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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 11

Speedup: 1.0×

• 26.2% 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: 46.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{0.5}{t}\\ t_2 := \frac{-0.5}{\frac{t}{z}}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ 0.5 t))) (t_2 (/ -0.5 (/ t z))))
   (if (<= y -6.2e-153)
     t_1
     (if (<= y -1.25e-205)
       (* z (/ -0.5 t))
       (if (<= y 1.05e-291)
         t_1
         (if (<= y 8.4e-14)
           t_2
           (if (<= y 4.8e+14)
             t_1
             (if (<= y 6.5e+79) t_2 (/ y (* t 2.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (0.5 / t);
	double t_2 = -0.5 / (t / z);
	double tmp;
	if (y <= -6.2e-153) {
		tmp = t_1;
	} else if (y <= -1.25e-205) {
		tmp = z * (-0.5 / t);
	} else if (y <= 1.05e-291) {
		tmp = t_1;
	} else if (y <= 8.4e-14) {
		tmp = t_2;
	} else if (y <= 4.8e+14) {
		tmp = t_1;
	} else if (y <= 6.5e+79) {
		tmp = t_2;
	} 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 = x * (0.5d0 / t)
    t_2 = (-0.5d0) / (t / z)
    if (y <= (-6.2d-153)) then
        tmp = t_1
    else if (y <= (-1.25d-205)) then
        tmp = z * ((-0.5d0) / t)
    else if (y <= 1.05d-291) then
        tmp = t_1
    else if (y <= 8.4d-14) then
        tmp = t_2
    else if (y <= 4.8d+14) then
        tmp = t_1
    else if (y <= 6.5d+79) then
        tmp = t_2
    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 = x * (0.5 / t);
	double t_2 = -0.5 / (t / z);
	double tmp;
	if (y <= -6.2e-153) {
		tmp = t_1;
	} else if (y <= -1.25e-205) {
		tmp = z * (-0.5 / t);
	} else if (y <= 1.05e-291) {
		tmp = t_1;
	} else if (y <= 8.4e-14) {
		tmp = t_2;
	} else if (y <= 4.8e+14) {
		tmp = t_1;
	} else if (y <= 6.5e+79) {
		tmp = t_2;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (0.5 / t)
	t_2 = -0.5 / (t / z)
	tmp = 0
	if y <= -6.2e-153:
		tmp = t_1
	elif y <= -1.25e-205:
		tmp = z * (-0.5 / t)
	elif y <= 1.05e-291:
		tmp = t_1
	elif y <= 8.4e-14:
		tmp = t_2
	elif y <= 4.8e+14:
		tmp = t_1
	elif y <= 6.5e+79:
		tmp = t_2
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(0.5 / t))
	t_2 = Float64(-0.5 / Float64(t / z))
	tmp = 0.0
	if (y <= -6.2e-153)
		tmp = t_1;
	elseif (y <= -1.25e-205)
		tmp = Float64(z * Float64(-0.5 / t));
	elseif (y <= 1.05e-291)
		tmp = t_1;
	elseif (y <= 8.4e-14)
		tmp = t_2;
	elseif (y <= 4.8e+14)
		tmp = t_1;
	elseif (y <= 6.5e+79)
		tmp = t_2;
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (0.5 / t);
	t_2 = -0.5 / (t / z);
	tmp = 0.0;
	if (y <= -6.2e-153)
		tmp = t_1;
	elseif (y <= -1.25e-205)
		tmp = z * (-0.5 / t);
	elseif (y <= 1.05e-291)
		tmp = t_1;
	elseif (y <= 8.4e-14)
		tmp = t_2;
	elseif (y <= 4.8e+14)
		tmp = t_1;
	elseif (y <= 6.5e+79)
		tmp = t_2;
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e-153], t$95$1, If[LessEqual[y, -1.25e-205], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-291], t$95$1, If[LessEqual[y, 8.4e-14], t$95$2, If[LessEqual[y, 4.8e+14], t$95$1, If[LessEqual[y, 6.5e+79], t$95$2, N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.1999999999999999e-153 or -1.25e-205 < y < 1.05e-291 or 8.3999999999999995e-14 < y < 4.8e14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.5%

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

   3. Taylor expanded in x around inf 38.4%

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

      1. associate-*r/ 38.4%

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

      2. associate-/l* 38.3%

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

   5. Simplified 38.3%

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

      1. associate-/r/ 38.3%

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

   7. Applied egg-rr 38.3%

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

   if -6.1999999999999999e-153 < y < -1.25e-205

   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 inf 61.8%

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

   if 1.05e-291 < y < 8.3999999999999995e-14 or 4.8e14 < y < 6.49999999999999954e79

   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 inf 50.7%

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

      1. associate-*l/ 50.8%

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

      2. associate-/l* 50.6%

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

   6. Applied egg-rr 50.6%

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

   if 6.49999999999999954e79 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 65.1%

      \[\leadsto \frac{\color{blue}{y}}{t \cdot 2} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]

Alternative 3: 47.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{0.5}{t}\\ t_2 := \frac{z}{\frac{t}{-0.5}}\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ 0.5 t))) (t_2 (/ z (/ t -0.5))))
   (if (<= y -1.42e-154)
     t_1
     (if (<= y -1.1e-205)
       (* z (/ -0.5 t))
       (if (<= y 2e-286)
         t_1
         (if (<= y 2.15e-11)
           t_2
           (if (<= y 5e+14) t_1 (if (<= y 7.2e+79) t_2 (/ y (* t 2.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (0.5 / t);
	double t_2 = z / (t / -0.5);
	double tmp;
	if (y <= -1.42e-154) {
		tmp = t_1;
	} else if (y <= -1.1e-205) {
		tmp = z * (-0.5 / t);
	} else if (y <= 2e-286) {
		tmp = t_1;
	} else if (y <= 2.15e-11) {
		tmp = t_2;
	} else if (y <= 5e+14) {
		tmp = t_1;
	} else if (y <= 7.2e+79) {
		tmp = t_2;
	} 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 = x * (0.5d0 / t)
    t_2 = z / (t / (-0.5d0))
    if (y <= (-1.42d-154)) then
        tmp = t_1
    else if (y <= (-1.1d-205)) then
        tmp = z * ((-0.5d0) / t)
    else if (y <= 2d-286) then
        tmp = t_1
    else if (y <= 2.15d-11) then
        tmp = t_2
    else if (y <= 5d+14) then
        tmp = t_1
    else if (y <= 7.2d+79) then
        tmp = t_2
    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 = x * (0.5 / t);
	double t_2 = z / (t / -0.5);
	double tmp;
	if (y <= -1.42e-154) {
		tmp = t_1;
	} else if (y <= -1.1e-205) {
		tmp = z * (-0.5 / t);
	} else if (y <= 2e-286) {
		tmp = t_1;
	} else if (y <= 2.15e-11) {
		tmp = t_2;
	} else if (y <= 5e+14) {
		tmp = t_1;
	} else if (y <= 7.2e+79) {
		tmp = t_2;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (0.5 / t)
	t_2 = z / (t / -0.5)
	tmp = 0
	if y <= -1.42e-154:
		tmp = t_1
	elif y <= -1.1e-205:
		tmp = z * (-0.5 / t)
	elif y <= 2e-286:
		tmp = t_1
	elif y <= 2.15e-11:
		tmp = t_2
	elif y <= 5e+14:
		tmp = t_1
	elif y <= 7.2e+79:
		tmp = t_2
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(0.5 / t))
	t_2 = Float64(z / Float64(t / -0.5))
	tmp = 0.0
	if (y <= -1.42e-154)
		tmp = t_1;
	elseif (y <= -1.1e-205)
		tmp = Float64(z * Float64(-0.5 / t));
	elseif (y <= 2e-286)
		tmp = t_1;
	elseif (y <= 2.15e-11)
		tmp = t_2;
	elseif (y <= 5e+14)
		tmp = t_1;
	elseif (y <= 7.2e+79)
		tmp = t_2;
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (0.5 / t);
	t_2 = z / (t / -0.5);
	tmp = 0.0;
	if (y <= -1.42e-154)
		tmp = t_1;
	elseif (y <= -1.1e-205)
		tmp = z * (-0.5 / t);
	elseif (y <= 2e-286)
		tmp = t_1;
	elseif (y <= 2.15e-11)
		tmp = t_2;
	elseif (y <= 5e+14)
		tmp = t_1;
	elseif (y <= 7.2e+79)
		tmp = t_2;
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.42e-154], t$95$1, If[LessEqual[y, -1.1e-205], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-286], t$95$1, If[LessEqual[y, 2.15e-11], t$95$2, If[LessEqual[y, 5e+14], t$95$1, If[LessEqual[y, 7.2e+79], t$95$2, N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.42e-154 or -1.10000000000000005e-205 < y < 2.0000000000000001e-286 or 2.15000000000000001e-11 < y < 5e14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.5%

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

   3. Taylor expanded in x around inf 37.8%

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

      1. associate-*r/ 37.8%

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

      2. associate-/l* 37.7%

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

   5. Simplified 37.7%

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

      1. associate-/r/ 37.7%

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

   7. Applied egg-rr 37.7%

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

   if -1.42e-154 < y < -1.10000000000000005e-205

   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 inf 58.4%

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

   if 2.0000000000000001e-286 < y < 2.15000000000000001e-11 or 5e14 < y < 7.1999999999999999e79

   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 inf 50.5%

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

      1. associate-*r/ 50.5%

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

      2. *-commutative 50.5%

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

      3. associate-/l* 50.5%

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

   6. Simplified 50.5%

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

   if 7.1999999999999999e79 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 65.1%

      \[\leadsto \frac{\color{blue}{y}}{t \cdot 2} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-11}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+79}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]

Alternative 4: 46.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 0.5}{t}\\ t_2 := \frac{z}{\frac{t}{-0.5}}\\ \mathbf{if}\;y \leq -7 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x 0.5) t)) (t_2 (/ z (/ t -0.5))))
   (if (<= y -7e-153)
     t_1
     (if (<= y -1.08e-197)
       (* z (/ -0.5 t))
       (if (<= y 4.8e-291)
         t_1
         (if (<= y 3.7e-14)
           t_2
           (if (<= y 4.8e+14)
             (* x (/ 0.5 t))
             (if (<= y 7e+79) t_2 (/ y (* t 2.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * 0.5) / t;
	double t_2 = z / (t / -0.5);
	double tmp;
	if (y <= -7e-153) {
		tmp = t_1;
	} else if (y <= -1.08e-197) {
		tmp = z * (-0.5 / t);
	} else if (y <= 4.8e-291) {
		tmp = t_1;
	} else if (y <= 3.7e-14) {
		tmp = t_2;
	} else if (y <= 4.8e+14) {
		tmp = x * (0.5 / t);
	} else if (y <= 7e+79) {
		tmp = t_2;
	} 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 = (x * 0.5d0) / t
    t_2 = z / (t / (-0.5d0))
    if (y <= (-7d-153)) then
        tmp = t_1
    else if (y <= (-1.08d-197)) then
        tmp = z * ((-0.5d0) / t)
    else if (y <= 4.8d-291) then
        tmp = t_1
    else if (y <= 3.7d-14) then
        tmp = t_2
    else if (y <= 4.8d+14) then
        tmp = x * (0.5d0 / t)
    else if (y <= 7d+79) then
        tmp = t_2
    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 = (x * 0.5) / t;
	double t_2 = z / (t / -0.5);
	double tmp;
	if (y <= -7e-153) {
		tmp = t_1;
	} else if (y <= -1.08e-197) {
		tmp = z * (-0.5 / t);
	} else if (y <= 4.8e-291) {
		tmp = t_1;
	} else if (y <= 3.7e-14) {
		tmp = t_2;
	} else if (y <= 4.8e+14) {
		tmp = x * (0.5 / t);
	} else if (y <= 7e+79) {
		tmp = t_2;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * 0.5) / t
	t_2 = z / (t / -0.5)
	tmp = 0
	if y <= -7e-153:
		tmp = t_1
	elif y <= -1.08e-197:
		tmp = z * (-0.5 / t)
	elif y <= 4.8e-291:
		tmp = t_1
	elif y <= 3.7e-14:
		tmp = t_2
	elif y <= 4.8e+14:
		tmp = x * (0.5 / t)
	elif y <= 7e+79:
		tmp = t_2
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * 0.5) / t)
	t_2 = Float64(z / Float64(t / -0.5))
	tmp = 0.0
	if (y <= -7e-153)
		tmp = t_1;
	elseif (y <= -1.08e-197)
		tmp = Float64(z * Float64(-0.5 / t));
	elseif (y <= 4.8e-291)
		tmp = t_1;
	elseif (y <= 3.7e-14)
		tmp = t_2;
	elseif (y <= 4.8e+14)
		tmp = Float64(x * Float64(0.5 / t));
	elseif (y <= 7e+79)
		tmp = t_2;
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * 0.5) / t;
	t_2 = z / (t / -0.5);
	tmp = 0.0;
	if (y <= -7e-153)
		tmp = t_1;
	elseif (y <= -1.08e-197)
		tmp = z * (-0.5 / t);
	elseif (y <= 4.8e-291)
		tmp = t_1;
	elseif (y <= 3.7e-14)
		tmp = t_2;
	elseif (y <= 4.8e+14)
		tmp = x * (0.5 / t);
	elseif (y <= 7e+79)
		tmp = t_2;
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e-153], t$95$1, If[LessEqual[y, -1.08e-197], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-291], t$95$1, If[LessEqual[y, 3.7e-14], t$95$2, If[LessEqual[y, 4.8e+14], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+79], t$95$2, N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.99999999999999961e-153 or -1.0800000000000001e-197 < y < 4.80000000000000025e-291

   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 x around inf 36.8%

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

      1. *-commutative 36.8%

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

      2. associate-*l/ 36.8%

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

   6. Simplified 36.8%

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

   if -6.99999999999999961e-153 < y < -1.0800000000000001e-197

   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 inf 64.9%

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

   if 4.80000000000000025e-291 < y < 3.70000000000000001e-14 or 4.8e14 < y < 6.99999999999999961e79

   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 inf 50.5%

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

      1. associate-*r/ 50.5%

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

      2. *-commutative 50.5%

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

      3. associate-/l* 50.5%

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

   6. Simplified 50.5%

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

   if 3.70000000000000001e-14 < y < 4.8e14

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in x around inf 54.0%

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

      1. associate-*r/ 54.0%

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

      2. associate-/l* 53.8%

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

   5. Simplified 53.8%

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

      1. associate-/r/ 54.0%

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

   7. Applied egg-rr 54.0%

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

   if 6.99999999999999961e79 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 65.1%

      \[\leadsto \frac{\color{blue}{y}}{t \cdot 2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-153}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-14}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+79}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]

Alternative 5: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z}{t \cdot 2}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -0.00076 \lor \neg \left(x \leq -2.45 \cdot 10^{-46}\right) \land x \leq -1.95 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x z) (* t 2.0))))
   (if (<= x -9.5e+86)
     t_1
     (if (<= x -1.15e+33)
       (* (+ x y) (/ 0.5 t))
       (if (or (<= x -0.00076) (and (not (<= x -2.45e-46)) (<= x -1.95e-72)))
         t_1
         (* (/ -0.5 t) (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - z) / (t * 2.0);
	double tmp;
	if (x <= -9.5e+86) {
		tmp = t_1;
	} else if (x <= -1.15e+33) {
		tmp = (x + y) * (0.5 / t);
	} else if ((x <= -0.00076) || (!(x <= -2.45e-46) && (x <= -1.95e-72))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x - z) / (t * 2.0d0)
    if (x <= (-9.5d+86)) then
        tmp = t_1
    else if (x <= (-1.15d+33)) then
        tmp = (x + y) * (0.5d0 / t)
    else if ((x <= (-0.00076d0)) .or. (.not. (x <= (-2.45d-46))) .and. (x <= (-1.95d-72))) then
        tmp = t_1
    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 t_1 = (x - z) / (t * 2.0);
	double tmp;
	if (x <= -9.5e+86) {
		tmp = t_1;
	} else if (x <= -1.15e+33) {
		tmp = (x + y) * (0.5 / t);
	} else if ((x <= -0.00076) || (!(x <= -2.45e-46) && (x <= -1.95e-72))) {
		tmp = t_1;
	} else {
		tmp = (-0.5 / t) * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - z) / (t * 2.0)
	tmp = 0
	if x <= -9.5e+86:
		tmp = t_1
	elif x <= -1.15e+33:
		tmp = (x + y) * (0.5 / t)
	elif (x <= -0.00076) or (not (x <= -2.45e-46) and (x <= -1.95e-72)):
		tmp = t_1
	else:
		tmp = (-0.5 / t) * (z - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - z) / Float64(t * 2.0))
	tmp = 0.0
	if (x <= -9.5e+86)
		tmp = t_1;
	elseif (x <= -1.15e+33)
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	elseif ((x <= -0.00076) || (!(x <= -2.45e-46) && (x <= -1.95e-72)))
		tmp = t_1;
	else
		tmp = Float64(Float64(-0.5 / t) * Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - z) / (t * 2.0);
	tmp = 0.0;
	if (x <= -9.5e+86)
		tmp = t_1;
	elseif (x <= -1.15e+33)
		tmp = (x + y) * (0.5 / t);
	elseif ((x <= -0.00076) || (~((x <= -2.45e-46)) && (x <= -1.95e-72)))
		tmp = t_1;
	else
		tmp = (-0.5 / t) * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+86], t$95$1, If[LessEqual[x, -1.15e+33], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -0.00076], And[N[Not[LessEqual[x, -2.45e-46]], $MachinePrecision], LessEqual[x, -1.95e-72]]], t$95$1, N[(N[(-0.5 / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000028e86 or -1.15000000000000005e33 < x < -7.6000000000000004e-4 or -2.45e-46 < x < -1.95e-72

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.3%

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

   if -9.50000000000000028e86 < x < -1.15000000000000005e33

   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/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

      2. +-commutative 98.5%

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

      3. associate-*l/ 98.5%

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

      4. associate-*r/ 98.4%

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

      5. +-commutative 98.4%

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

   6. Simplified 98.4%

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

   if -7.6000000000000004e-4 < x < -2.45e-46 or -1.95e-72 < x

   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/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 76.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+86}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -0.00076 \lor \neg \left(x \leq -2.45 \cdot 10^{-46}\right) \land x \leq -1.95 \cdot 10^{-72}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 6: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+163} \lor \neg \left(x \leq -3 \cdot 10^{+81}\right) \land x \leq -4.2 \cdot 10^{+43}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.8e+163) (and (not (<= x -3e+81)) (<= x -4.2e+43)))
   (* (+ x y) (/ 0.5 t))
   (* (/ -0.5 t) (- z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.8e+163) || (!(x <= -3e+81) && (x <= -4.2e+43))) {
		tmp = (x + y) * (0.5 / t);
	} 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 <= (-8.8d+163)) .or. (.not. (x <= (-3d+81))) .and. (x <= (-4.2d+43))) then
        tmp = (x + y) * (0.5d0 / t)
    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 <= -8.8e+163) || (!(x <= -3e+81) && (x <= -4.2e+43))) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = (-0.5 / t) * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.8e+163) or (not (x <= -3e+81) and (x <= -4.2e+43)):
		tmp = (x + y) * (0.5 / t)
	else:
		tmp = (-0.5 / t) * (z - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.8e+163) || (!(x <= -3e+81) && (x <= -4.2e+43)))
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	else
		tmp = Float64(Float64(-0.5 / t) * Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.8e+163) || (~((x <= -3e+81)) && (x <= -4.2e+43)))
		tmp = (x + y) * (0.5 / t);
	else
		tmp = (-0.5 / t) * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.8e+163], And[N[Not[LessEqual[x, -3e+81]], $MachinePrecision], LessEqual[x, -4.2e+43]]], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(N[(-0.5 / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999945e163 or -2.99999999999999997e81 < x < -4.20000000000000003e43

   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 97.0%

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

      1. *-commutative 97.0%

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

      2. +-commutative 97.0%

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

      3. associate-*l/ 97.0%

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

      4. associate-*r/ 96.7%

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

      5. +-commutative 96.7%

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

   6. Simplified 96.7%

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

   if -8.79999999999999945e163 < x < -2.99999999999999997e81 or -4.20000000000000003e43 < x

   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 x around 0 75.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+163} \lor \neg \left(x \leq -3 \cdot 10^{+81}\right) \land x \leq -4.2 \cdot 10^{+43}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 7: 44.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+164} \lor \neg \left(x \leq -2.2 \cdot 10^{+81}\right) \land x \leq -3 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1e+164) (and (not (<= x -2.2e+81)) (<= x -3e+43)))
   (* x (/ 0.5 t))
   (* z (/ -0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1e+164) || (!(x <= -2.2e+81) && (x <= -3e+43))) {
		tmp = x * (0.5 / t);
	} else {
		tmp = z * (-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 <= (-1d+164)) .or. (.not. (x <= (-2.2d+81))) .and. (x <= (-3d+43))) then
        tmp = x * (0.5d0 / t)
    else
        tmp = z * ((-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 <= -1e+164) || (!(x <= -2.2e+81) && (x <= -3e+43))) {
		tmp = x * (0.5 / t);
	} else {
		tmp = z * (-0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1e+164) or (not (x <= -2.2e+81) and (x <= -3e+43)):
		tmp = x * (0.5 / t)
	else:
		tmp = z * (-0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1e+164) || (!(x <= -2.2e+81) && (x <= -3e+43)))
		tmp = Float64(x * Float64(0.5 / t));
	else
		tmp = Float64(z * Float64(-0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1e+164) || (~((x <= -2.2e+81)) && (x <= -3e+43)))
		tmp = x * (0.5 / t);
	else
		tmp = z * (-0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1e+164], And[N[Not[LessEqual[x, -2.2e+81]], $MachinePrecision], LessEqual[x, -3e+43]]], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1e164 or -2.19999999999999987e81 < x < -3.00000000000000017e43

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.4%

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

   3. Taylor expanded in x around inf 90.1%

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

      1. associate-*r/ 90.1%

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

      2. associate-/l* 89.6%

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

   5. Simplified 89.6%

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

      1. associate-/r/ 89.8%

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

   7. Applied egg-rr 89.8%

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

   if -1e164 < x < -2.19999999999999987e81 or -3.00000000000000017e43 < x

   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 inf 46.1%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+164} \lor \neg \left(x \leq -2.2 \cdot 10^{+81}\right) \land x \leq -3 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \]

Alternative 8: 44.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{0.5}{t}\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ 0.5 t))))
   (if (<= x -8.8e+163)
     t_1
     (if (<= x -1.8e+81)
       (/ -0.5 (/ t z))
       (if (<= x -3.5e+43) t_1 (* z (/ -0.5 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (0.5 / t);
	double tmp;
	if (x <= -8.8e+163) {
		tmp = t_1;
	} else if (x <= -1.8e+81) {
		tmp = -0.5 / (t / z);
	} else if (x <= -3.5e+43) {
		tmp = t_1;
	} else {
		tmp = z * (-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) :: t_1
    real(8) :: tmp
    t_1 = x * (0.5d0 / t)
    if (x <= (-8.8d+163)) then
        tmp = t_1
    else if (x <= (-1.8d+81)) then
        tmp = (-0.5d0) / (t / z)
    else if (x <= (-3.5d+43)) then
        tmp = t_1
    else
        tmp = z * ((-0.5d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (0.5 / t);
	double tmp;
	if (x <= -8.8e+163) {
		tmp = t_1;
	} else if (x <= -1.8e+81) {
		tmp = -0.5 / (t / z);
	} else if (x <= -3.5e+43) {
		tmp = t_1;
	} else {
		tmp = z * (-0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (0.5 / t)
	tmp = 0
	if x <= -8.8e+163:
		tmp = t_1
	elif x <= -1.8e+81:
		tmp = -0.5 / (t / z)
	elif x <= -3.5e+43:
		tmp = t_1
	else:
		tmp = z * (-0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(0.5 / t))
	tmp = 0.0
	if (x <= -8.8e+163)
		tmp = t_1;
	elseif (x <= -1.8e+81)
		tmp = Float64(-0.5 / Float64(t / z));
	elseif (x <= -3.5e+43)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(-0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (0.5 / t);
	tmp = 0.0;
	if (x <= -8.8e+163)
		tmp = t_1;
	elseif (x <= -1.8e+81)
		tmp = -0.5 / (t / z);
	elseif (x <= -3.5e+43)
		tmp = t_1;
	else
		tmp = z * (-0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.8e+163], t$95$1, If[LessEqual[x, -1.8e+81], N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e+43], t$95$1, N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.79999999999999945e163 or -1.80000000000000003e81 < x < -3.5000000000000001e43

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.4%

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

   3. Taylor expanded in x around inf 90.1%

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

      1. associate-*r/ 90.1%

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

      2. associate-/l* 89.6%

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

   5. Simplified 89.6%

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

      1. associate-/r/ 89.8%

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

   7. Applied egg-rr 89.8%

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

   if -8.79999999999999945e163 < x < -1.80000000000000003e81

   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/ 99.1%

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

      8. *-commutative 99.1%

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

      9. associate-/r* 99.1%

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

      10. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around inf 35.4%

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

      1. associate-*l/ 35.9%

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

      2. associate-/l* 35.6%

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

   6. Applied egg-rr 35.6%

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

   if -3.5000000000000001e43 < x

   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 inf 46.5%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \]

Alternative 9: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+104} \lor \neg \left(z \leq 2.4 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e+104) (not (<= z 2.4e+76)))
   (/ z (/ t -0.5))
   (* (+ x y) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e+104) || !(z <= 2.4e+76)) {
		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 <= (-5.2d+104)) .or. (.not. (z <= 2.4d+76))) 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 <= -5.2e+104) || !(z <= 2.4e+76)) {
		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 <= -5.2e+104) or not (z <= 2.4e+76):
		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 <= -5.2e+104) || !(z <= 2.4e+76))
		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 <= -5.2e+104) || ~((z <= 2.4e+76)))
		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, -5.2e+104], N[Not[LessEqual[z, 2.4e+76]], $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 < -5.20000000000000001e104 or 2.4e76 < 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/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 73.8%

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

      1. associate-*r/ 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-/l* 73.8%

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

   6. Simplified 73.8%

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

   if -5.20000000000000001e104 < z < 2.4e76

   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 81.8%

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

      1. *-commutative 81.8%

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

      2. +-commutative 81.8%

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

      3. associate-*l/ 81.8%

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

      4. associate-*r/ 81.6%

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

      5. +-commutative 81.6%

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

   6. Simplified 81.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+104} \lor \neg \left(z \leq 2.4 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 10: 99.7% accurate, 1.0× speedup

Math

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

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(Float64(-0.5 / 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[(N[(-0.5 / t), $MachinePrecision] * N[(z - N[(x + y), $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/ 99.7%

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

   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. Final simplification 99.7%

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

Alternative 11: 37.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(z * 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/ 99.7%

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

   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 inf 41.0%

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

5. Final simplification 41.0%

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

Reproduce

herbie shell --seed 2023192 
(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)))