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

Percentage Accurate: 95.7% → 99.6%

Time: 12.4s

Alternatives: 15

Speedup: 1.4×

• 28.1% 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: 95.7% 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: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t_1 + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-30}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= (* z 3.0) -2e+35)
     (+ t_1 (/ t (* z (* y 3.0))))
     (if (<= (* z 3.0) 5e-30)
       (- x (/ (- y (/ t y)) (* z 3.0)))
       (+ t_1 (/ t (* y (* z 3.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -2e+35) {
		tmp = t_1 + (t / (z * (y * 3.0)));
	} else if ((z * 3.0) <= 5e-30) {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	} else {
		tmp = t_1 + (t / (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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if ((z * 3.0d0) <= (-2d+35)) then
        tmp = t_1 + (t / (z * (y * 3.0d0)))
    else if ((z * 3.0d0) <= 5d-30) then
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    else
        tmp = t_1 + (t / (y * (z * 3.0d0)))
    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));
	double tmp;
	if ((z * 3.0) <= -2e+35) {
		tmp = t_1 + (t / (z * (y * 3.0)));
	} else if ((z * 3.0) <= 5e-30) {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	} else {
		tmp = t_1 + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if (z * 3.0) <= -2e+35:
		tmp = t_1 + (t / (z * (y * 3.0)))
	elif (z * 3.0) <= 5e-30:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	else:
		tmp = t_1 + (t / (y * (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e+35)
		tmp = Float64(t_1 + Float64(t / Float64(z * Float64(y * 3.0))));
	elseif (Float64(z * 3.0) <= 5e-30)
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	else
		tmp = Float64(t_1 + Float64(t / Float64(y * Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if ((z * 3.0) <= -2e+35)
		tmp = t_1 + (t / (z * (y * 3.0)));
	elseif ((z * 3.0) <= 5e-30)
		tmp = x - ((y - (t / y)) / (z * 3.0));
	else
		tmp = t_1 + (t / (y * (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+35], N[(t$95$1 + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 5e-30], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -1.9999999999999999e35

   1. Initial program 99.6%

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

      1. associate-*l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   if -1.9999999999999999e35 < (*.f64 z 3) < 4.99999999999999972e-30

   1. Initial program 91.5%

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

      1. associate-*l* 91.5%

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

      2. *-commutative 91.5%

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

   3. Simplified 91.5%

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

      1. associate-+l- 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*l* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-/r* 99.0%

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

      6. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

   if 4.99999999999999972e-30 < (*.f64 z 3)

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-30}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+35} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{-30}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -2e+35) (not (<= (* z 3.0) 5e-30)))
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* y 3.0))))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+35) || !((z * 3.0) <= 5e-30)) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * 3.0d0) <= (-2d+35)) .or. (.not. ((z * 3.0d0) <= 5d-30))) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (y * 3.0d0)))
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+35) || !((z * 3.0) <= 5e-30)) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -2e+35) or not ((z * 3.0) <= 5e-30):
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -2e+35) || !(Float64(z * 3.0) <= 5e-30))
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(y * 3.0))));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -2e+35) || ~(((z * 3.0) <= 5e-30)))
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+35], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 5e-30]], $MachinePrecision]], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -1.9999999999999999e35 or 4.99999999999999972e-30 < (*.f64 z 3)

   1. Initial program 99.7%

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

      1. associate-*l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   if -1.9999999999999999e35 < (*.f64 z 3) < 4.99999999999999972e-30

   1. Initial program 91.5%

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

      1. associate-*l* 91.5%

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

      2. *-commutative 91.5%

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

   3. Simplified 91.5%

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

      1. associate-+l- 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*l* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-/r* 99.0%

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

      6. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+35} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{-30}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{if}\;y \leq -530000000000:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-110}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (/ 0.3333333333333333 z) y)))))
   (if (<= y -530000000000.0)
     (- x (* 0.3333333333333333 (/ y z)))
     (if (<= y 5.2e-165)
       t_1
       (if (<= y 1.16e-110)
         (* (/ 0.3333333333333333 z) (- (/ t y) y))
         (if (<= y 3.1e+28) t_1 (+ x (* y (/ -0.3333333333333333 z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (t * ((0.3333333333333333 / z) / y));
	double tmp;
	if (y <= -530000000000.0) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 5.2e-165) {
		tmp = t_1;
	} else if (y <= 1.16e-110) {
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	} else if (y <= 3.1e+28) {
		tmp = t_1;
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * ((0.3333333333333333d0 / z) / y))
    if (y <= (-530000000000.0d0)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 5.2d-165) then
        tmp = t_1
    else if (y <= 1.16d-110) then
        tmp = (0.3333333333333333d0 / z) * ((t / y) - y)
    else if (y <= 3.1d+28) then
        tmp = t_1
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (t * ((0.3333333333333333 / z) / y));
	double tmp;
	if (y <= -530000000000.0) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 5.2e-165) {
		tmp = t_1;
	} else if (y <= 1.16e-110) {
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	} else if (y <= 3.1e+28) {
		tmp = t_1;
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (t * ((0.3333333333333333 / z) / y))
	tmp = 0
	if y <= -530000000000.0:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 5.2e-165:
		tmp = t_1
	elif y <= 1.16e-110:
		tmp = (0.3333333333333333 / z) * ((t / y) - y)
	elif y <= 3.1e+28:
		tmp = t_1
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(t * Float64(Float64(0.3333333333333333 / z) / y)))
	tmp = 0.0
	if (y <= -530000000000.0)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 5.2e-165)
		tmp = t_1;
	elseif (y <= 1.16e-110)
		tmp = Float64(Float64(0.3333333333333333 / z) * Float64(Float64(t / y) - y));
	elseif (y <= 3.1e+28)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (t * ((0.3333333333333333 / z) / y));
	tmp = 0.0;
	if (y <= -530000000000.0)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 5.2e-165)
		tmp = t_1;
	elseif (y <= 1.16e-110)
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	elseif (y <= 3.1e+28)
		tmp = t_1;
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -530000000000.0], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-165], t$95$1, If[LessEqual[y, 1.16e-110], N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+28], t$95$1, N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.3e11

   1. Initial program 98.3%

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

      1. associate-*l* 98.2%

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

      2. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around 0 95.6%

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

   if -5.3e11 < y < 5.20000000000000015e-165 or 1.16000000000000001e-110 < y < 3.1000000000000001e28

   1. Initial program 95.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in t around inf 92.3%

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

      1. *-commutative 92.3%

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

      2. metadata-eval 92.3%

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

      3. times-frac 92.4%

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

      4. *-commutative 92.4%

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

      5. times-frac 92.3%

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

      6. associate-/r* 92.3%

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

      7. times-frac 86.3%

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

      8. *-commutative 86.3%

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

      9. associate-*r/ 92.3%

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

      10. associate-/l/ 92.3%

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

      11. associate-/r* 92.3%

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

      12. *-commutative 92.3%

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

      13. associate-/r* 92.2%

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

      14. metadata-eval 92.2%

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

   7. Simplified 92.2%

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

   if 5.20000000000000015e-165 < y < 1.16000000000000001e-110

   1. Initial program 63.3%

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

      1. associate-*l* 63.4%

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

      2. *-commutative 63.4%

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

   3. Simplified 63.4%

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

      1. +-commutative 63.4%

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

      2. *-commutative 63.4%

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

      3. associate-*l* 63.3%

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

      4. associate-+r- 63.3%

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

      5. associate-*l* 63.4%

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

      6. *-commutative 63.4%

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

      7. associate-/r* 100.0%

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

      8. div-inv 100.0%

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

      9. metadata-eval 100.0%

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

      10. div-inv 100.0%

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

      11. clear-num 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 88.2%

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

      1. distribute-lft-out-- 88.2%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

   9. Simplified 88.1%

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

   if 3.1000000000000001e28 < y

   1. Initial program 99.9%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 96.7%

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

      1. *-commutative 96.7%

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

      2. associate-*l/ 96.7%

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

      3. associate-*r/ 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -530000000000:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-165}:\\ \;\;\;\;x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-110}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+28}:\\ \;\;\;\;x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+63}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -1e+63)
   (+ x (* y (/ -0.3333333333333333 z)))
   (if (<= (* z 3.0) 2e+20)
     (* (/ 0.3333333333333333 z) (- (/ t y) y))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e+63) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if ((z * 3.0) <= 2e+20) {
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	} else {
		tmp = x - (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 ((z * 3.0d0) <= (-1d+63)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if ((z * 3.0d0) <= 2d+20) then
        tmp = (0.3333333333333333d0 / z) * ((t / y) - y)
    else
        tmp = x - (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 ((z * 3.0) <= -1e+63) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if ((z * 3.0) <= 2e+20) {
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -1e+63:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif (z * 3.0) <= 2e+20:
		tmp = (0.3333333333333333 / z) * ((t / y) - y)
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e+63)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (Float64(z * 3.0) <= 2e+20)
		tmp = Float64(Float64(0.3333333333333333 / z) * Float64(Float64(t / y) - y));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -1e+63)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif ((z * 3.0) <= 2e+20)
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e+63], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+20], N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -1.00000000000000006e63

   1. Initial program 99.7%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around 0 83.7%

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

      1. *-commutative 83.7%

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

      2. associate-*l/ 83.8%

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

      3. associate-*r/ 83.8%

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

   7. Simplified 83.8%

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

   if -1.00000000000000006e63 < (*.f64 z 3) < 2e20

   1. Initial program 92.3%

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

      1. associate-*l* 92.3%

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

      2. *-commutative 92.3%

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

   3. Simplified 92.3%

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

      1. +-commutative 92.3%

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

      2. *-commutative 92.3%

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

      3. associate-*l* 92.3%

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

      4. associate-+r- 92.3%

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

      5. associate-*l* 92.3%

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

      6. *-commutative 92.3%

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

      7. associate-/r* 95.5%

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

      8. div-inv 95.5%

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

      9. metadata-eval 95.5%

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

      10. div-inv 95.4%

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

      11. clear-num 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in z around 0 91.7%

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

      1. distribute-lft-out-- 91.7%

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

      2. associate-*l/ 91.6%

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

      3. *-commutative 91.6%

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

   9. Simplified 91.6%

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

   if 2e20 < (*.f64 z 3)

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 74.4%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+63}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-174}:\\ \;\;\;\;\left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.5e-174)
   (- (+ (/ (/ t z) (* y 3.0)) x) (* y (/ 0.3333333333333333 z)))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.5e-174) {
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	} else {
		tmp = x - ((y - (t / 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 <= 7.5d-174) then
        tmp = (((t / z) / (y * 3.0d0)) + x) - (y * (0.3333333333333333d0 / z))
    else
        tmp = x - ((y - (t / 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 <= 7.5e-174) {
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7.5e-174:
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.5e-174)
		tmp = Float64(Float64(Float64(Float64(t / z) / Float64(y * 3.0)) + x) - Float64(y * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 7.5e-174)
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.5e-174], N[(N[(N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.5000000000000003e-174

   1. Initial program 96.1%

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

      1. associate-*l* 96.1%

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

      2. *-commutative 96.1%

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

   3. Simplified 96.1%

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

      1. +-commutative 96.1%

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

      2. *-commutative 96.1%

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

      3. associate-*l* 96.1%

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

      4. associate-+r- 96.1%

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

      5. associate-*l* 96.1%

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

      6. *-commutative 96.1%

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

      7. associate-/r* 97.9%

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

      8. div-inv 97.9%

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

      9. metadata-eval 97.9%

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

      10. div-inv 97.8%

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

      11. clear-num 97.8%

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

   6. Applied egg-rr 97.8%

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

   if 7.5000000000000003e-174 < y

   1. Initial program 95.2%

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

      1. associate-*l* 95.2%

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

      2. *-commutative 95.2%

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

   3. Simplified 95.2%

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

      1. associate-+l- 95.2%

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

      2. *-commutative 95.2%

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

      3. associate-*l* 95.2%

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

      4. *-commutative 95.2%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-174}:\\ \;\;\;\;\left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -50000000000:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -50000000000.0)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 2.9e+22)
     (+ x (/ (* t (/ 0.3333333333333333 z)) y))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -50000000000.0) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 2.9e+22) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-50000000000.0d0)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 2.9d+22) then
        tmp = x + ((t * (0.3333333333333333d0 / z)) / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -50000000000.0) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 2.9e+22) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -50000000000.0:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 2.9e+22:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -50000000000.0)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 2.9e+22)
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -50000000000.0)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 2.9e+22)
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -50000000000.0], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+22], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e10

   1. Initial program 98.3%

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

      1. associate-*l* 98.2%

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

      2. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around 0 95.6%

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

   if -5e10 < y < 2.9e22

   1. Initial program 92.2%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t around inf 88.4%

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

      1. *-commutative 88.4%

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

      2. metadata-eval 88.4%

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

      3. times-frac 88.5%

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

      4. *-commutative 88.5%

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

      5. times-frac 88.5%

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

      6. associate-/r* 88.5%

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

      7. times-frac 86.2%

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

      8. *-commutative 86.2%

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

      9. associate-*r/ 88.5%

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

      10. associate-/l/ 88.5%

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

      11. associate-/r* 88.4%

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

      12. *-commutative 88.4%

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

      13. associate-/r* 88.4%

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

      14. metadata-eval 88.4%

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

   7. Simplified 88.4%

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

      1. associate-*r/ 92.9%

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

   9. Applied egg-rr 92.9%

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

   if 2.9e22 < y

   1. Initial program 99.9%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 96.7%

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

      1. *-commutative 96.7%

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

      2. associate-*l/ 96.7%

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

      3. associate-*r/ 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -50000000000:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -57000:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-121}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -57000.0)
   (/ (* y -0.3333333333333333) z)
   (if (<= y 5.5e-121)
     (* 0.3333333333333333 (/ t (* y z)))
     (if (<= y 3.2e+160) x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -57000.0) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 5.5e-121) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else if (y <= 3.2e+160) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-57000.0d0)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= 5.5d-121) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else if (y <= 3.2d+160) then
        tmp = x
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -57000.0) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 5.5e-121) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else if (y <= 3.2e+160) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -57000.0:
		tmp = (y * -0.3333333333333333) / z
	elif y <= 5.5e-121:
		tmp = 0.3333333333333333 * (t / (y * z))
	elif y <= 3.2e+160:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -57000.0)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= 5.5e-121)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	elseif (y <= 3.2e+160)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -57000.0)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= 5.5e-121)
		tmp = 0.3333333333333333 * (t / (y * z));
	elseif (y <= 3.2e+160)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -57000.0], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 5.5e-121], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+160], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -57000

   1. Initial program 98.3%

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

      1. associate-*l* 98.3%

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

      2. *-commutative 98.3%

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

   3. Simplified 98.3%

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

      1. +-commutative 98.3%

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

      2. *-commutative 98.3%

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

      3. associate-*l* 98.3%

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

      4. associate-+r- 98.3%

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

      5. associate-*l* 98.3%

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

      6. *-commutative 98.3%

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

      7. associate-/r* 98.3%

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

      8. div-inv 98.2%

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

      9. metadata-eval 98.2%

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

      10. div-inv 98.0%

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

      11. clear-num 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in y around inf 68.3%

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

      1. associate-*r/ 68.3%

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

      2. *-commutative 68.3%

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

   9. Simplified 68.3%

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

   if -57000 < y < 5.50000000000000031e-121

   1. Initial program 91.3%

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

      1. associate-*l* 91.3%

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

      2. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around 0 66.7%

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

      1. clear-num 66.7%

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

      2. inv-pow 66.7%

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

      3. *-un-lft-identity 66.7%

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

      4. distribute-lft-out-- 66.7%

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

      5. times-frac 66.8%

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

      6. metadata-eval 66.8%

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

   7. Applied egg-rr 66.8%

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

      1. unpow-1 66.8%

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

   9. Simplified 66.8%

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

   10. Taylor expanded in t around inf 67.6%

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

       1. *-commutative 67.6%

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

   12. Simplified 67.6%

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

   if 5.50000000000000031e-121 < y < 3.1999999999999998e160

   1. Initial program 97.6%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 54.7%

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

   if 3.1999999999999998e160 < y

   1. Initial program 99.9%

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

      1. associate-*l* 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 99.9%

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

      4. associate-+r- 99.9%

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

      5. associate-*l* 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/r* 91.0%

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

      8. div-inv 91.0%

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

      9. metadata-eval 91.0%

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

      10. div-inv 91.0%

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

      11. clear-num 90.9%

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

   6. Applied egg-rr 90.9%

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

   7. Taylor expanded in y around inf 82.4%

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

      1. associate-*r/ 82.5%

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

      2. associate-*l/ 82.5%

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

      3. metadata-eval 82.5%

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

      4. distribute-neg-frac 82.5%

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

      5. *-commutative 82.5%

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

      6. distribute-neg-frac 82.5%

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

      7. metadata-eval 82.5%

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

   9. Simplified 82.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -57000:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-121}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-52} \lor \neg \left(y \leq 2.8 \cdot 10^{-121}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.9e-52) (not (<= y 2.8e-121)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e-52) || !(y <= 2.8e-121)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.9d-52)) .or. (.not. (y <= 2.8d-121))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * (t / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e-52) || !(y <= 2.8e-121)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.9e-52) or not (y <= 2.8e-121):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (t / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.9e-52) || !(y <= 2.8e-121))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.9e-52) || ~((y <= 2.8e-121)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (t / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.9e-52], N[Not[LessEqual[y, 2.8e-121]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000002e-52 or 2.8000000000000001e-121 < y

   1. Initial program 98.6%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 90.1%

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

      1. *-commutative 90.1%

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

      2. associate-*l/ 90.1%

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

      3. associate-*r/ 90.1%

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

   7. Simplified 90.1%

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

   if -2.9000000000000002e-52 < y < 2.8000000000000001e-121

   1. Initial program 91.1%

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

      1. associate-*l* 91.1%

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

      2. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 67.1%

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

      1. clear-num 67.0%

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

      2. inv-pow 67.0%

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

      3. *-un-lft-identity 67.0%

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

      4. distribute-lft-out-- 67.0%

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

      5. times-frac 67.1%

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

      6. metadata-eval 67.1%

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

   7. Applied egg-rr 67.1%

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

      1. unpow-1 67.1%

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

   9. Simplified 67.1%

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

   10. Taylor expanded in t around inf 68.0%

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

       1. *-commutative 68.0%

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

   12. Simplified 68.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-52} \lor \neg \left(y \leq 2.8 \cdot 10^{-121}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-32}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-114}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e-32)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 7e-114)
     (* 0.3333333333333333 (/ t (* y z)))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-32) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 7e-114) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.4d-32)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 7d-114) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-32) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 7e-114) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e-32:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 7e-114:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e-32)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 7e-114)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e-32)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 7e-114)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e-32], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-114], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000001e-32

   1. Initial program 98.3%

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

      1. associate-*l* 98.3%

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

      2. *-commutative 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in t around 0 94.3%

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

   if -2.4000000000000001e-32 < y < 7e-114

   1. Initial program 91.1%

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

      1. associate-*l* 91.1%

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

      2. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 67.1%

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

      1. clear-num 67.0%

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

      2. inv-pow 67.0%

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

      3. *-un-lft-identity 67.0%

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

      4. distribute-lft-out-- 67.0%

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

      5. times-frac 67.1%

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

      6. metadata-eval 67.1%

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

   7. Applied egg-rr 67.1%

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

      1. unpow-1 67.1%

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

   9. Simplified 67.1%

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

   10. Taylor expanded in t around inf 68.0%

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

       1. *-commutative 68.0%

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

   12. Simplified 68.0%

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

   if 7e-114 < y

   1. Initial program 98.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*l/ 86.7%

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

      3. associate-*r/ 86.8%

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

   7. Simplified 86.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-32}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-114}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((0.3333333333333333d0 / z) * ((t / y) - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Simplified 95.3%

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

5. Final simplification 95.3%

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

Alternative 11: 95.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. associate-*l* 95.7%

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

   2. *-commutative 95.7%

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

3. Simplified 95.7%

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

   1. associate-+l- 95.7%

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

   2. *-commutative 95.7%

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

   3. associate-*l* 95.7%

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

   4. *-commutative 95.7%

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

   5. associate-/r* 95.0%

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

   6. sub-div 95.4%

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

6. Applied egg-rr 95.4%

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

7. Final simplification 95.4%

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

Alternative 12: 48.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+114}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.5e+93) x (if (<= x 7.8e+114) (* (/ y z) -0.3333333333333333) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e+93) {
		tmp = x;
	} else if (x <= 7.8e+114) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.5d+93)) then
        tmp = x
    else if (x <= 7.8d+114) then
        tmp = (y / z) * (-0.3333333333333333d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e+93) {
		tmp = x;
	} else if (x <= 7.8e+114) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.5e+93:
		tmp = x
	elif x <= 7.8e+114:
		tmp = (y / z) * -0.3333333333333333
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.5e+93)
		tmp = x;
	elseif (x <= 7.8e+114)
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.5e+93)
		tmp = x;
	elseif (x <= 7.8e+114)
		tmp = (y / z) * -0.3333333333333333;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.5e+93], x, If[LessEqual[x, 7.8e+114], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999991e93 or 7.8000000000000001e114 < x

   1. Initial program 98.8%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf 61.4%

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

   if -4.49999999999999991e93 < x < 7.8000000000000001e114

   1. Initial program 94.2%

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

      1. associate-*l* 94.2%

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

      2. *-commutative 94.2%

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

   3. Simplified 94.2%

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

      1. +-commutative 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-*l* 94.2%

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

      4. associate-+r- 94.2%

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

      5. associate-*l* 94.2%

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

      6. *-commutative 94.2%

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

      7. associate-/r* 95.1%

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

      8. div-inv 95.0%

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

      9. metadata-eval 95.0%

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

      10. div-inv 95.0%

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

      11. clear-num 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in y around inf 49.5%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+114}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.5e+93)
   x
   (if (<= x 2.25e+114) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e+93) {
		tmp = x;
	} else if (x <= 2.25e+114) {
		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 <= (-5.5d+93)) then
        tmp = x
    else if (x <= 2.25d+114) 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 <= -5.5e+93) {
		tmp = x;
	} else if (x <= 2.25e+114) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.5e+93:
		tmp = x
	elif x <= 2.25e+114:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.5e+93)
		tmp = x;
	elseif (x <= 2.25e+114)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.5e+93)
		tmp = x;
	elseif (x <= 2.25e+114)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.5e+93], x, If[LessEqual[x, 2.25e+114], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000003e93 or 2.25e114 < x

   1. Initial program 98.8%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf 61.4%

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

   if -5.5000000000000003e93 < x < 2.25e114

   1. Initial program 94.2%

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

      1. associate-*l* 94.2%

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

      2. *-commutative 94.2%

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

   3. Simplified 94.2%

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

      1. +-commutative 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-*l* 94.2%

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

      4. associate-+r- 94.2%

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

      5. associate-*l* 94.2%

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

      6. *-commutative 94.2%

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

      7. associate-/r* 95.1%

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

      8. div-inv 95.0%

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

      9. metadata-eval 95.0%

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

      10. div-inv 95.0%

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

      11. clear-num 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in y around inf 49.5%

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

      1. associate-*r/ 49.5%

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

      2. associate-*l/ 49.5%

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

      3. metadata-eval 49.5%

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

      4. distribute-neg-frac 49.5%

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

      5. *-commutative 49.5%

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

      6. distribute-neg-frac 49.5%

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

      7. metadata-eval 49.5%

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

   9. Simplified 49.5%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.8e+92) x (if (<= x 2.9e+114) (/ (* y -0.3333333333333333) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e+92) {
		tmp = x;
	} else if (x <= 2.9e+114) {
		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 <= (-6.8d+92)) then
        tmp = x
    else if (x <= 2.9d+114) 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 <= -6.8e+92) {
		tmp = x;
	} else if (x <= 2.9e+114) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.8e+92:
		tmp = x
	elif x <= 2.9e+114:
		tmp = (y * -0.3333333333333333) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.8e+92)
		tmp = x;
	elseif (x <= 2.9e+114)
		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 <= -6.8e+92)
		tmp = x;
	elseif (x <= 2.9e+114)
		tmp = (y * -0.3333333333333333) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.8e+92], x, If[LessEqual[x, 2.9e+114], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7999999999999996e92 or 2.9e114 < x

   1. Initial program 98.8%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf 61.4%

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

   if -6.7999999999999996e92 < x < 2.9e114

   1. Initial program 94.2%

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

      1. associate-*l* 94.2%

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

      2. *-commutative 94.2%

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

   3. Simplified 94.2%

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

      1. +-commutative 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-*l* 94.2%

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

      4. associate-+r- 94.2%

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

      5. associate-*l* 94.2%

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

      6. *-commutative 94.2%

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

      7. associate-/r* 95.1%

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

      8. div-inv 95.0%

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

      9. metadata-eval 95.0%

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

      10. div-inv 95.0%

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

      11. clear-num 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in y around inf 49.5%

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

      1. associate-*r/ 49.5%

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

      2. *-commutative 49.5%

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

   9. Simplified 49.5%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.0% accurate, 29.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Simplified 95.3%

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

5. Taylor expanded in x around inf 30.1%

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

6. Final simplification 30.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024011 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))