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

Percentage Accurate: 95.3% → 97.7%

Time: 8.2s

Alternatives: 10

Speedup: 1.4×

• 28.5% 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: 95.3% 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: 97.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2e-22)
   (+ (- x (/ y (* z 3.0))) (* (/ t z) (/ 0.3333333333333333 y)))
   (+ x (* (/ -0.3333333333333333 z) (- y (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2e-22) {
		tmp = (x - (y / (z * 3.0))) + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / 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 <= 2d-22) then
        tmp = (x - (y / (z * 3.0d0))) + ((t / z) * (0.3333333333333333d0 / y))
    else
        tmp = x + (((-0.3333333333333333d0) / z) * (y - (t / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2e-22) {
		tmp = (x - (y / (z * 3.0))) + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2e-22:
		tmp = (x - (y / (z * 3.0))) + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2e-22)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 / z) * Float64(y - Float64(t / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2e-22)
		tmp = (x - (y / (z * 3.0))) + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2e-22], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(-0.3333333333333333 / z), $MachinePrecision] * N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.0000000000000001e-22

   1. Initial program 96.3%

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

      1. associate-/r* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around 0 96.2%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 96.2%

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

      2. associate-*l/ 96.3%

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

      3. *-commutative 96.3%

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

      4. times-frac 98.1%

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

   6. Simplified 98.1%

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

   if 2.0000000000000001e-22 < y

   1. Initial program 96.9%

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

      1. associate-+l- 96.9%

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

      2. sub-neg 96.9%

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

      3. sub-neg 96.9%

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

      4. distribute-neg-in 96.9%

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

      5. unsub-neg 96.9%

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

      6. neg-mul-1 96.9%

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

      7. associate-*r/ 96.9%

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

      8. associate-*l/ 96.9%

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

      9. distribute-neg-frac 96.9%

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

      10. neg-mul-1 96.9%

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

      11. times-frac 98.3%

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

      12. distribute-lft-out-- 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.8%

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

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \]

Alternative 2: 62.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4800000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ t z) (/ 0.3333333333333333 y))))
   (if (<= y -9.5e+115)
     (/ y (* z -3.0))
     (if (<= y -3.7e-18)
       x
       (if (<= y 6e-122)
         t_1
         (if (<= y 1.02e-48)
           x
           (if (<= y 4800000000.0)
             t_1
             (if (<= y 2e+60) x (/ (* y -0.3333333333333333) z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / z) * (0.3333333333333333 / y);
	double tmp;
	if (y <= -9.5e+115) {
		tmp = y / (z * -3.0);
	} else if (y <= -3.7e-18) {
		tmp = x;
	} else if (y <= 6e-122) {
		tmp = t_1;
	} else if (y <= 1.02e-48) {
		tmp = x;
	} else if (y <= 4800000000.0) {
		tmp = t_1;
	} else if (y <= 2e+60) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (t / z) * (0.3333333333333333d0 / y)
    if (y <= (-9.5d+115)) then
        tmp = y / (z * (-3.0d0))
    else if (y <= (-3.7d-18)) then
        tmp = x
    else if (y <= 6d-122) then
        tmp = t_1
    else if (y <= 1.02d-48) then
        tmp = x
    else if (y <= 4800000000.0d0) then
        tmp = t_1
    else if (y <= 2d+60) 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 t_1 = (t / z) * (0.3333333333333333 / y);
	double tmp;
	if (y <= -9.5e+115) {
		tmp = y / (z * -3.0);
	} else if (y <= -3.7e-18) {
		tmp = x;
	} else if (y <= 6e-122) {
		tmp = t_1;
	} else if (y <= 1.02e-48) {
		tmp = x;
	} else if (y <= 4800000000.0) {
		tmp = t_1;
	} else if (y <= 2e+60) {
		tmp = x;
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t / z) * (0.3333333333333333 / y)
	tmp = 0
	if y <= -9.5e+115:
		tmp = y / (z * -3.0)
	elif y <= -3.7e-18:
		tmp = x
	elif y <= 6e-122:
		tmp = t_1
	elif y <= 1.02e-48:
		tmp = x
	elif y <= 4800000000.0:
		tmp = t_1
	elif y <= 2e+60:
		tmp = x
	else:
		tmp = (y * -0.3333333333333333) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / z) * Float64(0.3333333333333333 / y))
	tmp = 0.0
	if (y <= -9.5e+115)
		tmp = Float64(y / Float64(z * -3.0));
	elseif (y <= -3.7e-18)
		tmp = x;
	elseif (y <= 6e-122)
		tmp = t_1;
	elseif (y <= 1.02e-48)
		tmp = x;
	elseif (y <= 4800000000.0)
		tmp = t_1;
	elseif (y <= 2e+60)
		tmp = x;
	else
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t / z) * (0.3333333333333333 / y);
	tmp = 0.0;
	if (y <= -9.5e+115)
		tmp = y / (z * -3.0);
	elseif (y <= -3.7e-18)
		tmp = x;
	elseif (y <= 6e-122)
		tmp = t_1;
	elseif (y <= 1.02e-48)
		tmp = x;
	elseif (y <= 4800000000.0)
		tmp = t_1;
	elseif (y <= 2e+60)
		tmp = x;
	else
		tmp = (y * -0.3333333333333333) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+115], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.7e-18], x, If[LessEqual[y, 6e-122], t$95$1, If[LessEqual[y, 1.02e-48], x, If[LessEqual[y, 4800000000.0], t$95$1, If[LessEqual[y, 2e+60], x, N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.4999999999999997e115

   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-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 80.2%

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

      1. associate-/r* 80.2%

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

      2. associate-*r/ 80.2%

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

      3. associate-*r/ 80.3%

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

      4. div-sub 80.3%

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

      5. distribute-lft-out-- 80.3%

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

   6. Simplified 80.3%

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

   7. Taylor expanded in t around 0 80.3%

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

      1. *-commutative 80.3%

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

   9. Simplified 80.3%

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

       1. associate-/l* 80.4%

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

       2. div-inv 80.3%

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

       3. clear-num 80.3%

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

   11. Applied egg-rr 80.3%

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

       1. clear-num 80.3%

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

       2. un-div-inv 80.4%

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

       3. div-inv 80.4%

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

       4. metadata-eval 80.4%

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

   13. Applied egg-rr 80.4%

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

   if -9.4999999999999997e115 < y < -3.7000000000000003e-18 or 6.00000000000000009e-122 < y < 1.02000000000000005e-48 or 4.8e9 < y < 1.9999999999999999e60

   1. Initial program 99.9%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 55.1%

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

   if -3.7000000000000003e-18 < y < 6.00000000000000009e-122 or 1.02000000000000005e-48 < y < 4.8e9

   1. Initial program 93.5%

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

      1. associate-/r* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around 0 73.4%

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

      1. associate-/r* 70.0%

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

      2. associate-*r/ 70.0%

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

      3. associate-*r/ 70.0%

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

      4. div-sub 70.0%

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

      5. distribute-lft-out-- 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in t around inf 64.6%

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

      1. associate-*r/ 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-*r/ 64.5%

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

   9. Simplified 64.5%

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

       1. associate-/l* 68.8%

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

       2. associate-/r/ 71.6%

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

   11. Applied egg-rr 71.6%

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

   if 1.9999999999999999e60 < y

   1. Initial program 95.6%

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

      1. associate-/r* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around 0 71.3%

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

      1. associate-/r* 73.3%

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

      2. associate-*r/ 73.3%

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

      3. associate-*r/ 75.0%

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

      4. div-sub 77.2%

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

      5. distribute-lft-out-- 77.2%

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

   6. Simplified 77.2%

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

   7. Taylor expanded in t around 0 73.2%

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

      1. *-commutative 73.2%

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

   9. Simplified 73.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-122}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4800000000:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]

Alternative 3: 45.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+119} \lor \neg \left(x \leq -53\right) \land x \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.3e+140)
   x
   (if (or (<= x -1.6e+119) (and (not (<= x -53.0)) (<= x 1.05e-58)))
     (* y (/ -0.3333333333333333 z))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.3e+140) {
		tmp = x;
	} else if ((x <= -1.6e+119) || (!(x <= -53.0) && (x <= 1.05e-58))) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.3d+140)) then
        tmp = x
    else if ((x <= (-1.6d+119)) .or. (.not. (x <= (-53.0d0))) .and. (x <= 1.05d-58)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.3e+140) {
		tmp = x;
	} else if ((x <= -1.6e+119) || (!(x <= -53.0) && (x <= 1.05e-58))) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.3e+140:
		tmp = x
	elif (x <= -1.6e+119) or (not (x <= -53.0) and (x <= 1.05e-58)):
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.3e+140)
		tmp = x;
	elseif ((x <= -1.6e+119) || (!(x <= -53.0) && (x <= 1.05e-58)))
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.3e+140)
		tmp = x;
	elseif ((x <= -1.6e+119) || (~((x <= -53.0)) && (x <= 1.05e-58)))
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.3e+140], x, If[Or[LessEqual[x, -1.6e+119], And[N[Not[LessEqual[x, -53.0]], $MachinePrecision], LessEqual[x, 1.05e-58]]], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999999e140 or -1.59999999999999995e119 < x < -53 or 1.04999999999999994e-58 < 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-/r* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 53.7%

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

   if -2.2999999999999999e140 < x < -1.59999999999999995e119 or -53 < x < 1.04999999999999994e-58

   1. Initial program 94.8%

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

      1. associate-/r* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 86.8%

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

      1. associate-/r* 87.0%

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

      2. associate-*r/ 87.0%

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

      3. associate-*r/ 87.0%

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

      4. div-sub 87.8%

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

      5. distribute-lft-out-- 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in t around 0 51.4%

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

      1. *-commutative 51.4%

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

   9. Simplified 51.4%

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

       1. associate-/l* 51.5%

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

       2. div-inv 51.4%

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

       3. clear-num 51.4%

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

   11. Applied egg-rr 51.4%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+119} \lor \neg \left(x \leq -53\right) \land x \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 45.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+118}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -40:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.3e+140)
   x
   (if (<= x -4.6e+118)
     (* -0.3333333333333333 (/ y z))
     (if (<= x -40.0)
       x
       (if (<= x 1.05e-58) (* y (/ -0.3333333333333333 z)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.3e+140) {
		tmp = x;
	} else if (x <= -4.6e+118) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (x <= -40.0) {
		tmp = x;
	} else if (x <= 1.05e-58) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.3d+140)) then
        tmp = x
    else if (x <= (-4.6d+118)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (x <= (-40.0d0)) then
        tmp = x
    else if (x <= 1.05d-58) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.3e+140) {
		tmp = x;
	} else if (x <= -4.6e+118) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (x <= -40.0) {
		tmp = x;
	} else if (x <= 1.05e-58) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.3e+140:
		tmp = x
	elif x <= -4.6e+118:
		tmp = -0.3333333333333333 * (y / z)
	elif x <= -40.0:
		tmp = x
	elif x <= 1.05e-58:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.3e+140)
		tmp = x;
	elseif (x <= -4.6e+118)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (x <= -40.0)
		tmp = x;
	elseif (x <= 1.05e-58)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.3e+140)
		tmp = x;
	elseif (x <= -4.6e+118)
		tmp = -0.3333333333333333 * (y / z);
	elseif (x <= -40.0)
		tmp = x;
	elseif (x <= 1.05e-58)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.3e+140], x, If[LessEqual[x, -4.6e+118], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -40.0], x, If[LessEqual[x, 1.05e-58], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999999e140 or -4.60000000000000032e118 < x < -40 or 1.04999999999999994e-58 < 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-/r* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 53.7%

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

   if -2.2999999999999999e140 < x < -4.60000000000000032e118

   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-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 61.7%

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

      1. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   if -40 < x < 1.04999999999999994e-58

   1. Initial program 94.5%

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

      1. associate-/r* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around 0 87.1%

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

      1. associate-/r* 87.3%

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

      2. associate-*r/ 87.3%

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

      3. associate-*r/ 87.3%

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

      4. div-sub 88.1%

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

      5. distribute-lft-out-- 88.1%

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

   6. Simplified 88.1%

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

   7. Taylor expanded in t around 0 50.7%

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

      1. *-commutative 50.7%

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

   9. Simplified 50.7%

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

       1. associate-/l* 50.8%

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

       2. div-inv 50.7%

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

       3. clear-num 50.7%

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

   11. Applied egg-rr 50.7%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+118}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -40:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 45.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.1 \cdot 10^{+118}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -55:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.3e+140)
   x
   (if (<= x -7.1e+118)
     (* -0.3333333333333333 (/ y z))
     (if (<= x -55.0) x (if (<= x 1.05e-58) (/ y (* z -3.0)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.3e+140) {
		tmp = x;
	} else if (x <= -7.1e+118) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (x <= -55.0) {
		tmp = x;
	} else if (x <= 1.05e-58) {
		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 <= (-2.3d+140)) then
        tmp = x
    else if (x <= (-7.1d+118)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (x <= (-55.0d0)) then
        tmp = x
    else if (x <= 1.05d-58) 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 <= -2.3e+140) {
		tmp = x;
	} else if (x <= -7.1e+118) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (x <= -55.0) {
		tmp = x;
	} else if (x <= 1.05e-58) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.3e+140:
		tmp = x
	elif x <= -7.1e+118:
		tmp = -0.3333333333333333 * (y / z)
	elif x <= -55.0:
		tmp = x
	elif x <= 1.05e-58:
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.3e+140)
		tmp = x;
	elseif (x <= -7.1e+118)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (x <= -55.0)
		tmp = x;
	elseif (x <= 1.05e-58)
		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 <= -2.3e+140)
		tmp = x;
	elseif (x <= -7.1e+118)
		tmp = -0.3333333333333333 * (y / z);
	elseif (x <= -55.0)
		tmp = x;
	elseif (x <= 1.05e-58)
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.3e+140], x, If[LessEqual[x, -7.1e+118], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -55.0], x, If[LessEqual[x, 1.05e-58], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999999e140 or -7.0999999999999997e118 < x < -55 or 1.04999999999999994e-58 < 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-/r* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 53.7%

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

   if -2.2999999999999999e140 < x < -7.0999999999999997e118

   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-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 61.7%

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

      1. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   if -55 < x < 1.04999999999999994e-58

   1. Initial program 94.5%

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

      1. associate-/r* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around 0 87.1%

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

      1. associate-/r* 87.3%

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

      2. associate-*r/ 87.3%

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

      3. associate-*r/ 87.3%

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

      4. div-sub 88.1%

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

      5. distribute-lft-out-- 88.1%

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

   6. Simplified 88.1%

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

   7. Taylor expanded in t around 0 50.7%

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

      1. *-commutative 50.7%

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

   9. Simplified 50.7%

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

       1. associate-/l* 50.8%

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

       2. div-inv 50.7%

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

       3. clear-num 50.7%

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

   11. Applied egg-rr 50.7%

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

       1. clear-num 50.7%

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

       2. un-div-inv 50.8%

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

       3. div-inv 50.8%

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

       4. metadata-eval 50.8%

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

   13. Applied egg-rr 50.8%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.1 \cdot 10^{+118}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -55:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 88.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+44} \lor \neg \left(y \leq 1.7 \cdot 10^{+53}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.2e+44) (not (<= y 1.7e+53)))
   (- x (* 0.3333333333333333 (/ y z)))
   (+ x (* 0.3333333333333333 (/ t (* y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.2e+44) || !(y <= 1.7e+53)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = x + (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 <= (-2.2d+44)) .or. (.not. (y <= 1.7d+53))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = x + (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 <= -2.2e+44) || !(y <= 1.7e+53)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.2e+44) or not (y <= 1.7e+53):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.2e+44) || !(y <= 1.7e+53))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.2e+44) || ~((y <= 1.7e+53)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.2e+44], N[Not[LessEqual[y, 1.7e+53]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.19999999999999996e44 or 1.69999999999999999e53 < y

   1. Initial program 98.0%

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

      1. associate-/r* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in t around 0 95.4%

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

   if -2.19999999999999996e44 < y < 1.69999999999999999e53

   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-/r* 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around 0 86.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+44} \lor \neg \left(y \leq 1.7 \cdot 10^{+53}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 7: 77.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-31} \lor \neg \left(y \leq 6 \cdot 10^{-122}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6e-31) (not (<= y 6e-122)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-31) || !(y <= 6e-122)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6d-31)) .or. (.not. (y <= 6d-122))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-31) || !(y <= 6e-122)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6e-31) or not (y <= 6e-122):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6e-31) || !(y <= 6e-122))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6e-31) || ~((y <= 6e-122)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6e-31], N[Not[LessEqual[y, 6e-122]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999962e-31 or 6.00000000000000009e-122 < y

   1. Initial program 98.6%

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

      1. associate-/r* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around 0 87.3%

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

   if -5.99999999999999962e-31 < y < 6.00000000000000009e-122

   1. Initial program 92.8%

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

      1. associate-/r* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around 0 71.3%

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

      1. associate-/r* 68.5%

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

      2. associate-*r/ 68.6%

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

      3. associate-*r/ 68.6%

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

      4. div-sub 68.6%

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

      5. distribute-lft-out-- 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in t around inf 66.5%

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

      1. associate-*r/ 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r/ 66.5%

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

   9. Simplified 66.5%

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

       1. associate-/l* 70.3%

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

       2. associate-/r/ 73.4%

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

   11. Applied egg-rr 73.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-31} \lor \neg \left(y \leq 6 \cdot 10^{-122}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 8: 77.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-32} \lor \neg \left(y \leq 6 \cdot 10^{-122}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.08e-32) (not (<= y 6e-122)))
   (- x (* 0.3333333333333333 (/ y z)))
   (/ 0.3333333333333333 (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.08e-32) || !(y <= 6e-122)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} 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 <= (-1.08d-32)) .or. (.not. (y <= 6d-122))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    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 <= -1.08e-32) || !(y <= 6e-122)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = 0.3333333333333333 / (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.08e-32) or not (y <= 6e-122):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = 0.3333333333333333 / (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.08e-32) || !(y <= 6e-122))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	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 <= -1.08e-32) || ~((y <= 6e-122)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = 0.3333333333333333 / (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.08e-32], N[Not[LessEqual[y, 6e-122]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.08e-32 or 6.00000000000000009e-122 < y

   1. Initial program 98.6%

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

      1. associate-/r* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around 0 87.3%

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

   if -1.08e-32 < y < 6.00000000000000009e-122

   1. Initial program 92.8%

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

      1. associate-/r* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around 0 71.3%

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

      1. associate-/r* 68.5%

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

      2. associate-*r/ 68.6%

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

      3. associate-*r/ 68.6%

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

      4. div-sub 68.6%

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

      5. distribute-lft-out-- 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in t around inf 66.5%

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

      1. associate-*r/ 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r/ 66.5%

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

   9. Simplified 66.5%

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

       1. associate-/l* 70.3%

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

       2. associate-/r/ 73.4%

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

   11. Applied egg-rr 73.4%

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

       1. clear-num 73.3%

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

       2. frac-times 73.4%

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

       3. metadata-eval 73.4%

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

   13. Applied egg-rr 73.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-32} \lor \neg \left(y \leq 6 \cdot 10^{-122}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \]

Alternative 9: 95.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. associate-+l- 96.4%

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

   2. sub-neg 96.4%

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

   3. sub-neg 96.4%

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

   4. distribute-neg-in 96.4%

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

   5. unsub-neg 96.4%

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

   6. neg-mul-1 96.4%

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

   7. associate-*r/ 96.4%

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

   8. associate-*l/ 96.4%

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

   9. distribute-neg-frac 96.4%

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

   10. neg-mul-1 96.4%

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

   11. times-frac 94.6%

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

   12. distribute-lft-out-- 95.0%

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

   13. *-commutative 95.0%

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

   14. associate-/r* 95.0%

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

   15. metadata-eval 95.0%

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

3. Simplified 95.0%

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

4. Final simplification 95.0%

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

Alternative 10: 29.6% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. associate-/r* 96.9%

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

3. Simplified 96.9%

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

4. Taylor expanded in x around inf 30.1%

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

5. Final simplification 30.1%

   \[\leadsto x \]

Developer target: 96.4% 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 2023173 
(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))))