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

Percentage Accurate: 95.6% → 97.9%

Time: 13.7s

Alternatives: 15

Speedup: 1.4×

• 28.0% 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: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -5e+23)
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* 3.0 y))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -5e+23) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-5d+23)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (3.0d0 * y)))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -5e+23) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -5e+23:
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -5e+23)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(3.0 * y))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -5e+23)
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -5e+23], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -4.9999999999999999e23

   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* 99.8%

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

      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

   if -4.9999999999999999e23 < (*.f64 z 3)

   1. Initial program 94.0%

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

      1. associate-*l* 94.0%

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

      2. *-commutative 94.0%

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

   3. Simplified 94.0%

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

      1. associate-+l- 94.0%

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

      2. *-commutative 94.0%

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

      3. associate-*l* 94.0%

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

      4. associate-/l/ 97.3%

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

      5. sub-div 98.3%

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

   6. Applied egg-rr 98.3%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{+19}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}{z}\\ \mathbf{elif}\;y \leq -0.00092:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{3} \cdot \frac{-1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* 0.3333333333333333 (/ y z)))))
   (if (<= y -5.5e+78)
     t_1
     (if (<= y -2.95e+19)
       (/ (* 0.3333333333333333 (- (/ t y) y)) z)
       (if (<= y -0.00092)
         t_1
         (if (<= y 3.6e+72)
           (+ x (* (/ t z) (/ 0.3333333333333333 y)))
           (+ x (* (/ y 3.0) (/ -1.0 z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (0.3333333333333333 * (y / z));
	double tmp;
	if (y <= -5.5e+78) {
		tmp = t_1;
	} else if (y <= -2.95e+19) {
		tmp = (0.3333333333333333 * ((t / y) - y)) / z;
	} else if (y <= -0.00092) {
		tmp = t_1;
	} else if (y <= 3.6e+72) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + ((y / 3.0) * (-1.0 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (0.3333333333333333d0 * (y / z))
    if (y <= (-5.5d+78)) then
        tmp = t_1
    else if (y <= (-2.95d+19)) then
        tmp = (0.3333333333333333d0 * ((t / y) - y)) / z
    else if (y <= (-0.00092d0)) then
        tmp = t_1
    else if (y <= 3.6d+72) then
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    else
        tmp = x + ((y / 3.0d0) * ((-1.0d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (0.3333333333333333 * (y / z));
	double tmp;
	if (y <= -5.5e+78) {
		tmp = t_1;
	} else if (y <= -2.95e+19) {
		tmp = (0.3333333333333333 * ((t / y) - y)) / z;
	} else if (y <= -0.00092) {
		tmp = t_1;
	} else if (y <= 3.6e+72) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + ((y / 3.0) * (-1.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (0.3333333333333333 * (y / z))
	tmp = 0
	if y <= -5.5e+78:
		tmp = t_1
	elif y <= -2.95e+19:
		tmp = (0.3333333333333333 * ((t / y) - y)) / z
	elif y <= -0.00092:
		tmp = t_1
	elif y <= 3.6e+72:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x + ((y / 3.0) * (-1.0 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(0.3333333333333333 * Float64(y / z)))
	tmp = 0.0
	if (y <= -5.5e+78)
		tmp = t_1;
	elseif (y <= -2.95e+19)
		tmp = Float64(Float64(0.3333333333333333 * Float64(Float64(t / y) - y)) / z);
	elseif (y <= -0.00092)
		tmp = t_1;
	elseif (y <= 3.6e+72)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x + Float64(Float64(y / 3.0) * Float64(-1.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (0.3333333333333333 * (y / z));
	tmp = 0.0;
	if (y <= -5.5e+78)
		tmp = t_1;
	elseif (y <= -2.95e+19)
		tmp = (0.3333333333333333 * ((t / y) - y)) / z;
	elseif (y <= -0.00092)
		tmp = t_1;
	elseif (y <= 3.6e+72)
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x + ((y / 3.0) * (-1.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+78], t$95$1, If[LessEqual[y, -2.95e+19], N[(N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -0.00092], t$95$1, If[LessEqual[y, 3.6e+72], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / 3.0), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.4999999999999997e78 or -2.95e19 < y < -9.2000000000000003e-4

   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 99.1%

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

   if -5.4999999999999997e78 < y < -2.95e19

   1. Initial program 93.6%

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

      1. *-un-lft-identity 93.6%

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

      2. times-frac 93.1%

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

   4. Applied egg-rr 93.1%

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

      1. clear-num 93.2%

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

      2. inv-pow 93.2%

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

      3. *-commutative 93.2%

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

   6. Applied egg-rr 93.2%

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

      1. unpow-1 93.2%

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

      2. associate-*r* 93.2%

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

   8. Simplified 93.2%

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

   9. Taylor expanded in x around 0 93.6%

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

       1. distribute-lft-out-- 93.6%

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

       2. associate-/r* 99.7%

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

       3. distribute-lft-out-- 99.7%

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

       4. associate-*r/ 99.4%

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

       5. associate-*r/ 99.4%

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

       6. div-sub 99.4%

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

       7. distribute-lft-out-- 99.4%

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

   11. Simplified 99.4%

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

   if -9.2000000000000003e-4 < y < 3.60000000000000035e72

   1. Initial program 93.1%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in t around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-/r* 89.6%

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

      4. metadata-eval 89.6%

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

      5. times-frac 89.7%

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

      6. associate-*r/ 89.7%

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

      7. associate-/r* 89.6%

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

      8. associate-/l/ 89.7%

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

      9. associate-/r* 89.7%

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

      10. metadata-eval 89.7%

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

   7. Simplified 89.7%

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

   if 3.60000000000000035e72 < y

   1. Initial program 97.6%

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

      1. associate-*l* 97.6%

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

      2. *-commutative 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in t around 0 95.5%

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

      1. metadata-eval 95.5%

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

      2. times-frac 95.5%

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

      3. *-commutative 95.5%

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

      4. *-un-lft-identity 95.5%

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

   7. Applied egg-rr 95.5%

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

      1. *-un-lft-identity 97.6%

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

      2. times-frac 97.6%

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

   9. Applied egg-rr 95.6%

      \[\leadsto x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+78}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{+19}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}{z}\\ \mathbf{elif}\;y \leq -0.00092:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{3} \cdot \frac{-1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0285:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.0285)
   (/ y (* z -3.0))
   (if (<= y 1.65e-99)
     (* t (/ (/ 0.3333333333333333 y) z))
     (if (<= y 3.3e+46) x (/ (* y -0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.0285) {
		tmp = y / (z * -3.0);
	} else if (y <= 1.65e-99) {
		tmp = t * ((0.3333333333333333 / y) / z);
	} else if (y <= 3.3e+46) {
		tmp = x;
	} else {
		tmp = (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 <= (-0.0285d0)) then
        tmp = y / (z * (-3.0d0))
    else if (y <= 1.65d-99) then
        tmp = t * ((0.3333333333333333d0 / y) / z)
    else if (y <= 3.3d+46) then
        tmp = x
    else
        tmp = (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 <= -0.0285) {
		tmp = y / (z * -3.0);
	} else if (y <= 1.65e-99) {
		tmp = t * ((0.3333333333333333 / y) / z);
	} else if (y <= 3.3e+46) {
		tmp = x;
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.0285:
		tmp = y / (z * -3.0)
	elif y <= 1.65e-99:
		tmp = t * ((0.3333333333333333 / y) / z)
	elif y <= 3.3e+46:
		tmp = x
	else:
		tmp = (y * -0.3333333333333333) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.0285)
		tmp = Float64(y / Float64(z * -3.0));
	elseif (y <= 1.65e-99)
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / y) / z));
	elseif (y <= 3.3e+46)
		tmp = x;
	else
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.0285)
		tmp = y / (z * -3.0);
	elseif (y <= 1.65e-99)
		tmp = t * ((0.3333333333333333 / y) / z);
	elseif (y <= 3.3e+46)
		tmp = x;
	else
		tmp = (y * -0.3333333333333333) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.0285], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-99], N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+46], x, N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.028500000000000001

   1. Initial program 98.5%

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

      1. *-un-lft-identity 98.5%

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

      2. times-frac 98.3%

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

   4. Applied egg-rr 98.3%

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

      1. clear-num 98.3%

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

      2. inv-pow 98.3%

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

      3. *-commutative 98.3%

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

   6. Applied egg-rr 98.3%

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

      1. unpow-1 98.3%

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

      2. associate-*r* 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in y around inf 71.2%

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

       1. associate-*r/ 71.1%

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

       2. associate-/l* 71.1%

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

       3. associate-/r/ 71.1%

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

   11. Simplified 71.1%

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

       1. *-commutative 71.1%

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

       2. clear-num 71.0%

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

       3. un-div-inv 71.1%

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

       4. div-inv 71.2%

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

       5. metadata-eval 71.2%

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

   13. Applied egg-rr 71.2%

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

   if -0.028500000000000001 < y < 1.64999999999999993e-99

   1. Initial program 92.2%

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

      1. *-un-lft-identity 92.2%

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

      2. times-frac 92.2%

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

   4. Applied egg-rr 92.2%

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

      1. clear-num 92.2%

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

      2. inv-pow 92.2%

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

      3. *-commutative 92.2%

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

   6. Applied egg-rr 92.2%

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

      1. unpow-1 92.2%

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

      2. associate-*r* 92.2%

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

   8. Simplified 92.2%

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

   9. Taylor expanded in y around 0 62.8%

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

       1. associate-*r/ 62.9%

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

       2. *-commutative 62.9%

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

       3. associate-*r/ 62.8%

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

       4. associate-/r* 62.8%

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

   11. Simplified 62.8%

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

   if 1.64999999999999993e-99 < y < 3.2999999999999998e46

   1. Initial program 96.9%

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

      1. associate-*l* 96.9%

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

      2. *-commutative 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf 57.0%

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

   if 3.2999999999999998e46 < y

   1. Initial program 96.0%

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

      1. associate-*l* 96.0%

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

      2. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around 0 88.8%

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

   6. Taylor expanded in x around 0 57.0%

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

      1. associate-*r/ 57.0%

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

   8. Simplified 57.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0285:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-104}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.85)
   (/ y (* z -3.0))
   (if (<= y 2.8e-104)
     (* 0.3333333333333333 (/ (/ t y) z))
     (if (<= y 1.65e+46) x (/ (* y -0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.85) {
		tmp = y / (z * -3.0);
	} else if (y <= 2.8e-104) {
		tmp = 0.3333333333333333 * ((t / y) / z);
	} else if (y <= 1.65e+46) {
		tmp = x;
	} else {
		tmp = (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 <= (-2.85d0)) then
        tmp = y / (z * (-3.0d0))
    else if (y <= 2.8d-104) then
        tmp = 0.3333333333333333d0 * ((t / y) / z)
    else if (y <= 1.65d+46) then
        tmp = x
    else
        tmp = (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 <= -2.85) {
		tmp = y / (z * -3.0);
	} else if (y <= 2.8e-104) {
		tmp = 0.3333333333333333 * ((t / y) / z);
	} else if (y <= 1.65e+46) {
		tmp = x;
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.85:
		tmp = y / (z * -3.0)
	elif y <= 2.8e-104:
		tmp = 0.3333333333333333 * ((t / y) / z)
	elif y <= 1.65e+46:
		tmp = x
	else:
		tmp = (y * -0.3333333333333333) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.85)
		tmp = Float64(y / Float64(z * -3.0));
	elseif (y <= 2.8e-104)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / y) / z));
	elseif (y <= 1.65e+46)
		tmp = x;
	else
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.85)
		tmp = y / (z * -3.0);
	elseif (y <= 2.8e-104)
		tmp = 0.3333333333333333 * ((t / y) / z);
	elseif (y <= 1.65e+46)
		tmp = x;
	else
		tmp = (y * -0.3333333333333333) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.85], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-104], N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+46], x, N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.85000000000000009

   1. Initial program 98.5%

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

      1. *-un-lft-identity 98.5%

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

      2. times-frac 98.3%

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

   4. Applied egg-rr 98.3%

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

      1. clear-num 98.3%

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

      2. inv-pow 98.3%

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

      3. *-commutative 98.3%

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

   6. Applied egg-rr 98.3%

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

      1. unpow-1 98.3%

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

      2. associate-*r* 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in y around inf 71.2%

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

       1. associate-*r/ 71.1%

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

       2. associate-/l* 71.1%

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

       3. associate-/r/ 71.1%

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

   11. Simplified 71.1%

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

       1. *-commutative 71.1%

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

       2. clear-num 71.0%

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

       3. un-div-inv 71.1%

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

       4. div-inv 71.2%

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

       5. metadata-eval 71.2%

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

   13. Applied egg-rr 71.2%

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

   if -2.85000000000000009 < y < 2.8e-104

   1. Initial program 92.2%

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

      1. associate-*l* 92.3%

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

      2. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. +-commutative 88.3%

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

   7. Simplified 88.3%

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

   8. Taylor expanded in t around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-/r* 64.6%

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

   10. Simplified 64.6%

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

   if 2.8e-104 < y < 1.6499999999999999e46

   1. Initial program 96.9%

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

      1. associate-*l* 96.9%

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

      2. *-commutative 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf 57.0%

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

   if 1.6499999999999999e46 < y

   1. Initial program 96.0%

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

      1. associate-*l* 96.0%

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

      2. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around 0 88.8%

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

   6. Taylor expanded in x around 0 57.0%

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

      1. associate-*r/ 57.0%

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

   8. Simplified 57.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-104}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00315 \lor \neg \left(y \leq 4.4 \cdot 10^{+75}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.00315) (not (<= y 4.4e+75)))
   (- x (/ y (* z 3.0)))
   (+ x (* (/ t z) (/ 0.3333333333333333 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.00315) || !(y <= 4.4e+75)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.00315d0)) .or. (.not. (y <= 4.4d+75))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.00315) || !(y <= 4.4e+75)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.00315) or not (y <= 4.4e+75):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.00315) || !(y <= 4.4e+75))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.00315) || ~((y <= 4.4e+75)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.00315], N[Not[LessEqual[y, 4.4e+75]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00315 or 4.40000000000000024e75 < y

   1. Initial program 98.1%

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

      1. associate-*l* 98.1%

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

      2. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around 0 93.6%

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

      1. metadata-eval 93.6%

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

      2. times-frac 93.6%

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

      3. *-commutative 93.6%

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

      4. *-un-lft-identity 93.6%

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

   7. Applied egg-rr 93.6%

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

   if -0.00315 < y < 4.40000000000000024e75

   1. Initial program 93.1%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in t around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-/r* 89.6%

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

      4. metadata-eval 89.6%

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

      5. times-frac 89.7%

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

      6. associate-*r/ 89.7%

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

      7. associate-/r* 89.6%

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

      8. associate-/l/ 89.7%

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

      9. associate-/r* 89.7%

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

      10. metadata-eval 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00315 \lor \neg \left(y \leq 4.4 \cdot 10^{+75}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.57:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{3} \cdot \frac{-1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.57)
   (- x (/ y (* z 3.0)))
   (if (<= y 3.5e+72)
     (+ x (* (/ t z) (/ 0.3333333333333333 y)))
     (+ x (* (/ y 3.0) (/ -1.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.57) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 3.5e+72) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + ((y / 3.0) * (-1.0 / 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 <= (-0.57d0)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 3.5d+72) then
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    else
        tmp = x + ((y / 3.0d0) * ((-1.0d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.57) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 3.5e+72) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + ((y / 3.0) * (-1.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.57:
		tmp = x - (y / (z * 3.0))
	elif y <= 3.5e+72:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x + ((y / 3.0) * (-1.0 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.57)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 3.5e+72)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x + Float64(Float64(y / 3.0) * Float64(-1.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.57)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 3.5e+72)
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x + ((y / 3.0) * (-1.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.57], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+72], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / 3.0), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.569999999999999951

   1. Initial program 98.5%

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

      1. associate-*l* 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 92.4%

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

      1. metadata-eval 92.4%

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

      2. times-frac 92.4%

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

      3. *-commutative 92.4%

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

      4. *-un-lft-identity 92.4%

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

   7. Applied egg-rr 92.4%

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

   if -0.569999999999999951 < y < 3.5000000000000001e72

   1. Initial program 93.1%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in t around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-/r* 89.6%

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

      4. metadata-eval 89.6%

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

      5. times-frac 89.7%

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

      6. associate-*r/ 89.7%

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

      7. associate-/r* 89.6%

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

      8. associate-/l/ 89.7%

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

      9. associate-/r* 89.7%

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

      10. metadata-eval 89.7%

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

   7. Simplified 89.7%

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

   if 3.5000000000000001e72 < y

   1. Initial program 97.6%

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

      1. associate-*l* 97.6%

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

      2. *-commutative 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in t around 0 95.5%

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

      1. metadata-eval 95.5%

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

      2. times-frac 95.5%

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

      3. *-commutative 95.5%

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

      4. *-un-lft-identity 95.5%

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

   7. Applied egg-rr 95.5%

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

      1. *-un-lft-identity 97.6%

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

      2. times-frac 97.6%

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

   9. Applied egg-rr 95.6%

      \[\leadsto x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.57:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{3} \cdot \frac{-1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-179} \lor \neg \left(y \leq 1.4 \cdot 10^{-106}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.2e-179) (not (<= y 1.4e-106)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* 0.3333333333333333 (/ (/ t y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-179) || !(y <= 1.4e-106)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.2d-179)) .or. (.not. (y <= 1.4d-106))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = 0.3333333333333333d0 * ((t / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-179) || !(y <= 1.4e-106)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.2e-179) or not (y <= 1.4e-106):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = 0.3333333333333333 * ((t / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.2e-179) || !(y <= 1.4e-106))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.2e-179) || ~((y <= 1.4e-106)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = 0.3333333333333333 * ((t / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.2e-179], N[Not[LessEqual[y, 1.4e-106]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000005e-179 or 1.39999999999999994e-106 < y

   1. Initial program 97.7%

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

      1. associate-*l* 97.8%

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

      2. *-commutative 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around 0 79.4%

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

   if -6.2000000000000005e-179 < y < 1.39999999999999994e-106

   1. Initial program 87.7%

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

      1. associate-*l* 87.8%

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

      2. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in y around 0 87.7%

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

      1. +-commutative 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in t around inf 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-/r* 76.3%

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

   10. Simplified 76.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-179} \lor \neg \left(y \leq 1.4 \cdot 10^{-106}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-179} \lor \neg \left(y \leq 2.1 \cdot 10^{-103}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.2e-179) (not (<= y 2.1e-103)))
   (- x (/ y (* z 3.0)))
   (* 0.3333333333333333 (/ (/ t y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-179) || !(y <= 2.1e-103)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.2d-179)) .or. (.not. (y <= 2.1d-103))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = 0.3333333333333333d0 * ((t / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-179) || !(y <= 2.1e-103)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.2e-179) or not (y <= 2.1e-103):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = 0.3333333333333333 * ((t / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.2e-179) || !(y <= 2.1e-103))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.2e-179) || ~((y <= 2.1e-103)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = 0.3333333333333333 * ((t / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.2e-179], N[Not[LessEqual[y, 2.1e-103]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000005e-179 or 2.10000000000000005e-103 < y

   1. Initial program 97.7%

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

      1. associate-*l* 97.8%

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

      2. *-commutative 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. metadata-eval 79.4%

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

      2. times-frac 79.5%

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

      3. *-commutative 79.5%

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

      4. *-un-lft-identity 79.5%

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

   7. Applied egg-rr 79.5%

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

   if -6.2000000000000005e-179 < y < 2.10000000000000005e-103

   1. Initial program 87.7%

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

      1. associate-*l* 87.8%

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

      2. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in y around 0 87.7%

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

      1. +-commutative 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in t around inf 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-/r* 76.3%

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

   10. Simplified 76.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-179} \lor \neg \left(y \leq 2.1 \cdot 10^{-103}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-179} \lor \neg \left(y \leq 2.1 \cdot 10^{-99}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.3e-179) (not (<= y 2.1e-99)))
   (- x (/ y (* z 3.0)))
   (/ 0.3333333333333333 (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.3e-179) || !(y <= 2.1e-99)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 / (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.3d-179)) .or. (.not. (y <= 2.1d-99))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = 0.3333333333333333d0 / (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.3e-179) || !(y <= 2.1e-99)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 / (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.3e-179) or not (y <= 2.1e-99):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = 0.3333333333333333 / (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.3e-179) || !(y <= 2.1e-99))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(0.3333333333333333 / Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.3e-179) || ~((y <= 2.1e-99)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = 0.3333333333333333 / (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.3e-179], N[Not[LessEqual[y, 2.1e-99]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 / N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.29999999999999994e-179 or 2.09999999999999984e-99 < y

   1. Initial program 97.7%

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

      1. associate-*l* 97.8%

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

      2. *-commutative 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. metadata-eval 79.4%

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

      2. times-frac 79.5%

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

      3. *-commutative 79.5%

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

      4. *-un-lft-identity 79.5%

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

   7. Applied egg-rr 79.5%

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

   if -5.29999999999999994e-179 < y < 2.09999999999999984e-99

   1. Initial program 87.7%

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

      1. associate-*l* 87.8%

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

      2. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in y around 0 87.7%

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

      1. +-commutative 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in t around inf 70.6%

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

      1. *-commutative 70.6%

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

   10. Simplified 70.6%

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

       1. associate-*l/ 70.6%

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

       2. *-commutative 70.6%

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

       3. associate-/l* 70.6%

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

       4. *-commutative 70.6%

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

       5. *-un-lft-identity 70.6%

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

       6. times-frac 76.8%

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

       7. /-rgt-identity 76.8%

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

   12. Applied egg-rr 76.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-179} \lor \neg \left(y \leq 2.1 \cdot 10^{-99}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-179} \lor \neg \left(y \leq 1.7 \cdot 10^{-98}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.2e-179) (not (<= y 1.7e-98)))
   (- x (/ y (* z 3.0)))
   (/ 0.3333333333333333 (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-179) || !(y <= 1.7e-98)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 / (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.2d-179)) .or. (.not. (y <= 1.7d-98))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = 0.3333333333333333d0 / (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-179) || !(y <= 1.7e-98)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 / (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.2e-179) or not (y <= 1.7e-98):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = 0.3333333333333333 / (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.2e-179) || !(y <= 1.7e-98))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(0.3333333333333333 / Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.2e-179) || ~((y <= 1.7e-98)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = 0.3333333333333333 / (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.2e-179], N[Not[LessEqual[y, 1.7e-98]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000005e-179 or 1.7000000000000001e-98 < y

   1. Initial program 97.7%

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

      1. associate-*l* 97.8%

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

      2. *-commutative 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. metadata-eval 79.4%

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

      2. times-frac 79.5%

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

      3. *-commutative 79.5%

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

      4. *-un-lft-identity 79.5%

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

   7. Applied egg-rr 79.5%

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

   if -6.2000000000000005e-179 < y < 1.7000000000000001e-98

   1. Initial program 87.7%

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

      1. *-un-lft-identity 87.7%

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

      2. times-frac 87.7%

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

   4. Applied egg-rr 87.7%

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

      1. clear-num 87.7%

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

      2. inv-pow 87.7%

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

      3. *-commutative 87.7%

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

   6. Applied egg-rr 87.7%

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

      1. unpow-1 87.7%

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

      2. associate-*r* 87.7%

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

   8. Simplified 87.7%

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

   9. Taylor expanded in y around 0 70.6%

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

       1. associate-*r/ 70.6%

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

       2. *-commutative 70.6%

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

       3. associate-*r/ 70.5%

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

       4. associate-/r* 70.5%

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

   11. Simplified 70.5%

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

       1. associate-*r/ 76.4%

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

       2. associate-*l/ 78.0%

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

       3. clear-num 78.0%

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

       4. frac-times 78.0%

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

       5. metadata-eval 78.0%

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

   13. Applied egg-rr 78.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-179} \lor \neg \left(y \leq 1.7 \cdot 10^{-98}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.25e+19) x (if (<= x 2.4e+31) (* (/ y z) -0.3333333333333333) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.25e+19) {
		tmp = x;
	} else if (x <= 2.4e+31) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.25d+19)) then
        tmp = x
    else if (x <= 2.4d+31) then
        tmp = (y / z) * (-0.3333333333333333d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.25e+19) {
		tmp = x;
	} else if (x <= 2.4e+31) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.25e+19:
		tmp = x
	elif x <= 2.4e+31:
		tmp = (y / z) * -0.3333333333333333
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.25e+19)
		tmp = x;
	elseif (x <= 2.4e+31)
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.25e+19)
		tmp = x;
	elseif (x <= 2.4e+31)
		tmp = (y / z) * -0.3333333333333333;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.25e+19], x, If[LessEqual[x, 2.4e+31], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.25e19 or 2.39999999999999982e31 < x

   1. Initial program 98.3%

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

      1. associate-*l* 98.3%

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

      2. *-commutative 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf 58.6%

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

   if -3.25e19 < x < 2.39999999999999982e31

   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* 92.7%

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

      2. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in t around 0 53.2%

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

   6. Taylor expanded in x around 0 48.2%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.6e+28) x (if (<= x 3.7e+27) (/ y (* z -3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e+28) {
		tmp = x;
	} else if (x <= 3.7e+27) {
		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 (x <= (-1.6d+28)) then
        tmp = x
    else if (x <= 3.7d+27) 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 (x <= -1.6e+28) {
		tmp = x;
	} else if (x <= 3.7e+27) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.6e+28:
		tmp = x
	elif x <= 3.7e+27:
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.6e+28)
		tmp = x;
	elseif (x <= 3.7e+27)
		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 (x <= -1.6e+28)
		tmp = x;
	elseif (x <= 3.7e+27)
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.6e+28], x, If[LessEqual[x, 3.7e+27], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e28 or 3.70000000000000002e27 < x

   1. Initial program 98.3%

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

      1. associate-*l* 98.3%

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

      2. *-commutative 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf 58.6%

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

   if -1.6e28 < x < 3.70000000000000002e27

   1. Initial program 92.7%

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

      1. *-un-lft-identity 92.7%

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

      2. times-frac 92.6%

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

   4. Applied egg-rr 92.6%

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

      1. clear-num 92.6%

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

      2. inv-pow 92.6%

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

      3. *-commutative 92.6%

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

   6. Applied egg-rr 92.6%

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

      1. unpow-1 92.6%

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

      2. associate-*r* 92.6%

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

   8. Simplified 92.6%

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

   9. Taylor expanded in y around inf 48.2%

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

       1. associate-*r/ 48.2%

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

       2. associate-/l* 48.2%

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

       3. associate-/r/ 48.2%

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

   11. Simplified 48.2%

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

       1. *-commutative 48.2%

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

       2. clear-num 48.1%

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

       3. un-div-inv 48.2%

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

       4. div-inv 48.3%

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

       5. metadata-eval 48.3%

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

   13. Applied egg-rr 48.3%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((0.3333333333333333 / z) * ((t / y) - 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 + ((0.3333333333333333d0 / z) * ((t / y) - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

3. Simplified 96.7%

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

5. Final simplification 96.7%

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

Alternative 14: 95.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. associate-*l* 95.3%

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

   2. *-commutative 95.3%

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

3. Simplified 95.3%

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

   1. associate-+l- 95.3%

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

   2. *-commutative 95.3%

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

   3. associate-*l* 95.3%

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

   4. associate-/l/ 96.0%

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

   5. sub-div 96.8%

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

6. Applied egg-rr 96.8%

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

7. Final simplification 96.8%

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

Alternative 15: 30.2% 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 95.3%

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

   1. associate-*l* 95.3%

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

   2. *-commutative 95.3%

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

3. Simplified 95.3%

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

5. Taylor expanded in x around inf 31.8%

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

6. Final simplification 31.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.1% 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 2024021 
(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))))