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

Percentage Accurate: 95.5% → 97.6%

Time: 13.5s

Alternatives: 18

Speedup: 1.0×

• 27.7% 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: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-40}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1e-40)
   (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1e-40) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} 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 <= (-1d-40)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    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 <= -1e-40) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1e-40:
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1e-40)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1e-40)
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1e-40], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.9999999999999993e-41

   1. Initial program 99.8%

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

   if -9.9999999999999993e-41 < t

   1. Initial program 94.5%

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

      1. associate-+l- 94.5%

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

      2. *-commutative 94.5%

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

   3. Simplified 94.5%

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

      1. sub-neg 94.5%

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

      2. associate-/r* 98.2%

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

      3. sub-div 98.2%

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

   5. Applied egg-rr 98.2%

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

      1. sub-neg 98.2%

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

   7. Simplified 98.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-40}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]

Alternative 2: 79.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+168}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;z \cdot 3 \leq -4 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot 3 \leq -5 \cdot 10^{-13}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.3333333333333333 (/ (- y (/ t y)) z))))
   (if (<= (* z 3.0) -4e+168)
     (+ x (* y (/ -0.3333333333333333 z)))
     (if (<= (* z 3.0) -4e+49)
       t_1
       (if (<= (* z 3.0) -5e-13)
         (- x (/ y (* z 3.0)))
         (if (<= (* z 3.0) 5e-36)
           t_1
           (- x (/ y (/ z 0.3333333333333333)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.3333333333333333 * ((y - (t / y)) / z);
	double tmp;
	if ((z * 3.0) <= -4e+168) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if ((z * 3.0) <= -4e+49) {
		tmp = t_1;
	} else if ((z * 3.0) <= -5e-13) {
		tmp = x - (y / (z * 3.0));
	} else if ((z * 3.0) <= 5e-36) {
		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 = (-0.3333333333333333d0) * ((y - (t / y)) / z)
    if ((z * 3.0d0) <= (-4d+168)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if ((z * 3.0d0) <= (-4d+49)) then
        tmp = t_1
    else if ((z * 3.0d0) <= (-5d-13)) then
        tmp = x - (y / (z * 3.0d0))
    else if ((z * 3.0d0) <= 5d-36) 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 = -0.3333333333333333 * ((y - (t / y)) / z);
	double tmp;
	if ((z * 3.0) <= -4e+168) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if ((z * 3.0) <= -4e+49) {
		tmp = t_1;
	} else if ((z * 3.0) <= -5e-13) {
		tmp = x - (y / (z * 3.0));
	} else if ((z * 3.0) <= 5e-36) {
		tmp = t_1;
	} else {
		tmp = x - (y / (z / 0.3333333333333333));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.3333333333333333 * ((y - (t / y)) / z)
	tmp = 0
	if (z * 3.0) <= -4e+168:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif (z * 3.0) <= -4e+49:
		tmp = t_1
	elif (z * 3.0) <= -5e-13:
		tmp = x - (y / (z * 3.0))
	elif (z * 3.0) <= 5e-36:
		tmp = t_1
	else:
		tmp = x - (y / (z / 0.3333333333333333))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z))
	tmp = 0.0
	if (Float64(z * 3.0) <= -4e+168)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (Float64(z * 3.0) <= -4e+49)
		tmp = t_1;
	elseif (Float64(z * 3.0) <= -5e-13)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (Float64(z * 3.0) <= 5e-36)
		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 = -0.3333333333333333 * ((y - (t / y)) / z);
	tmp = 0.0;
	if ((z * 3.0) <= -4e+168)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif ((z * 3.0) <= -4e+49)
		tmp = t_1;
	elseif ((z * 3.0) <= -5e-13)
		tmp = x - (y / (z * 3.0));
	elseif ((z * 3.0) <= 5e-36)
		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[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+168], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+49], t$95$1, If[LessEqual[N[(z * 3.0), $MachinePrecision], -5e-13], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 5e-36], t$95$1, N[(x - N[(y / N[(z / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z 3) < -3.9999999999999997e168

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. distribute-frac-neg 97.1%

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

      3. associate-+l+ 97.1%

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

      4. remove-double-neg 97.1%

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

      5. distribute-frac-neg 97.1%

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

      6. sub-neg 97.1%

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

      7. neg-mul-1 97.1%

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

      8. associate-*l/ 97.1%

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

      9. neg-mul-1 97.1%

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

      10. times-frac 86.2%

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

      11. distribute-lft-out-- 86.2%

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

      12. *-commutative 86.2%

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

      13. associate-/r* 86.2%

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

      14. metadata-eval 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in y around inf 71.8%

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

   if -3.9999999999999997e168 < (*.f64 z 3) < -3.99999999999999979e49 or -4.9999999999999999e-13 < (*.f64 z 3) < 5.00000000000000004e-36

   1. Initial program 93.3%

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

      1. sub-neg 93.3%

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

      2. distribute-frac-neg 93.3%

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

      3. associate-+l+ 93.3%

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

      4. remove-double-neg 93.3%

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

      5. distribute-frac-neg 93.3%

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

      6. sub-neg 93.3%

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

      7. neg-mul-1 93.3%

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

      8. associate-*l/ 93.2%

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

      9. neg-mul-1 93.2%

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

      10. times-frac 97.6%

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

      11. distribute-lft-out-- 97.6%

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

      12. *-commutative 97.6%

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

      13. associate-/r* 97.6%

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

      14. metadata-eval 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around 0 97.6%

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

   5. Taylor expanded in x around 0 92.4%

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

   if -3.99999999999999979e49 < (*.f64 z 3) < -4.9999999999999999e-13

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. associate-+l+ 99.9%

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

      4. remove-double-neg 99.9%

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

      5. distribute-frac-neg 99.9%

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

      6. sub-neg 99.9%

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

      7. neg-mul-1 99.9%

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

      8. associate-*l/ 99.7%

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

      9. neg-mul-1 99.7%

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

      10. times-frac 99.7%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.6%

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

      14. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 91.1%

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

   5. Taylor expanded in x around 0 91.1%

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

      1. metadata-eval 91.1%

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

      2. cancel-sign-sub-inv 91.1%

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

      3. *-commutative 91.1%

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

      4. associate-*l/ 91.4%

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

      5. associate-/l* 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in z around 0 91.4%

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

      1. *-commutative 91.4%

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

   10. Simplified 91.4%

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

   if 5.00000000000000004e-36 < (*.f64 z 3)

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. associate-+l+ 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-frac-neg 99.8%

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

      6. sub-neg 99.8%

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

      7. neg-mul-1 99.8%

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

      8. associate-*l/ 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 92.5%

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

      11. distribute-lft-out-- 92.5%

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

      12. *-commutative 92.5%

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

      13. associate-/r* 92.5%

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

      14. metadata-eval 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 77.0%

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

   5. Taylor expanded in x around 0 77.0%

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

      1. metadata-eval 77.0%

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

      2. cancel-sign-sub-inv 77.0%

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

      3. *-commutative 77.0%

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

      4. associate-*l/ 77.1%

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

      5. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+168}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;z \cdot 3 \leq -4 \cdot 10^{+49}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;z \cdot 3 \leq -5 \cdot 10^{-13}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-36}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \end{array} \]

Alternative 3: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;\left(x - y \cdot \frac{0.3333333333333333}{z}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.1e+73)
   (+
    (- x (* y (/ 0.3333333333333333 z)))
    (* t (/ (/ 0.3333333333333333 z) y)))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.1e+73) {
		tmp = (x - (y * (0.3333333333333333 / z))) + (t * ((0.3333333333333333 / z) / 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 (t <= (-1.1d+73)) then
        tmp = (x - (y * (0.3333333333333333d0 / z))) + (t * ((0.3333333333333333d0 / z) / 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 (t <= -1.1e+73) {
		tmp = (x - (y * (0.3333333333333333 / z))) + (t * ((0.3333333333333333 / z) / y));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.1e+73:
		tmp = (x - (y * (0.3333333333333333 / z))) + (t * ((0.3333333333333333 / z) / y))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.1e+73)
		tmp = Float64(Float64(x - Float64(y * Float64(0.3333333333333333 / z))) + Float64(t * Float64(Float64(0.3333333333333333 / z) / y)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.1e+73)
		tmp = (x - (y * (0.3333333333333333 / z))) + (t * ((0.3333333333333333 / z) / y));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.1e+73], N[(N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e73

   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. associate--r- 99.7%

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

      2. div-inv 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/r* 99.7%

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

      5. metadata-eval 99.7%

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

      6. div-inv 99.7%

         \[\leadsto \left(x - y \cdot \frac{0.3333333333333333}{z}\right) + \color{blue}{t \cdot \frac{1}{y \cdot \left(z \cdot 3\right)}} \]

      7. *-commutative 99.7%

         \[\leadsto \left(x - y \cdot \frac{0.3333333333333333}{z}\right) + t \cdot \frac{1}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      8. associate-/r* 99.6%

         \[\leadsto \left(x - y \cdot \frac{0.3333333333333333}{z}\right) + t \cdot \color{blue}{\frac{\frac{1}{z \cdot 3}}{y}} \]

      9. *-commutative 99.6%

         \[\leadsto \left(x - y \cdot \frac{0.3333333333333333}{z}\right) + t \cdot \frac{\frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      10. associate-/r* 99.7%

          \[\leadsto \left(x - y \cdot \frac{0.3333333333333333}{z}\right) + t \cdot \frac{\color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      11. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   if -1.1e73 < t

   1. Initial program 95.1%

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

      1. associate-+l- 95.1%

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

      2. *-commutative 95.1%

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

   3. Simplified 95.1%

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

      1. sub-neg 95.1%

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

      2. associate-/r* 98.4%

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

      3. sub-div 98.4%

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

   5. Applied egg-rr 98.4%

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

      1. sub-neg 98.4%

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

   7. Simplified 98.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;\left(x - y \cdot \frac{0.3333333333333333}{z}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]

Alternative 4: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-38} \lor \neg \left(y \leq 5.4 \cdot 10^{-124}\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.2e-38) (not (<= y 5.4e-124)))
   (+ 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 <= -9.2e-38) || !(y <= 5.4e-124)) {
		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 <= (-9.2d-38)) .or. (.not. (y <= 5.4d-124))) 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 <= -9.2e-38) || !(y <= 5.4e-124)) {
		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 <= -9.2e-38) or not (y <= 5.4e-124):
		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 <= -9.2e-38) || !(y <= 5.4e-124))
		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 <= -9.2e-38) || ~((y <= 5.4e-124)))
		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, -9.2e-38], N[Not[LessEqual[y, 5.4e-124]], $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 < -9.20000000000000007e-38 or 5.40000000000000035e-124 < 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. sub-neg 98.6%

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

      2. distribute-frac-neg 98.6%

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

      3. associate-+l+ 98.6%

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

      4. remove-double-neg 98.6%

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

      5. distribute-frac-neg 98.6%

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

      6. sub-neg 98.6%

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

      7. neg-mul-1 98.6%

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

      8. associate-*l/ 98.5%

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

      9. neg-mul-1 98.5%

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

      10. times-frac 99.7%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.8%

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

   if -9.20000000000000007e-38 < y < 5.40000000000000035e-124

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. distribute-frac-neg 92.1%

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

      3. associate-+l+ 92.1%

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

      4. remove-double-neg 92.1%

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

      5. distribute-frac-neg 92.1%

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

      6. sub-neg 92.1%

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

      7. neg-mul-1 92.1%

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

      8. associate-*l/ 92.1%

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

      9. neg-mul-1 92.1%

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

      10. times-frac 86.4%

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

      11. distribute-lft-out-- 86.4%

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

      12. *-commutative 86.4%

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

      13. associate-/r* 86.5%

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

      14. metadata-eval 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in y around 0 91.3%

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

      1. associate-/r* 84.7%

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

      2. associate-*r/ 84.7%

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

      3. associate-*l/ 84.7%

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

      4. associate-*r/ 94.7%

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

      5. associate-*l/ 91.2%

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

      6. /-rgt-identity 91.2%

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

      7. associate-*r/ 91.2%

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

      8. associate-*l/ 94.7%

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

      9. associate-*r/ 84.7%

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

      10. *-commutative 84.7%

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

      11. associate-*r/ 84.7%

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

      12. *-commutative 84.7%

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

      13. associate-*r/ 84.7%

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

      14. *-commutative 84.7%

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

      15. associate-/r* 91.3%

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

      16. associate-/l* 91.3%

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

      17. associate-/r* 84.8%

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

      18. metadata-eval 84.8%

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

      19. associate-/r* 84.7%

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

      20. associate-/l/ 91.2%

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

      21. associate-*r* 91.3%

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

      22. *-commutative 91.3%

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

   6. Simplified 91.3%

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

      1. associate-/r* 94.6%

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

      2. div-inv 94.6%

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

   8. Applied egg-rr 94.6%

      \[\leadsto x + \color{blue}{\frac{t}{z} \cdot \frac{1}{y \cdot 3}} \]
   9. Step-by-step derivation

      1. *-commutative 94.6%

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

      2. associate-/r* 94.7%

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

      3. metadata-eval 94.7%

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

   10. Simplified 94.7%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-38} \lor \neg \left(y \leq 5.4 \cdot 10^{-124}\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 5: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-38} \lor \neg \left(y \leq 5.9 \cdot 10^{-124}\right):\\ \;\;\;\;x + \frac{\left(y - \frac{t}{y}\right) \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.2e-38) (not (<= y 5.9e-124)))
   (+ x (/ (* (- y (/ t y)) -0.3333333333333333) z))
   (+ x (* (/ t z) (/ 0.3333333333333333 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.2e-38) || !(y <= 5.9e-124)) {
		tmp = x + (((y - (t / y)) * -0.3333333333333333) / 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 <= (-9.2d-38)) .or. (.not. (y <= 5.9d-124))) then
        tmp = x + (((y - (t / y)) * (-0.3333333333333333d0)) / 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 <= -9.2e-38) || !(y <= 5.9e-124)) {
		tmp = x + (((y - (t / y)) * -0.3333333333333333) / z);
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.2e-38) or not (y <= 5.9e-124):
		tmp = x + (((y - (t / y)) * -0.3333333333333333) / z)
	else:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.2e-38) || !(y <= 5.9e-124))
		tmp = Float64(x + Float64(Float64(Float64(y - Float64(t / y)) * -0.3333333333333333) / 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 <= -9.2e-38) || ~((y <= 5.9e-124)))
		tmp = x + (((y - (t / y)) * -0.3333333333333333) / z);
	else
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.2e-38], N[Not[LessEqual[y, 5.9e-124]], $MachinePrecision]], N[(x + N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * -0.3333333333333333), $MachinePrecision] / z), $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 < -9.20000000000000007e-38 or 5.9000000000000002e-124 < 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. sub-neg 98.6%

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

      2. distribute-frac-neg 98.6%

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

      3. associate-+l+ 98.6%

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

      4. remove-double-neg 98.6%

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

      5. distribute-frac-neg 98.6%

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

      6. sub-neg 98.6%

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

      7. neg-mul-1 98.6%

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

      8. associate-*l/ 98.5%

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

      9. neg-mul-1 98.5%

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

      10. times-frac 99.7%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*l/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -9.20000000000000007e-38 < y < 5.9000000000000002e-124

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. distribute-frac-neg 92.1%

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

      3. associate-+l+ 92.1%

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

      4. remove-double-neg 92.1%

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

      5. distribute-frac-neg 92.1%

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

      6. sub-neg 92.1%

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

      7. neg-mul-1 92.1%

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

      8. associate-*l/ 92.1%

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

      9. neg-mul-1 92.1%

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

      10. times-frac 86.4%

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

      11. distribute-lft-out-- 86.4%

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

      12. *-commutative 86.4%

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

      13. associate-/r* 86.5%

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

      14. metadata-eval 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in y around 0 91.3%

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

      1. associate-/r* 84.7%

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

      2. associate-*r/ 84.7%

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

      3. associate-*l/ 84.7%

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

      4. associate-*r/ 94.7%

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

      5. associate-*l/ 91.2%

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

      6. /-rgt-identity 91.2%

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

      7. associate-*r/ 91.2%

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

      8. associate-*l/ 94.7%

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

      9. associate-*r/ 84.7%

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

      10. *-commutative 84.7%

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

      11. associate-*r/ 84.7%

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

      12. *-commutative 84.7%

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

      13. associate-*r/ 84.7%

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

      14. *-commutative 84.7%

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

      15. associate-/r* 91.3%

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

      16. associate-/l* 91.3%

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

      17. associate-/r* 84.8%

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

      18. metadata-eval 84.8%

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

      19. associate-/r* 84.7%

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

      20. associate-/l/ 91.2%

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

      21. associate-*r* 91.3%

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

      22. *-commutative 91.3%

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

   6. Simplified 91.3%

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

      1. associate-/r* 94.6%

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

      2. div-inv 94.6%

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

   8. Applied egg-rr 94.6%

      \[\leadsto x + \color{blue}{\frac{t}{z} \cdot \frac{1}{y \cdot 3}} \]
   9. Step-by-step derivation

      1. *-commutative 94.6%

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

      2. associate-/r* 94.7%

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

      3. metadata-eval 94.7%

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

   10. Simplified 94.7%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-38} \lor \neg \left(y \leq 5.9 \cdot 10^{-124}\right):\\ \;\;\;\;x + \frac{\left(y - \frac{t}{y}\right) \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 6: 49.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 500000000000:\\ \;\;\;\;\frac{-y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -1e-20)
   x
   (if (<= (* z 3.0) 500000000000.0) (/ (- y) (* z 3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e-20) {
		tmp = x;
	} else if ((z * 3.0) <= 500000000000.0) {
		tmp = -y / (z * 3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-1d-20)) then
        tmp = x
    else if ((z * 3.0d0) <= 500000000000.0d0) then
        tmp = -y / (z * 3.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e-20) {
		tmp = x;
	} else if ((z * 3.0) <= 500000000000.0) {
		tmp = -y / (z * 3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -1e-20:
		tmp = x
	elif (z * 3.0) <= 500000000000.0:
		tmp = -y / (z * 3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e-20)
		tmp = x;
	elseif (Float64(z * 3.0) <= 500000000000.0)
		tmp = Float64(Float64(-y) / Float64(z * 3.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -1e-20)
		tmp = x;
	elseif ((z * 3.0) <= 500000000000.0)
		tmp = -y / (z * 3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e-20], x, If[LessEqual[N[(z * 3.0), $MachinePrecision], 500000000000.0], N[((-y) / N[(z * 3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -9.99999999999999945e-21 or 5e11 < (*.f64 z 3)

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. distribute-frac-neg 99.1%

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

      3. associate-+l+ 99.1%

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

      4. remove-double-neg 99.1%

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

      5. distribute-frac-neg 99.1%

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

      6. sub-neg 99.1%

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

      7. neg-mul-1 99.1%

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

      8. associate-*l/ 99.1%

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

      9. neg-mul-1 99.1%

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

      10. times-frac 90.1%

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

      11. distribute-lft-out-- 90.1%

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

      12. *-commutative 90.1%

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

      13. associate-/r* 90.1%

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

      14. metadata-eval 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in x around inf 50.7%

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

   if -9.99999999999999945e-21 < (*.f64 z 3) < 5e11

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. distribute-frac-neg 92.6%

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

      3. associate-+l+ 92.6%

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

      4. remove-double-neg 92.6%

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

      5. distribute-frac-neg 92.6%

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

      6. sub-neg 92.6%

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

      7. neg-mul-1 92.6%

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

      8. associate-*l/ 92.5%

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

      9. neg-mul-1 92.5%

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

      10. times-frac 99.7%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 94.8%

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

   6. Taylor expanded in y around inf 50.3%

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

      1. *-commutative 50.3%

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

      2. metadata-eval 50.3%

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

      3. distribute-rgt-neg-in 50.3%

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

      4. associate-/r/ 50.3%

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

      5. distribute-neg-frac 50.3%

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

      6. div-inv 50.3%

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

      7. metadata-eval 50.3%

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

   8. Applied egg-rr 50.3%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 500000000000:\\ \;\;\;\;\frac{-y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 89.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+45} \lor \neg \left(y \leq 6 \cdot 10^{-7}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e+45) (not (<= y 6e-7)))
   (- x (/ (* y 0.3333333333333333) z))
   (+ x (* 0.3333333333333333 (/ t (* y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e+45) || !(y <= 6e-7)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3d+45)) .or. (.not. (y <= 6d-7))) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else
        tmp = x + (0.3333333333333333d0 * (t / (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e+45) || !(y <= 6e-7)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3e+45) or not (y <= 6e-7):
		tmp = x - ((y * 0.3333333333333333) / z)
	else:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3e+45) || !(y <= 6e-7))
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3e+45) || ~((y <= 6e-7)))
		tmp = x - ((y * 0.3333333333333333) / z);
	else
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3e+45], N[Not[LessEqual[y, 6e-7]], $MachinePrecision]], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000011e45 or 5.9999999999999997e-7 < y

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around 0 93.3%

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

      1. associate-*r/ 93.4%

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

      2. *-commutative 93.4%

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

   6. Applied egg-rr 93.4%

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

   if -3.00000000000000011e45 < y < 5.9999999999999997e-7

   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. sub-neg 93.6%

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

      2. distribute-frac-neg 93.6%

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

      3. associate-+l+ 93.6%

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

      4. remove-double-neg 93.6%

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

      5. distribute-frac-neg 93.6%

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

      6. sub-neg 93.6%

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

      7. neg-mul-1 93.6%

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

      8. associate-*l/ 93.6%

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

      9. neg-mul-1 93.6%

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

      10. times-frac 90.2%

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

      11. distribute-lft-out-- 90.2%

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

      12. *-commutative 90.2%

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

      13. associate-/r* 90.3%

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

      14. metadata-eval 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around 0 88.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+45} \lor \neg \left(y \leq 6 \cdot 10^{-7}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 8: 49.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 500000000000:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -1e-20)
   x
   (if (<= (* z 3.0) 500000000000.0) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e-20) {
		tmp = x;
	} else if ((z * 3.0) <= 500000000000.0) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-1d-20)) then
        tmp = x
    else if ((z * 3.0d0) <= 500000000000.0d0) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e-20) {
		tmp = x;
	} else if ((z * 3.0) <= 500000000000.0) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -1e-20:
		tmp = x
	elif (z * 3.0) <= 500000000000.0:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e-20)
		tmp = x;
	elseif (Float64(z * 3.0) <= 500000000000.0)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -1e-20)
		tmp = x;
	elseif ((z * 3.0) <= 500000000000.0)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e-20], x, If[LessEqual[N[(z * 3.0), $MachinePrecision], 500000000000.0], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -9.99999999999999945e-21 or 5e11 < (*.f64 z 3)

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. distribute-frac-neg 99.1%

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

      3. associate-+l+ 99.1%

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

      4. remove-double-neg 99.1%

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

      5. distribute-frac-neg 99.1%

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

      6. sub-neg 99.1%

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

      7. neg-mul-1 99.1%

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

      8. associate-*l/ 99.1%

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

      9. neg-mul-1 99.1%

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

      10. times-frac 90.1%

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

      11. distribute-lft-out-- 90.1%

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

      12. *-commutative 90.1%

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

      13. associate-/r* 90.1%

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

      14. metadata-eval 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in x around inf 50.7%

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

   if -9.99999999999999945e-21 < (*.f64 z 3) < 5e11

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. distribute-frac-neg 92.6%

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

      3. associate-+l+ 92.6%

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

      4. remove-double-neg 92.6%

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

      5. distribute-frac-neg 92.6%

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

      6. sub-neg 92.6%

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

      7. neg-mul-1 92.6%

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

      8. associate-*l/ 92.5%

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

      9. neg-mul-1 92.5%

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

      10. times-frac 99.7%

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

      11. distribute-lft-out-- 99.7%

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

      12. *-commutative 99.7%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 94.8%

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

   6. Taylor expanded in y around inf 50.3%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \cdot 3 \leq 500000000000:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 78.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{-84}:\\ \;\;\;\;-0.3333333333333333 \cdot \left(\frac{t}{z} \cdot \frac{-1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-38)
   (- x (/ y (/ z 0.3333333333333333)))
   (if (<= y 1.82e-84)
     (* -0.3333333333333333 (* (/ t z) (/ -1.0 y)))
     (- x (/ (* y 0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-38) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 1.82e-84) {
		tmp = -0.3333333333333333 * ((t / z) * (-1.0 / y));
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.45d-38)) then
        tmp = x - (y / (z / 0.3333333333333333d0))
    else if (y <= 1.82d-84) then
        tmp = (-0.3333333333333333d0) * ((t / z) * ((-1.0d0) / y))
    else
        tmp = x - ((y * 0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-38) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 1.82e-84) {
		tmp = -0.3333333333333333 * ((t / z) * (-1.0 / y));
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-38:
		tmp = x - (y / (z / 0.3333333333333333))
	elif y <= 1.82e-84:
		tmp = -0.3333333333333333 * ((t / z) * (-1.0 / y))
	else:
		tmp = x - ((y * 0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-38)
		tmp = Float64(x - Float64(y / Float64(z / 0.3333333333333333)));
	elseif (y <= 1.82e-84)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(t / z) * Float64(-1.0 / y)));
	else
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e-38)
		tmp = x - (y / (z / 0.3333333333333333));
	elseif (y <= 1.82e-84)
		tmp = -0.3333333333333333 * ((t / z) * (-1.0 / y));
	else
		tmp = x - ((y * 0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-38], N[(x - N[(y / N[(z / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.82e-84], N[(-0.3333333333333333 * N[(N[(t / z), $MachinePrecision] * N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.44999999999999997e-38

   1. Initial program 98.4%

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

      1. sub-neg 98.4%

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

      2. distribute-frac-neg 98.4%

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

      3. associate-+l+ 98.4%

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

      4. remove-double-neg 98.4%

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

      5. distribute-frac-neg 98.4%

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

      6. sub-neg 98.4%

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

      7. neg-mul-1 98.4%

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

      8. associate-*l/ 98.2%

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

      9. neg-mul-1 98.2%

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

      10. times-frac 99.6%

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

      11. distribute-lft-out-- 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 85.6%

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

   5. Taylor expanded in x around 0 85.6%

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

      1. metadata-eval 85.6%

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

      2. cancel-sign-sub-inv 85.6%

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

      3. *-commutative 85.6%

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

      4. associate-*l/ 85.6%

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

      5. associate-/l* 85.6%

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

   7. Simplified 85.6%

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

   if -1.44999999999999997e-38 < y < 1.81999999999999991e-84

   1. Initial program 91.5%

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

      1. sub-neg 91.5%

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

      2. distribute-frac-neg 91.5%

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

      3. associate-+l+ 91.5%

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

      4. remove-double-neg 91.5%

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

      5. distribute-frac-neg 91.5%

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

      6. sub-neg 91.5%

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

      7. neg-mul-1 91.5%

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

      8. associate-*l/ 91.5%

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

      9. neg-mul-1 91.5%

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

      10. times-frac 87.1%

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

      11. distribute-lft-out-- 87.1%

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

      12. *-commutative 87.1%

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

      13. associate-/r* 87.1%

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

      14. metadata-eval 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in z around 0 87.1%

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

   5. Taylor expanded in x around 0 63.0%

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

   6. Taylor expanded in y around 0 67.5%

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

      1. *-commutative 67.5%

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

      2. associate-*r/ 67.5%

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

      3. neg-mul-1 67.5%

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

      4. *-commutative 67.5%

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

   8. Simplified 67.5%

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

      1. neg-mul-1 67.5%

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

      2. times-frac 70.2%

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

   10. Applied egg-rr 70.2%

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

   if 1.81999999999999991e-84 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 86.9%

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

      1. associate-*r/ 87.0%

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

      2. *-commutative 87.0%

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

   6. Applied egg-rr 87.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{-84}:\\ \;\;\;\;-0.3333333333333333 \cdot \left(\frac{t}{z} \cdot \frac{-1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 10: 92.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -750:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -750.0)
   (- x (/ y (/ z 0.3333333333333333)))
   (if (<= y 3.6e-7)
     (+ x (* (/ t z) (/ 0.3333333333333333 y)))
     (- x (/ (* y 0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -750.0) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 3.6e-7) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-750.0d0)) then
        tmp = x - (y / (z / 0.3333333333333333d0))
    else if (y <= 3.6d-7) then
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    else
        tmp = x - ((y * 0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -750.0) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 3.6e-7) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -750.0:
		tmp = x - (y / (z / 0.3333333333333333))
	elif y <= 3.6e-7:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x - ((y * 0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -750.0)
		tmp = Float64(x - Float64(y / Float64(z / 0.3333333333333333)));
	elseif (y <= 3.6e-7)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -750.0)
		tmp = x - (y / (z / 0.3333333333333333));
	elseif (y <= 3.6e-7)
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x - ((y * 0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -750.0], N[(x - N[(y / N[(z / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-7], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -750

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. distribute-frac-neg 98.1%

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

      3. associate-+l+ 98.1%

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

      4. remove-double-neg 98.1%

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

      5. distribute-frac-neg 98.1%

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

      6. sub-neg 98.1%

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

      7. neg-mul-1 98.1%

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

      8. associate-*l/ 98.0%

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

      9. neg-mul-1 98.0%

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

      10. times-frac 99.6%

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

      11. distribute-lft-out-- 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 89.9%

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

   5. Taylor expanded in x around 0 89.9%

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

      1. metadata-eval 89.9%

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

      2. cancel-sign-sub-inv 89.9%

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

      3. *-commutative 89.9%

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

      4. associate-*l/ 90.0%

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

      5. associate-/l* 90.0%

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

   7. Simplified 90.0%

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

   if -750 < y < 3.59999999999999994e-7

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. distribute-frac-neg 93.0%

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

      3. associate-+l+ 93.0%

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

      4. remove-double-neg 93.0%

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

      5. distribute-frac-neg 93.0%

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

      6. sub-neg 93.0%

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

      7. neg-mul-1 93.0%

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

      8. associate-*l/ 93.0%

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

      9. neg-mul-1 93.0%

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

      10. times-frac 89.4%

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

      11. distribute-lft-out-- 89.4%

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

      12. *-commutative 89.4%

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

      13. associate-/r* 89.5%

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

      14. metadata-eval 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in y around 0 89.3%

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

      1. associate-/r* 84.3%

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

      2. associate-*r/ 84.2%

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

      3. associate-*l/ 84.3%

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

      4. associate-*r/ 91.9%

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

      5. associate-*l/ 89.3%

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

      6. /-rgt-identity 89.3%

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

      7. associate-*r/ 89.3%

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

      8. associate-*l/ 91.9%

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

      9. associate-*r/ 84.3%

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

      10. *-commutative 84.3%

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

      11. associate-*r/ 84.2%

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

      12. *-commutative 84.2%

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

      13. associate-*r/ 84.3%

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

      14. *-commutative 84.3%

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

      15. associate-/r* 89.3%

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

      16. associate-/l* 89.3%

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

      17. associate-/r* 84.3%

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

      18. metadata-eval 84.3%

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

      19. associate-/r* 84.2%

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

      20. associate-/l/ 89.3%

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

      21. associate-*r* 89.3%

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

      22. *-commutative 89.3%

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

   6. Simplified 89.3%

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

      1. associate-/r* 92.0%

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

      2. div-inv 91.9%

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

   8. Applied egg-rr 91.9%

      \[\leadsto x + \color{blue}{\frac{t}{z} \cdot \frac{1}{y \cdot 3}} \]
   9. Step-by-step derivation

      1. *-commutative 91.9%

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

      2. associate-/r* 92.0%

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

      3. metadata-eval 92.0%

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

   10. Simplified 92.0%

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

   if 3.59999999999999994e-7 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 92.9%

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

      1. associate-*r/ 93.1%

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

      2. *-commutative 93.1%

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

   6. Applied egg-rr 93.1%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -750:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 11: 75.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-85}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{-t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e-16)
   (- x (/ y (/ z 0.3333333333333333)))
   (if (<= y 1.08e-85)
     (* -0.3333333333333333 (/ (- t) (* y z)))
     (- x (/ (* y 0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-16) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 1.08e-85) {
		tmp = -0.3333333333333333 * (-t / (y * z));
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.7d-16)) then
        tmp = x - (y / (z / 0.3333333333333333d0))
    else if (y <= 1.08d-85) then
        tmp = (-0.3333333333333333d0) * (-t / (y * z))
    else
        tmp = x - ((y * 0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-16) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 1.08e-85) {
		tmp = -0.3333333333333333 * (-t / (y * z));
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e-16:
		tmp = x - (y / (z / 0.3333333333333333))
	elif y <= 1.08e-85:
		tmp = -0.3333333333333333 * (-t / (y * z))
	else:
		tmp = x - ((y * 0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e-16)
		tmp = Float64(x - Float64(y / Float64(z / 0.3333333333333333)));
	elseif (y <= 1.08e-85)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(-t) / Float64(y * z)));
	else
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e-16)
		tmp = x - (y / (z / 0.3333333333333333));
	elseif (y <= 1.08e-85)
		tmp = -0.3333333333333333 * (-t / (y * z));
	else
		tmp = x - ((y * 0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e-16], N[(x - N[(y / N[(z / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e-85], N[(-0.3333333333333333 * N[((-t) / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e-16

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-frac-neg 98.3%

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

      3. associate-+l+ 98.3%

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

      4. remove-double-neg 98.3%

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

      5. distribute-frac-neg 98.3%

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

      6. sub-neg 98.3%

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

      7. neg-mul-1 98.3%

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

      8. associate-*l/ 98.1%

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

      9. neg-mul-1 98.1%

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

      10. times-frac 99.6%

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

      11. distribute-lft-out-- 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 87.8%

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

   5. Taylor expanded in x around 0 87.8%

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

      1. metadata-eval 87.8%

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

      2. cancel-sign-sub-inv 87.8%

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

      3. *-commutative 87.8%

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

      4. associate-*l/ 87.8%

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

      5. associate-/l* 87.8%

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

   7. Simplified 87.8%

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

   if -1.7e-16 < y < 1.07999999999999997e-85

   1. Initial program 91.8%

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

      1. sub-neg 91.8%

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

      2. distribute-frac-neg 91.8%

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

      3. associate-+l+ 91.8%

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

      4. remove-double-neg 91.8%

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

      5. distribute-frac-neg 91.8%

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

      6. sub-neg 91.8%

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

      7. neg-mul-1 91.8%

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

      8. associate-*l/ 91.8%

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

      9. neg-mul-1 91.8%

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

      10. times-frac 87.5%

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

      11. distribute-lft-out-- 87.5%

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

      12. *-commutative 87.5%

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

      13. associate-/r* 87.6%

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

      14. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around 0 87.6%

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

   5. Taylor expanded in x around 0 63.5%

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

   6. Taylor expanded in y around 0 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*r/ 66.9%

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

      3. neg-mul-1 66.9%

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

      4. *-commutative 66.9%

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

   8. Simplified 66.9%

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

   if 1.07999999999999997e-85 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 86.9%

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

      1. associate-*r/ 87.0%

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

      2. *-commutative 87.0%

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

   6. Applied egg-rr 87.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-85}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{-t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 12: 75.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-80}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{z}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-18)
   (- x (/ y (/ z 0.3333333333333333)))
   (if (<= y 2.45e-80)
     (/ 0.3333333333333333 (/ z (/ t y)))
     (- x (/ (* y 0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-18) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 2.45e-80) {
		tmp = 0.3333333333333333 / (z / (t / y));
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d-18)) then
        tmp = x - (y / (z / 0.3333333333333333d0))
    else if (y <= 2.45d-80) then
        tmp = 0.3333333333333333d0 / (z / (t / y))
    else
        tmp = x - ((y * 0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-18) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 2.45e-80) {
		tmp = 0.3333333333333333 / (z / (t / y));
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-18:
		tmp = x - (y / (z / 0.3333333333333333))
	elif y <= 2.45e-80:
		tmp = 0.3333333333333333 / (z / (t / y))
	else:
		tmp = x - ((y * 0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-18)
		tmp = Float64(x - Float64(y / Float64(z / 0.3333333333333333)));
	elseif (y <= 2.45e-80)
		tmp = Float64(0.3333333333333333 / Float64(z / Float64(t / y)));
	else
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e-18)
		tmp = x - (y / (z / 0.3333333333333333));
	elseif (y <= 2.45e-80)
		tmp = 0.3333333333333333 / (z / (t / y));
	else
		tmp = x - ((y * 0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-18], N[(x - N[(y / N[(z / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e-80], N[(0.3333333333333333 / N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000018e-18

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-frac-neg 98.3%

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

      3. associate-+l+ 98.3%

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

      4. remove-double-neg 98.3%

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

      5. distribute-frac-neg 98.3%

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

      6. sub-neg 98.3%

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

      7. neg-mul-1 98.3%

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

      8. associate-*l/ 98.1%

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

      9. neg-mul-1 98.1%

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

      10. times-frac 99.6%

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

      11. distribute-lft-out-- 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 87.8%

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

   5. Taylor expanded in x around 0 87.8%

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

      1. metadata-eval 87.8%

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

      2. cancel-sign-sub-inv 87.8%

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

      3. *-commutative 87.8%

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

      4. associate-*l/ 87.8%

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

      5. associate-/l* 87.8%

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

   7. Simplified 87.8%

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

   if -2.50000000000000018e-18 < y < 2.44999999999999995e-80

   1. Initial program 91.8%

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

      1. sub-neg 91.8%

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

      2. distribute-frac-neg 91.8%

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

      3. associate-+l+ 91.8%

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

      4. remove-double-neg 91.8%

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

      5. distribute-frac-neg 91.8%

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

      6. sub-neg 91.8%

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

      7. neg-mul-1 91.8%

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

      8. associate-*l/ 91.8%

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

      9. neg-mul-1 91.8%

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

      10. times-frac 87.5%

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

      11. distribute-lft-out-- 87.5%

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

      12. *-commutative 87.5%

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

      13. associate-/r* 87.6%

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

      14. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around 0 87.6%

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

   5. Taylor expanded in x around 0 63.5%

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

   6. Taylor expanded in y around 0 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*r/ 66.9%

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

      3. neg-mul-1 66.9%

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

      4. *-commutative 66.9%

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

   8. Simplified 66.9%

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

      1. associate-*r/ 66.8%

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

      2. neg-mul-1 66.8%

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

      3. associate-*r* 66.8%

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

      4. metadata-eval 66.8%

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

      5. associate-/l* 66.7%

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

      6. add-sqr-sqrt 25.6%

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

      7. sqrt-unprod 21.8%

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

      8. sqr-neg 21.8%

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

      9. sqrt-unprod 0.8%

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

      10. *-commutative 0.8%

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

      11. add-sqr-sqrt 1.5%

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

      12. associate-/l* 1.5%

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

      13. add-sqr-sqrt 0.7%

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

      14. sqrt-unprod 21.9%

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

      15. sqr-neg 21.9%

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

      16. sqrt-unprod 24.7%

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

      17. add-sqr-sqrt 59.9%

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

   10. Applied egg-rr 59.9%

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

   if 2.44999999999999995e-80 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 86.9%

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

      1. associate-*r/ 87.0%

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

      2. *-commutative 87.0%

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

   6. Applied egg-rr 87.0%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-80}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{z}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 13: 75.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{t}{\frac{y \cdot z}{0.3333333333333333}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.9e-18)
   (- x (/ y (/ z 0.3333333333333333)))
   (if (<= y 9.6e-79)
     (/ t (/ (* y z) 0.3333333333333333))
     (- x (/ (* y 0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-18) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 9.6e-79) {
		tmp = t / ((y * z) / 0.3333333333333333);
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.9d-18)) then
        tmp = x - (y / (z / 0.3333333333333333d0))
    else if (y <= 9.6d-79) then
        tmp = t / ((y * z) / 0.3333333333333333d0)
    else
        tmp = x - ((y * 0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-18) {
		tmp = x - (y / (z / 0.3333333333333333));
	} else if (y <= 9.6e-79) {
		tmp = t / ((y * z) / 0.3333333333333333);
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.9e-18:
		tmp = x - (y / (z / 0.3333333333333333))
	elif y <= 9.6e-79:
		tmp = t / ((y * z) / 0.3333333333333333)
	else:
		tmp = x - ((y * 0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.9e-18)
		tmp = Float64(x - Float64(y / Float64(z / 0.3333333333333333)));
	elseif (y <= 9.6e-79)
		tmp = Float64(t / Float64(Float64(y * z) / 0.3333333333333333));
	else
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.9e-18)
		tmp = x - (y / (z / 0.3333333333333333));
	elseif (y <= 9.6e-79)
		tmp = t / ((y * z) / 0.3333333333333333);
	else
		tmp = x - ((y * 0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.9e-18], N[(x - N[(y / N[(z / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e-79], N[(t / N[(N[(y * z), $MachinePrecision] / 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.90000000000000005e-18

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-frac-neg 98.3%

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

      3. associate-+l+ 98.3%

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

      4. remove-double-neg 98.3%

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

      5. distribute-frac-neg 98.3%

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

      6. sub-neg 98.3%

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

      7. neg-mul-1 98.3%

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

      8. associate-*l/ 98.1%

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

      9. neg-mul-1 98.1%

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

      10. times-frac 99.6%

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

      11. distribute-lft-out-- 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 87.8%

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

   5. Taylor expanded in x around 0 87.8%

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

      1. metadata-eval 87.8%

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

      2. cancel-sign-sub-inv 87.8%

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

      3. *-commutative 87.8%

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

      4. associate-*l/ 87.8%

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

      5. associate-/l* 87.8%

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

   7. Simplified 87.8%

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

   if -3.90000000000000005e-18 < y < 9.60000000000000023e-79

   1. Initial program 91.8%

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

      1. sub-neg 91.8%

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

      2. distribute-frac-neg 91.8%

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

      3. associate-+l+ 91.8%

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

      4. remove-double-neg 91.8%

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

      5. distribute-frac-neg 91.8%

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

      6. sub-neg 91.8%

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

      7. neg-mul-1 91.8%

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

      8. associate-*l/ 91.8%

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

      9. neg-mul-1 91.8%

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

      10. times-frac 87.5%

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

      11. distribute-lft-out-- 87.5%

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

      12. *-commutative 87.5%

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

      13. associate-/r* 87.6%

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

      14. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around 0 87.6%

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

   5. Taylor expanded in x around 0 63.5%

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

   6. Taylor expanded in y around 0 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*r/ 66.9%

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

      3. neg-mul-1 66.9%

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

      4. *-commutative 66.9%

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

   8. Simplified 66.9%

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

      1. associate-*r/ 66.8%

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

      2. neg-mul-1 66.8%

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

      3. associate-*r* 66.8%

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

      4. metadata-eval 66.8%

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

      5. *-commutative 66.8%

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

      6. associate-/l* 66.8%

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

      7. *-commutative 66.8%

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

   10. Applied egg-rr 66.8%

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

   if 9.60000000000000023e-79 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 86.9%

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

      1. associate-*r/ 87.0%

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

      2. *-commutative 87.0%

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

   6. Applied egg-rr 87.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{y}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{t}{\frac{y \cdot z}{0.3333333333333333}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 14: 65.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{-0.3333333333333333}{z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. sub-neg 96.1%

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

   2. distribute-frac-neg 96.1%

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

   3. associate-+l+ 96.1%

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

   4. remove-double-neg 96.1%

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

   5. distribute-frac-neg 96.1%

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

   6. sub-neg 96.1%

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

   7. neg-mul-1 96.1%

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

   8. associate-*l/ 96.0%

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

   9. neg-mul-1 96.0%

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

   10. times-frac 94.6%

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

   11. distribute-lft-out-- 94.6%

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

   12. *-commutative 94.6%

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

   13. associate-/r* 94.6%

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

   14. metadata-eval 94.6%

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

3. Simplified 94.6%

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

4. Taylor expanded in y around inf 63.1%

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

5. Final simplification 63.1%

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

Alternative 15: 65.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x - 0.3333333333333333 \cdot \frac{y}{z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. associate-+l- 96.1%

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

   2. *-commutative 96.1%

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

3. Simplified 96.1%

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

4. Taylor expanded in t around 0 63.1%

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

5. Final simplification 63.1%

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

Alternative 16: 65.3% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. sub-neg 96.1%

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

   2. distribute-frac-neg 96.1%

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

   3. associate-+l+ 96.1%

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

   4. remove-double-neg 96.1%

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

   5. distribute-frac-neg 96.1%

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

   6. sub-neg 96.1%

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

   7. neg-mul-1 96.1%

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

   8. associate-*l/ 96.0%

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

   9. neg-mul-1 96.0%

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

   10. times-frac 94.6%

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

   11. distribute-lft-out-- 94.6%

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

   12. *-commutative 94.6%

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

   13. associate-/r* 94.6%

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

   14. metadata-eval 94.6%

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

3. Simplified 94.6%

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

4. Taylor expanded in y around inf 63.1%

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

5. Taylor expanded in x around 0 63.1%

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

   1. metadata-eval 63.1%

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

   2. cancel-sign-sub-inv 63.1%

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

   3. *-commutative 63.1%

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

   4. associate-*l/ 63.1%

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

   5. associate-/l* 63.1%

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

7. Simplified 63.1%

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

8. Taylor expanded in z around 0 63.1%

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

   1. *-commutative 63.1%

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

10. Simplified 63.1%

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

11. Final simplification 63.1%

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

Alternative 17: 65.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x - \frac{y \cdot 0.3333333333333333}{z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. associate-+l- 96.1%

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

   2. *-commutative 96.1%

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

3. Simplified 96.1%

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

4. Taylor expanded in t around 0 63.1%

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

   1. associate-*r/ 63.1%

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

   2. *-commutative 63.1%

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

6. Applied egg-rr 63.1%

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

7. Final simplification 63.1%

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

Alternative 18: 31.1% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. sub-neg 96.1%

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

   2. distribute-frac-neg 96.1%

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

   3. associate-+l+ 96.1%

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

   4. remove-double-neg 96.1%

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

   5. distribute-frac-neg 96.1%

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

   6. sub-neg 96.1%

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

   7. neg-mul-1 96.1%

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

   8. associate-*l/ 96.0%

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

   9. neg-mul-1 96.0%

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

   10. times-frac 94.6%

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

   11. distribute-lft-out-- 94.6%

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

   12. *-commutative 94.6%

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

   13. associate-/r* 94.6%

       \[\leadsto x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]

   14. metadata-eval 94.6%

       \[\leadsto x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

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 30.4%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 30.4%

   \[\leadsto x \]

Developer target: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023301 
(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))))