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

Percentage Accurate: 95.5% → 99.4%

Time: 13.6s

Alternatives: 19

Speedup: 0.7×

• 27.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+87} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -4e+87) (not (<= (* z 3.0) 5e-49)))
   (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y)))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -4e+87) || !((z * 3.0) <= 5e-49)) {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * 3.0d0) <= (-4d+87)) .or. (.not. ((z * 3.0d0) <= 5d-49))) then
        tmp = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -4e+87) || !((z * 3.0) <= 5e-49)) {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -4e+87) or not ((z * 3.0) <= 5e-49):
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -4e+87) || !(Float64(z * 3.0) <= 5e-49))
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -4e+87) || ~(((z * 3.0) <= 5e-49)))
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+87], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 5e-49]], $MachinePrecision]], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -3.9999999999999998e87 or 4.9999999999999999e-49 < (*.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

   if -3.9999999999999998e87 < (*.f64 z 3) < 4.9999999999999999e-49

   1. Initial program 93.3%

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

      1. associate-*l* 93.3%

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

      2. *-commutative 93.3%

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

   3. Simplified 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l* 93.3%

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

      3. associate-+l- 93.3%

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

      4. *-commutative 93.3%

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

      5. associate-/r* 99.2%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+87} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-14} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-43}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -1e-14) (not (<= (* z 3.0) 2e-43)))
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* 3.0 y))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -1e-14) || !((z * 3.0) <= 2e-43)) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * 3.0d0) <= (-1d-14)) .or. (.not. ((z * 3.0d0) <= 2d-43))) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (3.0d0 * y)))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -1e-14) || !((z * 3.0) <= 2e-43)) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -1e-14) or not ((z * 3.0) <= 2e-43):
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -1e-14) || !(Float64(z * 3.0) <= 2e-43))
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(3.0 * y))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -1e-14) || ~(((z * 3.0) <= 2e-43)))
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -1e-14], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-43]], $MachinePrecision]], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -9.99999999999999999e-15 or 2.00000000000000015e-43 < (*.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

   if -9.99999999999999999e-15 < (*.f64 z 3) < 2.00000000000000015e-43

   1. Initial program 92.1%

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

      1. associate-*l* 92.0%

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

      2. *-commutative 92.0%

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

   3. Simplified 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*l* 92.1%

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

      3. associate-+l- 92.1%

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

      4. *-commutative 92.1%

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

      5. associate-/r* 99.1%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-14} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-43}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+46} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{+37}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -2e+46) (not (<= (* z 3.0) 5e+37)))
   (- x (/ y (* z 3.0)))
   (* -0.3333333333333333 (/ (- y (/ t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+46) || !((z * 3.0) <= 5e+37)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * 3.0d0) <= (-2d+46)) .or. (.not. ((z * 3.0d0) <= 5d+37))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (-0.3333333333333333d0) * ((y - (t / y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+46) || !((z * 3.0) <= 5e+37)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -2e+46) or not ((z * 3.0) <= 5e+37):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -2e+46) || !(Float64(z * 3.0) <= 5e+37))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -2e+46) || ~(((z * 3.0) <= 5e+37)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+46], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 5e+37]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -2e46 or 4.99999999999999989e37 < (*.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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 87.7%

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

      6. sub-div 87.7%

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

   6. Applied egg-rr 87.7%

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

   7. Taylor expanded in y around inf 70.9%

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

   if -2e46 < (*.f64 z 3) < 4.99999999999999989e37

   1. Initial program 93.8%

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

      1. associate-*l* 93.8%

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

      2. *-commutative 93.8%

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

   3. Simplified 93.8%

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

      1. *-commutative 93.8%

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

      2. associate-*l* 93.8%

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

      3. associate-+l- 93.8%

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

      4. *-commutative 93.8%

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

      5. associate-/r* 99.2%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 90.7%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+46} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{+37}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+19}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z -3.0))))
   (if (<= y -2.4e+46)
     t_1
     (if (<= y -8e-16)
       x
       (if (<= y 1.06e+19) (* 0.3333333333333333 (/ t (* z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -2.4e+46) {
		tmp = t_1;
	} else if (y <= -8e-16) {
		tmp = x;
	} else if (y <= 1.06e+19) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z * (-3.0d0))
    if (y <= (-2.4d+46)) then
        tmp = t_1
    else if (y <= (-8d-16)) then
        tmp = x
    else if (y <= 1.06d+19) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -2.4e+46) {
		tmp = t_1;
	} else if (y <= -8e-16) {
		tmp = x;
	} else if (y <= 1.06e+19) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * -3.0)
	tmp = 0
	if y <= -2.4e+46:
		tmp = t_1
	elif y <= -8e-16:
		tmp = x
	elif y <= 1.06e+19:
		tmp = 0.3333333333333333 * (t / (z * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * -3.0))
	tmp = 0.0
	if (y <= -2.4e+46)
		tmp = t_1;
	elseif (y <= -8e-16)
		tmp = x;
	elseif (y <= 1.06e+19)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * -3.0);
	tmp = 0.0;
	if (y <= -2.4e+46)
		tmp = t_1;
	elseif (y <= -8e-16)
		tmp = x;
	elseif (y <= 1.06e+19)
		tmp = 0.3333333333333333 * (t / (z * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+46], t$95$1, If[LessEqual[y, -8e-16], x, If[LessEqual[y, 1.06e+19], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000008e46 or 1.06e19 < y

   1. Initial program 99.0%

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

      1. associate-*l* 99.0%

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

      2. *-commutative 99.0%

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

   3. Simplified 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-*l* 99.0%

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

      3. associate-+l- 99.0%

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

      4. *-commutative 99.0%

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

      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 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around 0 79.7%

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

       1. metadata-eval 79.7%

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

       2. distribute-lft-neg-in 79.7%

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

       3. associate-*r/ 79.7%

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

       4. associate-*l/ 79.7%

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

       5. metadata-eval 79.7%

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

       6. associate-*r/ 79.7%

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

       7. distribute-lft-neg-out 79.7%

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

       8. associate-*r/ 79.7%

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

       9. metadata-eval 79.7%

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

       10. distribute-neg-frac 79.7%

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

       11. metadata-eval 79.7%

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

   11. Simplified 79.7%

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

   12. Taylor expanded in y around inf 71.8%

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

       1. metadata-eval 71.8%

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

       2. times-frac 71.9%

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

       3. *-commutative 71.9%

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

       4. associate-*l/ 71.8%

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

       5. associate-/r* 71.8%

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

       6. associate-*l/ 71.8%

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

       7. metadata-eval 71.8%

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

       8. associate-/r* 71.8%

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

       9. neg-mul-1 71.8%

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

       10. associate-*l/ 71.8%

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

       11. *-commutative 71.8%

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

       12. *-rgt-identity 71.8%

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

       13. associate-/r* 71.9%

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

       14. distribute-lft-neg-in 71.9%

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

       15. distribute-rgt-neg-in 71.9%

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

       16. metadata-eval 71.9%

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

   14. Simplified 71.9%

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

   if -2.40000000000000008e46 < y < -7.9999999999999998e-16

   1. Initial program 100.0%

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

   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 72.1%

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

   if -7.9999999999999998e-16 < y < 1.06e19

   1. Initial program 93.5%

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

      1. associate-*l* 93.4%

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

      2. *-commutative 93.4%

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

   3. Simplified 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-*l* 93.5%

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

      3. associate-+l- 93.5%

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

      4. *-commutative 93.5%

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

      5. associate-/r* 90.7%

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

      6. sub-div 90.7%

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

   6. Applied egg-rr 90.7%

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

   7. Taylor expanded in y around 0 64.9%

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

      1. *-commutative 64.9%

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

   9. Simplified 64.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+19}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-135} \lor \neg \left(y \leq 1.55 \cdot 10^{-65}\right):\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{z}}{3}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e-135) (not (<= y 1.55e-65)))
   (+ x (* (/ 0.3333333333333333 z) (- (/ t y) y)))
   (+ x (/ (/ (/ t z) 3.0) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-135) || !(y <= 1.55e-65)) {
		tmp = x + ((0.3333333333333333 / z) * ((t / y) - y));
	} else {
		tmp = x + (((t / z) / 3.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5d-135)) .or. (.not. (y <= 1.55d-65))) then
        tmp = x + ((0.3333333333333333d0 / z) * ((t / y) - y))
    else
        tmp = x + (((t / z) / 3.0d0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-135) || !(y <= 1.55e-65)) {
		tmp = x + ((0.3333333333333333 / z) * ((t / y) - y));
	} else {
		tmp = x + (((t / z) / 3.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5e-135) or not (y <= 1.55e-65):
		tmp = x + ((0.3333333333333333 / z) * ((t / y) - y))
	else:
		tmp = x + (((t / z) / 3.0) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e-135) || !(y <= 1.55e-65))
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / z) * Float64(Float64(t / y) - y)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / z) / 3.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5e-135) || ~((y <= 1.55e-65)))
		tmp = x + ((0.3333333333333333 / z) * ((t / y) - y));
	else
		tmp = x + (((t / z) / 3.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e-135], N[Not[LessEqual[y, 1.55e-65]], $MachinePrecision]], N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / z), $MachinePrecision] / 3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000002e-135 or 1.55000000000000008e-65 < y

   1. Initial program 98.2%

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

   3. Simplified 99.2%

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

   if -5.0000000000000002e-135 < y < 1.55000000000000008e-65

   1. Initial program 92.2%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in t around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. times-frac 97.5%

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

      3. metadata-eval 97.5%

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

      4. associate-/r* 97.5%

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

      5. associate-/l/ 97.5%

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

      6. associate-/r* 97.5%

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

      7. associate-*l/ 97.6%

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

      8. *-commutative 97.6%

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

      9. *-lft-identity 97.6%

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

      10. associate-/r* 97.6%

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

   7. Simplified 97.6%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-135} \lor \neg \left(y \leq 1.55 \cdot 10^{-65}\right):\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{z}}{3}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-136} \lor \neg \left(y \leq 2.8 \cdot 10^{-94}\right):\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{z}}{3}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.45e-136) (not (<= y 2.8e-94)))
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ x (/ (/ (/ t z) 3.0) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.45e-136) || !(y <= 2.8e-94)) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + (((t / z) / 3.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.45d-136)) .or. (.not. (y <= 2.8d-94))) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = x + (((t / z) / 3.0d0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.45e-136) || !(y <= 2.8e-94)) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + (((t / z) / 3.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.45e-136) or not (y <= 2.8e-94):
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = x + (((t / z) / 3.0) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.45e-136) || !(y <= 2.8e-94))
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / z) / 3.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.45e-136) || ~((y <= 2.8e-94)))
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = x + (((t / z) / 3.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.45e-136], N[Not[LessEqual[y, 2.8e-94]], $MachinePrecision]], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / z), $MachinePrecision] / 3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.45e-136 or 2.7999999999999998e-94 < y

   1. Initial program 98.2%

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

      1. associate-*l* 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. Step-by-step derivation

      1. *-commutative 98.2%

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

      2. associate-*l* 98.2%

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

      3. associate-+l- 98.2%

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

      4. *-commutative 98.2%

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

      5. associate-/r* 98.8%

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

      6. sub-div 99.3%

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

   6. Applied egg-rr 99.3%

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

   if -2.45e-136 < y < 2.7999999999999998e-94

   1. Initial program 92.0%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in t around inf 91.0%

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

      1. associate-*r/ 91.0%

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

      2. times-frac 97.4%

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

      3. metadata-eval 97.4%

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

      4. associate-/r* 97.5%

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

      5. associate-/l/ 97.5%

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

      6. associate-/r* 97.5%

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

      7. associate-*l/ 97.5%

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

      8. *-commutative 97.5%

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

      9. *-lft-identity 97.5%

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

      10. associate-/r* 97.6%

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

   7. Simplified 97.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-136} \lor \neg \left(y \leq 2.8 \cdot 10^{-94}\right):\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{z}}{3}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y} - y\\ \mathbf{if}\;y \leq -6 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{z}}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot t_1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ t y) y)))
   (if (<= y -6e-135)
     (+ x (* (/ 0.3333333333333333 z) t_1))
     (if (<= y 3.7e-66)
       (+ x (/ (/ (/ t z) 3.0) y))
       (+ x (/ (* 0.3333333333333333 t_1) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -6e-135) {
		tmp = x + ((0.3333333333333333 / z) * t_1);
	} else if (y <= 3.7e-66) {
		tmp = x + (((t / z) / 3.0) / y);
	} else {
		tmp = x + ((0.3333333333333333 * t_1) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t / y) - y
    if (y <= (-6d-135)) then
        tmp = x + ((0.3333333333333333d0 / z) * t_1)
    else if (y <= 3.7d-66) then
        tmp = x + (((t / z) / 3.0d0) / y)
    else
        tmp = x + ((0.3333333333333333d0 * t_1) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -6e-135) {
		tmp = x + ((0.3333333333333333 / z) * t_1);
	} else if (y <= 3.7e-66) {
		tmp = x + (((t / z) / 3.0) / y);
	} else {
		tmp = x + ((0.3333333333333333 * t_1) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t / y) - y
	tmp = 0
	if y <= -6e-135:
		tmp = x + ((0.3333333333333333 / z) * t_1)
	elif y <= 3.7e-66:
		tmp = x + (((t / z) / 3.0) / y)
	else:
		tmp = x + ((0.3333333333333333 * t_1) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / y) - y)
	tmp = 0.0
	if (y <= -6e-135)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / z) * t_1));
	elseif (y <= 3.7e-66)
		tmp = Float64(x + Float64(Float64(Float64(t / z) / 3.0) / y));
	else
		tmp = Float64(x + Float64(Float64(0.3333333333333333 * t_1) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t / y) - y;
	tmp = 0.0;
	if (y <= -6e-135)
		tmp = x + ((0.3333333333333333 / z) * t_1);
	elseif (y <= 3.7e-66)
		tmp = x + (((t / z) / 3.0) / y);
	else
		tmp = x + ((0.3333333333333333 * t_1) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[y, -6e-135], N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-66], N[(x + N[(N[(N[(t / z), $MachinePrecision] / 3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(0.3333333333333333 * t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000024e-135

   1. Initial program 96.6%

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

   3. Simplified 99.7%

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

   if -6.00000000000000024e-135 < y < 3.7000000000000002e-66

   1. Initial program 92.2%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in t around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. times-frac 97.5%

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

      3. metadata-eval 97.5%

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

      4. associate-/r* 97.5%

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

      5. associate-/l/ 97.5%

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

      6. associate-/r* 97.5%

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

      7. associate-*l/ 97.6%

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

      8. *-commutative 97.6%

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

      9. *-lft-identity 97.6%

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

      10. associate-/r* 97.6%

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

   7. Simplified 97.6%

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

   if 3.7000000000000002e-66 < 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 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*r/ 98.6%

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

   6. Applied egg-rr 98.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{z}}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-47} \lor \neg \left(y \leq 3.5 \cdot 10^{+49}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e-47) (not (<= y 3.5e+49)))
   (- x (/ y (* z 3.0)))
   (+ x (* 0.3333333333333333 (/ t (* z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e-47) || !(y <= 3.5e+49)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.6d-47)) .or. (.not. (y <= 3.5d+49))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e-47) || !(y <= 3.5e+49)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.6e-47) or not (y <= 3.5e+49):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e-47) || !(y <= 3.5e+49))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.6e-47) || ~((y <= 3.5e+49)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.6e-47], N[Not[LessEqual[y, 3.5e+49]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e-47 or 3.49999999999999975e49 < y

   1. Initial program 98.2%

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

      1. associate-*l* 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. Step-by-step derivation

      1. *-commutative 98.2%

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

      2. associate-*l* 98.2%

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

      3. associate-+l- 98.2%

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

      4. *-commutative 98.2%

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

      5. associate-/r* 99.1%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 92.7%

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

   if -2.6e-47 < y < 3.49999999999999975e49

   1. Initial program 94.4%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around inf 88.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-47} \lor \neg \left(y \leq 3.5 \cdot 10^{+49}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+69} \lor \neg \left(y \leq 3.4 \cdot 10^{+49}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.2e+69) (not (<= y 3.4e+49)))
   (- x (/ y (* z 3.0)))
   (+ x (/ (/ (* t 0.3333333333333333) z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e+69) || !(y <= 3.4e+49)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.2d+69)) .or. (.not. (y <= 3.4d+49))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (((t * 0.3333333333333333d0) / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e+69) || !(y <= 3.4e+49)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.2e+69) or not (y <= 3.4e+49):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (((t * 0.3333333333333333) / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.2e+69) || !(y <= 3.4e+49))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t * 0.3333333333333333) / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.2e+69) || ~((y <= 3.4e+49)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.2e+69], N[Not[LessEqual[y, 3.4e+49]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2000000000000001e69 or 3.4000000000000001e49 < 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%

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

      2. associate-*l* 99.9%

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

      3. associate-+l- 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 97.0%

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

   if -1.2000000000000001e69 < y < 3.4000000000000001e49

   1. Initial program 93.8%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around inf 85.6%

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

      1. associate-*r/ 85.6%

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

      2. times-frac 90.2%

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

      3. metadata-eval 90.2%

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

      4. associate-/r* 90.2%

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

      5. associate-/l/ 90.2%

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

      6. associate-/r* 90.2%

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

      7. associate-*l/ 90.2%

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

      8. *-commutative 90.2%

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

      9. *-lft-identity 90.2%

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

      10. associate-/r* 90.3%

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

   7. Simplified 90.3%

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

   8. Taylor expanded in t around 0 90.2%

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

      1. *-commutative 90.2%

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

      2. associate-*l/ 90.2%

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

   10. Simplified 90.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+69} \lor \neg \left(y \leq 3.4 \cdot 10^{+49}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+67} \lor \neg \left(y \leq 3.8 \cdot 10^{+49}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{z}}{3}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.05e+67) (not (<= y 3.8e+49)))
   (- x (/ y (* z 3.0)))
   (+ x (/ (/ (/ t z) 3.0) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.05e+67) || !(y <= 3.8e+49)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (((t / z) / 3.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.05d+67)) .or. (.not. (y <= 3.8d+49))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (((t / z) / 3.0d0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.05e+67) || !(y <= 3.8e+49)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (((t / z) / 3.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.05e+67) or not (y <= 3.8e+49):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (((t / z) / 3.0) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.05e+67) || !(y <= 3.8e+49))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / z) / 3.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.05e+67) || ~((y <= 3.8e+49)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (((t / z) / 3.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.05e+67], N[Not[LessEqual[y, 3.8e+49]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / z), $MachinePrecision] / 3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0499999999999999e67 or 3.7999999999999999e49 < 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%

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

      2. associate-*l* 99.9%

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

      3. associate-+l- 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 97.0%

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

   if -2.0499999999999999e67 < y < 3.7999999999999999e49

   1. Initial program 93.8%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around inf 85.6%

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

      1. associate-*r/ 85.6%

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

      2. times-frac 90.2%

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

      3. metadata-eval 90.2%

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

      4. associate-/r* 90.2%

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

      5. associate-/l/ 90.2%

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

      6. associate-/r* 90.2%

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

      7. associate-*l/ 90.2%

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

      8. *-commutative 90.2%

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

      9. *-lft-identity 90.2%

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

      10. associate-/r* 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+67} \lor \neg \left(y \leq 3.8 \cdot 10^{+49}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{z}}{3}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-48} \lor \neg \left(y \leq 1.05 \cdot 10^{-22}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.18e-48) (not (<= y 1.05e-22)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ t (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.18e-48) || !(y <= 1.05e-22)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.18d-48)) .or. (.not. (y <= 1.05d-22))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * (t / (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.18e-48) || !(y <= 1.05e-22)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.18e-48) or not (y <= 1.05e-22):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (t / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.18e-48) || !(y <= 1.05e-22))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.18e-48) || ~((y <= 1.05e-22)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (t / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.18e-48], N[Not[LessEqual[y, 1.05e-22]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.18000000000000007e-48 or 1.05000000000000004e-22 < y

   1. Initial program 98.5%

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

   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 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*l/ 88.1%

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

      3. associate-*r/ 88.1%

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

   7. Simplified 88.1%

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

   if -1.18000000000000007e-48 < y < 1.05000000000000004e-22

   1. Initial program 93.5%

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

      1. associate-*l* 93.5%

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

      2. *-commutative 93.5%

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

   3. Simplified 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l* 93.5%

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

      3. associate-+l- 93.5%

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

      4. *-commutative 93.5%

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

      5. associate-/r* 89.5%

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

      6. sub-div 89.5%

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

   6. Applied egg-rr 89.5%

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

   7. Taylor expanded in y around 0 67.8%

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

      1. *-commutative 67.8%

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

   9. Simplified 67.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-48} \lor \neg \left(y \leq 1.05 \cdot 10^{-22}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-48} \lor \neg \left(y \leq 6.5 \cdot 10^{-23}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e-48) (not (<= y 6.5e-23)))
   (- x (/ y (* z 3.0)))
   (* 0.3333333333333333 (/ t (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-48) || !(y <= 6.5e-23)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.02d-48)) .or. (.not. (y <= 6.5d-23))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = 0.3333333333333333d0 * (t / (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-48) || !(y <= 6.5e-23)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e-48) or not (y <= 6.5e-23):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = 0.3333333333333333 * (t / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e-48) || !(y <= 6.5e-23))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.02e-48) || ~((y <= 6.5e-23)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = 0.3333333333333333 * (t / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e-48], N[Not[LessEqual[y, 6.5e-23]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000005e-48 or 6.5e-23 < y

   1. Initial program 98.5%

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

      1. associate-*l* 98.4%

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

      2. *-commutative 98.4%

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

   3. Simplified 98.4%

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

      1. *-commutative 98.4%

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

      2. associate-*l* 98.5%

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

      3. associate-+l- 98.5%

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

      4. *-commutative 98.5%

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

      5. associate-/r* 99.2%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 88.2%

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

   if -1.02000000000000005e-48 < y < 6.5e-23

   1. Initial program 93.5%

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

      1. associate-*l* 93.5%

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

      2. *-commutative 93.5%

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

   3. Simplified 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l* 93.5%

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

      3. associate-+l- 93.5%

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

      4. *-commutative 93.5%

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

      5. associate-/r* 89.5%

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

      6. sub-div 89.5%

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

   6. Applied egg-rr 89.5%

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

   7. Taylor expanded in y around 0 67.8%

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

      1. *-commutative 67.8%

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

   9. Simplified 67.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-48} \lor \neg \left(y \leq 6.5 \cdot 10^{-23}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{-48} \lor \neg \left(y \leq 1.45 \cdot 10^{-22}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.26e-48) (not (<= y 1.45e-22)))
   (- x (/ y (* z 3.0)))
   (/ (* t 0.3333333333333333) (* z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.26e-48) || !(y <= 1.45e-22)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (t * 0.3333333333333333) / (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.26d-48)) .or. (.not. (y <= 1.45d-22))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (t * 0.3333333333333333d0) / (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.26e-48) || !(y <= 1.45e-22)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (t * 0.3333333333333333) / (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.26e-48) or not (y <= 1.45e-22):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (t * 0.3333333333333333) / (z * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.26e-48) || !(y <= 1.45e-22))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(t * 0.3333333333333333) / Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.26e-48) || ~((y <= 1.45e-22)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (t * 0.3333333333333333) / (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.26e-48], N[Not[LessEqual[y, 1.45e-22]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * 0.3333333333333333), $MachinePrecision] / N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2599999999999999e-48 or 1.4500000000000001e-22 < y

   1. Initial program 98.5%

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

      1. associate-*l* 98.4%

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

      2. *-commutative 98.4%

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

   3. Simplified 98.4%

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

      1. *-commutative 98.4%

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

      2. associate-*l* 98.5%

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

      3. associate-+l- 98.5%

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

      4. *-commutative 98.5%

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

      5. associate-/r* 99.2%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 88.2%

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

   if -1.2599999999999999e-48 < y < 1.4500000000000001e-22

   1. Initial program 93.5%

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

      1. associate-*l* 93.5%

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

      2. *-commutative 93.5%

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

   3. Simplified 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l* 93.5%

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

      3. associate-+l- 93.5%

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

      4. *-commutative 93.5%

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

      5. associate-/r* 89.5%

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

      6. sub-div 89.5%

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

   6. Applied egg-rr 89.5%

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

   7. Taylor expanded in y around 0 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-/r* 64.6%

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

   9. Simplified 64.6%

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

       1. *-commutative 64.6%

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

       2. associate-/l/ 67.8%

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

       3. associate-*r/ 67.8%

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

       4. *-commutative 67.8%

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

   11. Applied egg-rr 67.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{-48} \lor \neg \left(y \leq 1.45 \cdot 10^{-22}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-45} \lor \neg \left(y \leq 9.5 \cdot 10^{-23}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.5e-45) (not (<= y 9.5e-23)))
   (- x (/ y (* z 3.0)))
   (/ (* (/ t z) 0.3333333333333333) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e-45) || !(y <= 9.5e-23)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = ((t / z) * 0.3333333333333333) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.5d-45)) .or. (.not. (y <= 9.5d-23))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = ((t / z) * 0.3333333333333333d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e-45) || !(y <= 9.5e-23)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = ((t / z) * 0.3333333333333333) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.5e-45) or not (y <= 9.5e-23):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = ((t / z) * 0.3333333333333333) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.5e-45) || !(y <= 9.5e-23))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(Float64(t / z) * 0.3333333333333333) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.5e-45) || ~((y <= 9.5e-23)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = ((t / z) * 0.3333333333333333) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.5e-45], N[Not[LessEqual[y, 9.5e-23]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000002e-45 or 9.50000000000000058e-23 < y

   1. Initial program 99.2%

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

      1. associate-*l* 99.1%

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

      2. *-commutative 99.1%

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

   3. Simplified 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-*l* 99.2%

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

      3. associate-+l- 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-/r* 99.2%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 88.8%

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

   if -9.5000000000000002e-45 < y < 9.50000000000000058e-23

   1. Initial program 92.7%

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

      1. associate-*l* 92.7%

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

      2. *-commutative 92.7%

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

   3. Simplified 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l* 92.7%

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

      3. associate-+l- 92.7%

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

      4. *-commutative 92.7%

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

      5. associate-/r* 89.7%

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

      6. sub-div 89.7%

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

   6. Applied egg-rr 89.7%

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

   7. Taylor expanded in y around 0 67.5%

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

      1. *-commutative 67.5%

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

   9. Simplified 67.5%

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

       1. associate-*l/ 67.5%

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

       2. *-commutative 67.5%

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

       3. times-frac 71.0%

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

       4. associate-*r/ 71.1%

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

   11. Applied egg-rr 71.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-45} \lor \neg \left(y \leq 9.5 \cdot 10^{-23}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-23}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e-49)
   (+ x (* y (/ -0.3333333333333333 z)))
   (if (<= y 7.5e-23)
     (* 0.3333333333333333 (/ t (* z y)))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-49) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 7.5e-23) {
		tmp = 0.3333333333333333 * (t / (z * 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 (y <= (-1.8d-49)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if (y <= 7.5d-23) then
        tmp = 0.3333333333333333d0 * (t / (z * 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 (y <= -1.8e-49) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 7.5e-23) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e-49:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif y <= 7.5e-23:
		tmp = 0.3333333333333333 * (t / (z * y))
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e-49)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (y <= 7.5e-23)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * 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 (y <= -1.8e-49)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif (y <= 7.5e-23)
		tmp = 0.3333333333333333 * (t / (z * y));
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e-49], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-23], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999985e-49

   1. Initial program 97.0%

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

   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 90.0%

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

      1. *-commutative 90.0%

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

      2. associate-*l/ 89.9%

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

      3. associate-*r/ 90.0%

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

   7. Simplified 90.0%

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

   if -1.79999999999999985e-49 < y < 7.4999999999999998e-23

   1. Initial program 93.5%

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

      1. associate-*l* 93.5%

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

      2. *-commutative 93.5%

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

   3. Simplified 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l* 93.5%

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

      3. associate-+l- 93.5%

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

      4. *-commutative 93.5%

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

      5. associate-/r* 89.5%

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

      6. sub-div 89.5%

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

   6. Applied egg-rr 89.5%

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

   7. Taylor expanded in y around 0 67.8%

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

      1. *-commutative 67.8%

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

   9. Simplified 67.8%

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

   if 7.4999999999999998e-23 < 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. Taylor expanded in t around 0 86.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-23}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+47} \lor \neg \left(y \leq 3.9 \cdot 10^{+29}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.35e+47) (not (<= y 3.9e+29)))
   (* -0.3333333333333333 (/ y z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e+47) || !(y <= 3.9e+29)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.35d+47)) .or. (.not. (y <= 3.9d+29))) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e+47) || !(y <= 3.9e+29)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.35e+47) or not (y <= 3.9e+29):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.35e+47) || !(y <= 3.9e+29))
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.35e+47) || ~((y <= 3.9e+29)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.35e+47], N[Not[LessEqual[y, 3.9e+29]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.34999999999999998e47 or 3.89999999999999968e29 < y

   1. Initial program 99.0%

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

      1. associate-*l* 99.0%

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

      2. *-commutative 99.0%

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

   3. Simplified 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-*l* 99.0%

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

      3. associate-+l- 99.0%

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

      4. *-commutative 99.0%

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

      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 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 73.0%

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

   if -1.34999999999999998e47 < y < 3.89999999999999968e29

   1. Initial program 94.0%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in x around inf 30.5%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+47} \lor \neg \left(y \leq 3.9 \cdot 10^{+29}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+47} \lor \neg \left(y \leq 7 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e+47) (not (<= y 7e+29))) (/ y (* z -3.0)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+47) || !(y <= 7e+29)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7.5d+47)) .or. (.not. (y <= 7d+29))) then
        tmp = y / (z * (-3.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+47) || !(y <= 7e+29)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e+47) or not (y <= 7e+29):
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e+47) || !(y <= 7e+29))
		tmp = Float64(y / Float64(z * -3.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.5e+47) || ~((y <= 7e+29)))
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e+47], N[Not[LessEqual[y, 7e+29]], $MachinePrecision]], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999999e47 or 6.99999999999999958e29 < y

   1. Initial program 99.0%

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

      1. associate-*l* 99.0%

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

      2. *-commutative 99.0%

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

   3. Simplified 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-*l* 99.0%

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

      3. associate-+l- 99.0%

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

      4. *-commutative 99.0%

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

      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 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around 0 81.1%

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

       1. metadata-eval 81.1%

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

       2. distribute-lft-neg-in 81.1%

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

       3. associate-*r/ 81.1%

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

       4. associate-*l/ 81.1%

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

       5. metadata-eval 81.1%

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

       6. associate-*r/ 81.1%

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

       7. distribute-lft-neg-out 81.1%

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

       8. associate-*r/ 81.1%

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

       9. metadata-eval 81.1%

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

       10. distribute-neg-frac 81.1%

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

       11. metadata-eval 81.1%

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

   11. Simplified 81.1%

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

   12. Taylor expanded in y around inf 73.0%

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

       1. metadata-eval 73.0%

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

       2. times-frac 73.2%

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

       3. *-commutative 73.2%

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

       4. associate-*l/ 73.0%

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

       5. associate-/r* 73.1%

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

       6. associate-*l/ 73.1%

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

       7. metadata-eval 73.1%

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

       8. associate-/r* 73.1%

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

       9. neg-mul-1 73.1%

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

       10. associate-*l/ 73.1%

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

       11. *-commutative 73.1%

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

       12. *-rgt-identity 73.1%

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

       13. associate-/r* 73.2%

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

       14. distribute-lft-neg-in 73.2%

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

       15. distribute-rgt-neg-in 73.2%

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

       16. metadata-eval 73.2%

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

   14. Simplified 73.2%

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

   if -7.4999999999999999e47 < y < 6.99999999999999958e29

   1. Initial program 94.0%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in x around inf 30.5%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+47} \lor \neg \left(y \leq 7 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+47}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3e+47)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 2.95e+29) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e+47) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 2.95e+29) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.3d+47)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 2.95d+29) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e+47) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 2.95e+29) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.3e+47:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 2.95e+29:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3e+47)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 2.95e+29)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.3e+47)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 2.95e+29)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.3e+47], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+29], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2999999999999999e47

   1. Initial program 98.0%

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

      1. associate-*l* 98.0%

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

      2. *-commutative 98.0%

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

   3. Simplified 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-*l* 98.0%

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

      3. associate-+l- 98.0%

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

      4. *-commutative 98.0%

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

      5. associate-/r* 98.0%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 68.4%

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

   if -2.2999999999999999e47 < y < 2.9499999999999999e29

   1. Initial program 94.0%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in x around inf 30.5%

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

   if 2.9499999999999999e29 < 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%

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

      2. associate-*l* 99.9%

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

      3. associate-+l- 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 77.2%

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

      1. clear-num 77.2%

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

      2. un-div-inv 77.3%

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

   9. Applied egg-rr 77.3%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+47}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.5% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

3. Simplified 95.0%

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

5. Taylor expanded in x around inf 25.5%

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

6. Final simplification 25.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.2% 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 2024018 
(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))))