3333333333333333 / Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 5000000000.0)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = (t / (z * (3.0 * y))) + (x - (0.3333333333333333 / (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 5000000000.0], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 5e9

   1. Initial program 93.4%

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

      1. associate-*l* 93.4%

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

      2. *-commutative 93.4%

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

   3. Simplified 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-*l* 93.4%

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

      3. associate-+l- 93.4%

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

      4. *-commutative 93.4%

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

      5. associate-/r* 96.7%

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

      6. sub-div 98.3%

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

   6. Applied egg-rr 98.3%

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

   if 5e9 < (*.f64 z 3)

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

      3. *-commutative 99.7%

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

      4. *-un-lft-identity 99.7%

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

      5. times-frac 99.8%

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

      6. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

      2. associate-/r* 99.8%

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

      3. metadata-eval 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 5000000000:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)} + \left(x - \frac{0.3333333333333333}{\frac{z}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 20000000:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 20000000.0)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* 3.0 y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 20000000.0) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 20000000.0d0) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (3.0d0 * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 20000000.0) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 20000000.0:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 20000000.0)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(3.0 * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 20000000.0)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 20000000.0], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 2e7

   1. Initial program 93.3%

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

      1. associate-*l* 93.3%

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

      2. *-commutative 93.3%

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

   3. Simplified 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l* 93.3%

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

      3. associate-+l- 93.3%

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

      4. *-commutative 93.3%

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

      5. associate-/r* 96.7%

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

      6. sub-div 98.3%

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

   6. Applied egg-rr 98.3%

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

   if 2e7 < (*.f64 z 3)

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 20000000:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 0.038:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 0.038)
     (+ x (* t (/ 0.3333333333333333 (* z y))))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 0.038) {
		tmp = x + (t * (0.3333333333333333 / (z * y)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.65d0)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 0.038d0) then
        tmp = x + (t * (0.3333333333333333d0 / (z * y)))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 0.038) {
		tmp = x + (t * (0.3333333333333333 / (z * y)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 0.038:
		tmp = x + (t * (0.3333333333333333 / (z * y)))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 0.038)
		tmp = Float64(x + Float64(t * Float64(0.3333333333333333 / Float64(z * y))));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 0.038)
		tmp = x + (t * (0.3333333333333333 / (z * y)));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.038], N[(x + N[(t * N[(0.3333333333333333 / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around 0 95.0%

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

   if -1.6499999999999999 < y < 0.0379999999999999991

   1. Initial program 92.7%

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

      1. sub-neg 92.7%

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

      2. associate-+l+ 92.7%

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

      3. remove-double-neg 92.7%

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

      4. distribute-frac-neg 92.7%

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

      5. unsub-neg 92.7%

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

      6. neg-mul-1 92.7%

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

      7. associate-*r/ 92.7%

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

      8. associate-*l/ 92.7%

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

      9. neg-mul-1 92.7%

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

      10. times-frac 92.0%

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

      11. distribute-lft-out-- 92.0%

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

      12. *-commutative 92.0%

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

      13. associate-/r* 91.9%

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

      14. metadata-eval 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around 0 90.2%

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

      1. *-commutative 90.2%

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

      2. metadata-eval 90.2%

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

      3. times-frac 90.2%

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

      4. associate-*r* 90.2%

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

      5. associate-*r/ 89.4%

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

      6. associate-*r* 89.4%

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

      7. *-commutative 89.4%

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

      8. associate-/r* 89.4%

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

      9. metadata-eval 89.4%

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

   7. Simplified 89.4%

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

   if 0.0379999999999999991 < y

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. associate-+l+ 96.8%

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

      3. remove-double-neg 96.8%

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

      4. distribute-frac-neg 96.8%

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

      5. unsub-neg 96.8%

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

      6. neg-mul-1 96.8%

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

      7. associate-*r/ 96.8%

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

      8. associate-*l/ 96.8%

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

      9. neg-mul-1 96.8%

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

      10. times-frac 96.8%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.1%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 0.038:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 0.0225:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1500.0)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 0.0225)
     (+ x (* 0.3333333333333333 (/ t (* z y))))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1500.0) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 0.0225) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1500.0d0)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 0.0225d0) then
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1500.0) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 0.0225) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1500.0:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 0.0225:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1500.0)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 0.0225)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1500.0)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 0.0225)
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1500.0], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0225], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1500

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around 0 95.0%

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

   if -1500 < y < 0.022499999999999999

   1. Initial program 92.7%

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

      1. sub-neg 92.7%

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

      2. associate-+l+ 92.7%

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

      3. remove-double-neg 92.7%

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

      4. distribute-frac-neg 92.7%

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

      5. unsub-neg 92.7%

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

      6. neg-mul-1 92.7%

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

      7. associate-*r/ 92.7%

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

      8. associate-*l/ 92.7%

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

      9. neg-mul-1 92.7%

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

      10. times-frac 92.0%

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

      11. distribute-lft-out-- 92.0%

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

      12. *-commutative 92.0%

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

      13. associate-/r* 91.9%

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

      14. metadata-eval 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around 0 90.2%

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

      1. +-commutative 90.2%

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

   7. Simplified 90.2%

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

   if 0.022499999999999999 < y

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. associate-+l+ 96.8%

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

      3. remove-double-neg 96.8%

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

      4. distribute-frac-neg 96.8%

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

      5. unsub-neg 96.8%

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

      6. neg-mul-1 96.8%

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

      7. associate-*r/ 96.8%

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

      8. associate-*l/ 96.8%

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

      9. neg-mul-1 96.8%

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

      10. times-frac 96.8%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.1%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 0.0225:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -100000:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 0.0062:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot y}}{3}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -100000.0)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 0.0062)
     (+ x (/ (/ t (* z y)) 3.0))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -100000.0) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 0.0062) {
		tmp = x + ((t / (z * y)) / 3.0);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-100000.0d0)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 0.0062d0) then
        tmp = x + ((t / (z * y)) / 3.0d0)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -100000.0) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 0.0062) {
		tmp = x + ((t / (z * y)) / 3.0);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -100000.0:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 0.0062:
		tmp = x + ((t / (z * y)) / 3.0)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -100000.0)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 0.0062)
		tmp = Float64(x + Float64(Float64(t / Float64(z * y)) / 3.0));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -100000.0)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 0.0062)
		tmp = x + ((t / (z * y)) / 3.0);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -100000.0], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0062], N[(x + N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e5

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around 0 95.0%

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

   if -1e5 < y < 0.00619999999999999978

   1. Initial program 92.7%

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

      1. sub-neg 92.7%

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

      2. associate-+l+ 92.7%

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

      3. remove-double-neg 92.7%

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

      4. distribute-frac-neg 92.7%

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

      5. unsub-neg 92.7%

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

      6. neg-mul-1 92.7%

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

      7. associate-*r/ 92.7%

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

      8. associate-*l/ 92.7%

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

      9. neg-mul-1 92.7%

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

      10. times-frac 92.0%

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

      11. distribute-lft-out-- 92.0%

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

      12. *-commutative 92.0%

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

      13. associate-/r* 91.9%

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

      14. metadata-eval 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around 0 90.2%

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

      1. +-commutative 90.2%

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

   7. Simplified 90.2%

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

      1. metadata-eval 90.2%

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

      2. associate-/r* 88.0%

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

      3. times-frac 88.1%

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

      4. *-un-lft-identity 88.1%

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

      5. *-commutative 88.1%

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

      6. associate-/r* 88.0%

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

      7. associate-/r* 90.2%

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

   9. Applied egg-rr 90.2%

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

   if 0.00619999999999999978 < y

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. associate-+l+ 96.8%

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

      3. remove-double-neg 96.8%

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

      4. distribute-frac-neg 96.8%

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

      5. unsub-neg 96.8%

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

      6. neg-mul-1 96.8%

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

      7. associate-*r/ 96.8%

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

      8. associate-*l/ 96.8%

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

      9. neg-mul-1 96.8%

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

      10. times-frac 96.8%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.1%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -100000:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 0.0062:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot y}}{3}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 92.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 6:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.9)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 6.0)
     (+ x (/ (/ (* t 0.3333333333333333) z) y))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.9) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 6.0) {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.9d0)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 6.0d0) then
        tmp = x + (((t * 0.3333333333333333d0) / z) / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.9) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 6.0) {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.9:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 6.0:
		tmp = x + (((t * 0.3333333333333333) / z) / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.9)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 6.0)
		tmp = Float64(x + Float64(Float64(Float64(t * 0.3333333333333333) / z) / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.9)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 6.0)
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.9], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.0], N[(x + N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9000000000000004

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around 0 95.0%

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

   if -5.9000000000000004 < y < 6

   1. Initial program 92.7%

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

      1. sub-neg 92.7%

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

      2. associate-+l+ 92.7%

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

      3. remove-double-neg 92.7%

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

      4. distribute-frac-neg 92.7%

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

      5. unsub-neg 92.7%

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

      6. neg-mul-1 92.7%

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

      7. associate-*r/ 92.7%

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

      8. associate-*l/ 92.7%

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

      9. neg-mul-1 92.7%

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

      10. times-frac 92.0%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      11. distribute-lft-out-- 92.0%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      12. *-commutative 92.0%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      13. associate-/r* 91.9%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. metadata-eval 91.9%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 90.2%

      \[\leadsto \color{blue}{x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   6. Step-by-step derivation

      1. +-commutative 90.2%

         \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z} + x} \]

   7. Simplified 90.2%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z} + x} \]
   8. Step-by-step derivation

      1. associate-*r/ 90.2%

         \[\leadsto \color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}} + x \]

      2. *-commutative 90.2%

         \[\leadsto \frac{0.3333333333333333 \cdot t}{\color{blue}{z \cdot y}} + x \]

      3. associate-/r* 94.3%

         \[\leadsto \color{blue}{\frac{\frac{0.3333333333333333 \cdot t}{z}}{y}} + x \]

      4. *-commutative 94.3%

         \[\leadsto \frac{\frac{\color{blue}{t \cdot 0.3333333333333333}}{z}}{y} + x \]

   9. Applied egg-rr 94.3%

      \[\leadsto \color{blue}{\frac{\frac{t \cdot 0.3333333333333333}{z}}{y}} + x \]

   if 6 < y

   1. Initial program 96.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg 96.8%

         \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ 96.8%

         \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. remove-double-neg 96.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 96.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. unsub-neg 96.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      6. neg-mul-1 96.8%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      7. associate-*r/ 96.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      8. associate-*l/ 96.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. neg-mul-1 96.8%

         \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. times-frac 96.8%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      11. distribute-lft-out-- 99.7%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      12. *-commutative 99.7%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      13. associate-/r* 99.7%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. metadata-eval 99.7%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 94.1%

      \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 6:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 94.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 3.6 \cdot 10^{+210}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot y}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 3.6e+210)
   (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z)))
   (+ x (/ (/ t (* z y)) 3.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 3.6e+210) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else {
		tmp = x + ((t / (z * y)) / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 3.6d+210) then
        tmp = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
    else
        tmp = x + ((t / (z * y)) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 3.6e+210) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else {
		tmp = x + ((t / (z * y)) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 3.6e+210:
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z))
	else:
		tmp = x + ((t / (z * y)) / 3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 3.6e+210)
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(Float64(t / Float64(z * y)) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 3.6e+210)
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	else
		tmp = x + ((t / (z * y)) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 3.6e+210], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 3.6000000000000003e210

   1. Initial program 94.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg 94.5%

         \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ 94.5%

         \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. remove-double-neg 94.5%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 94.5%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. unsub-neg 94.5%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      6. neg-mul-1 94.5%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      7. associate-*r/ 94.5%

         \[\leadsto x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      8. associate-*l/ 94.4%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. neg-mul-1 94.4%

         \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. times-frac 96.4%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      11. distribute-lft-out-- 97.7%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      12. *-commutative 97.7%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      13. associate-/r* 97.7%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. metadata-eval 97.7%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   if 3.6000000000000003e210 < (*.f64 z 3)

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ 99.8%

         \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. remove-double-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. unsub-neg 99.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      6. neg-mul-1 99.8%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      7. associate-*r/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      8. associate-*l/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. neg-mul-1 99.8%

         \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. times-frac 73.8%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      11. distribute-lft-out-- 73.8%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      12. *-commutative 73.8%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      13. associate-/r* 73.8%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. metadata-eval 73.8%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 92.7%

      \[\leadsto \color{blue}{x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   6. Step-by-step derivation

      1. +-commutative 92.7%

         \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z} + x} \]

   7. Simplified 92.7%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z} + x} \]
   8. Step-by-step derivation

      1. metadata-eval 92.7%

         \[\leadsto \color{blue}{\frac{1}{3}} \cdot \frac{t}{y \cdot z} + x \]

      2. associate-/r* 66.7%

         \[\leadsto \frac{1}{3} \cdot \color{blue}{\frac{\frac{t}{y}}{z}} + x \]

      3. times-frac 66.6%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{t}{y}}{3 \cdot z}} + x \]

      4. *-un-lft-identity 66.6%

         \[\leadsto \frac{\color{blue}{\frac{t}{y}}}{3 \cdot z} + x \]

      5. *-commutative 66.6%

         \[\leadsto \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}} + x \]

      6. associate-/r* 66.7%

         \[\leadsto \color{blue}{\frac{\frac{\frac{t}{y}}{z}}{3}} + x \]

      7. associate-/r* 92.8%

         \[\leadsto \frac{\color{blue}{\frac{t}{y \cdot z}}}{3} + x \]

   9. Applied egg-rr 92.8%

      \[\leadsto \color{blue}{\frac{\frac{t}{y \cdot z}}{3}} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 3.6 \cdot 10^{+210}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot y}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 3.6 \cdot 10^{+210}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot y}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 3.6e+210)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ x (/ (/ t (* z y)) 3.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 3.6e+210) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + ((t / (z * y)) / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 3.6d+210) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = x + ((t / (z * y)) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 3.6e+210) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + ((t / (z * y)) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 3.6e+210:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = x + ((t / (z * y)) / 3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 3.6e+210)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / Float64(z * y)) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 3.6e+210)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = x + ((t / (z * y)) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 3.6e+210], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 3.6000000000000003e210

   1. Initial program 94.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 94.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 94.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 94.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 94.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 94.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 94.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 96.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 97.8%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   if 3.6000000000000003e210 < (*.f64 z 3)

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ 99.8%

         \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. remove-double-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. unsub-neg 99.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      6. neg-mul-1 99.8%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      7. associate-*r/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      8. associate-*l/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. neg-mul-1 99.8%

         \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. times-frac 73.8%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      11. distribute-lft-out-- 73.8%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      12. *-commutative 73.8%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      13. associate-/r* 73.8%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. metadata-eval 73.8%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 92.7%

      \[\leadsto \color{blue}{x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   6. Step-by-step derivation

      1. +-commutative 92.7%

         \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z} + x} \]

   7. Simplified 92.7%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z} + x} \]
   8. Step-by-step derivation

      1. metadata-eval 92.7%

         \[\leadsto \color{blue}{\frac{1}{3}} \cdot \frac{t}{y \cdot z} + x \]

      2. associate-/r* 66.7%

         \[\leadsto \frac{1}{3} \cdot \color{blue}{\frac{\frac{t}{y}}{z}} + x \]

      3. times-frac 66.6%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{t}{y}}{3 \cdot z}} + x \]

      4. *-un-lft-identity 66.6%

         \[\leadsto \frac{\color{blue}{\frac{t}{y}}}{3 \cdot z} + x \]

      5. *-commutative 66.6%

         \[\leadsto \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}} + x \]

      6. associate-/r* 66.7%

         \[\leadsto \color{blue}{\frac{\frac{\frac{t}{y}}{z}}{3}} + x \]

      7. associate-/r* 92.8%

         \[\leadsto \frac{\color{blue}{\frac{t}{y \cdot z}}}{3} + x \]

   9. Applied egg-rr 92.8%

      \[\leadsto \color{blue}{\frac{\frac{t}{y \cdot z}}{3}} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 3.6 \cdot 10^{+210}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot y}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+20) x (if (<= z 1.8e+17) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+20) {
		tmp = x;
	} else if (z <= 1.8e+17) {
		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 <= (-2.7d+20)) then
        tmp = x
    else if (z <= 1.8d+17) 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 <= -2.7e+20) {
		tmp = x;
	} else if (z <= 1.8e+17) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+20:
		tmp = x
	elif z <= 1.8e+17:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+20)
		tmp = x;
	elseif (z <= 1.8e+17)
		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 <= -2.7e+20)
		tmp = x;
	elseif (z <= 1.8e+17)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+20], x, If[LessEqual[z, 1.8e+17], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e20 or 1.8e17 < z

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ 99.8%

         \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. remove-double-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. unsub-neg 99.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      6. neg-mul-1 99.8%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      7. associate-*r/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      8. associate-*l/ 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. neg-mul-1 99.7%

         \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. times-frac 90.6%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      11. distribute-lft-out-- 90.6%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      12. *-commutative 90.6%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      13. associate-/r* 90.6%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. metadata-eval 90.6%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 53.4%

      \[\leadsto \color{blue}{x} \]

   if -2.7e20 < z < 1.8e17

   1. Initial program 91.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 91.1%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 91.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 97.7%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 99.8%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   7. Taylor expanded in y around inf 46.3%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+16}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e+20) x (if (<= z 9e+16) (/ y (* z -3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e+20) {
		tmp = x;
	} else if (z <= 9e+16) {
		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 <= (-3.7d+20)) then
        tmp = x
    else if (z <= 9d+16) 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 <= -3.7e+20) {
		tmp = x;
	} else if (z <= 9e+16) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e+20:
		tmp = x
	elif z <= 9e+16:
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e+20)
		tmp = x;
	elseif (z <= 9e+16)
		tmp = Float64(y / Float64(z * -3.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.7e+20)
		tmp = x;
	elseif (z <= 9e+16)
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e+20], x, If[LessEqual[z, 9e+16], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7e20 or 9e16 < z

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ 99.8%

         \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. remove-double-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. unsub-neg 99.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      6. neg-mul-1 99.8%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      7. associate-*r/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      8. associate-*l/ 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. neg-mul-1 99.7%

         \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. times-frac 90.6%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      11. distribute-lft-out-- 90.6%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      12. *-commutative 90.6%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      13. associate-/r* 90.6%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. metadata-eval 90.6%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 53.4%

      \[\leadsto \color{blue}{x} \]

   if -3.7e20 < z < 9e16

   1. Initial program 91.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 91.1%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 91.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 97.7%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 99.8%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   7. Taylor expanded in y around inf 46.3%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-/r/ 46.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{-0.3333333333333333}}} \]

      3. div-inv 46.3%

         \[\leadsto \frac{y}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}} \]

      4. metadata-eval 46.3%

         \[\leadsto \frac{y}{z \cdot \color{blue}{-3}} \]

   9. Applied egg-rr 46.3%

      \[\leadsto \color{blue}{\frac{y}{z \cdot -3}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+16}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 42000000000000:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e+20) x (if (<= z 42000000000000.0) (/ (/ y z) -3.0) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e+20) {
		tmp = x;
	} else if (z <= 42000000000000.0) {
		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 <= (-3.7d+20)) then
        tmp = x
    else if (z <= 42000000000000.0d0) 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 <= -3.7e+20) {
		tmp = x;
	} else if (z <= 42000000000000.0) {
		tmp = (y / z) / -3.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e+20:
		tmp = x
	elif z <= 42000000000000.0:
		tmp = (y / z) / -3.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e+20)
		tmp = x;
	elseif (z <= 42000000000000.0)
		tmp = 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 <= -3.7e+20)
		tmp = x;
	elseif (z <= 42000000000000.0)
		tmp = (y / z) / -3.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e+20], x, If[LessEqual[z, 42000000000000.0], N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7e20 or 4.2e13 < z

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

      2. associate-+l+ 99.8%

         \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      3. remove-double-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

      4. distribute-frac-neg 99.8%

         \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      5. unsub-neg 99.8%

         \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      6. neg-mul-1 99.8%

         \[\leadsto x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      7. associate-*r/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      8. associate-*l/ 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

      9. neg-mul-1 99.7%

         \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

      10. times-frac 90.6%

          \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

      11. distribute-lft-out-- 90.6%

          \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

      12. *-commutative 90.6%

          \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

      13. associate-/r* 90.6%

          \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

      14. metadata-eval 90.6%

          \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 53.4%

      \[\leadsto \color{blue}{x} \]

   if -3.7e20 < z < 4.2e13

   1. Initial program 91.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 91.1%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 91.1%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 91.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 97.7%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 99.8%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   7. Taylor expanded in y around inf 46.3%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 46.3%

         \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 46.3%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

      3. clear-num 46.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot -0.3333333333333333}}} \]

      4. reciprocal-define 32.9%

         \[\leadsto \color{blue}{\mathsf{reciprocal}\left(\left(\frac{z}{y \cdot -0.3333333333333333}\right)\right)} \]

      5. *-commutative 32.9%

         \[\leadsto \mathsf{reciprocal}\left(\left(\frac{z}{\color{blue}{-0.3333333333333333 \cdot y}}\right)\right) \]

      6. associate-/r* 32.9%

         \[\leadsto \mathsf{reciprocal}\left(\color{blue}{\left(\frac{\frac{z}{-0.3333333333333333}}{y}\right)}\right) \]

      7. div-inv 32.9%

         \[\leadsto \mathsf{reciprocal}\left(\left(\frac{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}}{y}\right)\right) \]

      8. metadata-eval 32.9%

         \[\leadsto \mathsf{reciprocal}\left(\left(\frac{z \cdot \color{blue}{-3}}{y}\right)\right) \]

   9. Applied egg-rr 32.9%

      \[\leadsto \color{blue}{\mathsf{reciprocal}\left(\left(\frac{z \cdot -3}{y}\right)\right)} \]
   10. Step-by-step derivation

       1. reciprocal-undefine 46.3%

          \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot -3}{y}}} \]

       2. clear-num 46.3%

          \[\leadsto \color{blue}{\frac{y}{z \cdot -3}} \]

       3. associate-/r* 46.4%

          \[\leadsto \color{blue}{\frac{\frac{y}{z}}{-3}} \]

   11. Applied egg-rr 46.4%

       \[\leadsto \color{blue}{\frac{\frac{y}{z}}{-3}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 42000000000000:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 94.9%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. sub-neg 94.9%

      \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. associate-+l+ 94.9%

      \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   3. remove-double-neg 94.9%

      \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]

   4. distribute-frac-neg 94.9%

      \[\leadsto x + \left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

   5. unsub-neg 94.9%

      \[\leadsto x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   6. neg-mul-1 94.9%

      \[\leadsto x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

   7. associate-*r/ 94.9%

      \[\leadsto x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

   8. associate-*l/ 94.9%

      \[\leadsto x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \frac{-t}{\left(z \cdot 3\right) \cdot y}\right) \]

   9. neg-mul-1 94.9%

      \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]

   10. times-frac 94.5%

       \[\leadsto x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]

   11. distribute-lft-out-- 95.7%

       \[\leadsto x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]

   12. *-commutative 95.7%

       \[\leadsto x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]

   13. associate-/r* 95.7%

       \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

   14. metadata-eval 95.7%

       \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

3. Simplified 95.7%

   \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 28.3%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 28.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 95.7% 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 2024024 
(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))))