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

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 11

Speedup: 1.0×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\left(-y\right) - x, z, x + y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- (- y) x) z (+ x y)))

C

double code(double x, double y, double z) {
	return fma((-y - x), z, (x + y));
}

Julia

function code(x, y, z)
	return fma(Float64(Float64(-y) - x), z, Float64(x + y))
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

   1. +-commutative 100.0%

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

   2. distribute-rgt-neg-out 100.0%

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

   3. distribute-lft-neg-in 100.0%

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

   4. add-sqr-sqrt 46.8%

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

   5. sqrt-unprod 68.0%

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

   6. sqr-neg 68.0%

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

   7. sqrt-unprod 25.2%

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

   8. add-sqr-sqrt 47.5%

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

   9. fma-define 47.5%

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

   10. add-sqr-sqrt 25.2%

       \[\leadsto \mathsf{fma}\left(-\left(x + y\right), \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}, x + y\right) \]

   11. sqrt-unprod 68.0%

       \[\leadsto \mathsf{fma}\left(-\left(x + y\right), \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}, x + y\right) \]

   12. sqr-neg 68.0%

       \[\leadsto \mathsf{fma}\left(-\left(x + y\right), \sqrt{\color{blue}{z \cdot z}}, x + y\right) \]

   13. sqrt-unprod 46.8%

       \[\leadsto \mathsf{fma}\left(-\left(x + y\right), \color{blue}{\sqrt{z} \cdot \sqrt{z}}, x + y\right) \]

   14. add-sqr-sqrt 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(\left(-y\right) - x, z, x + y\right) \]
8. Add Preprocessing

Alternative 2: 75.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -5.35 \cdot 10^{+185}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1950000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.24:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+125} \lor \neg \left(z \leq 1.02 \cdot 10^{+154} \lor \neg \left(z \leq 6 \cdot 10^{+177}\right) \land z \leq 2.3 \cdot 10^{+260}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* y (- z))))
   (if (<= z -5.35e+185)
     t_0
     (if (<= z -3.35e+133)
       t_1
       (if (<= z -1.9e+73)
         t_0
         (if (<= z -1.2e+37)
           t_1
           (if (<= z -1950000.0)
             t_0
             (if (<= z 0.24)
               (+ x y)
               (if (or (<= z 2.55e+125)
                       (not
                        (or (<= z 1.02e+154)
                            (and (not (<= z 6e+177)) (<= z 2.3e+260)))))
                 t_0
                 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * -z;
	double tmp;
	if (z <= -5.35e+185) {
		tmp = t_0;
	} else if (z <= -3.35e+133) {
		tmp = t_1;
	} else if (z <= -1.9e+73) {
		tmp = t_0;
	} else if (z <= -1.2e+37) {
		tmp = t_1;
	} else if (z <= -1950000.0) {
		tmp = t_0;
	} else if (z <= 0.24) {
		tmp = x + y;
	} else if ((z <= 2.55e+125) || !((z <= 1.02e+154) || (!(z <= 6e+177) && (z <= 2.3e+260)))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * -z
    t_1 = y * -z
    if (z <= (-5.35d+185)) then
        tmp = t_0
    else if (z <= (-3.35d+133)) then
        tmp = t_1
    else if (z <= (-1.9d+73)) then
        tmp = t_0
    else if (z <= (-1.2d+37)) then
        tmp = t_1
    else if (z <= (-1950000.0d0)) then
        tmp = t_0
    else if (z <= 0.24d0) then
        tmp = x + y
    else if ((z <= 2.55d+125) .or. (.not. (z <= 1.02d+154) .or. (.not. (z <= 6d+177)) .and. (z <= 2.3d+260))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * -z;
	double tmp;
	if (z <= -5.35e+185) {
		tmp = t_0;
	} else if (z <= -3.35e+133) {
		tmp = t_1;
	} else if (z <= -1.9e+73) {
		tmp = t_0;
	} else if (z <= -1.2e+37) {
		tmp = t_1;
	} else if (z <= -1950000.0) {
		tmp = t_0;
	} else if (z <= 0.24) {
		tmp = x + y;
	} else if ((z <= 2.55e+125) || !((z <= 1.02e+154) || (!(z <= 6e+177) && (z <= 2.3e+260)))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = y * -z
	tmp = 0
	if z <= -5.35e+185:
		tmp = t_0
	elif z <= -3.35e+133:
		tmp = t_1
	elif z <= -1.9e+73:
		tmp = t_0
	elif z <= -1.2e+37:
		tmp = t_1
	elif z <= -1950000.0:
		tmp = t_0
	elif z <= 0.24:
		tmp = x + y
	elif (z <= 2.55e+125) or not ((z <= 1.02e+154) or (not (z <= 6e+177) and (z <= 2.3e+260))):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -5.35e+185)
		tmp = t_0;
	elseif (z <= -3.35e+133)
		tmp = t_1;
	elseif (z <= -1.9e+73)
		tmp = t_0;
	elseif (z <= -1.2e+37)
		tmp = t_1;
	elseif (z <= -1950000.0)
		tmp = t_0;
	elseif (z <= 0.24)
		tmp = Float64(x + y);
	elseif ((z <= 2.55e+125) || !((z <= 1.02e+154) || (!(z <= 6e+177) && (z <= 2.3e+260))))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = y * -z;
	tmp = 0.0;
	if (z <= -5.35e+185)
		tmp = t_0;
	elseif (z <= -3.35e+133)
		tmp = t_1;
	elseif (z <= -1.9e+73)
		tmp = t_0;
	elseif (z <= -1.2e+37)
		tmp = t_1;
	elseif (z <= -1950000.0)
		tmp = t_0;
	elseif (z <= 0.24)
		tmp = x + y;
	elseif ((z <= 2.55e+125) || ~(((z <= 1.02e+154) || (~((z <= 6e+177)) && (z <= 2.3e+260)))))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -5.35e+185], t$95$0, If[LessEqual[z, -3.35e+133], t$95$1, If[LessEqual[z, -1.9e+73], t$95$0, If[LessEqual[z, -1.2e+37], t$95$1, If[LessEqual[z, -1950000.0], t$95$0, If[LessEqual[z, 0.24], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 2.55e+125], N[Not[Or[LessEqual[z, 1.02e+154], And[N[Not[LessEqual[z, 6e+177]], $MachinePrecision], LessEqual[z, 2.3e+260]]]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3500000000000001e185 or -3.35000000000000015e133 < z < -1.90000000000000011e73 or -1.2e37 < z < -1.95e6 or 0.23999999999999999 < z < 2.5499999999999999e125 or 1.02000000000000007e154 < z < 6e177 or 2.30000000000000011e260 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 52.5%

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

   6. Taylor expanded in z around inf 51.4%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 51.4%

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

      2. neg-mul-1 51.4%

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

   8. Simplified 51.4%

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

   if -5.3500000000000001e185 < z < -3.35000000000000015e133 or -1.90000000000000011e73 < z < -1.2e37 or 2.5499999999999999e125 < z < 1.02000000000000007e154 or 6e177 < z < 2.30000000000000011e260

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. distribute-lft-in 99.9%

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

      3. *-commutative 99.9%

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

      4. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around 0 60.6%

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

      1. associate-*r* 60.6%

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

      2. mul-1-neg 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in z around inf 60.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 60.6%

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

      2. distribute-rgt-neg-in 60.6%

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

   10. Simplified 60.6%

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

   if -1.95e6 < z < 0.23999999999999999

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.6%

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

      1. +-commutative 94.6%

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

   5. Simplified 94.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.35 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1950000:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 0.24:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+125} \lor \neg \left(z \leq 1.02 \cdot 10^{+154} \lor \neg \left(z \leq 6 \cdot 10^{+177}\right) \land z \leq 2.3 \cdot 10^{+260}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;1 - z \leq -1 \cdot 10^{+270}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq -1 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -1 \cdot 10^{+39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+61} \lor \neg \left(1 - z \leq 5 \cdot 10^{+118}\right) \land 1 - z \leq 5.35 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= (- 1.0 z) -1e+270)
     t_0
     (if (<= (- 1.0 z) -1e+205)
       (* y (- z))
       (if (<= (- 1.0 z) -1e+39)
         t_0
         (if (<= (- 1.0 z) 1.0)
           (+ x y)
           (if (or (<= (- 1.0 z) 1e+61)
                   (and (not (<= (- 1.0 z) 5e+118)) (<= (- 1.0 z) 5.35e+185)))
             (* y (- 1.0 z))
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if ((1.0 - z) <= -1e+270) {
		tmp = t_0;
	} else if ((1.0 - z) <= -1e+205) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -1e+39) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.0) {
		tmp = x + y;
	} else if (((1.0 - z) <= 1e+61) || (!((1.0 - z) <= 5e+118) && ((1.0 - z) <= 5.35e+185))) {
		tmp = y * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * -z
    if ((1.0d0 - z) <= (-1d+270)) then
        tmp = t_0
    else if ((1.0d0 - z) <= (-1d+205)) then
        tmp = y * -z
    else if ((1.0d0 - z) <= (-1d+39)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 1.0d0) then
        tmp = x + y
    else if (((1.0d0 - z) <= 1d+61) .or. (.not. ((1.0d0 - z) <= 5d+118)) .and. ((1.0d0 - z) <= 5.35d+185)) then
        tmp = y * (1.0d0 - z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if ((1.0 - z) <= -1e+270) {
		tmp = t_0;
	} else if ((1.0 - z) <= -1e+205) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -1e+39) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.0) {
		tmp = x + y;
	} else if (((1.0 - z) <= 1e+61) || (!((1.0 - z) <= 5e+118) && ((1.0 - z) <= 5.35e+185))) {
		tmp = y * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if (1.0 - z) <= -1e+270:
		tmp = t_0
	elif (1.0 - z) <= -1e+205:
		tmp = y * -z
	elif (1.0 - z) <= -1e+39:
		tmp = t_0
	elif (1.0 - z) <= 1.0:
		tmp = x + y
	elif ((1.0 - z) <= 1e+61) or (not ((1.0 - z) <= 5e+118) and ((1.0 - z) <= 5.35e+185)):
		tmp = y * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (Float64(1.0 - z) <= -1e+270)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= -1e+205)
		tmp = Float64(y * Float64(-z));
	elseif (Float64(1.0 - z) <= -1e+39)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 1.0)
		tmp = Float64(x + y);
	elseif ((Float64(1.0 - z) <= 1e+61) || (!(Float64(1.0 - z) <= 5e+118) && (Float64(1.0 - z) <= 5.35e+185)))
		tmp = Float64(y * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if ((1.0 - z) <= -1e+270)
		tmp = t_0;
	elseif ((1.0 - z) <= -1e+205)
		tmp = y * -z;
	elseif ((1.0 - z) <= -1e+39)
		tmp = t_0;
	elseif ((1.0 - z) <= 1.0)
		tmp = x + y;
	elseif (((1.0 - z) <= 1e+61) || (~(((1.0 - z) <= 5e+118)) && ((1.0 - z) <= 5.35e+185)))
		tmp = y * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -1e+270], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], -1e+205], N[(y * (-z)), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], -1e+39], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], 1e+61], And[N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 5e+118]], $MachinePrecision], LessEqual[N[(1.0 - z), $MachinePrecision], 5.35e+185]]], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -1e270 or -1.00000000000000002e205 < (-.f64 #s(literal 1 binary64) z) < -9.9999999999999994e38 or 9.99999999999999949e60 < (-.f64 #s(literal 1 binary64) z) < 4.99999999999999972e118 or 5.3500000000000001e185 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 48.2%

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

   6. Taylor expanded in z around inf 48.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.2%

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

      2. neg-mul-1 48.2%

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

   8. Simplified 48.2%

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

   if -1e270 < (-.f64 #s(literal 1 binary64) z) < -1.00000000000000002e205

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 70.9%

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

      1. associate-*r* 70.9%

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

      2. mul-1-neg 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in z around inf 70.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 70.9%

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

      2. distribute-rgt-neg-in 70.9%

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

   10. Simplified 70.9%

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

   if -9.9999999999999994e38 < (-.f64 #s(literal 1 binary64) z) < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.2%

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

      1. +-commutative 94.2%

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

   5. Simplified 94.2%

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

   if 1 < (-.f64 #s(literal 1 binary64) z) < 9.99999999999999949e60 or 4.99999999999999972e118 < (-.f64 #s(literal 1 binary64) z) < 5.3500000000000001e185

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 48.9%

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -1 \cdot 10^{+270}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -1 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -1 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+61} \lor \neg \left(1 - z \leq 5 \cdot 10^{+118}\right) \land 1 - z \leq 5.35 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-123} \lor \neg \left(x \leq -1.55 \cdot 10^{-180}\right) \land x \leq -1.6 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.4e-123) (and (not (<= x -1.55e-180)) (<= x -1.6e-186)))
   (* x (- 1.0 z))
   (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e-123) || (!(x <= -1.55e-180) && (x <= -1.6e-186))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.4d-123)) .or. (.not. (x <= (-1.55d-180))) .and. (x <= (-1.6d-186))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e-123) || (!(x <= -1.55e-180) && (x <= -1.6e-186))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.4e-123) or (not (x <= -1.55e-180) and (x <= -1.6e-186)):
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.4e-123) || (!(x <= -1.55e-180) && (x <= -1.6e-186)))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.4e-123) || (~((x <= -1.55e-180)) && (x <= -1.6e-186)))
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.4e-123], And[N[Not[LessEqual[x, -1.55e-180]], $MachinePrecision], LessEqual[x, -1.6e-186]]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e-123 or -1.5499999999999999e-180 < x < -1.6e-186

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 62.1%

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

      1. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   if -2.4e-123 < x < -1.5499999999999999e-180 or -1.6e-186 < x

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 60.6%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-123} \lor \neg \left(x \leq -1.55 \cdot 10^{-180}\right) \land x \leq -1.6 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.7% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -1e+15) (not (<= (- 1.0 z) 1.0)))
   (* (- (- y) x) z)
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -1e+15) || !((1.0 - z) <= 1.0)) {
		tmp = (-y - x) * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - z) <= (-1d+15)) .or. (.not. ((1.0d0 - z) <= 1.0d0))) then
        tmp = (-y - x) * z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -1e+15) || !((1.0 - z) <= 1.0)) {
		tmp = (-y - x) * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -1e+15) or not ((1.0 - z) <= 1.0):
		tmp = (-y - x) * z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -1e+15) || !(Float64(1.0 - z) <= 1.0))
		tmp = Float64(Float64(Float64(-y) - x) * z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -1e+15) || ~(((1.0 - z) <= 1.0)))
		tmp = (-y - x) * z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -1e+15], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[((-y) - x), $MachinePrecision] * z), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -1e15 or 1 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 95.3%

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

      1. mul-1-neg 95.3%

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

      2. distribute-lft-neg-out 95.3%

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

      3. *-commutative 95.3%

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

      4. +-commutative 95.3%

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

   5. Simplified 95.3%

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

   if -1e15 < (-.f64 #s(literal 1 binary64) z) < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 97.3%

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

      1. +-commutative 97.3%

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

   5. Simplified 97.3%

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

4. Final simplification 96.3%

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

Alternative 6: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+38} \lor \neg \left(z \leq 1.6 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e+38) (not (<= z 1.6e-5))) (* y (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e+38) || !(z <= 1.6e-5)) {
		tmp = y * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.8d+38)) .or. (.not. (z <= 1.6d-5))) then
        tmp = y * -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e+38) || !(z <= 1.6e-5)) {
		tmp = y * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e+38) or not (z <= 1.6e-5):
		tmp = y * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e+38) || !(z <= 1.6e-5))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.8e+38) || ~((z <= 1.6e-5)))
		tmp = y * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e+38], N[Not[LessEqual[z, 1.6e-5]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e38 or 1.59999999999999993e-5 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-lft-in 99.9%

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

      3. *-commutative 99.9%

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

      4. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around 0 55.3%

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

      1. associate-*r* 55.3%

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

      2. mul-1-neg 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in z around inf 53.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 53.7%

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

      2. distribute-rgt-neg-in 53.7%

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

   10. Simplified 53.7%

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

   if -2.8e38 < z < 1.59999999999999993e-5

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 90.9%

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

      1. +-commutative 90.9%

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

   5. Simplified 90.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+38} \lor \neg \left(z \leq 1.6 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \left(x + y\right) - \left(x + y\right) \cdot z \]
6. Add Preprocessing

Alternative 8: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 9: 29.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 2.7e-219) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.7e-219) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.7d-219) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.7e-219) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.7e-219:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.7e-219)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.7e-219)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.7e-219], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.7e-219

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 54.9%

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

      1. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in z around 0 27.2%

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

   if 2.7e-219 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.4%

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

   4. Taylor expanded in z around 0 36.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 50.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x y))

C

double code(double x, double y, double z) {
	return x + y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + y
end function

Java

public static double code(double x, double y, double z) {
	return x + y;
}

Python

def code(x, y, z):
	return x + y

Julia

function code(x, y, z)
	return Float64(x + y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + y;
end

Wolfram

code[x_, y_, z_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 49.3%

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

   1. +-commutative 49.3%

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

5. Simplified 49.3%

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

6. Final simplification 49.3%

   \[\leadsto x + y \]
7. Add Preprocessing

Alternative 11: 26.4% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 48.4%

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

   1. *-commutative 48.4%

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

5. Simplified 48.4%

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

6. Taylor expanded in z around 0 24.0%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))