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

Percentage Accurate: 95.0% → 98.9%

Time: 12.1s

Alternatives: 17

Speedup: 1.0×

• 28.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.0% 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: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-36} \lor \neg \left(t \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + -0.3333333333333333 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.8e-36) (not (<= t 5e-8)))
   (+ x (+ (/ t (* z (* y 3.0))) (* -0.3333333333333333 (/ y z))))
   (+ x (/ (/ (- (/ t y) y) z) 3.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.8e-36) || !(t <= 5e-8)) {
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)));
	} 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 ((t <= (-8.8d-36)) .or. (.not. (t <= 5d-8))) then
        tmp = x + ((t / (z * (y * 3.0d0))) + ((-0.3333333333333333d0) * (y / z)))
    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 ((t <= -8.8e-36) || !(t <= 5e-8)) {
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)));
	} else {
		tmp = x + ((((t / y) - y) / z) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.8e-36) or not (t <= 5e-8):
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)))
	else:
		tmp = x + ((((t / y) - y) / z) / 3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.8e-36) || !(t <= 5e-8))
		tmp = Float64(x + Float64(Float64(t / Float64(z * Float64(y * 3.0))) + Float64(-0.3333333333333333 * Float64(y / z))));
	else
		tmp = Float64(x + Float64(Float64(Float64(Float64(t / y) - y) / z) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.8e-36) || ~((t <= 5e-8)))
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)));
	else
		tmp = x + ((((t / y) - y) / z) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.8e-36], N[Not[LessEqual[t, 5e-8]], $MachinePrecision]], N[(x + N[(N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.7999999999999997e-36 or 4.9999999999999998e-8 < t

   1. Initial program 99.7%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -8.7999999999999997e-36 < t < 4.9999999999999998e-8

   1. Initial program 92.3%

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

      1. associate-+l- 92.3%

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

      2. *-commutative 92.3%

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

   3. Simplified 92.3%

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

      1. sub-neg 92.3%

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

      2. associate-/r* 99.8%

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

      3. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-/r* 99.8%

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

      2. div-sub 99.8%

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

      3. div-sub 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. unsub-neg 99.8%

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

      2. sub-div 99.8%

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

      3. sub-div 99.8%

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

   9. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-36} \lor \neg \left(t \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + -0.3333333333333333 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\ \end{array} \]

Alternative 2: 87.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{if}\;y \leq -1465000000:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-293}:\\ \;\;\;\;\frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{-0.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ 0.3333333333333333 (* y z))))))
   (if (<= y -1465000000.0)
     (+ x (/ y (* z -3.0)))
     (if (<= y -6e-228)
       t_1
       (if (<= y 2.4e-293)
         (/ (/ (* t 0.3333333333333333) z) y)
         (if (<= y 7.5e+39) t_1 (+ x (/ y (/ z -0.3333333333333333)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (t * (0.3333333333333333 / (y * z)));
	double tmp;
	if (y <= -1465000000.0) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -6e-228) {
		tmp = t_1;
	} else if (y <= 2.4e-293) {
		tmp = ((t * 0.3333333333333333) / z) / y;
	} else if (y <= 7.5e+39) {
		tmp = t_1;
	} else {
		tmp = x + (y / (z / -0.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (0.3333333333333333d0 / (y * z)))
    if (y <= (-1465000000.0d0)) then
        tmp = x + (y / (z * (-3.0d0)))
    else if (y <= (-6d-228)) then
        tmp = t_1
    else if (y <= 2.4d-293) then
        tmp = ((t * 0.3333333333333333d0) / z) / y
    else if (y <= 7.5d+39) then
        tmp = t_1
    else
        tmp = x + (y / (z / (-0.3333333333333333d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (t * (0.3333333333333333 / (y * z)));
	double tmp;
	if (y <= -1465000000.0) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -6e-228) {
		tmp = t_1;
	} else if (y <= 2.4e-293) {
		tmp = ((t * 0.3333333333333333) / z) / y;
	} else if (y <= 7.5e+39) {
		tmp = t_1;
	} else {
		tmp = x + (y / (z / -0.3333333333333333));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (t * (0.3333333333333333 / (y * z)))
	tmp = 0
	if y <= -1465000000.0:
		tmp = x + (y / (z * -3.0))
	elif y <= -6e-228:
		tmp = t_1
	elif y <= 2.4e-293:
		tmp = ((t * 0.3333333333333333) / z) / y
	elif y <= 7.5e+39:
		tmp = t_1
	else:
		tmp = x + (y / (z / -0.3333333333333333))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(t * Float64(0.3333333333333333 / Float64(y * z))))
	tmp = 0.0
	if (y <= -1465000000.0)
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	elseif (y <= -6e-228)
		tmp = t_1;
	elseif (y <= 2.4e-293)
		tmp = Float64(Float64(Float64(t * 0.3333333333333333) / z) / y);
	elseif (y <= 7.5e+39)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(z / -0.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (t * (0.3333333333333333 / (y * z)));
	tmp = 0.0;
	if (y <= -1465000000.0)
		tmp = x + (y / (z * -3.0));
	elseif (y <= -6e-228)
		tmp = t_1;
	elseif (y <= 2.4e-293)
		tmp = ((t * 0.3333333333333333) / z) / y;
	elseif (y <= 7.5e+39)
		tmp = t_1;
	else
		tmp = x + (y / (z / -0.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(t * N[(0.3333333333333333 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1465000000.0], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-228], t$95$1, If[LessEqual[y, 2.4e-293], N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7.5e+39], t$95$1, N[(x + N[(y / N[(z / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.465e9

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 95.8%

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

      1. *-commutative 95.8%

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

      2. clear-num 95.8%

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

      3. un-div-inv 95.8%

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

      4. div-inv 95.9%

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

      5. metadata-eval 95.9%

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

   6. Applied egg-rr 95.9%

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

   if -1.465e9 < y < -5.9999999999999999e-228 or 2.3999999999999999e-293 < y < 7.5000000000000005e39

   1. Initial program 95.5%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in y around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. metadata-eval 88.8%

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

      3. times-frac 88.8%

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

      4. *-commutative 88.8%

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

      5. associate-*r* 88.8%

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

      6. associate-*r/ 88.3%

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

      7. associate-*r* 88.4%

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

      8. *-commutative 88.4%

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

      9. *-commutative 88.4%

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

      10. associate-/r* 88.3%

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

      11. metadata-eval 88.3%

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

   6. Simplified 88.3%

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

   if -5.9999999999999999e-228 < y < 2.3999999999999999e-293

   1. Initial program 72.8%

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

      1. associate-+l- 72.8%

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

      2. *-commutative 72.8%

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

   3. Simplified 72.8%

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

      1. sub-neg 72.8%

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

      2. associate-/r* 83.4%

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

      3. sub-div 83.4%

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

   5. Applied egg-rr 83.4%

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

      1. associate-/r* 83.3%

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

      2. div-sub 83.3%

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

      3. div-sub 83.3%

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

   7. Applied egg-rr 83.3%

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

      1. unsub-neg 83.3%

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

      2. sub-div 83.3%

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

      3. sub-div 83.3%

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

   9. Applied egg-rr 83.3%

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

   10. Taylor expanded in y around 0 72.8%

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

       1. *-commutative 72.8%

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

       2. associate-*l/ 72.8%

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

       3. associate-/l/ 99.5%

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

   12. Simplified 99.5%

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

   if 7.5000000000000005e39 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 98.1%

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

      1. associate-*r/ 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-/l* 98.2%

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

   6. Simplified 98.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1465000000:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-228}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-293}:\\ \;\;\;\;\frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{-0.3333333333333333}}\\ \end{array} \]

Alternative 3: 96.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-164}:\\ \;\;\;\;x + \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + -0.3333333333333333 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{\frac{-0.3333333333333333 \cdot t}{z}}{y} + \frac{y}{z \cdot 3}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.2e-164)
   (+ x (+ (/ t (* z (* y 3.0))) (* -0.3333333333333333 (/ y z))))
   (- x (+ (/ (/ (* -0.3333333333333333 t) z) y) (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e-164) {
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)));
	} else {
		tmp = x - ((((-0.3333333333333333 * t) / z) / 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 (y <= (-8.2d-164)) then
        tmp = x + ((t / (z * (y * 3.0d0))) + ((-0.3333333333333333d0) * (y / z)))
    else
        tmp = x - (((((-0.3333333333333333d0) * t) / z) / 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 (y <= -8.2e-164) {
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)));
	} else {
		tmp = x - ((((-0.3333333333333333 * t) / z) / y) + (y / (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e-164:
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)))
	else:
		tmp = x - ((((-0.3333333333333333 * t) / z) / y) + (y / (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e-164)
		tmp = Float64(x + Float64(Float64(t / Float64(z * Float64(y * 3.0))) + Float64(-0.3333333333333333 * Float64(y / z))));
	else
		tmp = Float64(x - Float64(Float64(Float64(Float64(-0.3333333333333333 * t) / z) / y) + Float64(y / Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e-164)
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)));
	else
		tmp = x - ((((-0.3333333333333333 * t) / z) / y) + (y / (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.2e-164], N[(x + N[(N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(N[(-0.3333333333333333 * t), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision] + N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999996e-164

   1. Initial program 99.7%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -8.1999999999999996e-164 < y

   1. Initial program 93.6%

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

      1. associate-+l- 93.6%

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

      2. sub-neg 93.6%

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

      3. distribute-frac-neg 93.6%

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

      4. associate-/r* 99.2%

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

      5. neg-mul-1 99.2%

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

      6. *-commutative 99.2%

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

      7. times-frac 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. associate-*r/ 99.2%

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

   5. Applied egg-rr 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-164}:\\ \;\;\;\;x + \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + -0.3333333333333333 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{\frac{-0.3333333333333333 \cdot t}{z}}{y} + \frac{y}{z \cdot 3}\right)\\ \end{array} \]

Alternative 4: 96.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-139}:\\ \;\;\;\;x + \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + -0.3333333333333333 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{-0.3333333333333333 \cdot \frac{t}{z}}{y} + \frac{y}{z \cdot 3}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.1e-139)
   (+ x (+ (/ t (* z (* y 3.0))) (* -0.3333333333333333 (/ y z))))
   (- x (+ (/ (* -0.3333333333333333 (/ t z)) y) (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.1e-139) {
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)));
	} else {
		tmp = x - (((-0.3333333333333333 * (t / z)) / 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 (y <= (-5.1d-139)) then
        tmp = x + ((t / (z * (y * 3.0d0))) + ((-0.3333333333333333d0) * (y / z)))
    else
        tmp = x - ((((-0.3333333333333333d0) * (t / z)) / 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 (y <= -5.1e-139) {
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)));
	} else {
		tmp = x - (((-0.3333333333333333 * (t / z)) / y) + (y / (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.1e-139:
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)))
	else:
		tmp = x - (((-0.3333333333333333 * (t / z)) / y) + (y / (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.1e-139)
		tmp = Float64(x + Float64(Float64(t / Float64(z * Float64(y * 3.0))) + Float64(-0.3333333333333333 * Float64(y / z))));
	else
		tmp = Float64(x - Float64(Float64(Float64(-0.3333333333333333 * Float64(t / z)) / y) + Float64(y / Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.1e-139)
		tmp = x + ((t / (z * (y * 3.0))) + (-0.3333333333333333 * (y / z)));
	else
		tmp = x - (((-0.3333333333333333 * (t / z)) / y) + (y / (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.1e-139], N[(x + N[(N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(-0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.10000000000000036e-139

   1. Initial program 99.7%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -5.10000000000000036e-139 < y

   1. Initial program 93.8%

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

      1. associate-+l- 93.8%

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

      2. sub-neg 93.8%

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

      3. distribute-frac-neg 93.8%

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

      4. associate-/r* 99.2%

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

      5. neg-mul-1 99.2%

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

      6. *-commutative 99.2%

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

      7. times-frac 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-139}:\\ \;\;\;\;x + \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + -0.3333333333333333 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{-0.3333333333333333 \cdot \frac{t}{z}}{y} + \frac{y}{z \cdot 3}\right)\\ \end{array} \]

Alternative 5: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-139} \lor \neg \left(y \leq 3.7 \cdot 10^{-106}\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.6e-139) (not (<= y 3.7e-106)))
   (+ x (* -0.3333333333333333 (/ (- y (/ t y)) z)))
   (+ x (* (/ t z) (/ 0.3333333333333333 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e-139) || !(y <= 3.7e-106)) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} 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 <= (-4.6d-139)) .or. (.not. (y <= 3.7d-106))) then
        tmp = x + ((-0.3333333333333333d0) * ((y - (t / y)) / z))
    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 <= -4.6e-139) || !(y <= 3.7e-106)) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.6e-139) or not (y <= 3.7e-106):
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z))
	else:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.6e-139) || !(y <= 3.7e-106))
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z)));
	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 <= -4.6e-139) || ~((y <= 3.7e-106)))
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	else
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.6e-139], N[Not[LessEqual[y, 3.7e-106]], $MachinePrecision]], N[(x + N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $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 < -4.60000000000000025e-139 or 3.69999999999999979e-106 < y

   1. Initial program 99.2%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 98.6%

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

   if -4.60000000000000025e-139 < y < 3.69999999999999979e-106

   1. Initial program 89.0%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in y around 0 88.9%

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

      1. *-commutative 88.9%

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

      2. metadata-eval 88.9%

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

      3. times-frac 88.9%

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

      4. *-commutative 88.9%

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

      5. associate-*r* 88.9%

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

      6. associate-*r/ 88.1%

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

      7. associate-*r* 88.2%

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

      8. *-commutative 88.2%

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

      9. *-commutative 88.2%

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

      10. associate-/r* 88.2%

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

      11. metadata-eval 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in t around 0 88.9%

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

      1. associate-*r/ 88.8%

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

      2. *-commutative 88.8%

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

      3. *-commutative 88.8%

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

      4. times-frac 99.6%

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

   9. Simplified 99.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-139} \lor \neg \left(y \leq 3.7 \cdot 10^{-106}\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 6: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{-139}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{t_1}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + t_1 \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- y (/ t y))))
   (if (<= y -4.6e-139)
     (+ x (* -0.3333333333333333 (/ t_1 z)))
     (if (<= y 3.4e-107)
       (+ x (* (/ t z) (/ 0.3333333333333333 y)))
       (+ x (* t_1 (/ -0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -4.6e-139) {
		tmp = x + (-0.3333333333333333 * (t_1 / z));
	} else if (y <= 3.4e-107) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + (t_1 * (-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 = y - (t / y)
    if (y <= (-4.6d-139)) then
        tmp = x + ((-0.3333333333333333d0) * (t_1 / z))
    else if (y <= 3.4d-107) then
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    else
        tmp = x + (t_1 * ((-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 = y - (t / y);
	double tmp;
	if (y <= -4.6e-139) {
		tmp = x + (-0.3333333333333333 * (t_1 / z));
	} else if (y <= 3.4e-107) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y - (t / y)
	tmp = 0
	if y <= -4.6e-139:
		tmp = x + (-0.3333333333333333 * (t_1 / z))
	elif y <= 3.4e-107:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x + (t_1 * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y - Float64(t / y))
	tmp = 0.0
	if (y <= -4.6e-139)
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(t_1 / z)));
	elseif (y <= 3.4e-107)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x + Float64(t_1 * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y - (t / y);
	tmp = 0.0;
	if (y <= -4.6e-139)
		tmp = x + (-0.3333333333333333 * (t_1 / z));
	elseif (y <= 3.4e-107)
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e-139], N[(x + N[(-0.3333333333333333 * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-107], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000025e-139

   1. Initial program 99.7%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around 0 97.8%

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

   if -4.60000000000000025e-139 < y < 3.39999999999999994e-107

   1. Initial program 88.8%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in y around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. metadata-eval 88.8%

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

      3. times-frac 88.8%

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

      4. *-commutative 88.8%

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

      5. associate-*r* 88.8%

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

      6. associate-*r/ 88.0%

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

      7. associate-*r* 88.1%

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

      8. *-commutative 88.1%

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

      9. *-commutative 88.1%

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

      10. associate-/r* 88.0%

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

      11. metadata-eval 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in t around 0 88.8%

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

      1. associate-*r/ 88.7%

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

      2. *-commutative 88.7%

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

      3. *-commutative 88.7%

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

      4. times-frac 99.6%

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

   9. Simplified 99.6%

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

   if 3.39999999999999994e-107 < y

   1. Initial program 98.6%

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

   3. Simplified 99.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-139}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 7: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-139}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-0.3333333333333333}{\frac{z}{\frac{t}{y} - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e-139)
   (+ x (* -0.3333333333333333 (/ (- y (/ t y)) z)))
   (if (<= y 2e-81)
     (+ x (* (/ t z) (/ 0.3333333333333333 y)))
     (- x (/ -0.3333333333333333 (/ z (- (/ t y) y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e-139) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} else if (y <= 2e-81) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x - (-0.3333333333333333 / (z / ((t / y) - 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 <= (-4.6d-139)) then
        tmp = x + ((-0.3333333333333333d0) * ((y - (t / y)) / z))
    else if (y <= 2d-81) then
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    else
        tmp = x - ((-0.3333333333333333d0) / (z / ((t / y) - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e-139) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} else if (y <= 2e-81) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x - (-0.3333333333333333 / (z / ((t / y) - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e-139:
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z))
	elif y <= 2e-81:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x - (-0.3333333333333333 / (z / ((t / y) - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e-139)
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z)));
	elseif (y <= 2e-81)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x - Float64(-0.3333333333333333 / Float64(z / Float64(Float64(t / y) - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e-139)
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	elseif (y <= 2e-81)
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x - (-0.3333333333333333 / (z / ((t / y) - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e-139], N[(x + N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-81], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(-0.3333333333333333 / N[(z / N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000025e-139

   1. Initial program 99.7%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around 0 97.8%

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

   if -4.60000000000000025e-139 < y < 1.9999999999999999e-81

   1. Initial program 88.9%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in y around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. metadata-eval 88.8%

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

      3. times-frac 88.8%

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

      4. *-commutative 88.8%

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

      5. associate-*r* 88.8%

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

      6. associate-*r/ 88.1%

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

      7. associate-*r* 88.2%

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

      8. *-commutative 88.2%

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

      9. *-commutative 88.2%

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

      10. associate-/r* 88.1%

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

      11. metadata-eval 88.1%

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

   6. Simplified 88.1%

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

   7. Taylor expanded in t around 0 88.8%

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

      1. associate-*r/ 88.8%

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

      2. *-commutative 88.8%

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

      3. *-commutative 88.8%

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

      4. times-frac 99.6%

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

   9. Simplified 99.6%

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

   if 1.9999999999999999e-81 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-139}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-0.3333333333333333}{\frac{z}{\frac{t}{y} - y}}\\ \end{array} \]

Alternative 8: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-139}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e-139)
   (+ x (* -0.3333333333333333 (/ (- y (/ t y)) z)))
   (if (<= y 1.95e-107)
     (+ x (* (/ t z) (/ 0.3333333333333333 y)))
     (+ x (/ (/ (- (/ t y) y) z) 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e-139) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} else if (y <= 1.95e-107) {
		tmp = x + ((t / z) * (0.3333333333333333 / 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 (y <= (-4.6d-139)) then
        tmp = x + ((-0.3333333333333333d0) * ((y - (t / y)) / z))
    else if (y <= 1.95d-107) then
        tmp = x + ((t / z) * (0.3333333333333333d0 / 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 (y <= -4.6e-139) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} else if (y <= 1.95e-107) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + ((((t / y) - y) / z) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e-139:
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z))
	elif y <= 1.95e-107:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x + ((((t / y) - y) / z) / 3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e-139)
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z)));
	elseif (y <= 1.95e-107)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x + Float64(Float64(Float64(Float64(t / y) - y) / z) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e-139)
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	elseif (y <= 1.95e-107)
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x + ((((t / y) - y) / z) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e-139], N[(x + N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-107], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000025e-139

   1. Initial program 99.7%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around 0 97.8%

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

   if -4.60000000000000025e-139 < y < 1.95e-107

   1. Initial program 88.8%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in y around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. metadata-eval 88.8%

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

      3. times-frac 88.8%

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

      4. *-commutative 88.8%

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

      5. associate-*r* 88.8%

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

      6. associate-*r/ 88.0%

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

      7. associate-*r* 88.1%

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

      8. *-commutative 88.1%

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

      9. *-commutative 88.1%

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

      10. associate-/r* 88.0%

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

      11. metadata-eval 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in t around 0 88.8%

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

      1. associate-*r/ 88.7%

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

      2. *-commutative 88.7%

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

      3. *-commutative 88.7%

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

      4. times-frac 99.6%

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

   9. Simplified 99.6%

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

   if 1.95e-107 < 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-+l- 98.6%

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

      2. *-commutative 98.6%

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

   3. Simplified 98.6%

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

      1. sub-neg 98.6%

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

      2. associate-/r* 99.7%

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

      3. sub-div 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-/r* 99.8%

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

      2. div-sub 99.8%

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

      3. div-sub 99.7%

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

   7. Applied egg-rr 99.7%

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

      1. unsub-neg 99.7%

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

      2. sub-div 99.8%

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

      3. sub-div 99.8%

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

   9. Applied egg-rr 99.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-139}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{z}}{3}\\ \end{array} \]

Alternative 9: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1465000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-58}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e+89)
   (/ (* y -0.3333333333333333) z)
   (if (<= y -1465000000.0)
     x
     (if (<= y 2.15e-58)
       (* 0.3333333333333333 (/ t (* y z)))
       (if (<= y 1.12e+55) x (/ -0.3333333333333333 (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e+89) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -1465000000.0) {
		tmp = x;
	} else if (y <= 2.15e-58) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else if (y <= 1.12e+55) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.6d+89)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= (-1465000000.0d0)) then
        tmp = x
    else if (y <= 2.15d-58) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else if (y <= 1.12d+55) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e+89) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -1465000000.0) {
		tmp = x;
	} else if (y <= 2.15e-58) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else if (y <= 1.12e+55) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e+89:
		tmp = (y * -0.3333333333333333) / z
	elif y <= -1465000000.0:
		tmp = x
	elif y <= 2.15e-58:
		tmp = 0.3333333333333333 * (t / (y * z))
	elif y <= 1.12e+55:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e+89)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= -1465000000.0)
		tmp = x;
	elseif (y <= 2.15e-58)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	elseif (y <= 1.12e+55)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e+89)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= -1465000000.0)
		tmp = x;
	elseif (y <= 2.15e-58)
		tmp = 0.3333333333333333 * (t / (y * z));
	elseif (y <= 1.12e+55)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e+89], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -1465000000.0], x, If[LessEqual[y, 2.15e-58], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+55], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.5999999999999998e89

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. sub-neg 99.7%

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

      2. associate-/r* 99.7%

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

      3. sub-div 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-/r* 99.7%

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

      2. div-sub 99.7%

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

      3. div-sub 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around inf 77.6%

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

      1. associate-*r/ 77.7%

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

      2. *-commutative 77.7%

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

   10. Simplified 77.7%

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

   if -4.5999999999999998e89 < y < -1.465e9 or 2.15e-58 < y < 1.12000000000000006e55

   1. Initial program 99.9%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 54.8%

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

   if -1.465e9 < y < 2.15e-58

   1. Initial program 91.4%

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

      1. associate-+l- 91.4%

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

      2. *-commutative 91.4%

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

   3. Simplified 91.4%

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

      1. sub-neg 91.4%

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

      2. associate-/r* 88.4%

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

      3. sub-div 88.5%

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

   5. Applied egg-rr 88.5%

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

      1. associate-/r* 88.6%

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

      2. div-sub 88.6%

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

      3. div-sub 88.6%

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

   7. Applied egg-rr 88.6%

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

      1. unsub-neg 88.6%

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

      2. sub-div 88.6%

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

      3. sub-div 88.6%

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

   9. Applied egg-rr 88.6%

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

   10. Taylor expanded in y around 0 65.7%

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

   if 1.12000000000000006e55 < y

   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%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-/r* 99.8%

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

      3. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-/r* 99.8%

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

      2. div-sub 99.8%

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

      3. div-sub 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around inf 76.5%

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

      1. *-commutative 76.5%

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

   10. Simplified 76.5%

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

       1. *-commutative 76.5%

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

       2. clear-num 76.5%

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

       3. un-div-inv 76.5%

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

   12. Applied egg-rr 76.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1465000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-58}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]

Alternative 10: 91.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1465000000:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{-0.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1465000000.0)
   (+ x (/ y (* z -3.0)))
   (if (<= y 7e+39)
     (+ x (* (/ t z) (/ 0.3333333333333333 y)))
     (+ x (/ y (/ z -0.3333333333333333))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1465000000.0) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= 7e+39) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + (y / (z / -0.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1465000000.0d0)) then
        tmp = x + (y / (z * (-3.0d0)))
    else if (y <= 7d+39) then
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    else
        tmp = x + (y / (z / (-0.3333333333333333d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1465000000.0) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= 7e+39) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + (y / (z / -0.3333333333333333));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1465000000.0:
		tmp = x + (y / (z * -3.0))
	elif y <= 7e+39:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x + (y / (z / -0.3333333333333333))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1465000000.0)
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	elseif (y <= 7e+39)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x + Float64(y / Float64(z / -0.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1465000000.0)
		tmp = x + (y / (z * -3.0));
	elseif (y <= 7e+39)
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x + (y / (z / -0.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1465000000.0], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+39], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.465e9

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 95.8%

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

      1. *-commutative 95.8%

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

      2. clear-num 95.8%

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

      3. un-div-inv 95.8%

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

      4. div-inv 95.9%

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

      5. metadata-eval 95.9%

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

   6. Applied egg-rr 95.9%

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

   if -1.465e9 < y < 7.0000000000000003e39

   1. Initial program 92.7%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around 0 86.8%

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

      1. *-commutative 86.8%

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

      2. metadata-eval 86.8%

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

      3. times-frac 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-*r* 86.9%

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

      6. associate-*r/ 86.4%

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

      7. associate-*r* 86.5%

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

      8. *-commutative 86.5%

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

      9. *-commutative 86.5%

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

      10. associate-/r* 86.4%

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

      11. metadata-eval 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in t around 0 86.8%

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

      1. associate-*r/ 86.8%

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

      2. *-commutative 86.8%

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

      3. *-commutative 86.8%

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

      4. times-frac 93.1%

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

   9. Simplified 93.1%

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

   if 7.0000000000000003e39 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 98.1%

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

      1. associate-*r/ 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-/l* 98.2%

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

   6. Simplified 98.2%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1465000000:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{-0.3333333333333333}}\\ \end{array} \]

Alternative 11: 76.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-48} \lor \neg \left(y \leq 7.4 \cdot 10^{-78}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e-48) (not (<= y 7.4e-78)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-48) || !(y <= 7.4e-78)) {
		tmp = x + (y * (-0.3333333333333333 / 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 <= (-1.4d-48)) .or. (.not. (y <= 7.4d-78))) then
        tmp = x + (y * ((-0.3333333333333333d0) / 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 <= -1.4e-48) || !(y <= 7.4e-78)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e-48) or not (y <= 7.4e-78):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (t / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e-48) || !(y <= 7.4e-78))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = 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 <= -1.4e-48) || ~((y <= 7.4e-78)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (t / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e-48], N[Not[LessEqual[y, 7.4e-78]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000002e-48 or 7.40000000000000011e-78 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 90.3%

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

   if -1.40000000000000002e-48 < y < 7.40000000000000011e-78

   1. Initial program 90.6%

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

      1. associate-+l- 90.6%

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

      2. *-commutative 90.6%

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

   3. Simplified 90.6%

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

      1. sub-neg 90.6%

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

      2. associate-/r* 87.4%

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

      3. sub-div 87.4%

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

   5. Applied egg-rr 87.4%

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

      1. associate-/r* 87.5%

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

      2. div-sub 87.5%

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

      3. div-sub 87.5%

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

   7. Applied egg-rr 87.5%

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

      1. unsub-neg 87.5%

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

      2. sub-div 87.5%

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

      3. sub-div 87.5%

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

   9. Applied egg-rr 87.5%

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

   10. Taylor expanded in y around 0 68.0%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-48} \lor \neg \left(y \leq 7.4 \cdot 10^{-78}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 12: 76.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-40} \lor \neg \left(y \leq 1.35 \cdot 10^{-77}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.8e-40) (not (<= y 1.35e-77)))
   (+ 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 <= -5.8e-40) || !(y <= 1.35e-77)) {
		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 <= (-5.8d-40)) .or. (.not. (y <= 1.35d-77))) 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 <= -5.8e-40) || !(y <= 1.35e-77)) {
		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 <= -5.8e-40) or not (y <= 1.35e-77):
		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 <= -5.8e-40) || !(y <= 1.35e-77))
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	else
		tmp = 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 <= -5.8e-40) || ~((y <= 1.35e-77)))
		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, -5.8e-40], N[Not[LessEqual[y, 1.35e-77]], $MachinePrecision]], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999998e-40 or 1.35e-77 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 90.3%

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

      1. *-commutative 90.3%

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

      2. clear-num 90.2%

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

      3. un-div-inv 90.3%

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

      4. div-inv 90.4%

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

      5. metadata-eval 90.4%

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

   6. Applied egg-rr 90.4%

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

   if -5.7999999999999998e-40 < y < 1.35e-77

   1. Initial program 90.6%

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

      1. associate-+l- 90.6%

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

      2. *-commutative 90.6%

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

   3. Simplified 90.6%

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

      1. sub-neg 90.6%

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

      2. associate-/r* 87.4%

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

      3. sub-div 87.4%

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

   5. Applied egg-rr 87.4%

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

      1. associate-/r* 87.5%

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

      2. div-sub 87.5%

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

      3. div-sub 87.5%

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

   7. Applied egg-rr 87.5%

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

      1. unsub-neg 87.5%

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

      2. sub-div 87.5%

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

      3. sub-div 87.5%

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

   9. Applied egg-rr 87.5%

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

   10. Taylor expanded in y around 0 68.0%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-40} \lor \neg \left(y \leq 1.35 \cdot 10^{-77}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 13: 78.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-31} \lor \neg \left(y \leq 8 \cdot 10^{-78}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e-31) (not (<= y 8e-78)))
   (+ x (/ y (* z -3.0)))
   (/ (/ (* t 0.3333333333333333) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e-31) || !(y <= 8e-78)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = ((t * 0.3333333333333333) / z) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.5d-31)) .or. (.not. (y <= 8d-78))) then
        tmp = x + (y / (z * (-3.0d0)))
    else
        tmp = ((t * 0.3333333333333333d0) / z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e-31) || !(y <= 8e-78)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = ((t * 0.3333333333333333) / z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.5e-31) or not (y <= 8e-78):
		tmp = x + (y / (z * -3.0))
	else:
		tmp = ((t * 0.3333333333333333) / z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.5e-31) || !(y <= 8e-78))
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(Float64(Float64(t * 0.3333333333333333) / z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.5e-31) || ~((y <= 8e-78)))
		tmp = x + (y / (z * -3.0));
	else
		tmp = ((t * 0.3333333333333333) / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.5e-31], N[Not[LessEqual[y, 8e-78]], $MachinePrecision]], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000004e-31 or 7.99999999999999999e-78 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 90.3%

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

      1. *-commutative 90.3%

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

      2. clear-num 90.2%

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

      3. un-div-inv 90.3%

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

      4. div-inv 90.4%

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

      5. metadata-eval 90.4%

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

   6. Applied egg-rr 90.4%

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

   if -4.5000000000000004e-31 < y < 7.99999999999999999e-78

   1. Initial program 90.6%

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

      1. associate-+l- 90.6%

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

      2. *-commutative 90.6%

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

   3. Simplified 90.6%

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

      1. sub-neg 90.6%

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

      2. associate-/r* 87.4%

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

      3. sub-div 87.4%

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

   5. Applied egg-rr 87.4%

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

      1. associate-/r* 87.5%

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

      2. div-sub 87.5%

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

      3. div-sub 87.5%

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

   7. Applied egg-rr 87.5%

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

      1. unsub-neg 87.5%

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

      2. sub-div 87.5%

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

      3. sub-div 87.5%

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

   9. Applied egg-rr 87.5%

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

   10. Taylor expanded in y around 0 68.0%

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

       1. *-commutative 68.0%

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

       2. associate-*l/ 67.9%

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

       3. associate-/l/ 75.3%

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

   12. Simplified 75.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-31} \lor \neg \left(y \leq 8 \cdot 10^{-78}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 14: 47.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+89} \lor \neg \left(y \leq 1.5 \cdot 10^{+44}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.6e+89) (not (<= y 1.5e+44)))
   (* -0.3333333333333333 (/ y z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.6e+89) || !(y <= 1.5e+44)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.6d+89)) .or. (.not. (y <= 1.5d+44))) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.6e+89) || !(y <= 1.5e+44)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.6e+89) or not (y <= 1.5e+44):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.6e+89) || !(y <= 1.5e+44))
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.6e+89) || ~((y <= 1.5e+44)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.6e+89], N[Not[LessEqual[y, 1.5e+44]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.60000000000000018e89 or 1.49999999999999993e44 < y

   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%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-/r* 99.8%

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

      3. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-/r* 99.7%

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

      2. div-sub 99.7%

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

      3. div-sub 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around inf 77.1%

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

      1. *-commutative 77.1%

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

   10. Simplified 77.1%

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

   if -9.60000000000000018e89 < y < 1.49999999999999993e44

   1. Initial program 93.8%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around inf 33.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+89} \lor \neg \left(y \leq 1.5 \cdot 10^{+44}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 47.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+89}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e+89)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 3e+53) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e+89) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 3e+53) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5d+89)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 3d+53) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e+89) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 3e+53) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5e+89:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 3e+53:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e+89)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 3e+53)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e+89)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 3e+53)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5e+89], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+53], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999983e89

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. sub-neg 99.7%

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

      2. associate-/r* 99.7%

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

      3. sub-div 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-/r* 99.7%

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

      2. div-sub 99.7%

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

      3. div-sub 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around inf 77.6%

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

      1. *-commutative 77.6%

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

   10. Simplified 77.6%

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

   if -4.99999999999999983e89 < y < 2.99999999999999998e53

   1. Initial program 93.8%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around inf 33.5%

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

   if 2.99999999999999998e53 < y

   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%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-/r* 99.8%

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

      3. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-/r* 99.8%

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

      2. div-sub 99.8%

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

      3. div-sub 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around inf 76.5%

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

      1. *-commutative 76.5%

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

   10. Simplified 76.5%

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

       1. *-commutative 76.5%

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

       2. clear-num 76.5%

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

       3. un-div-inv 76.5%

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

   12. Applied egg-rr 76.5%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+89}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]

Alternative 16: 47.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e+89)
   (/ (* y -0.3333333333333333) z)
   (if (<= y 9e+42) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e+89) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 9e+42) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.6d+89)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= 9d+42) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e+89) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 9e+42) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e+89:
		tmp = (y * -0.3333333333333333) / z
	elif y <= 9e+42:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e+89)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= 9e+42)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e+89)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= 9e+42)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e+89], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 9e+42], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5999999999999998e89

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. sub-neg 99.7%

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

      2. associate-/r* 99.7%

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

      3. sub-div 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-/r* 99.7%

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

      2. div-sub 99.7%

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

      3. div-sub 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around inf 77.6%

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

      1. associate-*r/ 77.7%

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

      2. *-commutative 77.7%

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

   10. Simplified 77.7%

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

   if -4.5999999999999998e89 < y < 9.00000000000000025e42

   1. Initial program 93.8%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around inf 33.5%

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

   if 9.00000000000000025e42 < y

   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%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-/r* 99.8%

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

      3. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-/r* 99.8%

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

      2. div-sub 99.8%

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

      3. div-sub 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around inf 76.5%

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

      1. *-commutative 76.5%

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

   10. Simplified 76.5%

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

       1. *-commutative 76.5%

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

       2. clear-num 76.5%

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

       3. un-div-inv 76.5%

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

   12. Applied egg-rr 76.5%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]

Alternative 17: 29.8% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

3. Simplified 94.6%

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

4. Taylor expanded in x around inf 29.6%

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

5. Final simplification 29.6%

   \[\leadsto x \]

Developer target: 95.9% 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 2023318 
(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))))