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

Percentage Accurate: 95.7% → 99.6%

Time: 13.8s

Alternatives: 16

Speedup: 1.0×

• 27.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-58}:\\ \;\;\;\;t_1 + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{1}{z \cdot \frac{-3}{y - \frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= (* z 3.0) -1e-58)
     (+ t_1 (/ t (* z (* 3.0 y))))
     (if (<= (* z 3.0) 4e+21)
       (+ x (/ 1.0 (* z (/ -3.0 (- y (/ t y))))))
       (+ t_1 (/ t (* (* z 3.0) y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -1e-58) {
		tmp = t_1 + (t / (z * (3.0 * y)));
	} else if ((z * 3.0) <= 4e+21) {
		tmp = x + (1.0 / (z * (-3.0 / (y - (t / y)))));
	} else {
		tmp = t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if ((z * 3.0d0) <= (-1d-58)) then
        tmp = t_1 + (t / (z * (3.0d0 * y)))
    else if ((z * 3.0d0) <= 4d+21) then
        tmp = x + (1.0d0 / (z * ((-3.0d0) / (y - (t / y)))))
    else
        tmp = t_1 + (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 t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -1e-58) {
		tmp = t_1 + (t / (z * (3.0 * y)));
	} else if ((z * 3.0) <= 4e+21) {
		tmp = x + (1.0 / (z * (-3.0 / (y - (t / y)))));
	} else {
		tmp = t_1 + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if (z * 3.0) <= -1e-58:
		tmp = t_1 + (t / (z * (3.0 * y)))
	elif (z * 3.0) <= 4e+21:
		tmp = x + (1.0 / (z * (-3.0 / (y - (t / y)))))
	else:
		tmp = t_1 + (t / ((z * 3.0) * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e-58)
		tmp = Float64(t_1 + Float64(t / Float64(z * Float64(3.0 * y))));
	elseif (Float64(z * 3.0) <= 4e+21)
		tmp = Float64(x + Float64(1.0 / Float64(z * Float64(-3.0 / Float64(y - Float64(t / y))))));
	else
		tmp = Float64(t_1 + Float64(t / Float64(Float64(z * 3.0) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if ((z * 3.0) <= -1e-58)
		tmp = t_1 + (t / (z * (3.0 * y)));
	elseif ((z * 3.0) <= 4e+21)
		tmp = x + (1.0 / (z * (-3.0 / (y - (t / y)))));
	else
		tmp = t_1 + (t / ((z * 3.0) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e-58], N[(t$95$1 + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 4e+21], N[(x + N[(1.0 / N[(z * N[(-3.0 / N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -1e-58

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 98.6%

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

      1. associate-*r* 98.6%

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

      2. *-commutative 98.6%

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

      3. *-commutative 98.6%

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

   4. Simplified 98.6%

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

   if -1e-58 < (*.f64 z 3) < 4e21

   1. Initial program 88.7%

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

   3. Simplified 99.7%

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

      1. associate-*l/ 99.6%

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

      2. clear-num 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r/ 99.9%

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

   8. Simplified 99.9%

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

   if 4e21 < (*.f64 z 3)

   1. Initial program 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-58}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{1}{z \cdot \frac{-3}{y - \frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

Alternative 2: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-58} \lor \neg \left(z \cdot 3 \leq 4 \cdot 10^{+21}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z \cdot \frac{-3}{y - \frac{t}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -1e-58) (not (<= (* z 3.0) 4e+21)))
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* 3.0 y))))
   (+ x (/ 1.0 (* z (/ -3.0 (- y (/ t y))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -1e-58) || !((z * 3.0) <= 4e+21)) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (1.0 / (z * (-3.0 / (y - (t / 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 (((z * 3.0d0) <= (-1d-58)) .or. (.not. ((z * 3.0d0) <= 4d+21))) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (3.0d0 * y)))
    else
        tmp = x + (1.0d0 / (z * ((-3.0d0) / (y - (t / y)))))
    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-58) || !((z * 3.0) <= 4e+21)) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (1.0 / (z * (-3.0 / (y - (t / y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -1e-58) or not ((z * 3.0) <= 4e+21):
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)))
	else:
		tmp = x + (1.0 / (z * (-3.0 / (y - (t / y)))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -1e-58) || !(Float64(z * 3.0) <= 4e+21))
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(3.0 * y))));
	else
		tmp = Float64(x + Float64(1.0 / Float64(z * Float64(-3.0 / Float64(y - Float64(t / y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -1e-58) || ~(((z * 3.0) <= 4e+21)))
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	else
		tmp = x + (1.0 / (z * (-3.0 / (y - (t / y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -1e-58], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 4e+21]], $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[(1.0 / N[(z * N[(-3.0 / N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -1e-58 or 4e21 < (*.f64 z 3)

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 99.1%

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

      1. associate-*r* 99.1%

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

      2. *-commutative 99.1%

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

      3. *-commutative 99.1%

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

   4. Simplified 99.1%

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

   if -1e-58 < (*.f64 z 3) < 4e21

   1. Initial program 88.7%

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

   3. Simplified 99.7%

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

      1. associate-*l/ 99.6%

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

      2. clear-num 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r/ 99.9%

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

   8. Simplified 99.9%

      \[\leadsto x + \frac{1}{\color{blue}{z \cdot \frac{-3}{y - \frac{t}{y}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-58} \lor \neg \left(z \cdot 3 \leq 4 \cdot 10^{+21}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z \cdot \frac{-3}{y - \frac{t}{y}}}\\ \end{array} \]

Alternative 3: 87.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ t_2 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-16}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* 0.3333333333333333 (/ t (* z y)))))
        (t_2 (- x (* (/ y z) 0.3333333333333333))))
   (if (<= y -1.65e+65)
     t_2
     (if (<= y 3.1e-88)
       t_1
       (if (<= y 2.05e-16)
         (* (- (/ t y) y) (/ 0.3333333333333333 z))
         (if (<= y 9.2e+21) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (0.3333333333333333 * (t / (z * y)));
	double t_2 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -1.65e+65) {
		tmp = t_2;
	} else if (y <= 3.1e-88) {
		tmp = t_1;
	} else if (y <= 2.05e-16) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else if (y <= 9.2e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + (0.3333333333333333d0 * (t / (z * y)))
    t_2 = x - ((y / z) * 0.3333333333333333d0)
    if (y <= (-1.65d+65)) then
        tmp = t_2
    else if (y <= 3.1d-88) then
        tmp = t_1
    else if (y <= 2.05d-16) then
        tmp = ((t / y) - y) * (0.3333333333333333d0 / z)
    else if (y <= 9.2d+21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (0.3333333333333333 * (t / (z * y)));
	double t_2 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -1.65e+65) {
		tmp = t_2;
	} else if (y <= 3.1e-88) {
		tmp = t_1;
	} else if (y <= 2.05e-16) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else if (y <= 9.2e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (0.3333333333333333 * (t / (z * y)))
	t_2 = x - ((y / z) * 0.3333333333333333)
	tmp = 0
	if y <= -1.65e+65:
		tmp = t_2
	elif y <= 3.1e-88:
		tmp = t_1
	elif y <= 2.05e-16:
		tmp = ((t / y) - y) * (0.3333333333333333 / z)
	elif y <= 9.2e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))))
	t_2 = Float64(x - Float64(Float64(y / z) * 0.3333333333333333))
	tmp = 0.0
	if (y <= -1.65e+65)
		tmp = t_2;
	elseif (y <= 3.1e-88)
		tmp = t_1;
	elseif (y <= 2.05e-16)
		tmp = Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z));
	elseif (y <= 9.2e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (0.3333333333333333 * (t / (z * y)));
	t_2 = x - ((y / z) * 0.3333333333333333);
	tmp = 0.0;
	if (y <= -1.65e+65)
		tmp = t_2;
	elseif (y <= 3.1e-88)
		tmp = t_1;
	elseif (y <= 2.05e-16)
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	elseif (y <= 9.2e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+65], t$95$2, If[LessEqual[y, 3.1e-88], t$95$1, If[LessEqual[y, 2.05e-16], N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65000000000000012e65 or 9.2e21 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 96.1%

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

   if -1.65000000000000012e65 < y < 3.0999999999999998e-88 or 2.05000000000000003e-16 < y < 9.2e21

   1. Initial program 90.8%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in y around 0 86.2%

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

   if 3.0999999999999998e-88 < y < 2.05000000000000003e-16

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. associate-*r* 92.9%

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

      2. *-commutative 92.9%

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

      3. *-commutative 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in x around 0 92.8%

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

      1. associate-/r* 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.4%

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

      4. div-sub 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

      1. associate-/r/ 99.4%

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

   9. Applied egg-rr 99.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-88}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-16}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+21}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \end{array} \]

Alternative 4: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-13}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+22}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* (/ y z) 0.3333333333333333))))
   (if (<= y -1.65e+65)
     t_1
     (if (<= y 3.3e-88)
       (+ x (/ 0.3333333333333333 (/ y (/ t z))))
       (if (<= y 2.25e-13)
         (* (- (/ t y) y) (/ 0.3333333333333333 z))
         (if (<= y 3.5e+22)
           (+ x (* 0.3333333333333333 (/ t (* z y))))
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -1.65e+65) {
		tmp = t_1;
	} else if (y <= 3.3e-88) {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	} else if (y <= 2.25e-13) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else if (y <= 3.5e+22) {
		tmp = x + (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 = x - ((y / z) * 0.3333333333333333d0)
    if (y <= (-1.65d+65)) then
        tmp = t_1
    else if (y <= 3.3d-88) then
        tmp = x + (0.3333333333333333d0 / (y / (t / z)))
    else if (y <= 2.25d-13) then
        tmp = ((t / y) - y) * (0.3333333333333333d0 / z)
    else if (y <= 3.5d+22) then
        tmp = x + (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 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -1.65e+65) {
		tmp = t_1;
	} else if (y <= 3.3e-88) {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	} else if (y <= 2.25e-13) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else if (y <= 3.5e+22) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) * 0.3333333333333333)
	tmp = 0
	if y <= -1.65e+65:
		tmp = t_1
	elif y <= 3.3e-88:
		tmp = x + (0.3333333333333333 / (y / (t / z)))
	elif y <= 2.25e-13:
		tmp = ((t / y) - y) * (0.3333333333333333 / z)
	elif y <= 3.5e+22:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) * 0.3333333333333333))
	tmp = 0.0
	if (y <= -1.65e+65)
		tmp = t_1;
	elseif (y <= 3.3e-88)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y / Float64(t / z))));
	elseif (y <= 2.25e-13)
		tmp = Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z));
	elseif (y <= 3.5e+22)
		tmp = Float64(x + 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 = x - ((y / z) * 0.3333333333333333);
	tmp = 0.0;
	if (y <= -1.65e+65)
		tmp = t_1;
	elseif (y <= 3.3e-88)
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	elseif (y <= 2.25e-13)
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	elseif (y <= 3.5e+22)
		tmp = x + (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[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+65], t$95$1, If[LessEqual[y, 3.3e-88], N[(x + N[(0.3333333333333333 / N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e-13], N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+22], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.65000000000000012e65 or 3.5e22 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 96.1%

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

   if -1.65000000000000012e65 < y < 3.29999999999999994e-88

   1. Initial program 90.2%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around 0 85.3%

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

      1. metadata-eval 85.3%

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

      2. clear-num 85.3%

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

      3. inv-pow 85.3%

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

      4. unpow-prod-down 85.2%

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

      5. inv-pow 85.2%

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

      6. associate-/r* 85.3%

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

      7. metadata-eval 85.3%

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

      8. associate-/l* 93.6%

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

   6. Applied egg-rr 93.6%

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

   if 3.29999999999999994e-88 < y < 2.25e-13

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. associate-*r* 92.9%

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

      2. *-commutative 92.9%

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

      3. *-commutative 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in x around 0 92.8%

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

      1. associate-/r* 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.4%

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

      4. div-sub 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

      1. associate-/r/ 99.4%

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

   9. Applied egg-rr 99.4%

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

   if 2.25e-13 < y < 3.5e22

   1. Initial program 99.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in y around 0 100.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-13}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+22}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \end{array} \]

Alternative 5: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-17}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{z}{\frac{t}{y} - y}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+20}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* (/ y z) 0.3333333333333333))))
   (if (<= y -1.65e+65)
     t_1
     (if (<= y 3.3e-88)
       (+ x (/ 0.3333333333333333 (/ y (/ t z))))
       (if (<= y 8e-17)
         (/ 0.3333333333333333 (/ z (- (/ t y) y)))
         (if (<= y 1.02e+20)
           (+ x (* 0.3333333333333333 (/ t (* z y))))
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -1.65e+65) {
		tmp = t_1;
	} else if (y <= 3.3e-88) {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	} else if (y <= 8e-17) {
		tmp = 0.3333333333333333 / (z / ((t / y) - y));
	} else if (y <= 1.02e+20) {
		tmp = x + (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 = x - ((y / z) * 0.3333333333333333d0)
    if (y <= (-1.65d+65)) then
        tmp = t_1
    else if (y <= 3.3d-88) then
        tmp = x + (0.3333333333333333d0 / (y / (t / z)))
    else if (y <= 8d-17) then
        tmp = 0.3333333333333333d0 / (z / ((t / y) - y))
    else if (y <= 1.02d+20) then
        tmp = x + (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 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -1.65e+65) {
		tmp = t_1;
	} else if (y <= 3.3e-88) {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	} else if (y <= 8e-17) {
		tmp = 0.3333333333333333 / (z / ((t / y) - y));
	} else if (y <= 1.02e+20) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) * 0.3333333333333333)
	tmp = 0
	if y <= -1.65e+65:
		tmp = t_1
	elif y <= 3.3e-88:
		tmp = x + (0.3333333333333333 / (y / (t / z)))
	elif y <= 8e-17:
		tmp = 0.3333333333333333 / (z / ((t / y) - y))
	elif y <= 1.02e+20:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) * 0.3333333333333333))
	tmp = 0.0
	if (y <= -1.65e+65)
		tmp = t_1;
	elseif (y <= 3.3e-88)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y / Float64(t / z))));
	elseif (y <= 8e-17)
		tmp = Float64(0.3333333333333333 / Float64(z / Float64(Float64(t / y) - y)));
	elseif (y <= 1.02e+20)
		tmp = Float64(x + 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 = x - ((y / z) * 0.3333333333333333);
	tmp = 0.0;
	if (y <= -1.65e+65)
		tmp = t_1;
	elseif (y <= 3.3e-88)
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	elseif (y <= 8e-17)
		tmp = 0.3333333333333333 / (z / ((t / y) - y));
	elseif (y <= 1.02e+20)
		tmp = x + (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[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+65], t$95$1, If[LessEqual[y, 3.3e-88], N[(x + N[(0.3333333333333333 / N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-17], N[(0.3333333333333333 / N[(z / N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+20], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.65000000000000012e65 or 1.02e20 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 96.1%

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

   if -1.65000000000000012e65 < y < 3.29999999999999994e-88

   1. Initial program 90.2%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around 0 85.3%

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

      1. metadata-eval 85.3%

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

      2. clear-num 85.3%

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

      3. inv-pow 85.3%

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

      4. unpow-prod-down 85.2%

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

      5. inv-pow 85.2%

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

      6. associate-/r* 85.3%

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

      7. metadata-eval 85.3%

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

      8. associate-/l* 93.6%

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

   6. Applied egg-rr 93.6%

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

   if 3.29999999999999994e-88 < y < 8.00000000000000057e-17

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. associate-*r* 92.9%

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

      2. *-commutative 92.9%

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

      3. *-commutative 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in x around 0 92.8%

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

      1. associate-/r* 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.4%

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

      4. div-sub 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   if 8.00000000000000057e-17 < y < 1.02e20

   1. Initial program 99.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in y around 0 100.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-17}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{z}{\frac{t}{y} - y}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+20}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \end{array} \]

Alternative 6: 97.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-153}:\\ \;\;\;\;\left(x + -0.3333333333333333 \cdot \frac{y}{z}\right) + \frac{\frac{\frac{t}{y}}{3}}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-121}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e-153)
   (+ (+ x (* -0.3333333333333333 (/ y z))) (/ (/ (/ t y) 3.0) z))
   (if (<= y 2.8e-121)
     (+ x (/ 0.3333333333333333 (/ y (/ t z))))
     (+ x (/ (- y (/ t y)) (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e-153) {
		tmp = (x + (-0.3333333333333333 * (y / z))) + (((t / y) / 3.0) / z);
	} else if (y <= 2.8e-121) {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	} else {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.6d-153)) then
        tmp = (x + ((-0.3333333333333333d0) * (y / z))) + (((t / y) / 3.0d0) / z)
    else if (y <= 2.8d-121) then
        tmp = x + (0.3333333333333333d0 / (y / (t / z)))
    else
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e-153) {
		tmp = (x + (-0.3333333333333333 * (y / z))) + (((t / y) / 3.0) / z);
	} else if (y <= 2.8e-121) {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	} else {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e-153:
		tmp = (x + (-0.3333333333333333 * (y / z))) + (((t / y) / 3.0) / z)
	elif y <= 2.8e-121:
		tmp = x + (0.3333333333333333 / (y / (t / z)))
	else:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.6e-153)
		tmp = Float64(Float64(x + Float64(-0.3333333333333333 * Float64(y / z))) + Float64(Float64(Float64(t / y) / 3.0) / z));
	elseif (y <= 2.8e-121)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y / Float64(t / z))));
	else
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.6e-153)
		tmp = (x + (-0.3333333333333333 * (y / z))) + (((t / y) / 3.0) / z);
	elseif (y <= 2.8e-121)
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	else
		tmp = x + ((y - (t / y)) / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.6e-153], N[(N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t / y), $MachinePrecision] / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-121], N[(x + N[(0.3333333333333333 / N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6000000000000001e-153

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. distribute-frac-neg 96.7%

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

      3. neg-mul-1 96.7%

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

      4. *-commutative 96.7%

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

      5. times-frac 96.7%

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

      6. metadata-eval 96.7%

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

      7. associate-/l/ 99.7%

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

      8. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   if -5.6000000000000001e-153 < y < 2.8000000000000001e-121

   1. Initial program 87.7%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in y around 0 87.6%

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

      1. metadata-eval 87.6%

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

      2. clear-num 87.6%

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

      3. inv-pow 87.6%

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

      4. unpow-prod-down 87.6%

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

      5. inv-pow 87.6%

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

      6. associate-/r* 87.7%

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

      7. metadata-eval 87.7%

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

      8. associate-/l* 98.9%

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

   6. Applied egg-rr 98.9%

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

   if 2.8000000000000001e-121 < 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 98.3%

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

      1. *-commutative 98.3%

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

      2. clear-num 98.3%

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

      3. un-div-inv 98.4%

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

      4. div-inv 98.5%

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

      5. metadata-eval 98.5%

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

   5. Applied egg-rr 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-153}:\\ \;\;\;\;\left(x + -0.3333333333333333 \cdot \frac{y}{z}\right) + \frac{\frac{\frac{t}{y}}{3}}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-121}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternative 7: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ t_2 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 0.3333333333333333 (* y (/ z t))))
        (t_2 (- x (* (/ y z) 0.3333333333333333))))
   (if (<= y -7.4e-77)
     t_2
     (if (<= y 3.5e-197)
       t_1
       (if (<= y 1.48e-155) x (if (<= y 9.2e-8) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 / (y * (z / t));
	double t_2 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -7.4e-77) {
		tmp = t_2;
	} else if (y <= 3.5e-197) {
		tmp = t_1;
	} else if (y <= 1.48e-155) {
		tmp = x;
	} else if (y <= 9.2e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 / (y * (z / t))
    t_2 = x - ((y / z) * 0.3333333333333333d0)
    if (y <= (-7.4d-77)) then
        tmp = t_2
    else if (y <= 3.5d-197) then
        tmp = t_1
    else if (y <= 1.48d-155) then
        tmp = x
    else if (y <= 9.2d-8) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 / (y * (z / t));
	double t_2 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -7.4e-77) {
		tmp = t_2;
	} else if (y <= 3.5e-197) {
		tmp = t_1;
	} else if (y <= 1.48e-155) {
		tmp = x;
	} else if (y <= 9.2e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 / (y * (z / t))
	t_2 = x - ((y / z) * 0.3333333333333333)
	tmp = 0
	if y <= -7.4e-77:
		tmp = t_2
	elif y <= 3.5e-197:
		tmp = t_1
	elif y <= 1.48e-155:
		tmp = x
	elif y <= 9.2e-8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 / Float64(y * Float64(z / t)))
	t_2 = Float64(x - Float64(Float64(y / z) * 0.3333333333333333))
	tmp = 0.0
	if (y <= -7.4e-77)
		tmp = t_2;
	elseif (y <= 3.5e-197)
		tmp = t_1;
	elseif (y <= 1.48e-155)
		tmp = x;
	elseif (y <= 9.2e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 / (y * (z / t));
	t_2 = x - ((y / z) * 0.3333333333333333);
	tmp = 0.0;
	if (y <= -7.4e-77)
		tmp = t_2;
	elseif (y <= 3.5e-197)
		tmp = t_1;
	elseif (y <= 1.48e-155)
		tmp = x;
	elseif (y <= 9.2e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4e-77], t$95$2, If[LessEqual[y, 3.5e-197], t$95$1, If[LessEqual[y, 1.48e-155], x, If[LessEqual[y, 9.2e-8], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.39999999999999992e-77 or 9.2000000000000003e-8 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 86.5%

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

   if -7.39999999999999992e-77 < y < 3.4999999999999998e-197 or 1.48e-155 < y < 9.2000000000000003e-8

   1. Initial program 89.2%

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

   2. Taylor expanded in z around 0 89.2%

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

      1. associate-*r* 89.2%

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

      2. *-commutative 89.2%

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

      3. *-commutative 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in x around 0 71.0%

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

      1. associate-/r* 67.7%

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

      2. associate-*r/ 67.7%

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

      3. associate-*r/ 67.6%

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

      4. div-sub 67.6%

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

      5. distribute-lft-out-- 67.6%

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

      6. associate-/l* 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in t around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-*l/ 73.4%

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

   10. Simplified 73.4%

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

   if 3.4999999999999998e-197 < y < 1.48e-155

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \end{array} \]

Alternative 8: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-196}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* (/ y z) 0.3333333333333333))))
   (if (<= y -2.9e-77)
     t_1
     (if (<= y 3.2e-196)
       (/ 0.3333333333333333 (/ y (/ t z)))
       (if (<= y 1.6e-155)
         x
         (if (<= y 9.2e-8) (/ 0.3333333333333333 (* y (/ z t))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -2.9e-77) {
		tmp = t_1;
	} else if (y <= 3.2e-196) {
		tmp = 0.3333333333333333 / (y / (t / z));
	} else if (y <= 1.6e-155) {
		tmp = x;
	} else if (y <= 9.2e-8) {
		tmp = 0.3333333333333333 / (y * (z / t));
	} 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 = x - ((y / z) * 0.3333333333333333d0)
    if (y <= (-2.9d-77)) then
        tmp = t_1
    else if (y <= 3.2d-196) then
        tmp = 0.3333333333333333d0 / (y / (t / z))
    else if (y <= 1.6d-155) then
        tmp = x
    else if (y <= 9.2d-8) then
        tmp = 0.3333333333333333d0 / (y * (z / t))
    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 = x - ((y / z) * 0.3333333333333333);
	double tmp;
	if (y <= -2.9e-77) {
		tmp = t_1;
	} else if (y <= 3.2e-196) {
		tmp = 0.3333333333333333 / (y / (t / z));
	} else if (y <= 1.6e-155) {
		tmp = x;
	} else if (y <= 9.2e-8) {
		tmp = 0.3333333333333333 / (y * (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y / z) * 0.3333333333333333)
	tmp = 0
	if y <= -2.9e-77:
		tmp = t_1
	elif y <= 3.2e-196:
		tmp = 0.3333333333333333 / (y / (t / z))
	elif y <= 1.6e-155:
		tmp = x
	elif y <= 9.2e-8:
		tmp = 0.3333333333333333 / (y * (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y / z) * 0.3333333333333333))
	tmp = 0.0
	if (y <= -2.9e-77)
		tmp = t_1;
	elseif (y <= 3.2e-196)
		tmp = Float64(0.3333333333333333 / Float64(y / Float64(t / z)));
	elseif (y <= 1.6e-155)
		tmp = x;
	elseif (y <= 9.2e-8)
		tmp = Float64(0.3333333333333333 / Float64(y * Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((y / z) * 0.3333333333333333);
	tmp = 0.0;
	if (y <= -2.9e-77)
		tmp = t_1;
	elseif (y <= 3.2e-196)
		tmp = 0.3333333333333333 / (y / (t / z));
	elseif (y <= 1.6e-155)
		tmp = x;
	elseif (y <= 9.2e-8)
		tmp = 0.3333333333333333 / (y * (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e-77], t$95$1, If[LessEqual[y, 3.2e-196], N[(0.3333333333333333 / N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-155], x, If[LessEqual[y, 9.2e-8], N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.8999999999999999e-77 or 9.2000000000000003e-8 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 86.5%

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

   if -2.8999999999999999e-77 < y < 3.2e-196

   1. Initial program 87.9%

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

   2. Taylor expanded in z around 0 88.0%

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

      1. associate-*r* 88.0%

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

      2. *-commutative 88.0%

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

      3. *-commutative 88.0%

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

   4. Simplified 88.0%

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

   5. Taylor expanded in x around 0 67.3%

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

      1. associate-/r* 61.8%

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

      2. associate-*r/ 61.7%

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

      3. associate-*r/ 61.7%

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

      4. div-sub 61.7%

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

      5. distribute-lft-out-- 61.7%

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

      6. associate-/l* 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in t around inf 65.8%

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

      1. associate-/l* 74.5%

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

   10. Simplified 74.5%

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

   if 3.2e-196 < y < 1.60000000000000006e-155

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   if 1.60000000000000006e-155 < y < 9.2000000000000003e-8

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 93.1%

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

      1. associate-*r* 93.0%

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

      2. *-commutative 93.0%

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

      3. *-commutative 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in x around 0 82.5%

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

      1. associate-/r* 85.9%

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

      2. associate-*r/ 86.0%

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

      3. associate-*r/ 85.8%

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

      4. div-sub 85.8%

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

      5. distribute-lft-out-- 85.8%

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

      6. associate-/l* 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in t around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-*l/ 72.0%

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

   10. Simplified 72.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-196}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \end{array} \]

Alternative 9: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-150} \lor \neg \left(y \leq 2.36 \cdot 10^{-122}\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.05e-150) (not (<= y 2.36e-122)))
   (+ x (* -0.3333333333333333 (/ (- y (/ t y)) z)))
   (+ x (/ 0.3333333333333333 (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.05e-150) || !(y <= 2.36e-122)) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} else {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.05d-150)) .or. (.not. (y <= 2.36d-122))) then
        tmp = x + ((-0.3333333333333333d0) * ((y - (t / y)) / z))
    else
        tmp = x + (0.3333333333333333d0 / (y / (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.05e-150) || !(y <= 2.36e-122)) {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	} else {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.05e-150) or not (y <= 2.36e-122):
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z))
	else:
		tmp = x + (0.3333333333333333 / (y / (t / z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.05e-150) || !(y <= 2.36e-122))
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y / Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.05e-150) || ~((y <= 2.36e-122)))
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	else
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.05e-150], N[Not[LessEqual[y, 2.36e-122]], $MachinePrecision]], N[(x + N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 / N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0499999999999999e-150 or 2.35999999999999995e-122 < y

   1. Initial program 97.5%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 99.2%

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

   if -2.0499999999999999e-150 < y < 2.35999999999999995e-122

   1. Initial program 87.7%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in y around 0 87.6%

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

      1. metadata-eval 87.6%

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

      2. clear-num 87.6%

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

      3. inv-pow 87.6%

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

      4. unpow-prod-down 87.6%

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

      5. inv-pow 87.6%

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

      6. associate-/r* 87.7%

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

      7. metadata-eval 87.7%

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

      8. associate-/l* 98.9%

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

   6. Applied egg-rr 98.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-150} \lor \neg \left(y \leq 2.36 \cdot 10^{-122}\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \]

Alternative 10: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{-150}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{t_1}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- y (/ t y))))
   (if (<= y -3.9e-150)
     (+ x (* -0.3333333333333333 (/ t_1 z)))
     (if (<= y 4.5e-124)
       (+ x (/ 0.3333333333333333 (/ y (/ t z))))
       (+ x (/ t_1 (* z -3.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -3.9e-150) {
		tmp = x + (-0.3333333333333333 * (t_1 / z));
	} else if (y <= 4.5e-124) {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	} else {
		tmp = x + (t_1 / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (t / y)
    if (y <= (-3.9d-150)) then
        tmp = x + ((-0.3333333333333333d0) * (t_1 / z))
    else if (y <= 4.5d-124) then
        tmp = x + (0.3333333333333333d0 / (y / (t / z)))
    else
        tmp = x + (t_1 / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -3.9e-150) {
		tmp = x + (-0.3333333333333333 * (t_1 / z));
	} else if (y <= 4.5e-124) {
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	} else {
		tmp = x + (t_1 / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y - (t / y)
	tmp = 0
	if y <= -3.9e-150:
		tmp = x + (-0.3333333333333333 * (t_1 / z))
	elif y <= 4.5e-124:
		tmp = x + (0.3333333333333333 / (y / (t / z)))
	else:
		tmp = x + (t_1 / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y - Float64(t / y))
	tmp = 0.0
	if (y <= -3.9e-150)
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(t_1 / z)));
	elseif (y <= 4.5e-124)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y / Float64(t / z))));
	else
		tmp = Float64(x + Float64(t_1 / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y - (t / y);
	tmp = 0.0;
	if (y <= -3.9e-150)
		tmp = x + (-0.3333333333333333 * (t_1 / z));
	elseif (y <= 4.5e-124)
		tmp = x + (0.3333333333333333 / (y / (t / z)));
	else
		tmp = x + (t_1 / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e-150], N[(x + N[(-0.3333333333333333 * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-124], N[(x + N[(0.3333333333333333 / N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000002e-150

   1. Initial program 96.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

   if -3.9000000000000002e-150 < y < 4.4999999999999996e-124

   1. Initial program 87.7%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in y around 0 87.6%

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

      1. metadata-eval 87.6%

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

      2. clear-num 87.6%

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

      3. inv-pow 87.6%

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

      4. unpow-prod-down 87.6%

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

      5. inv-pow 87.6%

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

      6. associate-/r* 87.7%

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

      7. metadata-eval 87.7%

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

      8. associate-/l* 98.9%

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

   6. Applied egg-rr 98.9%

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

   if 4.4999999999999996e-124 < 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 98.3%

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

      1. *-commutative 98.3%

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

      2. clear-num 98.3%

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

      3. un-div-inv 98.4%

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

      4. div-inv 98.5%

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

      5. metadata-eval 98.5%

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

   5. Applied egg-rr 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-150}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternative 11: 80.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+95} \lor \neg \left(z \leq 4.8 \cdot 10^{+140}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.35e+95) (not (<= z 4.8e+140)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* (- (/ t y) y) (/ 0.3333333333333333 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e+95) || !(z <= 4.8e+140)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.35d+95)) .or. (.not. (z <= 4.8d+140))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = ((t / y) - y) * (0.3333333333333333d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e+95) || !(z <= 4.8e+140)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.35e+95) or not (z <= 4.8e+140):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = ((t / y) - y) * (0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.35e+95) || !(z <= 4.8e+140))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.35e+95) || ~((z <= 4.8e+140)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.35e+95], N[Not[LessEqual[z, 4.8e+140]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e95 or 4.7999999999999999e140 < z

   1. Initial program 98.7%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in y around inf 73.1%

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

   if -1.35e95 < z < 4.7999999999999999e140

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 92.1%

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

      1. associate-*r* 92.1%

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

      2. *-commutative 92.1%

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

      3. *-commutative 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in x around 0 80.8%

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

      1. associate-/r* 86.0%

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

      2. associate-*r/ 85.9%

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

      3. associate-*r/ 85.8%

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

      4. div-sub 85.8%

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

      5. distribute-lft-out-- 85.8%

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

      6. associate-/l* 85.9%

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

   7. Simplified 85.9%

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

      1. associate-/r/ 85.8%

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

   9. Applied egg-rr 85.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+95} \lor \neg \left(z \leq 4.8 \cdot 10^{+140}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \end{array} \]

Alternative 12: 47.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+35}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.3e+92) x (if (<= x 4.8e+35) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e+92) {
		tmp = x;
	} else if (x <= 4.8e+35) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.3d+92)) then
        tmp = x
    else if (x <= 4.8d+35) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e+92) {
		tmp = x;
	} else if (x <= 4.8e+35) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.3e+92:
		tmp = x
	elif x <= 4.8e+35:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.3e+92)
		tmp = x;
	elseif (x <= 4.8e+35)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.3e+92)
		tmp = x;
	elseif (x <= 4.8e+35)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.3e+92], x, If[LessEqual[x, 4.8e+35], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2999999999999999e92 or 4.80000000000000029e35 < x

   1. Initial program 95.7%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around inf 55.3%

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

   if -1.2999999999999999e92 < x < 4.80000000000000029e35

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 93.5%

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

      1. associate-*r* 93.5%

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

      2. *-commutative 93.5%

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

      3. *-commutative 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in y around inf 44.1%

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

      1. *-commutative 44.1%

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

   7. Simplified 44.1%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+35}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 64.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{-0.3333333333333333}{z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

3. Simplified 92.7%

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

4. Taylor expanded in y around inf 59.9%

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

5. Final simplification 59.9%

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

Alternative 14: 64.6% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

3. Simplified 92.7%

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

   1. *-commutative 92.7%

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

   2. clear-num 92.7%

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

   3. un-div-inv 92.7%

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

   4. div-inv 92.8%

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

   5. metadata-eval 92.8%

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

5. Applied egg-rr 92.8%

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

6. Taylor expanded in y around inf 59.9%

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

7. Final simplification 59.9%

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

Alternative 15: 64.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{z} \cdot 0.3333333333333333 \end{array} \]

FPCore

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

C

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

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) * 0.3333333333333333d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

2. Taylor expanded in t around 0 59.9%

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

3. Final simplification 59.9%

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

Alternative 16: 31.2% 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 94.3%

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

3. Simplified 92.7%

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

4. Taylor expanded in x around inf 26.8%

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

5. Final simplification 26.8%

   \[\leadsto x \]

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 2023276 
(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))))