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

Percentage Accurate: 95.6% → 97.5%

Time: 12.3s

Alternatives: 19

Speedup: 1.4×

• 26.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+289}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))))
   (if (<= t_1 4e+289) t_1 (+ x (* -0.3333333333333333 (/ (- y (/ t y)) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 4e+289) {
		tmp = t_1;
	} else {
		tmp = x + (-0.3333333333333333 * ((y - (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) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    if (t_1 <= 4d+289) then
        tmp = t_1
    else
        tmp = x + ((-0.3333333333333333d0) * ((y - (t / y)) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 4e+289) {
		tmp = t_1;
	} else {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	tmp = 0
	if t_1 <= 4e+289:
		tmp = t_1
	else:
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))))
	tmp = 0.0
	if (t_1 <= 4e+289)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	tmp = 0.0;
	if (t_1 <= 4e+289)
		tmp = t_1;
	else
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+289], t$95$1, N[(x + N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 4.0000000000000002e289

   1. Initial program 98.3%

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

   if 4.0000000000000002e289 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))

   1. Initial program 87.2%

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

      1. sub-neg 87.2%

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

      2. associate-+l+ 87.2%

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

      3. remove-double-neg 87.2%

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

      4. distribute-frac-neg 87.2%

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

      5. sub-neg 87.2%

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

      6. distribute-frac-neg 87.2%

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

      7. neg-mul-1 87.2%

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

      8. *-commutative 87.2%

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

      9. associate-/l* 87.2%

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

      10. *-commutative 87.2%

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

      11. neg-mul-1 87.2%

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

      12. times-frac 97.6%

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

      13. distribute-lft-out-- 99.8%

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

      14. *-commutative 99.8%

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

      15. associate-/r* 99.9%

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 100.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 4 \cdot 10^{+289}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+16} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{+90}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -2e+16) (not (<= (* z 3.0) 5e+90)))
   (- x (/ (* y 0.3333333333333333) z))
   (* 0.3333333333333333 (/ (- (/ t y) y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+16) || !((z * 3.0) <= 5e+90)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = 0.3333333333333333 * (((t / y) - 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 (((z * 3.0d0) <= (-2d+16)) .or. (.not. ((z * 3.0d0) <= 5d+90))) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else
        tmp = 0.3333333333333333d0 * (((t / y) - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+16) || !((z * 3.0) <= 5e+90)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -2e+16) or not ((z * 3.0) <= 5e+90):
		tmp = x - ((y * 0.3333333333333333) / z)
	else:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -2e+16) || !(Float64(z * 3.0) <= 5e+90))
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -2e+16) || ~(((z * 3.0) <= 5e+90)))
		tmp = x - ((y * 0.3333333333333333) / z);
	else
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+16], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 5e+90]], $MachinePrecision]], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -2e16 or 5.0000000000000004e90 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. associate-+l+ 98.8%

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

      3. distribute-frac-neg 98.8%

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

      4. neg-mul-1 98.8%

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

      5. *-commutative 98.8%

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

      6. times-frac 98.9%

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

      7. fma-define 98.9%

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

      8. metadata-eval 98.9%

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

      9. associate-*l* 98.8%

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

      10. *-commutative 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around 0 81.1%

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

      1. metadata-eval 81.1%

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

      2. cancel-sign-sub-inv 81.1%

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

      3. associate-*r/ 81.2%

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

      4. *-commutative 81.2%

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

   7. Simplified 81.2%

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

   if -2e16 < (*.f64 z #s(literal 3 binary64)) < 5.0000000000000004e90

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 90.0%

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

      1. distribute-lft-out-- 90.0%

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

      2. associate-/l* 90.1%

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

   5. Applied egg-rr 90.1%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+16} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{+90}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{-3}}{z}\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ y -3.0) z)))
   (if (<= y -1.06e+105)
     t_1
     (if (<= y -2.65e-135)
       x
       (if (<= y 6.9e+72) (* t (/ (/ 0.3333333333333333 y) z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / -3.0) / z;
	double tmp;
	if (y <= -1.06e+105) {
		tmp = t_1;
	} else if (y <= -2.65e-135) {
		tmp = x;
	} else if (y <= 6.9e+72) {
		tmp = t * ((0.3333333333333333 / y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / (-3.0d0)) / z
    if (y <= (-1.06d+105)) then
        tmp = t_1
    else if (y <= (-2.65d-135)) then
        tmp = x
    else if (y <= 6.9d+72) then
        tmp = t * ((0.3333333333333333d0 / y) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / -3.0) / z;
	double tmp;
	if (y <= -1.06e+105) {
		tmp = t_1;
	} else if (y <= -2.65e-135) {
		tmp = x;
	} else if (y <= 6.9e+72) {
		tmp = t * ((0.3333333333333333 / y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / -3.0) / z
	tmp = 0
	if y <= -1.06e+105:
		tmp = t_1
	elif y <= -2.65e-135:
		tmp = x
	elif y <= 6.9e+72:
		tmp = t * ((0.3333333333333333 / y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / -3.0) / z)
	tmp = 0.0
	if (y <= -1.06e+105)
		tmp = t_1;
	elseif (y <= -2.65e-135)
		tmp = x;
	elseif (y <= 6.9e+72)
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / -3.0) / z;
	tmp = 0.0;
	if (y <= -1.06e+105)
		tmp = t_1;
	elseif (y <= -2.65e-135)
		tmp = x;
	elseif (y <= 6.9e+72)
		tmp = t * ((0.3333333333333333 / y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.06e+105], t$95$1, If[LessEqual[y, -2.65e-135], x, If[LessEqual[y, 6.9e+72], N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e105 or 6.90000000000000034e72 < 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. associate-+l+ 98.6%

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

      3. distribute-frac-neg 98.6%

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

      4. neg-mul-1 98.6%

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

      5. *-commutative 98.6%

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

      6. times-frac 98.6%

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

      7. fma-define 98.6%

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

      8. metadata-eval 98.6%

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

      9. associate-*l* 98.6%

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

      10. *-commutative 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around 0 99.6%

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

      1. metadata-eval 99.6%

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

      2. cancel-sign-sub-inv 99.6%

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

      3. associate-*r/ 99.6%

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

      4. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. metadata-eval 75.1%

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

      3. distribute-lft-neg-in 75.1%

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

      4. add-sqr-sqrt 30.7%

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

      5. sqrt-unprod 27.1%

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

      6. sqr-neg 27.1%

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

      7. sqrt-unprod 1.0%

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

      8. add-sqr-sqrt 1.6%

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

      9. frac-2neg 1.6%

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

      10. clear-num 1.6%

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

      11. frac-2neg 1.6%

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

      12. metadata-eval 1.6%

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

      13. distribute-frac-neg2 1.6%

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

      14. metadata-eval 1.6%

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

      15. distribute-neg-frac 1.6%

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

      16. clear-num 1.6%

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

      17. distribute-neg-frac 1.6%

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

      18. distribute-lft-neg-in 1.6%

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

      19. metadata-eval 1.6%

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

      20. associate-*r/ 1.6%

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

   10. Applied egg-rr 1.6%

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

       1. add-sqr-sqrt 0.7%

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

       2. sqrt-unprod 36.9%

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

       3. sqr-neg 36.9%

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

       4. sqrt-unprod 41.5%

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

       5. add-sqr-sqrt 75.1%

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

       6. metadata-eval 75.1%

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

       7. times-frac 75.0%

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

       8. *-un-lft-identity 75.0%

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

       9. associate-/r* 75.2%

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

   12. Applied egg-rr 75.2%

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

   if -1.06e105 < y < -2.65e-135

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-+l+ 98.0%

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

      3. distribute-frac-neg 98.0%

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

      4. neg-mul-1 98.0%

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

      5. *-commutative 98.0%

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

      6. times-frac 97.9%

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

      7. fma-define 97.9%

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

      8. metadata-eval 97.9%

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

      9. associate-*l* 97.9%

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

      10. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 55.1%

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

   if -2.65e-135 < y < 6.90000000000000034e72

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0 71.7%

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

   4. Taylor expanded in t around inf 67.9%

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

      1. associate-*r/ 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*r/ 67.9%

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

      4. associate-/r* 67.9%

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

   6. Simplified 67.9%

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

Alternative 4: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{-3}}{z}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.75 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+72}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ y -3.0) z)))
   (if (<= y -9e+104)
     t_1
     (if (<= y -4.75e-135)
       x
       (if (<= y 6.9e+72) (* 0.3333333333333333 (/ t (* y z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / -3.0) / z;
	double tmp;
	if (y <= -9e+104) {
		tmp = t_1;
	} else if (y <= -4.75e-135) {
		tmp = x;
	} else if (y <= 6.9e+72) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / (-3.0d0)) / z
    if (y <= (-9d+104)) then
        tmp = t_1
    else if (y <= (-4.75d-135)) then
        tmp = x
    else if (y <= 6.9d+72) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / -3.0) / z;
	double tmp;
	if (y <= -9e+104) {
		tmp = t_1;
	} else if (y <= -4.75e-135) {
		tmp = x;
	} else if (y <= 6.9e+72) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / -3.0) / z
	tmp = 0
	if y <= -9e+104:
		tmp = t_1
	elif y <= -4.75e-135:
		tmp = x
	elif y <= 6.9e+72:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / -3.0) / z)
	tmp = 0.0
	if (y <= -9e+104)
		tmp = t_1;
	elseif (y <= -4.75e-135)
		tmp = x;
	elseif (y <= 6.9e+72)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / -3.0) / z;
	tmp = 0.0;
	if (y <= -9e+104)
		tmp = t_1;
	elseif (y <= -4.75e-135)
		tmp = x;
	elseif (y <= 6.9e+72)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -9e+104], t$95$1, If[LessEqual[y, -4.75e-135], x, If[LessEqual[y, 6.9e+72], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999997e104 or 6.90000000000000034e72 < 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. associate-+l+ 98.6%

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

      3. distribute-frac-neg 98.6%

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

      4. neg-mul-1 98.6%

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

      5. *-commutative 98.6%

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

      6. times-frac 98.6%

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

      7. fma-define 98.6%

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

      8. metadata-eval 98.6%

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

      9. associate-*l* 98.6%

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

      10. *-commutative 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around 0 99.6%

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

      1. metadata-eval 99.6%

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

      2. cancel-sign-sub-inv 99.6%

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

      3. associate-*r/ 99.6%

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

      4. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. metadata-eval 75.1%

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

      3. distribute-lft-neg-in 75.1%

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

      4. add-sqr-sqrt 30.7%

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

      5. sqrt-unprod 27.1%

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

      6. sqr-neg 27.1%

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

      7. sqrt-unprod 1.0%

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

      8. add-sqr-sqrt 1.6%

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

      9. frac-2neg 1.6%

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

      10. clear-num 1.6%

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

      11. frac-2neg 1.6%

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

      12. metadata-eval 1.6%

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

      13. distribute-frac-neg2 1.6%

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

      14. metadata-eval 1.6%

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

      15. distribute-neg-frac 1.6%

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

      16. clear-num 1.6%

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

      17. distribute-neg-frac 1.6%

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

      18. distribute-lft-neg-in 1.6%

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

      19. metadata-eval 1.6%

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

      20. associate-*r/ 1.6%

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

   10. Applied egg-rr 1.6%

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

       1. add-sqr-sqrt 0.7%

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

       2. sqrt-unprod 36.9%

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

       3. sqr-neg 36.9%

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

       4. sqrt-unprod 41.5%

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

       5. add-sqr-sqrt 75.1%

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

       6. metadata-eval 75.1%

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

       7. times-frac 75.0%

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

       8. *-un-lft-identity 75.0%

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

       9. associate-/r* 75.2%

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

   12. Applied egg-rr 75.2%

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

   if -8.9999999999999997e104 < y < -4.75000000000000004e-135

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-+l+ 98.0%

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

      3. distribute-frac-neg 98.0%

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

      4. neg-mul-1 98.0%

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

      5. *-commutative 98.0%

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

      6. times-frac 97.9%

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

      7. fma-define 97.9%

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

      8. metadata-eval 97.9%

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

      9. associate-*l* 97.9%

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

      10. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 55.1%

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

   if -4.75000000000000004e-135 < y < 6.90000000000000034e72

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0 71.7%

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

   4. Taylor expanded in t around inf 67.9%

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

Alternative 5: 96.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 10^{-220}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 1e-220)
   (+ x (* -0.3333333333333333 (/ (- y (/ t y)) z)))
   (+ (/ y (* z -3.0)) (+ x (/ t (* z (* y 3.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 1e-220) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} else {
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 1d-220) then
        tmp = x + ((-0.3333333333333333d0) * ((y - (t / y)) / z))
    else
        tmp = (y / (z * (-3.0d0))) + (x + (t / (z * (y * 3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 1e-220) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} else {
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 1e-220:
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z))
	else:
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 1e-220)
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z)));
	else
		tmp = Float64(Float64(y / Float64(z * -3.0)) + Float64(x + Float64(t / Float64(z * Float64(y * 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 1e-220)
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	else
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e-220], N[(x + N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < 9.99999999999999992e-221

   1. Initial program 94.3%

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

      1. sub-neg 94.3%

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

      2. associate-+l+ 94.3%

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

      3. remove-double-neg 94.3%

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

      4. distribute-frac-neg 94.3%

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

      5. sub-neg 94.3%

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

      6. distribute-frac-neg 94.3%

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

      7. neg-mul-1 94.3%

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

      8. *-commutative 94.3%

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

      9. associate-/l* 94.3%

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

      10. *-commutative 94.3%

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

      11. neg-mul-1 94.3%

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

      12. times-frac 97.2%

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

      13. distribute-lft-out-- 97.8%

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

      14. *-commutative 97.8%

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

      15. associate-/r* 97.9%

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

      16. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 97.9%

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

   if 9.99999999999999992e-221 < (*.f64 z #s(literal 3 binary64))

   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. +-commutative 99.7%

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

      2. associate-+r- 99.7%

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

      3. sub-neg 99.7%

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

      4. associate-*l* 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-frac-neg2 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 10^{-220}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+52} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7e+52) (not (<= y 6.9e+72)))
   (- x (/ (* y 0.3333333333333333) z))
   (- x (* -0.3333333333333333 (/ (/ t z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e+52) || !(y <= 6.9e+72)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = x - (-0.3333333333333333 * ((t / z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7d+52)) .or. (.not. (y <= 6.9d+72))) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else
        tmp = x - ((-0.3333333333333333d0) * ((t / z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e+52) || !(y <= 6.9e+72)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = x - (-0.3333333333333333 * ((t / z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7e+52) or not (y <= 6.9e+72):
		tmp = x - ((y * 0.3333333333333333) / z)
	else:
		tmp = x - (-0.3333333333333333 * ((t / z) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7e+52) || !(y <= 6.9e+72))
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	else
		tmp = Float64(x - Float64(-0.3333333333333333 * Float64(Float64(t / z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7e+52) || ~((y <= 6.9e+72)))
		tmp = x - ((y * 0.3333333333333333) / z);
	else
		tmp = x - (-0.3333333333333333 * ((t / z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7e+52], N[Not[LessEqual[y, 6.9e+72]], $MachinePrecision]], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(-0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e52 or 6.90000000000000034e72 < y

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-+l+ 98.7%

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

      3. distribute-frac-neg 98.7%

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

      4. neg-mul-1 98.7%

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

      5. *-commutative 98.7%

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

      6. times-frac 98.7%

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

      7. fma-define 98.7%

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

      8. metadata-eval 98.7%

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

      9. associate-*l* 98.7%

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

      10. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around 0 98.8%

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

      1. metadata-eval 98.8%

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

      2. cancel-sign-sub-inv 98.8%

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

      3. associate-*r/ 98.9%

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

      4. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   if -7e52 < y < 6.90000000000000034e72

   1. Initial program 94.5%

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

      1. sub-neg 94.5%

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

      2. associate-+l+ 94.5%

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

      3. remove-double-neg 94.5%

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

      4. distribute-frac-neg 94.5%

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

      5. sub-neg 94.5%

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

      6. distribute-frac-neg 94.5%

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

      7. neg-mul-1 94.5%

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

      8. *-commutative 94.5%

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

      9. associate-/l* 94.4%

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

      10. *-commutative 94.4%

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

      11. neg-mul-1 94.4%

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

      12. times-frac 93.1%

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

      13. distribute-lft-out-- 93.1%

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

      14. *-commutative 93.1%

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

      15. associate-/r* 93.1%

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

      16. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0 93.1%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. associate-*r/ 89.3%

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

      2. neg-mul-1 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-/r* 91.4%

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

      5. distribute-frac-neg 91.4%

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

      6. distribute-neg-frac2 91.4%

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

   8. Simplified 91.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+52} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+52} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e+52) (not (<= y 6.9e+72)))
   (- x (/ (* y 0.3333333333333333) z))
   (- x (/ -0.3333333333333333 (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+52) || !(y <= 6.9e+72)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = x - (-0.3333333333333333 / (y / (t / 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 <= (-3.8d+52)) .or. (.not. (y <= 6.9d+72))) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else
        tmp = x - ((-0.3333333333333333d0) / (y / (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+52) || !(y <= 6.9e+72)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = x - (-0.3333333333333333 / (y / (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e+52) or not (y <= 6.9e+72):
		tmp = x - ((y * 0.3333333333333333) / z)
	else:
		tmp = x - (-0.3333333333333333 / (y / (t / z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e+52) || !(y <= 6.9e+72))
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	else
		tmp = Float64(x - Float64(-0.3333333333333333 / Float64(y / Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.8e+52) || ~((y <= 6.9e+72)))
		tmp = x - ((y * 0.3333333333333333) / z);
	else
		tmp = x - (-0.3333333333333333 / (y / (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e+52], N[Not[LessEqual[y, 6.9e+72]], $MachinePrecision]], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(-0.3333333333333333 / N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8e52 or 6.90000000000000034e72 < y

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-+l+ 98.7%

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

      3. distribute-frac-neg 98.7%

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

      4. neg-mul-1 98.7%

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

      5. *-commutative 98.7%

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

      6. times-frac 98.7%

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

      7. fma-define 98.7%

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

      8. metadata-eval 98.7%

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

      9. associate-*l* 98.7%

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

      10. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around 0 98.8%

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

      1. metadata-eval 98.8%

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

      2. cancel-sign-sub-inv 98.8%

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

      3. associate-*r/ 98.9%

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

      4. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   if -3.8e52 < y < 6.90000000000000034e72

   1. Initial program 94.5%

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

      1. sub-neg 94.5%

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

      2. associate-+l+ 94.5%

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

      3. remove-double-neg 94.5%

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

      4. distribute-frac-neg 94.5%

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

      5. sub-neg 94.5%

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

      6. distribute-frac-neg 94.5%

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

      7. neg-mul-1 94.5%

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

      8. *-commutative 94.5%

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

      9. associate-/l* 94.4%

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

      10. *-commutative 94.4%

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

      11. neg-mul-1 94.4%

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

      12. times-frac 93.1%

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

      13. distribute-lft-out-- 93.1%

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

      14. *-commutative 93.1%

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

      15. associate-/r* 93.1%

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

      16. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0 93.1%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. associate-*r/ 89.3%

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

      2. neg-mul-1 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-/r* 91.4%

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

      5. distribute-frac-neg 91.4%

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

      6. distribute-neg-frac2 91.4%

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

   8. Simplified 91.4%

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

      1. *-commutative 91.4%

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

      2. frac-2neg 91.4%

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

      3. distribute-frac-neg 91.4%

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

      4. add-sqr-sqrt 45.5%

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

      5. sqrt-unprod 56.3%

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

      6. sqr-neg 56.3%

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

      7. sqrt-unprod 18.6%

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

      8. add-sqr-sqrt 29.8%

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

      9. frac-2neg 29.8%

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

      10. distribute-neg-frac 29.8%

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

      11. frac-2neg 29.8%

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

      12. cancel-sign-sub-inv 29.8%

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

      13. *-commutative 29.8%

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

      14. clear-num 29.8%

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

      15. un-div-inv 29.8%

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

      16. add-sqr-sqrt 11.2%

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

      17. sqrt-unprod 51.6%

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

   10. Applied egg-rr 91.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+52} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+52} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e+52) (not (<= y 6.9e+72)))
   (- x (/ (* y 0.3333333333333333) z))
   (+ x (/ (/ 0.3333333333333333 y) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e+52) || !(y <= 6.9e+72)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.5d+52)) .or. (.not. (y <= 6.9d+72))) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else
        tmp = x + ((0.3333333333333333d0 / y) / (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e+52) || !(y <= 6.9e+72)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e+52) or not (y <= 6.9e+72):
		tmp = x - ((y * 0.3333333333333333) / z)
	else:
		tmp = x + ((0.3333333333333333 / y) / (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e+52) || !(y <= 6.9e+72))
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	else
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / y) / Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.5e+52) || ~((y <= 6.9e+72)))
		tmp = x - ((y * 0.3333333333333333) / z);
	else
		tmp = x + ((0.3333333333333333 / y) / (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e+52], N[Not[LessEqual[y, 6.9e+72]], $MachinePrecision]], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(0.3333333333333333 / y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999996e52 or 6.90000000000000034e72 < y

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-+l+ 98.7%

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

      3. distribute-frac-neg 98.7%

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

      4. neg-mul-1 98.7%

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

      5. *-commutative 98.7%

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

      6. times-frac 98.7%

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

      7. fma-define 98.7%

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

      8. metadata-eval 98.7%

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

      9. associate-*l* 98.7%

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

      10. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around 0 98.8%

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

      1. metadata-eval 98.8%

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

      2. cancel-sign-sub-inv 98.8%

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

      3. associate-*r/ 98.9%

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

      4. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   if -6.49999999999999996e52 < y < 6.90000000000000034e72

   1. Initial program 94.5%

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

      1. sub-neg 94.5%

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

      2. associate-+l+ 94.5%

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

      3. remove-double-neg 94.5%

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

      4. distribute-frac-neg 94.5%

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

      5. sub-neg 94.5%

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

      6. distribute-frac-neg 94.5%

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

      7. neg-mul-1 94.5%

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

      8. *-commutative 94.5%

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

      9. associate-/l* 94.4%

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

      10. *-commutative 94.4%

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

      11. neg-mul-1 94.4%

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

      12. times-frac 93.1%

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

      13. distribute-lft-out-- 93.1%

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

      14. *-commutative 93.1%

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

      15. associate-/r* 93.1%

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

      16. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0 93.1%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. associate-*r/ 89.3%

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

      2. neg-mul-1 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-/r* 91.4%

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

      5. distribute-frac-neg 91.4%

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

      6. distribute-neg-frac2 91.4%

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

   8. Simplified 91.4%

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

      1. *-commutative 91.4%

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

      2. frac-2neg 91.4%

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

      3. distribute-frac-neg 91.4%

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

      4. add-sqr-sqrt 45.5%

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

      5. sqrt-unprod 56.3%

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

      6. sqr-neg 56.3%

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

      7. sqrt-unprod 18.6%

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

      8. add-sqr-sqrt 29.8%

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

      9. frac-2neg 29.8%

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

      10. distribute-neg-frac 29.8%

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

      11. frac-2neg 29.8%

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

      12. cancel-sign-sub-inv 29.8%

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

      13. *-commutative 29.8%

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

      14. clear-num 29.8%

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

      15. un-div-inv 29.8%

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

      16. add-sqr-sqrt 11.2%

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

      17. sqrt-unprod 51.6%

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

   10. Applied egg-rr 91.4%

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

       1. sub-neg 91.4%

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

       2. distribute-neg-frac 91.4%

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

       3. metadata-eval 91.4%

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

       4. associate-/r/ 87.4%

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

   12. Simplified 87.4%

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

       1. frac-2neg 87.4%

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

       2. metadata-eval 87.4%

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

       3. div-inv 87.4%

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

       4. associate-*l/ 89.3%

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

       5. distribute-neg-frac2 89.3%

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

   14. Applied egg-rr 89.3%

       \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{1}{\frac{y \cdot z}{-t}}} \]
   15. Step-by-step derivation

       1. associate-*r/ 89.4%

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

       2. metadata-eval 89.4%

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

       3. distribute-frac-neg2 89.4%

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

       4. associate-*r/ 90.6%

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

       5. distribute-neg-frac2 90.6%

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

       6. associate-/r* 90.6%

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

       7. metadata-eval 90.6%

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

       8. distribute-neg-frac 90.6%

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

       9. metadata-eval 90.6%

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

       10. associate-*r/ 90.5%

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

       11. distribute-neg-frac 90.5%

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

       12. associate-*r/ 90.6%

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

       13. metadata-eval 90.6%

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

       14. distribute-frac-neg2 90.6%

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

       15. distribute-frac-neg2 90.6%

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

       16. remove-double-neg 90.6%

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

   16. Simplified 90.6%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+52} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-7} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e-7) (not (<= y 6.9e+72)))
   (- 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 <= -4.2e-7) || !(y <= 6.9e+72)) {
		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 <= (-4.2d-7)) .or. (.not. (y <= 6.9d+72))) 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 <= -4.2e-7) || !(y <= 6.9e+72)) {
		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 <= -4.2e-7) or not (y <= 6.9e+72):
		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 <= -4.2e-7) || !(y <= 6.9e+72))
		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 <= -4.2e-7) || ~((y <= 6.9e+72)))
		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, -4.2e-7], N[Not[LessEqual[y, 6.9e+72]], $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 < -4.2e-7 or 6.90000000000000034e72 < y

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-+l+ 98.0%

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

      3. distribute-frac-neg 98.0%

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

      4. neg-mul-1 98.0%

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

      5. *-commutative 98.0%

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

      6. times-frac 98.1%

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

      7. fma-define 98.1%

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

      8. metadata-eval 98.1%

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

      9. associate-*l* 98.1%

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

      10. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around 0 97.4%

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

      1. metadata-eval 97.4%

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

      2. cancel-sign-sub-inv 97.4%

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

      3. associate-*r/ 97.5%

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

      4. *-commutative 97.5%

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

   7. Simplified 97.5%

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

   if -4.2e-7 < y < 6.90000000000000034e72

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. associate-+l+ 94.7%

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

      3. remove-double-neg 94.7%

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

      4. distribute-frac-neg 94.7%

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

      5. sub-neg 94.7%

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

      6. distribute-frac-neg 94.7%

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

      7. neg-mul-1 94.7%

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

      8. *-commutative 94.7%

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

      9. associate-/l* 94.7%

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

      10. *-commutative 94.7%

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

      11. neg-mul-1 94.7%

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

      12. times-frac 92.4%

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

      13. distribute-lft-out-- 92.4%

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

      14. *-commutative 92.4%

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

      15. associate-/r* 92.4%

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

      16. metadata-eval 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in y around 0 90.2%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-7} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-135} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.3e-135) (not (<= y 6.9e+72)))
   (- x (/ (* y 0.3333333333333333) z))
   (* t (/ (/ 0.3333333333333333 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.3e-135) || !(y <= 6.9e+72)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = t * ((0.3333333333333333 / 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 <= (-3.3d-135)) .or. (.not. (y <= 6.9d+72))) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else
        tmp = t * ((0.3333333333333333d0 / 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 <= -3.3e-135) || !(y <= 6.9e+72)) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else {
		tmp = t * ((0.3333333333333333 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.3e-135) or not (y <= 6.9e+72):
		tmp = x - ((y * 0.3333333333333333) / z)
	else:
		tmp = t * ((0.3333333333333333 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.3e-135) || !(y <= 6.9e+72))
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	else
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.3e-135) || ~((y <= 6.9e+72)))
		tmp = x - ((y * 0.3333333333333333) / z);
	else
		tmp = t * ((0.3333333333333333 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.3e-135], N[Not[LessEqual[y, 6.9e+72]], $MachinePrecision]], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2999999999999999e-135 or 6.90000000000000034e72 < y

   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. associate-+l+ 98.4%

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

      3. distribute-frac-neg 98.4%

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

      4. neg-mul-1 98.4%

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

      5. *-commutative 98.4%

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

      6. times-frac 98.4%

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

      7. fma-define 98.4%

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

      8. metadata-eval 98.4%

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

      9. associate-*l* 98.4%

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

      10. *-commutative 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around 0 90.3%

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

      1. metadata-eval 90.3%

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

      2. cancel-sign-sub-inv 90.3%

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

      3. associate-*r/ 90.3%

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

      4. *-commutative 90.3%

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

   7. Simplified 90.3%

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

   if -3.2999999999999999e-135 < y < 6.90000000000000034e72

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0 71.7%

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

   4. Taylor expanded in t around inf 67.9%

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

      1. associate-*r/ 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*r/ 67.9%

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

      4. associate-/r* 67.9%

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

   6. Simplified 67.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-135} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-135} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.3e-135) (not (<= y 6.9e+72)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* t (/ (/ 0.3333333333333333 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.3e-135) || !(y <= 6.9e+72)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = t * ((0.3333333333333333 / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.3d-135)) .or. (.not. (y <= 6.9d+72))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = t * ((0.3333333333333333d0 / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.3e-135) || !(y <= 6.9e+72)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = t * ((0.3333333333333333 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.3e-135) or not (y <= 6.9e+72):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = t * ((0.3333333333333333 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.3e-135) || !(y <= 6.9e+72))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.3e-135) || ~((y <= 6.9e+72)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = t * ((0.3333333333333333 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.3e-135], N[Not[LessEqual[y, 6.9e+72]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.3e-135 or 6.90000000000000034e72 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0 90.3%

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

   if -5.3e-135 < y < 6.90000000000000034e72

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0 71.7%

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

   4. Taylor expanded in t around inf 67.9%

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

      1. associate-*r/ 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*r/ 67.9%

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

      4. associate-/r* 67.9%

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

   6. Simplified 67.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-135} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-135} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.65e-135) (not (<= y 6.9e+72)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* t (/ (/ 0.3333333333333333 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.65e-135) || !(y <= 6.9e+72)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = t * ((0.3333333333333333 / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.65d-135)) .or. (.not. (y <= 6.9d+72))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = t * ((0.3333333333333333d0 / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.65e-135) || !(y <= 6.9e+72)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = t * ((0.3333333333333333 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.65e-135) or not (y <= 6.9e+72):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = t * ((0.3333333333333333 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.65e-135) || !(y <= 6.9e+72))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.65e-135) || ~((y <= 6.9e+72)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = t * ((0.3333333333333333 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.65e-135], N[Not[LessEqual[y, 6.9e+72]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.65e-135 or 6.90000000000000034e72 < y

   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. associate-+l+ 98.4%

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

      3. remove-double-neg 98.4%

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

      4. distribute-frac-neg 98.4%

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

      5. sub-neg 98.4%

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

      6. distribute-frac-neg 98.4%

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

      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. *-commutative 98.4%

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

      9. associate-/l* 98.3%

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

      10. *-commutative 98.3%

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

      11. neg-mul-1 98.3%

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

      12. times-frac 98.4%

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

      13. distribute-lft-out-- 99.1%

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

      14. *-commutative 99.1%

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

      15. associate-/r* 99.0%

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

      16. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around inf 90.2%

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

   if -2.65e-135 < y < 6.90000000000000034e72

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0 71.7%

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

   4. Taylor expanded in t around inf 67.9%

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

      1. associate-*r/ 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*r/ 67.9%

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

      4. associate-/r* 67.9%

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

   6. Simplified 67.9%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-135} \lor \neg \left(y \leq 6.9 \cdot 10^{+72}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-135}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-135)
   (+ x (* y (/ -0.3333333333333333 z)))
   (if (<= y 6.9e+72)
     (* t (/ (/ 0.3333333333333333 y) z))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-135) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 6.9e+72) {
		tmp = t * ((0.3333333333333333 / y) / z);
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.5d-135)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if (y <= 6.9d+72) then
        tmp = t * ((0.3333333333333333d0 / y) / z)
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-135) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 6.9e+72) {
		tmp = t * ((0.3333333333333333 / y) / z);
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-135:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif y <= 6.9e+72:
		tmp = t * ((0.3333333333333333 / y) / z)
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-135)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (y <= 6.9e+72)
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / y) / z));
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e-135)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif (y <= 6.9e+72)
		tmp = t * ((0.3333333333333333 / y) / z);
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-135], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.9e+72], N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999999e-135

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-+l+ 98.7%

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

      3. remove-double-neg 98.7%

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

      4. distribute-frac-neg 98.7%

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

      5. sub-neg 98.7%

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

      6. distribute-frac-neg 98.7%

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

      7. neg-mul-1 98.7%

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

      8. *-commutative 98.7%

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

      9. associate-/l* 98.6%

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

      10. *-commutative 98.6%

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

      11. neg-mul-1 98.6%

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

      12. times-frac 98.8%

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

      13. distribute-lft-out-- 98.8%

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

      14. *-commutative 98.8%

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

      15. associate-/r* 98.8%

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

      16. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around inf 85.6%

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

   if -5.4999999999999999e-135 < y < 6.90000000000000034e72

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0 71.7%

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

   4. Taylor expanded in t around inf 67.9%

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

      1. associate-*r/ 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*r/ 67.9%

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

      4. associate-/r* 67.9%

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

   6. Simplified 67.9%

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

   if 6.90000000000000034e72 < y

   1. Initial program 97.7%

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

      1. sub-neg 97.7%

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

      2. associate-+l+ 97.7%

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

      3. remove-double-neg 97.7%

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

      4. distribute-frac-neg 97.7%

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

      5. sub-neg 97.7%

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

      6. distribute-frac-neg 97.7%

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

      7. neg-mul-1 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-/l* 97.6%

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

      10. *-commutative 97.6%

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

      11. neg-mul-1 97.6%

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

      12. times-frac 97.6%

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

      13. distribute-lft-out-- 99.6%

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

      14. *-commutative 99.6%

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

      15. associate-/r* 99.5%

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

      16. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. metadata-eval 99.7%

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

      3. times-frac 99.7%

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

      4. *-rgt-identity 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-135}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 96.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \left(\frac{1}{y \cdot \frac{z \cdot 3}{t}} + x\right) + \frac{y}{z \cdot -3} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (+ (/ 1.0 (* y (/ (* z 3.0) t))) x) (/ y (* z -3.0))))

C

double code(double x, double y, double z, double t) {
	return ((1.0 / (y * ((z * 3.0) / t))) + 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 = ((1.0d0 / (y * ((z * 3.0d0) / t))) + x) + (y / (z * (-3.0d0)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((1.0 / (y * ((z * 3.0) / t))) + x) + (y / (z * -3.0));
}

Python

def code(x, y, z, t):
	return ((1.0 / (y * ((z * 3.0) / t))) + x) + (y / (z * -3.0))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(1.0 / Float64(y * Float64(Float64(z * 3.0) / t))) + x) + Float64(y / Float64(z * -3.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((1.0 / (y * ((z * 3.0) / t))) + x) + (y / (z * -3.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(1.0 / N[(y * N[(N[(z * 3.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.4%

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

   1. +-commutative 96.4%

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

   2. associate-+r- 96.4%

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

   3. sub-neg 96.4%

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

   4. associate-*l* 96.4%

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

   5. *-commutative 96.4%

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

   6. distribute-frac-neg2 96.4%

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

   7. distribute-rgt-neg-in 96.4%

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

   8. metadata-eval 96.4%

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

3. Simplified 96.4%

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

   1. clear-num 96.3%

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

   2. inv-pow 96.3%

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

   3. *-commutative 96.3%

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

   4. associate-*l* 96.3%

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

   5. *-commutative 96.3%

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

6. Applied egg-rr 96.3%

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

   1. unpow-1 96.3%

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

   2. associate-/l* 97.1%

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

8. Simplified 97.1%

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

Alternative 15: 48.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.4e+67) x (if (<= x 9.5e-10) (/ (/ y -3.0) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e+67) {
		tmp = x;
	} else if (x <= 9.5e-10) {
		tmp = (y / -3.0) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.4d+67)) then
        tmp = x
    else if (x <= 9.5d-10) then
        tmp = (y / (-3.0d0)) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e+67) {
		tmp = x;
	} else if (x <= 9.5e-10) {
		tmp = (y / -3.0) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.4e+67:
		tmp = x
	elif x <= 9.5e-10:
		tmp = (y / -3.0) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.4e+67)
		tmp = x;
	elseif (x <= 9.5e-10)
		tmp = Float64(Float64(y / -3.0) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.4e+67)
		tmp = x;
	elseif (x <= 9.5e-10)
		tmp = (y / -3.0) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.4e+67], x, If[LessEqual[x, 9.5e-10], N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999e67 or 9.50000000000000028e-10 < x

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. associate-+l+ 96.7%

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

      3. distribute-frac-neg 96.7%

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

      4. neg-mul-1 96.7%

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

      5. *-commutative 96.7%

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

      6. times-frac 96.7%

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

      7. fma-define 96.7%

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

      8. metadata-eval 96.7%

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

      9. associate-*l* 96.7%

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

      10. *-commutative 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around inf 52.8%

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

   if -1.3999999999999999e67 < x < 9.50000000000000028e-10

   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. associate-+l+ 96.1%

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

      3. distribute-frac-neg 96.1%

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

      4. neg-mul-1 96.1%

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

      5. *-commutative 96.1%

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

      6. times-frac 96.1%

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

      7. fma-define 96.0%

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

      8. metadata-eval 96.0%

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

      9. associate-*l* 96.0%

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

      10. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around 0 56.8%

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

      1. metadata-eval 56.8%

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

      2. cancel-sign-sub-inv 56.8%

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

      3. associate-*r/ 56.9%

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

      4. *-commutative 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in x around 0 47.6%

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

      1. associate-*r/ 47.7%

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

      2. metadata-eval 47.7%

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

      3. distribute-lft-neg-in 47.7%

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

      4. add-sqr-sqrt 18.4%

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

      5. sqrt-unprod 18.8%

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

      6. sqr-neg 18.8%

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

      7. sqrt-unprod 0.9%

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

      8. add-sqr-sqrt 1.9%

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

      9. frac-2neg 1.9%

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

      10. clear-num 1.9%

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

      11. frac-2neg 1.9%

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

      12. metadata-eval 1.9%

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

      13. distribute-frac-neg2 1.9%

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

      14. metadata-eval 1.9%

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

      15. distribute-neg-frac 1.9%

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

      16. clear-num 1.9%

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

      17. distribute-neg-frac 1.9%

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

      18. distribute-lft-neg-in 1.9%

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

      19. metadata-eval 1.9%

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

      20. associate-*r/ 1.9%

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

   10. Applied egg-rr 1.9%

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

       1. add-sqr-sqrt 1.0%

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

       2. sqrt-unprod 23.6%

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

       3. sqr-neg 23.6%

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

       4. sqrt-unprod 25.6%

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

       5. add-sqr-sqrt 47.6%

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

       6. metadata-eval 47.6%

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

       7. times-frac 47.6%

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

       8. *-un-lft-identity 47.6%

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

       9. associate-/r* 47.7%

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

   12. Applied egg-rr 47.7%

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

Alternative 16: 48.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.65e+66) x (if (<= x 9.5e-10) (/ (* y -0.3333333333333333) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e+66) {
		tmp = x;
	} else if (x <= 9.5e-10) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.65d+66)) then
        tmp = x
    else if (x <= 9.5d-10) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e+66) {
		tmp = x;
	} else if (x <= 9.5e-10) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.65e+66:
		tmp = x
	elif x <= 9.5e-10:
		tmp = (y * -0.3333333333333333) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.65e+66)
		tmp = x;
	elseif (x <= 9.5e-10)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.65e+66)
		tmp = x;
	elseif (x <= 9.5e-10)
		tmp = (y * -0.3333333333333333) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.65e+66], x, If[LessEqual[x, 9.5e-10], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6500000000000001e66 or 9.50000000000000028e-10 < x

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. associate-+l+ 96.7%

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

      3. distribute-frac-neg 96.7%

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

      4. neg-mul-1 96.7%

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

      5. *-commutative 96.7%

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

      6. times-frac 96.7%

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

      7. fma-define 96.7%

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

      8. metadata-eval 96.7%

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

      9. associate-*l* 96.7%

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

      10. *-commutative 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around inf 52.8%

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

   if -1.6500000000000001e66 < x < 9.50000000000000028e-10

   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. associate-+l+ 96.1%

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

      3. distribute-frac-neg 96.1%

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

      4. neg-mul-1 96.1%

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

      5. *-commutative 96.1%

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

      6. times-frac 96.1%

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

      7. fma-define 96.0%

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

      8. metadata-eval 96.0%

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

      9. associate-*l* 96.0%

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

      10. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around 0 56.8%

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

      1. metadata-eval 56.8%

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

      2. cancel-sign-sub-inv 56.8%

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

      3. associate-*r/ 56.9%

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

      4. *-commutative 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in x around 0 47.6%

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

      1. *-commutative 47.6%

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

      2. associate-*l/ 47.7%

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

   10. Simplified 47.7%

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

Alternative 17: 48.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.7e+69) x (if (<= x 4.6e-10) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.7e+69) {
		tmp = x;
	} else if (x <= 4.6e-10) {
		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 (x <= (-6.7d+69)) then
        tmp = x
    else if (x <= 4.6d-10) 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 (x <= -6.7e+69) {
		tmp = x;
	} else if (x <= 4.6e-10) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.7e+69:
		tmp = x
	elif x <= 4.6e-10:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.7e+69)
		tmp = x;
	elseif (x <= 4.6e-10)
		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 (x <= -6.7e+69)
		tmp = x;
	elseif (x <= 4.6e-10)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.7e+69], x, If[LessEqual[x, 4.6e-10], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7000000000000001e69 or 4.60000000000000014e-10 < x

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. associate-+l+ 96.7%

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

      3. distribute-frac-neg 96.7%

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

      4. neg-mul-1 96.7%

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

      5. *-commutative 96.7%

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

      6. times-frac 96.7%

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

      7. fma-define 96.7%

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

      8. metadata-eval 96.7%

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

      9. associate-*l* 96.7%

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

      10. *-commutative 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around inf 52.8%

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

   if -6.7000000000000001e69 < x < 4.60000000000000014e-10

   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. associate-+l+ 96.1%

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

      3. distribute-frac-neg 96.1%

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

      4. neg-mul-1 96.1%

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

      5. *-commutative 96.1%

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

      6. times-frac 96.1%

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

      7. fma-define 96.0%

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

      8. metadata-eval 96.0%

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

      9. associate-*l* 96.0%

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

      10. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around 0 56.8%

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

      1. metadata-eval 56.8%

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

      2. cancel-sign-sub-inv 56.8%

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

      3. associate-*r/ 56.9%

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

      4. *-commutative 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in x around 0 47.6%

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

Alternative 18: 95.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. sub-neg 96.4%

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

   2. associate-+l+ 96.4%

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

   3. remove-double-neg 96.4%

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

   4. distribute-frac-neg 96.4%

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

   5. sub-neg 96.4%

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

   6. distribute-frac-neg 96.4%

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

   7. neg-mul-1 96.4%

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

   8. *-commutative 96.4%

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

   9. associate-/l* 96.3%

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

   10. *-commutative 96.3%

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

   11. neg-mul-1 96.3%

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

   12. times-frac 95.6%

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

   13. distribute-lft-out-- 96.0%

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

   14. *-commutative 96.0%

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

   15. associate-/r* 96.0%

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

   16. metadata-eval 96.0%

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

3. Simplified 96.0%

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

5. Taylor expanded in z around 0 96.1%

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

Alternative 19: 30.4% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. sub-neg 96.4%

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

   2. associate-+l+ 96.4%

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

   3. distribute-frac-neg 96.4%

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

   4. neg-mul-1 96.4%

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

   5. *-commutative 96.4%

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

   6. times-frac 96.4%

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

   7. fma-define 96.4%

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

   8. metadata-eval 96.4%

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

   9. associate-*l* 96.3%

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

   10. *-commutative 96.3%

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

3. Simplified 96.3%

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

5. Taylor expanded in x around inf 30.3%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 96.0% 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 2024180 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y)))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))