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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 13

Speedup: 1.0×

• 26.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 47.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{-0.5}}\\ t_2 := \frac{x \cdot 0.5}{t}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+34} \lor \neg \left(y \leq 4.4 \cdot 10^{+56}\right) \land y \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ t -0.5))) (t_2 (/ (* x 0.5) t)))
   (if (<= y -1.6e-301)
     t_2
     (if (<= y 1.6e-212)
       t_1
       (if (<= y 7.6e-164)
         t_2
         (if (or (<= y 6.5e+34) (and (not (<= y 4.4e+56)) (<= y 1.15e+73)))
           t_1
           (/ y (* t 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (t / -0.5);
	double t_2 = (x * 0.5) / t;
	double tmp;
	if (y <= -1.6e-301) {
		tmp = t_2;
	} else if (y <= 1.6e-212) {
		tmp = t_1;
	} else if (y <= 7.6e-164) {
		tmp = t_2;
	} else if ((y <= 6.5e+34) || (!(y <= 4.4e+56) && (y <= 1.15e+73))) {
		tmp = t_1;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z / (t / (-0.5d0))
    t_2 = (x * 0.5d0) / t
    if (y <= (-1.6d-301)) then
        tmp = t_2
    else if (y <= 1.6d-212) then
        tmp = t_1
    else if (y <= 7.6d-164) then
        tmp = t_2
    else if ((y <= 6.5d+34) .or. (.not. (y <= 4.4d+56)) .and. (y <= 1.15d+73)) then
        tmp = t_1
    else
        tmp = y / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (t / -0.5);
	double t_2 = (x * 0.5) / t;
	double tmp;
	if (y <= -1.6e-301) {
		tmp = t_2;
	} else if (y <= 1.6e-212) {
		tmp = t_1;
	} else if (y <= 7.6e-164) {
		tmp = t_2;
	} else if ((y <= 6.5e+34) || (!(y <= 4.4e+56) && (y <= 1.15e+73))) {
		tmp = t_1;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (t / -0.5)
	t_2 = (x * 0.5) / t
	tmp = 0
	if y <= -1.6e-301:
		tmp = t_2
	elif y <= 1.6e-212:
		tmp = t_1
	elif y <= 7.6e-164:
		tmp = t_2
	elif (y <= 6.5e+34) or (not (y <= 4.4e+56) and (y <= 1.15e+73)):
		tmp = t_1
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(t / -0.5))
	t_2 = Float64(Float64(x * 0.5) / t)
	tmp = 0.0
	if (y <= -1.6e-301)
		tmp = t_2;
	elseif (y <= 1.6e-212)
		tmp = t_1;
	elseif (y <= 7.6e-164)
		tmp = t_2;
	elseif ((y <= 6.5e+34) || (!(y <= 4.4e+56) && (y <= 1.15e+73)))
		tmp = t_1;
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (t / -0.5);
	t_2 = (x * 0.5) / t;
	tmp = 0.0;
	if (y <= -1.6e-301)
		tmp = t_2;
	elseif (y <= 1.6e-212)
		tmp = t_1;
	elseif (y <= 7.6e-164)
		tmp = t_2;
	elseif ((y <= 6.5e+34) || (~((y <= 4.4e+56)) && (y <= 1.15e+73)))
		tmp = t_1;
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[y, -1.6e-301], t$95$2, If[LessEqual[y, 1.6e-212], t$95$1, If[LessEqual[y, 7.6e-164], t$95$2, If[Or[LessEqual[y, 6.5e+34], And[N[Not[LessEqual[y, 4.4e+56]], $MachinePrecision], LessEqual[y, 1.15e+73]]], t$95$1, N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5999999999999999e-301 or 1.5999999999999999e-212 < y < 7.59999999999999979e-164

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.6%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]

   4. Taylor expanded in x around inf 35.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 35.1%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot 0.5} \]

      2. associate-*l/ 35.1%

         \[\leadsto \color{blue}{\frac{x \cdot 0.5}{t}} \]

   6. Simplified 35.1%

      \[\leadsto \color{blue}{\frac{x \cdot 0.5}{t}} \]

   if -1.5999999999999999e-301 < y < 1.5999999999999999e-212 or 7.59999999999999979e-164 < y < 6.50000000000000017e34 or 4.40000000000000032e56 < y < 1.15e73

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.6%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]

   4. Taylor expanded in z around inf 48.4%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 48.4%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot z}{t}} \]

      2. *-commutative 48.4%

         \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

      3. associate-/l* 48.4%

         \[\leadsto \color{blue}{\frac{z}{\frac{t}{-0.5}}} \]

   6. Simplified 48.4%

      \[\leadsto \color{blue}{\frac{z}{\frac{t}{-0.5}}} \]

   if 6.50000000000000017e34 < y < 4.40000000000000032e56 or 1.15e73 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 73.0%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-301}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-164}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+34} \lor \neg \left(y \leq 4.4 \cdot 10^{+56}\right) \land y \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]

Alternative 3: 47.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+35} \lor \neg \left(y \leq 2.4 \cdot 10^{+55}\right) \land y \leq 8.7 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y 1.55e+35) (and (not (<= y 2.4e+55)) (<= y 8.7e+71)))
   (/ z (/ t -0.5))
   (/ y (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 1.55e+35) || (!(y <= 2.4e+55) && (y <= 8.7e+71))) {
		tmp = z / (t / -0.5);
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= 1.55d+35) .or. (.not. (y <= 2.4d+55)) .and. (y <= 8.7d+71)) then
        tmp = z / (t / (-0.5d0))
    else
        tmp = y / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 1.55e+35) || (!(y <= 2.4e+55) && (y <= 8.7e+71))) {
		tmp = z / (t / -0.5);
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= 1.55e+35) or (not (y <= 2.4e+55) and (y <= 8.7e+71)):
		tmp = z / (t / -0.5)
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= 1.55e+35) || (!(y <= 2.4e+55) && (y <= 8.7e+71)))
		tmp = Float64(z / Float64(t / -0.5));
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= 1.55e+35) || (~((y <= 2.4e+55)) && (y <= 8.7e+71)))
		tmp = z / (t / -0.5);
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, 1.55e+35], And[N[Not[LessEqual[y, 2.4e+55]], $MachinePrecision], LessEqual[y, 8.7e+71]]], N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.54999999999999993e35 or 2.3999999999999999e55 < y < 8.6999999999999997e71

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.6%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]

   4. Taylor expanded in z around inf 41.3%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 41.3%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot z}{t}} \]

      2. *-commutative 41.3%

         \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

      3. associate-/l* 41.3%

         \[\leadsto \color{blue}{\frac{z}{\frac{t}{-0.5}}} \]

   6. Simplified 41.3%

      \[\leadsto \color{blue}{\frac{z}{\frac{t}{-0.5}}} \]

   if 1.54999999999999993e35 < y < 2.3999999999999999e55 or 8.6999999999999997e71 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 71.7%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+35} \lor \neg \left(y \leq 2.4 \cdot 10^{+55}\right) \land y \leq 8.7 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]

Alternative 4: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+102} \lor \neg \left(z \leq 1.15 \cdot 10^{+131}\right):\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.5e+102) (not (<= z 1.15e+131)))
   (/ z (/ t -0.5))
   (* (+ x y) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.5e+102) || !(z <= 1.15e+131)) {
		tmp = z / (t / -0.5);
	} else {
		tmp = (x + y) * (0.5 / 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 <= (-2.5d+102)) .or. (.not. (z <= 1.15d+131))) then
        tmp = z / (t / (-0.5d0))
    else
        tmp = (x + y) * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.5e+102) || !(z <= 1.15e+131)) {
		tmp = z / (t / -0.5);
	} else {
		tmp = (x + y) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.5e+102) or not (z <= 1.15e+131):
		tmp = z / (t / -0.5)
	else:
		tmp = (x + y) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.5e+102) || !(z <= 1.15e+131))
		tmp = Float64(z / Float64(t / -0.5));
	else
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.5e+102) || ~((z <= 1.15e+131)))
		tmp = z / (t / -0.5);
	else
		tmp = (x + y) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.5e+102], N[Not[LessEqual[z, 1.15e+131]], $MachinePrecision]], N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e102 or 1.14999999999999996e131 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.5%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.5%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.5%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.5%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]

   4. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 76.8%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot z}{t}} \]

      2. *-commutative 76.8%

         \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

      3. associate-/l* 76.8%

         \[\leadsto \color{blue}{\frac{z}{\frac{t}{-0.5}}} \]

   6. Simplified 76.8%

      \[\leadsto \color{blue}{\frac{z}{\frac{t}{-0.5}}} \]

   if -2.5e102 < z < 1.14999999999999996e131

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.6%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]

   4. Taylor expanded in z around 0 87.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y + x}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 87.0%

         \[\leadsto \color{blue}{\frac{y + x}{t} \cdot 0.5} \]

      2. +-commutative 87.0%

         \[\leadsto \frac{\color{blue}{x + y}}{t} \cdot 0.5 \]

      3. associate-*l/ 87.0%

         \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot 0.5}{t}} \]

      4. associate-*r/ 86.7%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \frac{0.5}{t}} \]

      5. +-commutative 86.7%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \frac{0.5}{t} \]

   6. Simplified 86.7%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \frac{0.5}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+102} \lor \neg \left(z \leq 1.15 \cdot 10^{+131}\right):\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 5: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2e+31) (/ -0.5 (/ t (- z x))) (* (+ x y) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e+31) {
		tmp = -0.5 / (t / (z - x));
	} else {
		tmp = (x + y) * (0.5 / 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 + y) <= 2d+31) then
        tmp = (-0.5d0) / (t / (z - x))
    else
        tmp = (x + y) * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e+31) {
		tmp = -0.5 / (t / (z - x));
	} else {
		tmp = (x + y) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 2e+31:
		tmp = -0.5 / (t / (z - x))
	else:
		tmp = (x + y) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 2e+31)
		tmp = Float64(-0.5 / Float64(t / Float64(z - x)));
	else
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 2e+31)
		tmp = -0.5 / (t / (z - x));
	else
		tmp = (x + y) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 2e+31], N[(-0.5 / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1.9999999999999999e31

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.6%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z - \left(x + y\right)\right)}{t}} \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   6. Taylor expanded in y around 0 72.1%

      \[\leadsto \frac{-0.5}{\color{blue}{\frac{t}{z - x}}} \]

   if 1.9999999999999999e31 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.7%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.7%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]

   4. Taylor expanded in z around 0 86.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y + x}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto \color{blue}{\frac{y + x}{t} \cdot 0.5} \]

      2. +-commutative 86.7%

         \[\leadsto \frac{\color{blue}{x + y}}{t} \cdot 0.5 \]

      3. associate-*l/ 86.7%

         \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot 0.5}{t}} \]

      4. associate-*r/ 86.4%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \frac{0.5}{t}} \]

      5. +-commutative 86.4%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \frac{0.5}{t} \]

   6. Simplified 86.4%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \frac{0.5}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 6: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-151}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -4e-151) (/ -0.5 (/ t (- z x))) (/ -0.5 (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -4e-151) {
		tmp = -0.5 / (t / (z - x));
	} else {
		tmp = -0.5 / (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-4d-151)) then
        tmp = (-0.5d0) / (t / (z - x))
    else
        tmp = (-0.5d0) / (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -4e-151) {
		tmp = -0.5 / (t / (z - x));
	} else {
		tmp = -0.5 / (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -4e-151:
		tmp = -0.5 / (t / (z - x))
	else:
		tmp = -0.5 / (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -4e-151)
		tmp = Float64(-0.5 / Float64(t / Float64(z - x)));
	else
		tmp = Float64(-0.5 / Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -4e-151)
		tmp = -0.5 / (t / (z - x));
	else
		tmp = -0.5 / (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -4e-151], N[(-0.5 / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.5 / N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -3.9999999999999998e-151

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.7%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.7%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z - \left(x + y\right)\right)}{t}} \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   6. Taylor expanded in y around 0 63.0%

      \[\leadsto \frac{-0.5}{\color{blue}{\frac{t}{z - x}}} \]

   if -3.9999999999999998e-151 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.5%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.5%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.5%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.5%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z - \left(x + y\right)\right)}{t}} \]

      2. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   6. Taylor expanded in x around 0 62.8%

      \[\leadsto \frac{-0.5}{\color{blue}{\frac{t}{z - y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-151}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - y}}\\ \end{array} \]

Alternative 7: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{-212}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2e-212) (/ (- x z) (* t 2.0)) (/ -0.5 (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e-212) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = -0.5 / (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= 2d-212) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (-0.5d0) / (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e-212) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = -0.5 / (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 2e-212:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = -0.5 / (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 2e-212)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(-0.5 / Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 2e-212)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = -0.5 / (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 2e-212], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(-0.5 / N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1.99999999999999991e-212

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 66.5%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if 1.99999999999999991e-212 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.6%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z - \left(x + y\right)\right)}{t}} \]

      2. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   6. Taylor expanded in x around 0 59.8%

      \[\leadsto \frac{-0.5}{\color{blue}{\frac{t}{z - y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{-212}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - y}}\\ \end{array} \]

Alternative 8: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-151}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -4e-151) (/ (- x z) (* t 2.0)) (/ (- y z) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -4e-151) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-4d-151)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -4e-151) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -4e-151:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -4e-151)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -4e-151)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -4e-151], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -3.9999999999999998e-151

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 63.2%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if -3.9999999999999998e-151 < (+.f64 x y)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 63.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-151}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \]

Alternative 9: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(z - \left(x + y\right)\right) \cdot \frac{-0.5}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (- z (+ x y)) (/ -0.5 t)))

C

double code(double x, double y, double z, double t) {
	return (z - (x + y)) * (-0.5 / 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 = (z - (x + y)) * ((-0.5d0) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (z - (x + y)) * (-0.5 / t);
}

Python

def code(x, y, z, t):
	return (z - (x + y)) * (-0.5 / t)

Julia

function code(x, y, z, t)
	return Float64(Float64(z - Float64(x + y)) * Float64(-0.5 / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (z - (x + y)) * (-0.5 / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(z - N[(x + y), $MachinePrecision]), $MachinePrecision] * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

      \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

   2. +-commutative 100.0%

      \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

   3. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   5. sub0-neg 100.0%

      \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   6. neg-mul-1 100.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   7. associate-*l/ 99.6%

      \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

   8. *-commutative 99.6%

      \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

   9. associate-/r* 99.6%

      \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

   10. metadata-eval 99.6%

       \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]

4. Final simplification 99.6%

   \[\leadsto \left(z - \left(x + y\right)\right) \cdot \frac{-0.5}{t} \]

Alternative 10: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{-0.5}{\frac{t}{z - \left(x + y\right)}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ -0.5 (/ t (- z (+ x y)))))

C

double code(double x, double y, double z, double t) {
	return -0.5 / (t / (z - (x + y)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (-0.5d0) / (t / (z - (x + y)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return -0.5 / (t / (z - (x + y)));
}

Python

def code(x, y, z, t):
	return -0.5 / (t / (z - (x + y)))

Julia

function code(x, y, z, t)
	return Float64(-0.5 / Float64(t / Float64(z - Float64(x + y))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = -0.5 / (t / (z - (x + y)));
end

Wolfram

code[x_, y_, z_, t_] := N[(-0.5 / N[(t / N[(z - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

      \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

   2. +-commutative 100.0%

      \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

   3. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   5. sub0-neg 100.0%

      \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   6. neg-mul-1 100.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   7. associate-*l/ 99.6%

      \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

   8. *-commutative 99.6%

      \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

   9. associate-/r* 99.6%

      \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

   10. metadata-eval 99.6%

       \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]
4. Step-by-step derivation

   1. associate-*l/ 100.0%

      \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z - \left(x + y\right)\right)}{t}} \]

   2. associate-/l* 99.7%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

5. Applied egg-rr 99.7%

   \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

6. Final simplification 99.7%

   \[\leadsto \frac{-0.5}{\frac{t}{z - \left(x + y\right)}} \]

Alternative 11: 47.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 5.6e+31) (* z (/ -0.5 t)) (* y (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.6e+31) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y * (0.5 / 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 <= 5.6d+31) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = y * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.6e+31) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 5.6e+31:
		tmp = z * (-0.5 / t)
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 5.6e+31)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 5.6e+31)
		tmp = z * (-0.5 / t);
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 5.6e+31], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.60000000000000034e31

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.6%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]

   4. Taylor expanded in z around inf 40.5%

      \[\leadsto \frac{-0.5}{t} \cdot \color{blue}{z} \]

   if 5.60000000000000034e31 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 99.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.6%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z - \left(x + y\right)\right)}{t}} \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

   6. Taylor expanded in y around inf 69.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 69.2%

         \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]

      2. *-commutative 69.2%

         \[\leadsto \frac{\color{blue}{y \cdot 0.5}}{t} \]

      3. associate-*r/ 68.9%

         \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]

   8. Simplified 68.9%

      \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 12: 47.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.3e+34) (* z (/ -0.5 t)) (/ y (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.3e+34) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.3d+34) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = y / (t * 2.0d0)
    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+34) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.3e+34:
		tmp = z * (-0.5 / t)
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.3e+34)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.3e+34)
		tmp = z * (-0.5 / t);
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.3e+34], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.29999999999999999e34

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      7. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

      8. *-commutative 99.6%

         \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

      9. associate-/r* 99.6%

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

      10. metadata-eval 99.6%

          \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]

   4. Taylor expanded in z around inf 40.5%

      \[\leadsto \frac{-0.5}{t} \cdot \color{blue}{z} \]

   if 1.29999999999999999e34 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 69.2%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]

Alternative 13: 37.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{0.5}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* y (/ 0.5 t)))

C

double code(double x, double y, double z, double t) {
	return y * (0.5 / 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 = y * (0.5d0 / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return y * (0.5 / t);
}

Python

def code(x, y, z, t):
	return y * (0.5 / t)

Julia

function code(x, y, z, t)
	return Float64(y * Float64(0.5 / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = y * (0.5 / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

      \[\leadsto \frac{\color{blue}{\left(x + y\right) + \left(-z\right)}}{t \cdot 2} \]

   2. +-commutative 100.0%

      \[\leadsto \frac{\color{blue}{\left(-z\right) + \left(x + y\right)}}{t \cdot 2} \]

   3. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   5. sub0-neg 100.0%

      \[\leadsto \frac{\color{blue}{-\left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   6. neg-mul-1 100.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   7. associate-*l/ 99.6%

      \[\leadsto \color{blue}{\frac{-1}{t \cdot 2} \cdot \left(z - \left(x + y\right)\right)} \]

   8. *-commutative 99.6%

      \[\leadsto \frac{-1}{\color{blue}{2 \cdot t}} \cdot \left(z - \left(x + y\right)\right) \]

   9. associate-/r* 99.6%

      \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t}} \cdot \left(z - \left(x + y\right)\right) \]

   10. metadata-eval 99.6%

       \[\leadsto \frac{\color{blue}{-0.5}}{t} \cdot \left(z - \left(x + y\right)\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot \left(z - \left(x + y\right)\right)} \]
4. Step-by-step derivation

   1. associate-*l/ 100.0%

      \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z - \left(x + y\right)\right)}{t}} \]

   2. associate-/l* 99.7%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

5. Applied egg-rr 99.7%

   \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z - \left(x + y\right)}}} \]

6. Taylor expanded in y around inf 37.4%

   \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
7. Step-by-step derivation

   1. associate-*r/ 37.4%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]

   2. *-commutative 37.4%

      \[\leadsto \frac{\color{blue}{y \cdot 0.5}}{t} \]

   3. associate-*r/ 37.3%

      \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]

8. Simplified 37.3%

   \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]

9. Final simplification 37.3%

   \[\leadsto y \cdot \frac{0.5}{t} \]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))