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

Percentage Accurate: 93.2% → 98.7%

Time: 9.5s

Alternatives: 16

Speedup: 1.0×

• 24.4% 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: 93.2% 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: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z x)) t))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (- z x) (/ y t)))
     (if (<= t_1 5e+278) t_1 (+ x (* y (/ (- z x) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - x) * (y / t));
	} else if (t_1 <= 5e+278) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z - x) / t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((z - x) * (y / t));
	} else if (t_1 <= 5e+278) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * (z - x)) / t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((z - x) * (y / t))
	elif t_1 <= 5e+278:
		tmp = t_1
	else:
		tmp = x + (y * ((z - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - x) * Float64(y / t)));
	elseif (t_1 <= 5e+278)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * (z - x)) / t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((z - x) * (y / t));
	elseif (t_1 <= 5e+278)
		tmp = t_1;
	else
		tmp = x + (y * ((z - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+278], t$95$1, N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 74.8%

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

   3. Taylor expanded in z around 0 54.2%

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

      1. +-commutative 54.2%

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

      2. *-commutative 54.2%

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

      3. associate-*r/ 57.3%

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

      4. mul-1-neg 57.3%

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

      5. associate-/l* 76.6%

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

      6. distribute-lft-neg-in 76.6%

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

      7. distribute-rgt-in 99.9%

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

      8. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 5.00000000000000029e278

   1. Initial program 99.3%

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

   if 5.00000000000000029e278 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 5 \cdot 10^{+278}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z x)) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+303)))
     (+ x (* (- z x) (/ y t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+303)) {
		tmp = x + ((z - x) * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+303)) {
		tmp = x + ((z - x) * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * (z - x)) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+303):
		tmp = x + ((z - x) * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+303))
		tmp = Float64(x + Float64(Float64(z - x) * Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * (z - x)) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+303)))
		tmp = x + ((z - x) * (y / 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 * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+303]], $MachinePrecision]], N[(x + N[(N[(z - x), $MachinePrecision] * N[(y / t), $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 4.9999999999999997e303 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 74.7%

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

   3. Taylor expanded in z around 0 57.5%

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

      1. +-commutative 57.5%

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

      2. *-commutative 57.5%

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

      3. associate-*r/ 64.0%

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

      4. mul-1-neg 64.0%

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

      5. associate-/l* 74.6%

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

      6. distribute-lft-neg-in 74.6%

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

      7. distribute-rgt-in 99.9%

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

      8. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 4.9999999999999997e303

   1. Initial program 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+303}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z x)) t))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (- z x) (/ y t)))
     (if (<= t_1 5e+303) t_1 (+ x (/ (- z x) (/ t y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - x) * (y / t));
	} else if (t_1 <= 5e+303) {
		tmp = t_1;
	} else {
		tmp = x + ((z - x) / (t / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((z - x) * (y / t));
	} else if (t_1 <= 5e+303) {
		tmp = t_1;
	} else {
		tmp = x + ((z - x) / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * (z - x)) / t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((z - x) * (y / t))
	elif t_1 <= 5e+303:
		tmp = t_1
	else:
		tmp = x + ((z - x) / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - x) * Float64(y / t)));
	elseif (t_1 <= 5e+303)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - x) / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * (z - x)) / t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((z - x) * (y / t));
	elseif (t_1 <= 5e+303)
		tmp = t_1;
	else
		tmp = x + ((z - x) / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+303], t$95$1, N[(x + N[(N[(z - x), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 74.8%

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

   3. Taylor expanded in z around 0 54.2%

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

      1. +-commutative 54.2%

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

      2. *-commutative 54.2%

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

      3. associate-*r/ 57.3%

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

      4. mul-1-neg 57.3%

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

      5. associate-/l* 76.6%

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

      6. distribute-lft-neg-in 76.6%

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

      7. distribute-rgt-in 99.9%

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

      8. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 4.9999999999999997e303

   1. Initial program 99.4%

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

   if 4.9999999999999997e303 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 74.6%

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

   3. Taylor expanded in z around 0 60.0%

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

      1. +-commutative 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-*r/ 69.0%

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

      4. mul-1-neg 69.0%

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

      5. associate-/l* 73.1%

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

      6. distribute-lft-neg-in 73.1%

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

      7. distribute-rgt-in 99.9%

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

      8. sub-neg 99.9%

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

   5. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 5 \cdot 10^{+303}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+140} \lor \neg \left(x \leq -3.6 \cdot 10^{+31} \lor \neg \left(x \leq -1.25 \cdot 10^{+18}\right) \land x \leq 1.95 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.2e+140)
         (not
          (or (<= x -3.6e+31) (and (not (<= x -1.25e+18)) (<= x 1.95e+51)))))
   (* x (- 1.0 (/ y t)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.2e+140) || !((x <= -3.6e+31) || (!(x <= -1.25e+18) && (x <= 1.95e+51)))) {
		tmp = x * (1.0 - (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 ((x <= (-6.2d+140)) .or. (.not. (x <= (-3.6d+31)) .or. (.not. (x <= (-1.25d+18))) .and. (x <= 1.95d+51))) then
        tmp = x * (1.0d0 - (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 ((x <= -6.2e+140) || !((x <= -3.6e+31) || (!(x <= -1.25e+18) && (x <= 1.95e+51)))) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.2e+140) or not ((x <= -3.6e+31) or (not (x <= -1.25e+18) and (x <= 1.95e+51))):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.2e+140) || !((x <= -3.6e+31) || (!(x <= -1.25e+18) && (x <= 1.95e+51))))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6.2e+140) || ~(((x <= -3.6e+31) || (~((x <= -1.25e+18)) && (x <= 1.95e+51)))))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.2e+140], N[Not[Or[LessEqual[x, -3.6e+31], And[N[Not[LessEqual[x, -1.25e+18]], $MachinePrecision], LessEqual[x, 1.95e+51]]]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000001e140 or -3.59999999999999996e31 < x < -1.25e18 or 1.94999999999999992e51 < x

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 92.4%

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

      1. mul-1-neg 92.4%

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

      2. unsub-neg 92.4%

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

   5. Simplified 92.4%

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

   if -6.2000000000000001e140 < x < -3.59999999999999996e31 or -1.25e18 < x < 1.94999999999999992e51

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 87.4%

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

      1. associate-/l* 49.3%

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

   5. Simplified 86.8%

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

      1. clear-num 48.7%

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

      2. un-div-inv 50.4%

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

   7. Applied egg-rr 87.8%

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

      1. associate-/r/ 52.5%

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

   9. Applied egg-rr 90.2%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+140} \lor \neg \left(x \leq -3.6 \cdot 10^{+31} \lor \neg \left(x \leq -1.25 \cdot 10^{+18}\right) \land x \leq 1.95 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+235}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+223} \lor \neg \left(z \leq -9.5 \cdot 10^{+78}\right) \land z \leq 6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e+235)
   (* y (/ z t))
   (if (or (<= z -2.35e+223) (and (not (<= z -9.5e+78)) (<= z 6e-26)))
     (* x (- 1.0 (/ y t)))
     (* (- z x) (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+235) {
		tmp = y * (z / t);
	} else if ((z <= -2.35e+223) || (!(z <= -9.5e+78) && (z <= 6e-26))) {
		tmp = x * (1.0 - (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 (z <= (-4.8d+235)) then
        tmp = y * (z / t)
    else if ((z <= (-2.35d+223)) .or. (.not. (z <= (-9.5d+78))) .and. (z <= 6d-26)) then
        tmp = x * (1.0d0 - (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 (z <= -4.8e+235) {
		tmp = y * (z / t);
	} else if ((z <= -2.35e+223) || (!(z <= -9.5e+78) && (z <= 6e-26))) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (z - x) * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e+235:
		tmp = y * (z / t)
	elif (z <= -2.35e+223) or (not (z <= -9.5e+78) and (z <= 6e-26)):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (z - x) * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e+235)
		tmp = Float64(y * Float64(z / t));
	elseif ((z <= -2.35e+223) || (!(z <= -9.5e+78) && (z <= 6e-26)))
		tmp = Float64(x * Float64(1.0 - Float64(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 (z <= -4.8e+235)
		tmp = y * (z / t);
	elseif ((z <= -2.35e+223) || (~((z <= -9.5e+78)) && (z <= 6e-26)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (z - x) * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e+235], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.35e+223], And[N[Not[LessEqual[z, -9.5e+78]], $MachinePrecision], LessEqual[z, 6e-26]]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999998e235

   1. Initial program 87.3%

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

   3. Taylor expanded in y around -inf 61.6%

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

   4. Taylor expanded in z around inf 54.9%

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

      1. associate-/l* 67.6%

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

   6. Simplified 67.6%

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

   if -4.7999999999999998e235 < z < -2.35000000000000021e223 or -9.5000000000000006e78 < z < 6.00000000000000023e-26

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

   5. Simplified 82.6%

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

   if -2.35000000000000021e223 < z < -9.5000000000000006e78 or 6.00000000000000023e-26 < z

   1. Initial program 92.3%

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

   3. Taylor expanded in y around -inf 70.9%

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

   4. Taylor expanded in z around 0 64.6%

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

      1. +-commutative 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-*r/ 91.7%

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

      4. mul-1-neg 91.7%

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

      5. associate-/l* 89.5%

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

      6. distribute-lft-neg-in 89.5%

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

      7. distribute-rgt-in 99.7%

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

      8. sub-neg 99.7%

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

   6. Simplified 78.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+235}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+223} \lor \neg \left(z \leq -9.5 \cdot 10^{+78}\right) \land z \leq 6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+234}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))))
   (if (<= z -1.12e+234)
     (* y (/ z t))
     (if (<= z -2.45e+177)
       t_1
       (if (<= z -2.3e+96)
         (/ (* y z) t)
         (if (<= z 1.32e+107) t_1 (* z (/ y t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (z <= -1.12e+234) {
		tmp = y * (z / t);
	} else if (z <= -2.45e+177) {
		tmp = t_1;
	} else if (z <= -2.3e+96) {
		tmp = (y * z) / t;
	} else if (z <= 1.32e+107) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    if (z <= (-1.12d+234)) then
        tmp = y * (z / t)
    else if (z <= (-2.45d+177)) then
        tmp = t_1
    else if (z <= (-2.3d+96)) then
        tmp = (y * z) / t
    else if (z <= 1.32d+107) then
        tmp = t_1
    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 t_1 = x * (1.0 - (y / t));
	double tmp;
	if (z <= -1.12e+234) {
		tmp = y * (z / t);
	} else if (z <= -2.45e+177) {
		tmp = t_1;
	} else if (z <= -2.3e+96) {
		tmp = (y * z) / t;
	} else if (z <= 1.32e+107) {
		tmp = t_1;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if z <= -1.12e+234:
		tmp = y * (z / t)
	elif z <= -2.45e+177:
		tmp = t_1
	elif z <= -2.3e+96:
		tmp = (y * z) / t
	elif z <= 1.32e+107:
		tmp = t_1
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (z <= -1.12e+234)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= -2.45e+177)
		tmp = t_1;
	elseif (z <= -2.3e+96)
		tmp = Float64(Float64(y * z) / t);
	elseif (z <= 1.32e+107)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (z <= -1.12e+234)
		tmp = y * (z / t);
	elseif (z <= -2.45e+177)
		tmp = t_1;
	elseif (z <= -2.3e+96)
		tmp = (y * z) / t;
	elseif (z <= 1.32e+107)
		tmp = t_1;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+234], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.45e+177], t$95$1, If[LessEqual[z, -2.3e+96], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.32e+107], t$95$1, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.12000000000000004e234

   1. Initial program 87.3%

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

   3. Taylor expanded in y around -inf 61.6%

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

   4. Taylor expanded in z around inf 54.9%

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

      1. associate-/l* 67.6%

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

   6. Simplified 67.6%

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

   if -1.12000000000000004e234 < z < -2.4500000000000001e177 or -2.30000000000000015e96 < z < 1.32000000000000003e107

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. unsub-neg 77.0%

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

   5. Simplified 77.0%

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

   if -2.4500000000000001e177 < z < -2.30000000000000015e96

   1. Initial program 99.8%

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

   3. Taylor expanded in y around -inf 93.7%

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

   4. Taylor expanded in z around inf 87.4%

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

   if 1.32000000000000003e107 < z

   1. Initial program 86.7%

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

   3. Taylor expanded in y around -inf 68.4%

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

   4. Taylor expanded in z around inf 68.2%

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

      1. associate-/l* 63.7%

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

   6. Simplified 63.7%

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

      1. clear-num 63.8%

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

      2. un-div-inv 66.0%

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

   8. Applied egg-rr 66.0%

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

      1. associate-/r/ 79.1%

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

   10. Applied egg-rr 79.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+234}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-295}:\\ \;\;\;\;\frac{-x \cdot y}{t}\\ \mathbf{elif}\;t \leq 1750000:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.8e+67)
   x
   (if (<= t -7.8e-60)
     (/ y (/ t z))
     (if (<= t -4.4e-295)
       (/ (- (* x y)) t)
       (if (<= t 1750000.0) (/ (* y z) t) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.8e+67) {
		tmp = x;
	} else if (t <= -7.8e-60) {
		tmp = y / (t / z);
	} else if (t <= -4.4e-295) {
		tmp = -(x * y) / t;
	} else if (t <= 1750000.0) {
		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 (t <= (-6.8d+67)) then
        tmp = x
    else if (t <= (-7.8d-60)) then
        tmp = y / (t / z)
    else if (t <= (-4.4d-295)) then
        tmp = -(x * y) / t
    else if (t <= 1750000.0d0) 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 (t <= -6.8e+67) {
		tmp = x;
	} else if (t <= -7.8e-60) {
		tmp = y / (t / z);
	} else if (t <= -4.4e-295) {
		tmp = -(x * y) / t;
	} else if (t <= 1750000.0) {
		tmp = (y * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.8e+67:
		tmp = x
	elif t <= -7.8e-60:
		tmp = y / (t / z)
	elif t <= -4.4e-295:
		tmp = -(x * y) / t
	elif t <= 1750000.0:
		tmp = (y * z) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.8e+67)
		tmp = x;
	elseif (t <= -7.8e-60)
		tmp = Float64(y / Float64(t / z));
	elseif (t <= -4.4e-295)
		tmp = Float64(Float64(-Float64(x * y)) / t);
	elseif (t <= 1750000.0)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.8e+67)
		tmp = x;
	elseif (t <= -7.8e-60)
		tmp = y / (t / z);
	elseif (t <= -4.4e-295)
		tmp = -(x * y) / t;
	elseif (t <= 1750000.0)
		tmp = (y * z) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.8e+67], x, If[LessEqual[t, -7.8e-60], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e-295], N[((-N[(x * y), $MachinePrecision]) / t), $MachinePrecision], If[LessEqual[t, 1750000.0], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.8000000000000003e67 or 1.75e6 < t

   1. Initial program 86.5%

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

   3. Taylor expanded in y around 0 65.1%

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

   if -6.8000000000000003e67 < t < -7.8000000000000004e-60

   1. Initial program 96.3%

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

   3. Taylor expanded in y around -inf 65.2%

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

   4. Taylor expanded in z around inf 49.2%

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

      1. associate-/l* 52.6%

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

   6. Simplified 52.6%

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

      1. clear-num 52.5%

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

      2. un-div-inv 52.8%

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

   8. Applied egg-rr 52.8%

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

   if -7.8000000000000004e-60 < t < -4.4000000000000004e-295

   1. Initial program 97.7%

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

   3. Taylor expanded in y around -inf 84.4%

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

   4. Taylor expanded in z around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-lft-neg-out 56.4%

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

      3. *-commutative 56.4%

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

   6. Simplified 56.4%

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

   if -4.4000000000000004e-295 < t < 1.75e6

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 88.2%

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

   4. Taylor expanded in z around inf 61.3%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-295}:\\ \;\;\;\;\frac{-x \cdot y}{t}\\ \mathbf{elif}\;t \leq 1750000:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ \mathbf{if}\;y \leq -18000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))))
   (if (<= y -18000000.0)
     t_1
     (if (<= y 3.2e-32) x (if (<= y 1.25e+192) t_1 (* x (/ y (- t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (y <= -18000000.0) {
		tmp = t_1;
	} else if (y <= 3.2e-32) {
		tmp = x;
	} else if (y <= 1.25e+192) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = z * (y / t)
    if (y <= (-18000000.0d0)) then
        tmp = t_1
    else if (y <= 3.2d-32) then
        tmp = x
    else if (y <= 1.25d+192) then
        tmp = t_1
    else
        tmp = x * (y / -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (y <= -18000000.0) {
		tmp = t_1;
	} else if (y <= 3.2e-32) {
		tmp = x;
	} else if (y <= 1.25e+192) {
		tmp = t_1;
	} else {
		tmp = x * (y / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	tmp = 0
	if y <= -18000000.0:
		tmp = t_1
	elif y <= 3.2e-32:
		tmp = x
	elif y <= 1.25e+192:
		tmp = t_1
	else:
		tmp = x * (y / -t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (y <= -18000000.0)
		tmp = t_1;
	elseif (y <= 3.2e-32)
		tmp = x;
	elseif (y <= 1.25e+192)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	tmp = 0.0;
	if (y <= -18000000.0)
		tmp = t_1;
	elseif (y <= 3.2e-32)
		tmp = x;
	elseif (y <= 1.25e+192)
		tmp = t_1;
	else
		tmp = x * (y / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -18000000.0], t$95$1, If[LessEqual[y, 3.2e-32], x, If[LessEqual[y, 1.25e+192], t$95$1, N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e7 or 3.2000000000000002e-32 < y < 1.25000000000000008e192

   1. Initial program 87.7%

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

   3. Taylor expanded in y around -inf 71.4%

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

   4. Taylor expanded in z around inf 47.6%

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

      1. associate-/l* 52.6%

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

   6. Simplified 52.6%

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

      1. clear-num 51.8%

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

      2. un-div-inv 51.8%

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

   8. Applied egg-rr 51.8%

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

      1. associate-/r/ 54.0%

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

   10. Applied egg-rr 54.0%

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

   if -1.8e7 < y < 3.2000000000000002e-32

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 65.8%

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

   if 1.25000000000000008e192 < y

   1. Initial program 82.7%

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

   3. Taylor expanded in y around -inf 74.1%

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

   4. Taylor expanded in z around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 57.1%

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

      3. distribute-rgt-neg-in 57.1%

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

      4. mul-1-neg 57.1%

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

      5. associate-*r/ 57.1%

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

      6. mul-1-neg 57.1%

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

   6. Simplified 57.1%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -18000000:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+192}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ \mathbf{if}\;y \leq -21000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))))
   (if (<= y -21000000.0)
     t_1
     (if (<= y 1.3e-44) x (if (<= y 7.8e+191) t_1 (/ x (/ t (- y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (y <= -21000000.0) {
		tmp = t_1;
	} else if (y <= 1.3e-44) {
		tmp = x;
	} else if (y <= 7.8e+191) {
		tmp = t_1;
	} else {
		tmp = x / (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) :: t_1
    real(8) :: tmp
    t_1 = z * (y / t)
    if (y <= (-21000000.0d0)) then
        tmp = t_1
    else if (y <= 1.3d-44) then
        tmp = x
    else if (y <= 7.8d+191) then
        tmp = t_1
    else
        tmp = x / (t / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (y <= -21000000.0) {
		tmp = t_1;
	} else if (y <= 1.3e-44) {
		tmp = x;
	} else if (y <= 7.8e+191) {
		tmp = t_1;
	} else {
		tmp = x / (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	tmp = 0
	if y <= -21000000.0:
		tmp = t_1
	elif y <= 1.3e-44:
		tmp = x
	elif y <= 7.8e+191:
		tmp = t_1
	else:
		tmp = x / (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (y <= -21000000.0)
		tmp = t_1;
	elseif (y <= 1.3e-44)
		tmp = x;
	elseif (y <= 7.8e+191)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	tmp = 0.0;
	if (y <= -21000000.0)
		tmp = t_1;
	elseif (y <= 1.3e-44)
		tmp = x;
	elseif (y <= 7.8e+191)
		tmp = t_1;
	else
		tmp = x / (t / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -21000000.0], t$95$1, If[LessEqual[y, 1.3e-44], x, If[LessEqual[y, 7.8e+191], t$95$1, N[(x / N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1e7 or 1.2999999999999999e-44 < y < 7.8000000000000001e191

   1. Initial program 87.7%

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

   3. Taylor expanded in y around -inf 71.4%

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

   4. Taylor expanded in z around inf 47.6%

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

      1. associate-/l* 52.6%

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

   6. Simplified 52.6%

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

      1. clear-num 51.8%

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

      2. un-div-inv 51.8%

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

   8. Applied egg-rr 51.8%

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

      1. associate-/r/ 54.0%

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

   10. Applied egg-rr 54.0%

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

   if -2.1e7 < y < 1.2999999999999999e-44

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 65.8%

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

   if 7.8000000000000001e191 < y

   1. Initial program 82.7%

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

   3. Taylor expanded in y around -inf 74.1%

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

   4. Taylor expanded in z around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 57.1%

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

      3. distribute-rgt-neg-in 57.1%

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

      4. mul-1-neg 57.1%

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

      5. associate-*r/ 57.1%

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

      6. mul-1-neg 57.1%

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

   6. Simplified 57.1%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 5.9%

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

      3. sqr-neg 5.9%

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

      4. sqrt-unprod 6.4%

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

      5. add-sqr-sqrt 6.4%

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

      6. clear-num 6.4%

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

      7. div-inv 6.4%

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

      8. frac-2neg 6.4%

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

      9. distribute-frac-neg2 6.4%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 38.1%

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

      12. sqr-neg 38.1%

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

      13. sqrt-unprod 57.1%

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

      14. add-sqr-sqrt 57.2%

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

   8. Applied egg-rr 57.2%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000000:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+191}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -18000000 \lor \neg \left(y \leq 3.3 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -18000000.0) (not (<= y 3.3e-33)))
   (* y (/ (- z x) t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -18000000.0) || !(y <= 3.3e-33)) {
		tmp = y * ((z - x) / 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 <= (-18000000.0d0)) .or. (.not. (y <= 3.3d-33))) then
        tmp = y * ((z - x) / 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 <= -18000000.0) || !(y <= 3.3e-33)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -18000000.0) or not (y <= 3.3e-33):
		tmp = y * ((z - x) / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -18000000.0) || !(y <= 3.3e-33))
		tmp = Float64(y * Float64(Float64(z - x) / 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 <= -18000000.0) || ~((y <= 3.3e-33)))
		tmp = y * ((z - x) / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -18000000.0], N[Not[LessEqual[y, 3.3e-33]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e7 or 3.3000000000000003e-33 < y

   1. Initial program 86.9%

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

   3. Taylor expanded in y around -inf 71.8%

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

      1. associate-/l* 80.3%

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

      2. *-commutative 80.3%

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

   5. Applied egg-rr 80.3%

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

   if -1.8e7 < y < 3.3000000000000003e-33

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -18000000 \lor \neg \left(y \leq 3.3 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+15} \lor \neg \left(x \leq 6.5 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.05e+15) (not (<= x 6.5e+48)))
   (* x (- 1.0 (/ y t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.05e+15) || !(x <= 6.5e+48)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.05d+15)) .or. (.not. (x <= 6.5d+48))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.05e+15) || !(x <= 6.5e+48)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.05e+15) or not (x <= 6.5e+48):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.05e+15) || !(x <= 6.5e+48))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.05e+15) || ~((x <= 6.5e+48)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.05e+15], N[Not[LessEqual[x, 6.5e+48]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.05e15 or 6.49999999999999972e48 < x

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf 88.9%

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

      1. mul-1-neg 88.9%

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

      2. unsub-neg 88.9%

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

   5. Simplified 88.9%

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

   if -3.05e15 < x < 6.49999999999999972e48

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 86.7%

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

      1. associate-/l* 52.8%

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

   5. Simplified 85.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+15} \lor \neg \left(x \leq 6.5 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 54:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.2e-59)
   (+ x (* y (/ z t)))
   (if (<= t 54.0) (/ (* y (- z x)) t) (+ x (* z (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.2e-59) {
		tmp = x + (y * (z / t));
	} else if (t <= 54.0) {
		tmp = (y * (z - x)) / 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 (t <= (-6.2d-59)) then
        tmp = x + (y * (z / t))
    else if (t <= 54.0d0) then
        tmp = (y * (z - x)) / 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 (t <= -6.2e-59) {
		tmp = x + (y * (z / t));
	} else if (t <= 54.0) {
		tmp = (y * (z - x)) / t;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.2e-59:
		tmp = x + (y * (z / t))
	elif t <= 54.0:
		tmp = (y * (z - x)) / t
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.2e-59)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 54.0)
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.2e-59)
		tmp = x + (y * (z / t));
	elseif (t <= 54.0)
		tmp = (y * (z - x)) / t;
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.2e-59], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 54.0], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.19999999999999998e-59

   1. Initial program 85.2%

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

   3. Taylor expanded in z around inf 80.6%

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

      1. associate-/l* 35.3%

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

   5. Simplified 84.9%

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

   if -6.19999999999999998e-59 < t < 54

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 86.7%

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

   if 54 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate-/l* 26.2%

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

   5. Simplified 93.7%

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

      1. clear-num 26.1%

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

      2. un-div-inv 26.1%

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

   7. Applied egg-rr 93.7%

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

      1. associate-/r/ 26.9%

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

   9. Applied egg-rr 95.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 54:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -21000000 \lor \neg \left(y \leq 3.8 \cdot 10^{-44}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -21000000.0) (not (<= y 3.8e-44))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -21000000.0) || !(y <= 3.8e-44)) {
		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 <= (-21000000.0d0)) .or. (.not. (y <= 3.8d-44))) 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 <= -21000000.0) || !(y <= 3.8e-44)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -21000000.0) or not (y <= 3.8e-44):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -21000000.0) || !(y <= 3.8e-44))
		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 <= -21000000.0) || ~((y <= 3.8e-44)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -21000000.0], N[Not[LessEqual[y, 3.8e-44]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.1e7 or 3.8000000000000001e-44 < y

   1. Initial program 86.9%

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

   3. Taylor expanded in y around -inf 71.8%

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

   4. Taylor expanded in z around inf 44.7%

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

      1. associate-/l* 50.3%

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

   6. Simplified 50.3%

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

   if -2.1e7 < y < 3.8000000000000001e-44

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 65.8%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000000 \lor \neg \left(y \leq 3.8 \cdot 10^{-44}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -21000000 \lor \neg \left(y \leq 4.6 \cdot 10^{-39}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -21000000.0) (not (<= y 4.6e-39))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -21000000.0) || !(y <= 4.6e-39)) {
		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 <= (-21000000.0d0)) .or. (.not. (y <= 4.6d-39))) 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 <= -21000000.0) || !(y <= 4.6e-39)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -21000000.0) or not (y <= 4.6e-39):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -21000000.0) || !(y <= 4.6e-39))
		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 <= -21000000.0) || ~((y <= 4.6e-39)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -21000000.0], N[Not[LessEqual[y, 4.6e-39]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.1e7 or 4.60000000000000016e-39 < y

   1. Initial program 86.9%

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

   3. Taylor expanded in y around -inf 71.8%

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

   4. Taylor expanded in z around inf 44.7%

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

      1. associate-/l* 50.3%

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

   6. Simplified 50.3%

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

      1. clear-num 49.7%

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

      2. un-div-inv 49.7%

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

   8. Applied egg-rr 49.7%

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

      1. associate-/r/ 51.6%

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

   10. Applied egg-rr 51.6%

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

   if -2.1e7 < y < 4.60000000000000016e-39

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 65.8%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000000 \lor \neg \left(y \leq 4.6 \cdot 10^{-39}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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 92.5%

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

3. Taylor expanded in z around 0 87.8%

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

   1. +-commutative 87.8%

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

   2. *-commutative 87.8%

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

   3. associate-*r/ 86.6%

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

   4. mul-1-neg 86.6%

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

   5. associate-/l* 89.4%

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

   6. distribute-lft-neg-in 89.4%

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

   7. distribute-rgt-in 96.6%

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

   8. sub-neg 96.6%

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

5. Simplified 96.6%

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

6. Final simplification 96.6%

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

Alternative 16: 39.1% 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 92.5%

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

3. Taylor expanded in y around 0 41.3%

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

4. Final simplification 41.3%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 90.9% 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 2024079 
(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)))