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

Percentage Accurate: 99.9% → 99.9%

Time: 6.7s

Alternatives: 9

Speedup: 1.0×

• 26.3% 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: 46.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.5 \cdot \frac{z}{t}\\ t_2 := 0.5 \cdot \frac{x}{t}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.5 (/ z t))) (t_2 (* 0.5 (/ x t))))
   (if (<= y -1.1e-92)
     t_2
     (if (<= y -1.5e-157)
       t_1
       (if (<= y 9.5e-106) t_2 (if (<= y 5.1e+66) 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 = 0.5 * (x / t);
	double tmp;
	if (y <= -1.1e-92) {
		tmp = t_2;
	} else if (y <= -1.5e-157) {
		tmp = t_1;
	} else if (y <= 9.5e-106) {
		tmp = t_2;
	} else if (y <= 5.1e+66) {
		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 = 0.5d0 * (x / t)
    if (y <= (-1.1d-92)) then
        tmp = t_2
    else if (y <= (-1.5d-157)) then
        tmp = t_1
    else if (y <= 9.5d-106) then
        tmp = t_2
    else if (y <= 5.1d+66) 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 = 0.5 * (x / t);
	double tmp;
	if (y <= -1.1e-92) {
		tmp = t_2;
	} else if (y <= -1.5e-157) {
		tmp = t_1;
	} else if (y <= 9.5e-106) {
		tmp = t_2;
	} else if (y <= 5.1e+66) {
		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 = 0.5 * (x / t)
	tmp = 0
	if y <= -1.1e-92:
		tmp = t_2
	elif y <= -1.5e-157:
		tmp = t_1
	elif y <= 9.5e-106:
		tmp = t_2
	elif y <= 5.1e+66:
		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(0.5 * Float64(x / t))
	tmp = 0.0
	if (y <= -1.1e-92)
		tmp = t_2;
	elseif (y <= -1.5e-157)
		tmp = t_1;
	elseif (y <= 9.5e-106)
		tmp = t_2;
	elseif (y <= 5.1e+66)
		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 = 0.5 * (x / t);
	tmp = 0.0;
	if (y <= -1.1e-92)
		tmp = t_2;
	elseif (y <= -1.5e-157)
		tmp = t_1;
	elseif (y <= 9.5e-106)
		tmp = t_2;
	elseif (y <= 5.1e+66)
		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[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e-92], t$95$2, If[LessEqual[y, -1.5e-157], t$95$1, If[LessEqual[y, 9.5e-106], t$95$2, If[LessEqual[y, 5.1e+66], t$95$1, N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.09999999999999994e-92 or -1.5e-157 < y < 9.4999999999999994e-106

   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. *-commutative 100.0%

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

      5. times-frac 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub0-neg 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.6%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.6%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.6%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.6%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.6%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.6%

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

      17. +-commutative 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. associate--r+ 99.6%

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

      21. *-commutative 99.6%

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

      22. associate-/r* 99.6%

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

      23. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 47.4%

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

   if -1.09999999999999994e-92 < y < -1.5e-157 or 9.4999999999999994e-106 < y < 5.10000000000000008e66

   1. Initial program 99.9%

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

      1. *-lft-identity 99.9%

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

      2. metadata-eval 99.9%

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

      3. times-frac 99.9%

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

      4. *-commutative 99.9%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 51.3%

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

   if 5.10000000000000008e66 < 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. *-commutative 100.0%

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

      5. times-frac 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.9%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.9%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.9%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.9%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.9%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.9%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.9%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.9%

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

      17. +-commutative 99.9%

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

      18. sub-neg 99.9%

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

      19. +-commutative 99.9%

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

      20. associate--r+ 99.9%

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

      21. *-commutative 99.9%

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

      22. associate-/r* 99.9%

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

      23. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 65.3%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-92}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-157}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-106}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+66}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+138} \lor \neg \left(x \leq -1.25 \cdot 10^{+119}\right) \land x \leq -1.5 \cdot 10^{+42}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.5e+138) (and (not (<= x -1.25e+119)) (<= x -1.5e+42)))
   (* 0.5 (/ x t))
   (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.5e+138) || (!(x <= -1.25e+119) && (x <= -1.5e+42))) {
		tmp = 0.5 * (x / 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 <= (-3.5d+138)) .or. (.not. (x <= (-1.25d+119))) .and. (x <= (-1.5d+42))) then
        tmp = 0.5d0 * (x / 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 <= -3.5e+138) || (!(x <= -1.25e+119) && (x <= -1.5e+42))) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.5e+138) or (not (x <= -1.25e+119) and (x <= -1.5e+42)):
		tmp = 0.5 * (x / t)
	else:
		tmp = -0.5 * ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.5e+138) || (!(x <= -1.25e+119) && (x <= -1.5e+42)))
		tmp = Float64(0.5 * Float64(x / 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 <= -3.5e+138) || (~((x <= -1.25e+119)) && (x <= -1.5e+42)))
		tmp = 0.5 * (x / t);
	else
		tmp = -0.5 * ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.5e+138], And[N[Not[LessEqual[x, -1.25e+119]], $MachinePrecision], LessEqual[x, -1.5e+42]]], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4999999999999998e138 or -1.25e119 < x < -1.50000000000000014e42

   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. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 77.5%

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

   if -3.4999999999999998e138 < x < -1.25e119 or -1.50000000000000014e42 < 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. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 75.6%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+138} \lor \neg \left(x \leq -1.25 \cdot 10^{+119}\right) \land x \leq -1.5 \cdot 10^{+42}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-242}:\\ \;\;\;\;\frac{-0.5 \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -2e-242) (/ (* -0.5 (- z x)) t) (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -2e-242) {
		tmp = (-0.5 * (z - x)) / 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 + y) <= (-2d-242)) then
        tmp = ((-0.5d0) * (z - x)) / 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 + y) <= -2e-242) {
		tmp = (-0.5 * (z - x)) / t;
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -2e-242:
		tmp = (-0.5 * (z - x)) / t
	else:
		tmp = -0.5 * ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -2e-242)
		tmp = Float64(Float64(-0.5 * Float64(z - x)) / 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 + y) <= -2e-242)
		tmp = (-0.5 * (z - x)) / t;
	else
		tmp = -0.5 * ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -2e-242], N[(N[(-0.5 * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(-0.5 * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -2e-242

   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. *-commutative 100.0%

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

      5. times-frac 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub0-neg 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.6%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.6%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.6%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.6%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.6%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.6%

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

      17. +-commutative 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. associate--r+ 99.6%

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

      21. *-commutative 99.6%

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

      22. associate-/r* 99.6%

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

      23. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 68.2%

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

      1. associate-*r/ 68.2%

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

   7. Simplified 68.2%

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

   if -2e-242 < (+.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. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 66.5%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-242}:\\ \;\;\;\;\frac{-0.5 \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 8.1e-13) (* (/ -0.5 t) (- z x)) (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.1e-13) {
		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 (y <= 8.1d-13) 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 (y <= 8.1e-13) {
		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 y <= 8.1e-13:
		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 (y <= 8.1e-13)
		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 (y <= 8.1e-13)
		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[y, 8.1e-13], 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 y < 8.0999999999999998e-13

   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. *-commutative 100.0%

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

      5. times-frac 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub0-neg 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.6%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.6%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.6%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.6%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.6%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.6%

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

      17. +-commutative 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. associate--r+ 99.6%

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

      21. *-commutative 99.6%

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

      22. associate-/r* 99.6%

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

      23. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.8%

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

   7. Simplified 77.8%

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

      1. associate-/l* 77.3%

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

      2. associate-/r/ 77.5%

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

   9. Applied egg-rr 77.5%

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

   if 8.0999999999999998e-13 < 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. *-commutative 100.0%

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

      5. times-frac 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub0-neg 99.8%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.8%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.8%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.8%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.8%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.8%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.8%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.8%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.8%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.8%

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

      17. +-commutative 99.8%

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

      18. sub-neg 99.8%

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

      19. +-commutative 99.8%

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

      20. associate--r+ 99.8%

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

      21. *-commutative 99.8%

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

      22. associate-/r* 99.8%

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

      23. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 80.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{-0.5}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.15e-12) (/ -0.5 (/ t (- z x))) (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.15e-12) {
		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 (y <= 1.15d-12) 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 (y <= 1.15e-12) {
		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 y <= 1.15e-12:
		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 (y <= 1.15e-12)
		tmp = Float64(-0.5 / Float64(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 (y <= 1.15e-12)
		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[y, 1.15e-12], N[(-0.5 / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.14999999999999995e-12

   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. *-commutative 100.0%

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

      5. times-frac 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub0-neg 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.6%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.6%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.6%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.6%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.6%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.6%

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

      17. +-commutative 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. associate--r+ 99.6%

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

      21. *-commutative 99.6%

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

      22. associate-/r* 99.6%

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

      23. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. associate-/l* 77.3%

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

   7. Simplified 77.3%

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

   if 1.14999999999999995e-12 < 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. *-commutative 100.0%

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

      5. times-frac 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub0-neg 99.8%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.8%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.8%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.8%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.8%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.8%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.8%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.8%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.8%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.8%

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

      17. +-commutative 99.8%

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

      18. sub-neg 99.8%

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

      19. +-commutative 99.8%

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

      20. associate--r+ 99.8%

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

      21. *-commutative 99.8%

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

      22. associate-/r* 99.8%

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

      23. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 80.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 45.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-35}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.8e-35) (* 0.5 (/ x t)) (* -0.5 (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.8e-35) {
		tmp = 0.5 * (x / 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 (x <= (-8.8d-35)) then
        tmp = 0.5d0 * (x / 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 (x <= -8.8e-35) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = -0.5 * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.8e-35:
		tmp = 0.5 * (x / t)
	else:
		tmp = -0.5 * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.8e-35)
		tmp = Float64(0.5 * Float64(x / 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 (x <= -8.8e-35)
		tmp = 0.5 * (x / t);
	else
		tmp = -0.5 * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.8e-35], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999975e-35

   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. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 61.5%

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

   if -8.79999999999999975e-35 < 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. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 45.4%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-35}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. *-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. *-commutative 100.0%

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

   5. times-frac 99.7%

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

   6. remove-double-neg 99.7%

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

   7. sub0-neg 99.7%

      \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

   8. div-sub 99.7%

      \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

   9. metadata-eval 99.7%

      \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   10. neg-mul-1 99.7%

       \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   11. *-commutative 99.7%

       \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   12. associate-/l* 99.7%

       \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

   13. metadata-eval 99.7%

       \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

   14. /-rgt-identity 99.7%

       \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

   15. associate--r- 99.7%

       \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

   16. neg-sub0 99.7%

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

   17. +-commutative 99.7%

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

   18. sub-neg 99.7%

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

   19. +-commutative 99.7%

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

   20. associate--r+ 99.7%

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

   21. *-commutative 99.7%

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

   22. associate-/r* 99.7%

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

   23. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Final simplification 99.7%

   \[\leadsto \left(\left(z - y\right) - x\right) \cdot \frac{-0.5}{t} \]
6. Add Preprocessing

Alternative 9: 37.5% 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. *-commutative 100.0%

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

   5. times-frac 99.7%

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

   6. remove-double-neg 99.7%

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

   7. sub0-neg 99.7%

      \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

   8. div-sub 99.7%

      \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

   9. metadata-eval 99.7%

      \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   10. neg-mul-1 99.7%

       \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   11. *-commutative 99.7%

       \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   12. associate-/l* 99.7%

       \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

   13. metadata-eval 99.7%

       \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

   14. /-rgt-identity 99.7%

       \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

   15. associate--r- 99.7%

       \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

   16. neg-sub0 99.7%

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

   17. +-commutative 99.7%

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

   18. sub-neg 99.7%

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

   19. +-commutative 99.7%

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

   20. associate--r+ 99.7%

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

   21. *-commutative 99.7%

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

   22. associate-/r* 99.7%

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

   23. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in z around inf 38.2%

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

6. Final simplification 38.2%

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

Reproduce

herbie shell --seed 2024021 
(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)))