Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Percentage Accurate: 92.9% → 98.5%

Time: 7.6s

Alternatives: 14

Speedup: 1.0×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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 - x)) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - x)) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+283}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- z x) y) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+283)))
     (+ x (/ y (/ t (- z x))))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+283)) {
		tmp = x + (y / (t / (z - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+283)) {
		tmp = x + (y / (t / (z - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((z - x) * y) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+283):
		tmp = x + (y / (t / (z - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(z - x) * y) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+283))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((z - x) * y) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+283)))
		tmp = x + (y / (t / (z - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+283]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0 or 1.99999999999999991e283 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 77.9%

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

      1. associate-/l* 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 1.99999999999999991e283

   1. Initial program 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \leq -\infty \lor \neg \left(x + \frac{\left(z - x\right) \cdot y}{t} \leq 2 \cdot 10^{+283}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+251}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.9e+26)
   (/ z (/ t y))
   (if (<= y -6.2e-7)
     (* y (/ (- x) t))
     (if (<= y 1.1e+68)
       x
       (if (<= y 4.2e+251) (* z (/ y t)) (* (/ y t) (- x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.9e+26) {
		tmp = z / (t / y);
	} else if (y <= -6.2e-7) {
		tmp = y * (-x / t);
	} else if (y <= 1.1e+68) {
		tmp = x;
	} else if (y <= 4.2e+251) {
		tmp = z * (y / t);
	} else {
		tmp = (y / t) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.9d+26)) then
        tmp = z / (t / y)
    else if (y <= (-6.2d-7)) then
        tmp = y * (-x / t)
    else if (y <= 1.1d+68) then
        tmp = x
    else if (y <= 4.2d+251) then
        tmp = z * (y / t)
    else
        tmp = (y / t) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.9e+26) {
		tmp = z / (t / y);
	} else if (y <= -6.2e-7) {
		tmp = y * (-x / t);
	} else if (y <= 1.1e+68) {
		tmp = x;
	} else if (y <= 4.2e+251) {
		tmp = z * (y / t);
	} else {
		tmp = (y / t) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.9e+26:
		tmp = z / (t / y)
	elif y <= -6.2e-7:
		tmp = y * (-x / t)
	elif y <= 1.1e+68:
		tmp = x
	elif y <= 4.2e+251:
		tmp = z * (y / t)
	else:
		tmp = (y / t) * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.9e+26)
		tmp = Float64(z / Float64(t / y));
	elseif (y <= -6.2e-7)
		tmp = Float64(y * Float64(Float64(-x) / t));
	elseif (y <= 1.1e+68)
		tmp = x;
	elseif (y <= 4.2e+251)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = Float64(Float64(y / t) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.9e+26)
		tmp = z / (t / y);
	elseif (y <= -6.2e-7)
		tmp = y * (-x / t);
	elseif (y <= 1.1e+68)
		tmp = x;
	elseif (y <= 4.2e+251)
		tmp = z * (y / t);
	else
		tmp = (y / t) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.9e+26], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-7], N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+68], x, If[LessEqual[y, 4.2e+251], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.9000000000000003e26

   1. Initial program 89.2%

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

   3. Taylor expanded in y around -inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/l* 83.0%

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

   5. Applied egg-rr 83.0%

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

   6. Taylor expanded in z around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-*r/ 58.4%

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

   8. Simplified 58.4%

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

      1. clear-num 58.4%

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

      2. un-div-inv 58.4%

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

   10. Applied egg-rr 58.4%

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

   if -5.9000000000000003e26 < y < -6.1999999999999999e-7

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in z around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. distribute-frac-neg2 89.6%

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

   6. Simplified 89.6%

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

   if -6.1999999999999999e-7 < y < 1.09999999999999994e68

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 70.5%

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

   if 1.09999999999999994e68 < y < 4.2000000000000001e251

   1. Initial program 87.1%

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

   3. Taylor expanded in y around -inf 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-/l* 94.6%

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

   5. Applied egg-rr 94.6%

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

   6. Taylor expanded in z around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-*r/ 71.5%

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

   8. Simplified 71.5%

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

   if 4.2000000000000001e251 < y

   1. Initial program 74.8%

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

   3. Taylor expanded in y around -inf 74.8%

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

   4. Taylor expanded in z around 0 42.8%

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

      1. mul-1-neg 42.8%

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

      2. associate-/l* 73.4%

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

      3. distribute-rgt-neg-in 73.4%

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

      4. mul-1-neg 73.4%

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

      5. associate-*r/ 73.4%

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

      6. mul-1-neg 73.4%

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

   6. Simplified 73.4%

      \[\leadsto \color{blue}{x \cdot \frac{-y}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+251}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+252}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y t) (- x))))
   (if (<= y -1.22e+27)
     (/ z (/ t y))
     (if (<= y -6.2e-7)
       t_1
       (if (<= y 4.1e+67) x (if (<= y 5.4e+252) (* z (/ y t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / t) * -x;
	double tmp;
	if (y <= -1.22e+27) {
		tmp = z / (t / y);
	} else if (y <= -6.2e-7) {
		tmp = t_1;
	} else if (y <= 4.1e+67) {
		tmp = x;
	} else if (y <= 5.4e+252) {
		tmp = z * (y / 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 = (y / t) * -x
    if (y <= (-1.22d+27)) then
        tmp = z / (t / y)
    else if (y <= (-6.2d-7)) then
        tmp = t_1
    else if (y <= 4.1d+67) then
        tmp = x
    else if (y <= 5.4d+252) then
        tmp = z * (y / 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 = (y / t) * -x;
	double tmp;
	if (y <= -1.22e+27) {
		tmp = z / (t / y);
	} else if (y <= -6.2e-7) {
		tmp = t_1;
	} else if (y <= 4.1e+67) {
		tmp = x;
	} else if (y <= 5.4e+252) {
		tmp = z * (y / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / t) * -x
	tmp = 0
	if y <= -1.22e+27:
		tmp = z / (t / y)
	elif y <= -6.2e-7:
		tmp = t_1
	elif y <= 4.1e+67:
		tmp = x
	elif y <= 5.4e+252:
		tmp = z * (y / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / t) * Float64(-x))
	tmp = 0.0
	if (y <= -1.22e+27)
		tmp = Float64(z / Float64(t / y));
	elseif (y <= -6.2e-7)
		tmp = t_1;
	elseif (y <= 4.1e+67)
		tmp = x;
	elseif (y <= 5.4e+252)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / t) * -x;
	tmp = 0.0;
	if (y <= -1.22e+27)
		tmp = z / (t / y);
	elseif (y <= -6.2e-7)
		tmp = t_1;
	elseif (y <= 4.1e+67)
		tmp = x;
	elseif (y <= 5.4e+252)
		tmp = z * (y / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.22e+27], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-7], t$95$1, If[LessEqual[y, 4.1e+67], x, If[LessEqual[y, 5.4e+252], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2200000000000001e27

   1. Initial program 89.2%

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

   3. Taylor expanded in y around -inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/l* 83.0%

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

   5. Applied egg-rr 83.0%

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

   6. Taylor expanded in z around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-*r/ 58.4%

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

   8. Simplified 58.4%

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

      1. clear-num 58.4%

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

      2. un-div-inv 58.4%

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

   10. Applied egg-rr 58.4%

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

   if -1.2200000000000001e27 < y < -6.1999999999999999e-7 or 5.40000000000000021e252 < y

   1. Initial program 82.0%

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

   3. Taylor expanded in y around -inf 82.0%

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

   4. Taylor expanded in z around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. associate-/l* 77.9%

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

      3. distribute-rgt-neg-in 77.9%

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

      4. mul-1-neg 77.9%

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

      5. associate-*r/ 77.9%

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

      6. mul-1-neg 77.9%

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

   6. Simplified 77.9%

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

   if -6.1999999999999999e-7 < y < 4.09999999999999979e67

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 70.5%

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

   if 4.09999999999999979e67 < y < 5.40000000000000021e252

   1. Initial program 87.1%

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

   3. Taylor expanded in y around -inf 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-/l* 94.6%

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

   5. Applied egg-rr 94.6%

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

   6. Taylor expanded in z around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-*r/ 71.5%

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

   8. Simplified 71.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+252}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-7} \lor \neg \left(y \leq 6 \cdot 10^{+72}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e-7) (not (<= y 6e+72)))
   (* (- z x) (/ y t))
   (+ x (/ (* z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-7) || !(y <= 6e+72)) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.5d-7)) .or. (.not. (y <= 6d+72))) then
        tmp = (z - x) * (y / t)
    else
        tmp = x + ((z * y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-7) || !(y <= 6e+72)) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e-7) or not (y <= 6e+72):
		tmp = (z - x) * (y / t)
	else:
		tmp = x + ((z * y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e-7) || !(y <= 6e+72))
		tmp = Float64(Float64(z - x) * Float64(y / t));
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.5e-7) || ~((y <= 6e+72)))
		tmp = (z - x) * (y / t);
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e-7], N[Not[LessEqual[y, 6e+72]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000024e-7 or 6.00000000000000006e72 < y

   1. Initial program 87.1%

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

   3. Taylor expanded in y around -inf 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-/l* 89.4%

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

   5. Applied egg-rr 89.4%

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

   if -6.50000000000000024e-7 < y < 6.00000000000000006e72

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 88.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-7} \lor \neg \left(y \leq 6 \cdot 10^{+72}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-79} \lor \neg \left(z \leq 2.6 \cdot 10^{-96}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.5e-79) (not (<= z 2.6e-96)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e-79) || !(z <= 2.6e-96)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.5d-79)) .or. (.not. (z <= 2.6d-96))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e-79) || !(z <= 2.6e-96)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.5e-79) or not (z <= 2.6e-96):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.5e-79) || !(z <= 2.6e-96))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.5e-79) || ~((z <= 2.6e-96)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.5e-79], N[Not[LessEqual[z, 2.6e-96]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000003e-79 or 2.6000000000000002e-96 < z

   1. Initial program 92.2%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. associate-/l* 86.1%

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

   5. Simplified 86.1%

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

   if -3.5000000000000003e-79 < z < 2.6000000000000002e-96

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 92.2%

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

      1. mul-1-neg 92.2%

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

      2. unsub-neg 92.2%

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

   5. Simplified 92.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-79} \lor \neg \left(z \leq 2.6 \cdot 10^{-96}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-42} \lor \neg \left(y \leq 4.5 \cdot 10^{+66}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.9e-42) (not (<= y 4.5e+66)))
   (* (- z x) (/ y t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e-42) || !(y <= 4.5e+66)) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.9d-42)) .or. (.not. (y <= 4.5d+66))) then
        tmp = (z - x) * (y / t)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e-42) || !(y <= 4.5e+66)) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.9e-42) or not (y <= 4.5e+66):
		tmp = (z - x) * (y / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.9e-42) || !(y <= 4.5e+66))
		tmp = Float64(Float64(z - x) * Float64(y / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.9e-42) || ~((y <= 4.5e+66)))
		tmp = (z - x) * (y / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.9e-42], N[Not[LessEqual[y, 4.5e+66]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000003e-42 or 4.4999999999999998e66 < y

   1. Initial program 88.0%

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

   3. Taylor expanded in y around -inf 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-/l* 87.8%

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

   5. Applied egg-rr 87.8%

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

   if -2.9000000000000003e-42 < y < 4.4999999999999998e66

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

   5. Simplified 81.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-42} \lor \neg \left(y \leq 4.5 \cdot 10^{+66}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e-7)
   (/ y (/ t (- z x)))
   (if (<= y 5.2e+72) (+ x (/ (* z y) t)) (* (- z x) (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-7) {
		tmp = y / (t / (z - x));
	} else if (y <= 5.2e+72) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = (z - x) * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.5d-7)) then
        tmp = y / (t / (z - x))
    else if (y <= 5.2d+72) then
        tmp = x + ((z * y) / t)
    else
        tmp = (z - x) * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-7) {
		tmp = y / (t / (z - x));
	} else if (y <= 5.2e+72) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = (z - x) * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e-7:
		tmp = y / (t / (z - x))
	elif y <= 5.2e+72:
		tmp = x + ((z * y) / t)
	else:
		tmp = (z - x) * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e-7)
		tmp = Float64(y / Float64(t / Float64(z - x)));
	elseif (y <= 5.2e+72)
		tmp = Float64(x + Float64(Float64(z * y) / t));
	else
		tmp = Float64(Float64(z - x) * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.5e-7)
		tmp = y / (t / (z - x));
	elseif (y <= 5.2e+72)
		tmp = x + ((z * y) / t);
	else
		tmp = (z - x) * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e-7], N[(y / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+72], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.50000000000000024e-7

   1. Initial program 90.2%

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

   3. Taylor expanded in y around -inf 77.7%

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

      1. associate-/l* 99.8%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.7%

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

   5. Applied egg-rr 85.9%

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

   if -6.50000000000000024e-7 < y < 5.19999999999999963e72

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 88.8%

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

   if 5.19999999999999963e72 < y

   1. Initial program 82.9%

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

   3. Taylor expanded in y around -inf 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-/l* 96.0%

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

   5. Applied egg-rr 96.0%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.1e+161)
   (* y (/ z t))
   (if (<= z 4e+149) (* x (- 1.0 (/ y t))) (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.1e+161) {
		tmp = y * (z / t);
	} else if (z <= 4e+149) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.1d+161)) then
        tmp = y * (z / t)
    else if (z <= 4d+149) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.1e+161) {
		tmp = y * (z / t);
	} else if (z <= 4e+149) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.1e+161:
		tmp = y * (z / t)
	elif z <= 4e+149:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.1e+161)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 4e+149)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.1e+161)
		tmp = y * (z / t);
	elseif (z <= 4e+149)
		tmp = x * (1.0 - (y / t));
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.1e+161], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+149], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0999999999999997e161

   1. Initial program 87.0%

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

   3. Taylor expanded in y around inf 76.4%

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

   4. Taylor expanded in z around inf 76.6%

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

   if -7.0999999999999997e161 < z < 4.0000000000000002e149

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

   5. Simplified 81.3%

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

   if 4.0000000000000002e149 < z

   1. Initial program 86.1%

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

   3. Taylor expanded in y around -inf 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-/l* 77.4%

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

   5. Applied egg-rr 77.4%

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

   6. Taylor expanded in z around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-*r/ 70.9%

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

   8. Simplified 70.9%

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

Alternative 9: 55.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-42} \lor \neg \left(y \leq 4.6 \cdot 10^{+67}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e-42) (not (<= y 4.6e+67))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e-42) || !(y <= 4.6e+67)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.3d-42)) .or. (.not. (y <= 4.6d+67))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e-42) || !(y <= 4.6e+67)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.3e-42) or not (y <= 4.6e+67):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.3e-42) || !(y <= 4.6e+67))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.3e-42) || ~((y <= 4.6e+67)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.3e-42], N[Not[LessEqual[y, 4.6e+67]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-42 or 4.5999999999999997e67 < y

   1. Initial program 87.9%

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

   3. Taylor expanded in y around -inf 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-/l* 87.7%

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

   5. Applied egg-rr 87.7%

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

   6. Taylor expanded in z around inf 48.3%

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

      1. *-commutative 48.3%

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

      2. associate-*r/ 57.7%

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

   8. Simplified 57.7%

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

   if -1.3e-42 < y < 4.5999999999999997e67

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 72.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-42} \lor \neg \left(y \leq 4.6 \cdot 10^{+67}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-40} \lor \neg \left(y \leq 3.85 \cdot 10^{+67}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.52e-40) (not (<= y 3.85e+67))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.52e-40) || !(y <= 3.85e+67)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.52d-40)) .or. (.not. (y <= 3.85d+67))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.52e-40) || !(y <= 3.85e+67)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.52e-40) or not (y <= 3.85e+67):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.52e-40) || !(y <= 3.85e+67))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.52e-40) || ~((y <= 3.85e+67)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.52e-40], N[Not[LessEqual[y, 3.85e+67]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.51999999999999992e-40 or 3.8500000000000001e67 < y

   1. Initial program 87.9%

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

   3. Taylor expanded in y around inf 85.4%

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

   4. Taylor expanded in z around inf 54.3%

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

   if -1.51999999999999992e-40 < y < 3.8500000000000001e67

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 72.1%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-40} \lor \neg \left(y \leq 3.85 \cdot 10^{+67}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-42}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e-42) (/ z (/ t y)) (if (<= y 5.2e+67) x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e-42) {
		tmp = z / (t / y);
	} else if (y <= 5.2e+67) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.7d-42)) then
        tmp = z / (t / y)
    else if (y <= 5.2d+67) then
        tmp = x
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e-42) {
		tmp = z / (t / y);
	} else if (y <= 5.2e+67) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e-42:
		tmp = z / (t / y)
	elif y <= 5.2e+67:
		tmp = x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e-42)
		tmp = Float64(z / Float64(t / y));
	elseif (y <= 5.2e+67)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.7e-42)
		tmp = z / (t / y);
	elseif (y <= 5.2e+67)
		tmp = x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e-42], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+67], x, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7000000000000002e-42

   1. Initial program 91.0%

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

   3. Taylor expanded in y around -inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/l* 83.1%

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

   5. Applied egg-rr 83.1%

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

   6. Taylor expanded in z around inf 44.9%

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

      1. *-commutative 44.9%

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

      2. associate-*r/ 53.2%

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

   8. Simplified 53.2%

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

      1. clear-num 53.2%

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

      2. un-div-inv 53.3%

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

   10. Applied egg-rr 53.3%

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

   if -3.7000000000000002e-42 < y < 5.2000000000000001e67

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 72.1%

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

   if 5.2000000000000001e67 < y

   1. Initial program 83.6%

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

   3. Taylor expanded in y around -inf 79.9%

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

      1. *-commutative 79.9%

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

      2. associate-/l* 94.3%

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

   5. Applied egg-rr 94.3%

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

   6. Taylor expanded in z around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-*r/ 64.0%

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

   8. Simplified 64.0%

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

Alternative 12: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - x) * (y / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. +-commutative 92.9%

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

   2. *-commutative 92.9%

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

   3. associate-/l* 98.7%

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

4. Applied egg-rr 98.7%

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

5. Final simplification 98.7%

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

Alternative 13: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + (y / (t / (z - 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 + (y / (t / (z - x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-/l* 95.0%

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

   2. clear-num 95.0%

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

   3. un-div-inv 95.2%

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

4. Applied egg-rr 95.2%

   \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z - x}}} \]
5. Add Preprocessing

Alternative 14: 38.5% accurate, 9.0× 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 92.9%

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

3. Taylor expanded in y around 0 43.1%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 91.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

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 - ((x * (y / t)) + (-z * (y / t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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