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

Percentage Accurate: 99.9% → 99.9%

Time: 7.1s

Alternatives: 9

Speedup: 1.0×

• 27.1% 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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 46.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.5 \cdot \frac{z}{t}\\ t_2 := \frac{x \cdot 0.5}{t}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-271}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.5 (/ z t))) (t_2 (/ (* x 0.5) t)))
   (if (<= y -5e+17)
     t_2
     (if (<= y -3.7e-61)
       t_1
       (if (<= y -6.8e-271)
         t_2
         (if (<= y 1.4e-230)
           t_1
           (if (<= y 2.5e-209)
             t_2
             (if (<= y 8.5e-107)
               t_1
               (if (<= y 6.8e-90)
                 t_2
                 (if (<= y 4.9e+117) t_1 (* 0.5 (/ y t))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (z / t);
	double t_2 = (x * 0.5) / t;
	double tmp;
	if (y <= -5e+17) {
		tmp = t_2;
	} else if (y <= -3.7e-61) {
		tmp = t_1;
	} else if (y <= -6.8e-271) {
		tmp = t_2;
	} else if (y <= 1.4e-230) {
		tmp = t_1;
	} else if (y <= 2.5e-209) {
		tmp = t_2;
	} else if (y <= 8.5e-107) {
		tmp = t_1;
	} else if (y <= 6.8e-90) {
		tmp = t_2;
	} else if (y <= 4.9e+117) {
		tmp = t_1;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-0.5d0) * (z / t)
    t_2 = (x * 0.5d0) / t
    if (y <= (-5d+17)) then
        tmp = t_2
    else if (y <= (-3.7d-61)) then
        tmp = t_1
    else if (y <= (-6.8d-271)) then
        tmp = t_2
    else if (y <= 1.4d-230) then
        tmp = t_1
    else if (y <= 2.5d-209) then
        tmp = t_2
    else if (y <= 8.5d-107) then
        tmp = t_1
    else if (y <= 6.8d-90) then
        tmp = t_2
    else if (y <= 4.9d+117) then
        tmp = t_1
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (z / t);
	double t_2 = (x * 0.5) / t;
	double tmp;
	if (y <= -5e+17) {
		tmp = t_2;
	} else if (y <= -3.7e-61) {
		tmp = t_1;
	} else if (y <= -6.8e-271) {
		tmp = t_2;
	} else if (y <= 1.4e-230) {
		tmp = t_1;
	} else if (y <= 2.5e-209) {
		tmp = t_2;
	} else if (y <= 8.5e-107) {
		tmp = t_1;
	} else if (y <= 6.8e-90) {
		tmp = t_2;
	} else if (y <= 4.9e+117) {
		tmp = t_1;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 * (z / t)
	t_2 = (x * 0.5) / t
	tmp = 0
	if y <= -5e+17:
		tmp = t_2
	elif y <= -3.7e-61:
		tmp = t_1
	elif y <= -6.8e-271:
		tmp = t_2
	elif y <= 1.4e-230:
		tmp = t_1
	elif y <= 2.5e-209:
		tmp = t_2
	elif y <= 8.5e-107:
		tmp = t_1
	elif y <= 6.8e-90:
		tmp = t_2
	elif y <= 4.9e+117:
		tmp = t_1
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.5 * Float64(z / t))
	t_2 = Float64(Float64(x * 0.5) / t)
	tmp = 0.0
	if (y <= -5e+17)
		tmp = t_2;
	elseif (y <= -3.7e-61)
		tmp = t_1;
	elseif (y <= -6.8e-271)
		tmp = t_2;
	elseif (y <= 1.4e-230)
		tmp = t_1;
	elseif (y <= 2.5e-209)
		tmp = t_2;
	elseif (y <= 8.5e-107)
		tmp = t_1;
	elseif (y <= 6.8e-90)
		tmp = t_2;
	elseif (y <= 4.9e+117)
		tmp = t_1;
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 * (z / t);
	t_2 = (x * 0.5) / t;
	tmp = 0.0;
	if (y <= -5e+17)
		tmp = t_2;
	elseif (y <= -3.7e-61)
		tmp = t_1;
	elseif (y <= -6.8e-271)
		tmp = t_2;
	elseif (y <= 1.4e-230)
		tmp = t_1;
	elseif (y <= 2.5e-209)
		tmp = t_2;
	elseif (y <= 8.5e-107)
		tmp = t_1;
	elseif (y <= 6.8e-90)
		tmp = t_2;
	elseif (y <= 4.9e+117)
		tmp = t_1;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[y, -5e+17], t$95$2, If[LessEqual[y, -3.7e-61], t$95$1, If[LessEqual[y, -6.8e-271], t$95$2, If[LessEqual[y, 1.4e-230], t$95$1, If[LessEqual[y, 2.5e-209], t$95$2, If[LessEqual[y, 8.5e-107], t$95$1, If[LessEqual[y, 6.8e-90], t$95$2, If[LessEqual[y, 4.9e+117], t$95$1, N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e17 or -3.7e-61 < y < -6.8000000000000001e-271 or 1.4e-230 < y < 2.5000000000000002e-209 or 8.49999999999999956e-107 < y < 6.79999999999999988e-90

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 44.8%

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

      1. associate-*r/ 44.8%

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

   7. Simplified 44.8%

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

   if -5e17 < y < -3.7e-61 or -6.8000000000000001e-271 < y < 1.4e-230 or 2.5000000000000002e-209 < y < 8.49999999999999956e-107 or 6.79999999999999988e-90 < y < 4.9000000000000001e117

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 57.9%

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

   if 4.9000000000000001e117 < y

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 88.8%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-61}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-271}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-230}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-209}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-107}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+117}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.5 \cdot \frac{z}{t}\\ t_2 := \frac{x \cdot 0.5}{t}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-281}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{z}{-2}}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.5 (/ z t))) (t_2 (/ (* x 0.5) t)))
   (if (<= y -5.5e+17)
     t_2
     (if (<= y -9e-60)
       t_1
       (if (<= y -1.12e-281)
         t_2
         (if (<= y 8.2e-232)
           (/ (/ z -2.0) t)
           (if (<= y 2e-205)
             t_2
             (if (<= y 1e-106)
               t_1
               (if (<= y 5.4e-90)
                 t_2
                 (if (<= y 2.7e+117) t_1 (* 0.5 (/ y t))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (z / t);
	double t_2 = (x * 0.5) / t;
	double tmp;
	if (y <= -5.5e+17) {
		tmp = t_2;
	} else if (y <= -9e-60) {
		tmp = t_1;
	} else if (y <= -1.12e-281) {
		tmp = t_2;
	} else if (y <= 8.2e-232) {
		tmp = (z / -2.0) / t;
	} else if (y <= 2e-205) {
		tmp = t_2;
	} else if (y <= 1e-106) {
		tmp = t_1;
	} else if (y <= 5.4e-90) {
		tmp = t_2;
	} else if (y <= 2.7e+117) {
		tmp = t_1;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-0.5d0) * (z / t)
    t_2 = (x * 0.5d0) / t
    if (y <= (-5.5d+17)) then
        tmp = t_2
    else if (y <= (-9d-60)) then
        tmp = t_1
    else if (y <= (-1.12d-281)) then
        tmp = t_2
    else if (y <= 8.2d-232) then
        tmp = (z / (-2.0d0)) / t
    else if (y <= 2d-205) then
        tmp = t_2
    else if (y <= 1d-106) then
        tmp = t_1
    else if (y <= 5.4d-90) then
        tmp = t_2
    else if (y <= 2.7d+117) then
        tmp = t_1
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (z / t);
	double t_2 = (x * 0.5) / t;
	double tmp;
	if (y <= -5.5e+17) {
		tmp = t_2;
	} else if (y <= -9e-60) {
		tmp = t_1;
	} else if (y <= -1.12e-281) {
		tmp = t_2;
	} else if (y <= 8.2e-232) {
		tmp = (z / -2.0) / t;
	} else if (y <= 2e-205) {
		tmp = t_2;
	} else if (y <= 1e-106) {
		tmp = t_1;
	} else if (y <= 5.4e-90) {
		tmp = t_2;
	} else if (y <= 2.7e+117) {
		tmp = t_1;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 * (z / t)
	t_2 = (x * 0.5) / t
	tmp = 0
	if y <= -5.5e+17:
		tmp = t_2
	elif y <= -9e-60:
		tmp = t_1
	elif y <= -1.12e-281:
		tmp = t_2
	elif y <= 8.2e-232:
		tmp = (z / -2.0) / t
	elif y <= 2e-205:
		tmp = t_2
	elif y <= 1e-106:
		tmp = t_1
	elif y <= 5.4e-90:
		tmp = t_2
	elif y <= 2.7e+117:
		tmp = t_1
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.5 * Float64(z / t))
	t_2 = Float64(Float64(x * 0.5) / t)
	tmp = 0.0
	if (y <= -5.5e+17)
		tmp = t_2;
	elseif (y <= -9e-60)
		tmp = t_1;
	elseif (y <= -1.12e-281)
		tmp = t_2;
	elseif (y <= 8.2e-232)
		tmp = Float64(Float64(z / -2.0) / t);
	elseif (y <= 2e-205)
		tmp = t_2;
	elseif (y <= 1e-106)
		tmp = t_1;
	elseif (y <= 5.4e-90)
		tmp = t_2;
	elseif (y <= 2.7e+117)
		tmp = t_1;
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 * (z / t);
	t_2 = (x * 0.5) / t;
	tmp = 0.0;
	if (y <= -5.5e+17)
		tmp = t_2;
	elseif (y <= -9e-60)
		tmp = t_1;
	elseif (y <= -1.12e-281)
		tmp = t_2;
	elseif (y <= 8.2e-232)
		tmp = (z / -2.0) / t;
	elseif (y <= 2e-205)
		tmp = t_2;
	elseif (y <= 1e-106)
		tmp = t_1;
	elseif (y <= 5.4e-90)
		tmp = t_2;
	elseif (y <= 2.7e+117)
		tmp = t_1;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[y, -5.5e+17], t$95$2, If[LessEqual[y, -9e-60], t$95$1, If[LessEqual[y, -1.12e-281], t$95$2, If[LessEqual[y, 8.2e-232], N[(N[(z / -2.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 2e-205], t$95$2, If[LessEqual[y, 1e-106], t$95$1, If[LessEqual[y, 5.4e-90], t$95$2, If[LessEqual[y, 2.7e+117], t$95$1, N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5e17 or -9.00000000000000001e-60 < y < -1.12e-281 or 8.19999999999999945e-232 < y < 2e-205 or 9.99999999999999941e-107 < y < 5.39999999999999993e-90

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 45.4%

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

      1. associate-*r/ 45.4%

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

   7. Simplified 45.4%

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

   if -5.5e17 < y < -9.00000000000000001e-60 or 2e-205 < y < 9.99999999999999941e-107 or 5.39999999999999993e-90 < y < 2.7000000000000002e117

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 50.6%

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

   if -1.12e-281 < y < 8.19999999999999945e-232

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.1%

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

      1. metadata-eval 82.1%

         \[\leadsto \color{blue}{\frac{1}{-2}} \cdot \frac{z}{t} \]

      2. times-frac 82.1%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{-2 \cdot t}} \]

      3. *-un-lft-identity 82.1%

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

      4. associate-/r* 82.1%

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

   7. Applied egg-rr 82.1%

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

   if 2.7000000000000002e117 < y

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 88.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-60}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-281}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{z}{-2}}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 10^{-106}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+117}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.5 \cdot \frac{z}{t}\\ t_2 := x \cdot \frac{0.5}{t}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.5 (/ z t))) (t_2 (* x (/ 0.5 t))))
   (if (<= y -9.5e+18)
     t_2
     (if (<= y -9.4e-60)
       t_1
       (if (<= y -1.8e-274)
         t_2
         (if (<= y 4.2e-106)
           t_1
           (if (<= y 3.5e-90)
             t_2
             (if (<= y 2.1e+118) t_1 (* 0.5 (/ y t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (z / t);
	double t_2 = x * (0.5 / t);
	double tmp;
	if (y <= -9.5e+18) {
		tmp = t_2;
	} else if (y <= -9.4e-60) {
		tmp = t_1;
	} else if (y <= -1.8e-274) {
		tmp = t_2;
	} else if (y <= 4.2e-106) {
		tmp = t_1;
	} else if (y <= 3.5e-90) {
		tmp = t_2;
	} else if (y <= 2.1e+118) {
		tmp = t_1;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-0.5d0) * (z / t)
    t_2 = x * (0.5d0 / t)
    if (y <= (-9.5d+18)) then
        tmp = t_2
    else if (y <= (-9.4d-60)) then
        tmp = t_1
    else if (y <= (-1.8d-274)) then
        tmp = t_2
    else if (y <= 4.2d-106) then
        tmp = t_1
    else if (y <= 3.5d-90) then
        tmp = t_2
    else if (y <= 2.1d+118) then
        tmp = t_1
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (z / t);
	double t_2 = x * (0.5 / t);
	double tmp;
	if (y <= -9.5e+18) {
		tmp = t_2;
	} else if (y <= -9.4e-60) {
		tmp = t_1;
	} else if (y <= -1.8e-274) {
		tmp = t_2;
	} else if (y <= 4.2e-106) {
		tmp = t_1;
	} else if (y <= 3.5e-90) {
		tmp = t_2;
	} else if (y <= 2.1e+118) {
		tmp = t_1;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 * (z / t)
	t_2 = x * (0.5 / t)
	tmp = 0
	if y <= -9.5e+18:
		tmp = t_2
	elif y <= -9.4e-60:
		tmp = t_1
	elif y <= -1.8e-274:
		tmp = t_2
	elif y <= 4.2e-106:
		tmp = t_1
	elif y <= 3.5e-90:
		tmp = t_2
	elif y <= 2.1e+118:
		tmp = t_1
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.5 * Float64(z / t))
	t_2 = Float64(x * Float64(0.5 / t))
	tmp = 0.0
	if (y <= -9.5e+18)
		tmp = t_2;
	elseif (y <= -9.4e-60)
		tmp = t_1;
	elseif (y <= -1.8e-274)
		tmp = t_2;
	elseif (y <= 4.2e-106)
		tmp = t_1;
	elseif (y <= 3.5e-90)
		tmp = t_2;
	elseif (y <= 2.1e+118)
		tmp = t_1;
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 * (z / t);
	t_2 = x * (0.5 / t);
	tmp = 0.0;
	if (y <= -9.5e+18)
		tmp = t_2;
	elseif (y <= -9.4e-60)
		tmp = t_1;
	elseif (y <= -1.8e-274)
		tmp = t_2;
	elseif (y <= 4.2e-106)
		tmp = t_1;
	elseif (y <= 3.5e-90)
		tmp = t_2;
	elseif (y <= 2.1e+118)
		tmp = t_1;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+18], t$95$2, If[LessEqual[y, -9.4e-60], t$95$1, If[LessEqual[y, -1.8e-274], t$95$2, If[LessEqual[y, 4.2e-106], t$95$1, If[LessEqual[y, 3.5e-90], t$95$2, If[LessEqual[y, 2.1e+118], t$95$1, N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5e18 or -9.4e-60 < y < -1.79999999999999991e-274 or 4.20000000000000007e-106 < y < 3.4999999999999999e-90

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 43.6%

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

      1. associate-*r/ 43.6%

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

      2. associate-/l* 43.5%

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

      3. associate-/r/ 43.6%

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

   7. Simplified 43.6%

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

   if -9.5e18 < y < -9.4e-60 or -1.79999999999999991e-274 < y < 4.20000000000000007e-106 or 3.4999999999999999e-90 < y < 2.1e118

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 56.6%

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

   if 2.1e118 < y

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 88.8%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-60}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-106}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+118}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+132} \lor \neg \left(x \leq -2 \cdot 10^{+103}\right) \land x \leq -4.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.2e+132) (and (not (<= x -2e+103)) (<= x -4.6e+58)))
   (/ (* x 0.5) t)
   (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.2e+132) || (!(x <= -2e+103) && (x <= -4.6e+58))) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-8.2d+132)) .or. (.not. (x <= (-2d+103))) .and. (x <= (-4.6d+58))) then
        tmp = (x * 0.5d0) / t
    else
        tmp = (-0.5d0) * ((z - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.2e+132) || (!(x <= -2e+103) && (x <= -4.6e+58))) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.2e+132) or (not (x <= -2e+103) and (x <= -4.6e+58)):
		tmp = (x * 0.5) / t
	else:
		tmp = -0.5 * ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.2e+132) || (!(x <= -2e+103) && (x <= -4.6e+58)))
		tmp = Float64(Float64(x * 0.5) / t);
	else
		tmp = Float64(-0.5 * Float64(Float64(z - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.2e+132) || (~((x <= -2e+103)) && (x <= -4.6e+58)))
		tmp = (x * 0.5) / t;
	else
		tmp = -0.5 * ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.2e+132], And[N[Not[LessEqual[x, -2e+103]], $MachinePrecision], LessEqual[x, -4.6e+58]]], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(-0.5 * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.19999999999999983e132 or -2e103 < x < -4.60000000000000005e58

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 82.9%

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

      1. associate-*r/ 82.9%

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

   7. Simplified 82.9%

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

   if -8.19999999999999983e132 < x < -2e103 or -4.60000000000000005e58 < x

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 82.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+132} \lor \neg \left(x \leq -2 \cdot 10^{+103}\right) \land x \leq -4.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+19} \lor \neg \left(y \leq 2.8 \cdot 10^{+117}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.75e+19) (not (<= y 2.8e+117)))
   (* 0.5 (/ y t))
   (* -0.5 (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.75e+19) || !(y <= 2.8e+117)) {
		tmp = 0.5 * (y / t);
	} else {
		tmp = -0.5 * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.75d+19)) .or. (.not. (y <= 2.8d+117))) then
        tmp = 0.5d0 * (y / t)
    else
        tmp = (-0.5d0) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.75e+19) || !(y <= 2.8e+117)) {
		tmp = 0.5 * (y / t);
	} else {
		tmp = -0.5 * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.75e+19) or not (y <= 2.8e+117):
		tmp = 0.5 * (y / t)
	else:
		tmp = -0.5 * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.75e+19) || !(y <= 2.8e+117))
		tmp = Float64(0.5 * Float64(y / t));
	else
		tmp = Float64(-0.5 * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.75e+19) || ~((y <= 2.8e+117)))
		tmp = 0.5 * (y / t);
	else
		tmp = -0.5 * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.75e+19], N[Not[LessEqual[y, 2.8e+117]], $MachinePrecision]], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e19 or 2.79999999999999997e117 < y

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 73.6%

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

   if -1.75e19 < y < 2.79999999999999997e117

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 51.5%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+19} \lor \neg \left(y \leq 2.8 \cdot 10^{+117}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-170}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1e-170) (* (/ -0.5 t) (- z x)) (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-170) {
		tmp = (-0.5 / t) * (z - x);
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1d-170)) then
        tmp = ((-0.5d0) / t) * (z - x)
    else
        tmp = (-0.5d0) * ((z - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-170) {
		tmp = (-0.5 / t) * (z - x);
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1e-170:
		tmp = (-0.5 / t) * (z - x)
	else:
		tmp = -0.5 * ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1e-170)
		tmp = Float64(Float64(-0.5 / t) * Float64(z - x));
	else
		tmp = Float64(-0.5 * Float64(Float64(z - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1e-170)
		tmp = (-0.5 / t) * (z - x);
	else
		tmp = -0.5 * ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-170], N[(N[(-0.5 / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.99999999999999983e-171

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 69.0%

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

      1. associate-*r/ 69.0%

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

      2. associate-/l* 68.8%

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

      3. associate-/r/ 68.9%

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

   7. Simplified 68.9%

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

   if -9.99999999999999983e-171 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 76.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-170}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.9e+51) (* 0.5 (/ (+ x y) t)) (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e+51) {
		tmp = 0.5 * ((x + y) / t);
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.9d+51)) then
        tmp = 0.5d0 * ((x + y) / t)
    else
        tmp = (-0.5d0) * ((z - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e+51) {
		tmp = 0.5 * ((x + y) / t);
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.9e+51:
		tmp = 0.5 * ((x + y) / t)
	else:
		tmp = -0.5 * ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.9e+51)
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	else
		tmp = Float64(-0.5 * Float64(Float64(z - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.9e+51)
		tmp = 0.5 * ((x + y) / t);
	else
		tmp = -0.5 * ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.9e+51], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8999999999999998e51

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 87.3%

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

   if -2.8999999999999998e51 < x

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 82.2%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. *-lft-identity 100.0%

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

   2. metadata-eval 100.0%

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

   3. times-frac 100.0%

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

   4. neg-mul-1 100.0%

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

   5. sub-neg 100.0%

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

   6. +-commutative 100.0%

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

   7. distribute-neg-in 100.0%

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

   8. remove-double-neg 100.0%

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

   9. sub-neg 100.0%

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

   10. +-commutative 100.0%

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

   11. associate--r+ 100.0%

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

   12. neg-mul-1 100.0%

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

   13. distribute-rgt-neg-in 100.0%

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

   14. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in z around inf 39.8%

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

6. Final simplification 39.8%

   \[\leadsto -0.5 \cdot \frac{z}{t} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(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)))