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

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 6

Speedup: 1.0×

• 20.3% 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, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (1.0 - z) * (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 = (1.0d0 - z) * (x + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 74.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;1 - z \leq -5 \cdot 10^{+226}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;1 - z \leq -400000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 2 \cdot 10^{+184}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* z (- y))))
   (if (<= (- 1.0 z) -5e+226)
     t_0
     (if (<= (- 1.0 z) -5e+74)
       t_1
       (if (<= (- 1.0 z) -400000.0)
         t_0
         (if (<= (- 1.0 z) 2.0)
           (+ x y)
           (if (<= (- 1.0 z) 2e+184) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = z * -y;
	double tmp;
	if ((1.0 - z) <= -5e+226) {
		tmp = t_0;
	} else if ((1.0 - z) <= -5e+74) {
		tmp = t_1;
	} else if ((1.0 - z) <= -400000.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 2e+184) {
		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 = z * -y
    if ((1.0d0 - z) <= (-5d+226)) then
        tmp = t_0
    else if ((1.0d0 - z) <= (-5d+74)) then
        tmp = t_1
    else if ((1.0d0 - z) <= (-400000.0d0)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 2.0d0) then
        tmp = x + y
    else if ((1.0d0 - z) <= 2d+184) 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 = z * -y;
	double tmp;
	if ((1.0 - z) <= -5e+226) {
		tmp = t_0;
	} else if ((1.0 - z) <= -5e+74) {
		tmp = t_1;
	} else if ((1.0 - z) <= -400000.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 2e+184) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = z * -y
	tmp = 0
	if (1.0 - z) <= -5e+226:
		tmp = t_0
	elif (1.0 - z) <= -5e+74:
		tmp = t_1
	elif (1.0 - z) <= -400000.0:
		tmp = t_0
	elif (1.0 - z) <= 2.0:
		tmp = x + y
	elif (1.0 - z) <= 2e+184:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (Float64(1.0 - z) <= -5e+226)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= -5e+74)
		tmp = t_1;
	elseif (Float64(1.0 - z) <= -400000.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 2.0)
		tmp = Float64(x + y);
	elseif (Float64(1.0 - z) <= 2e+184)
		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 = z * -y;
	tmp = 0.0;
	if ((1.0 - z) <= -5e+226)
		tmp = t_0;
	elseif ((1.0 - z) <= -5e+74)
		tmp = t_1;
	elseif ((1.0 - z) <= -400000.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 2.0)
		tmp = x + y;
	elseif ((1.0 - z) <= 2e+184)
		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[(z * (-y)), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -5e+226], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], -5e+74], t$95$1, If[LessEqual[N[(1.0 - z), $MachinePrecision], -400000.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(x + y), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 2e+184], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -5.0000000000000005e226 or -4.99999999999999963e74 < (-.f64 #s(literal 1 binary64) z) < -4e5 or 2 < (-.f64 #s(literal 1 binary64) z) < 2.00000000000000003e184

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.2%

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

      1. mul-1-neg 97.2%

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

      2. distribute-lft-neg-out 97.2%

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

      3. *-commutative 97.2%

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

      4. +-commutative 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in y around 0 42.0%

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

      1. associate-*r* 42.0%

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

      2. mul-1-neg 42.0%

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

   8. Simplified 42.0%

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

   if -5.0000000000000005e226 < (-.f64 #s(literal 1 binary64) z) < -4.99999999999999963e74 or 2.00000000000000003e184 < (-.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 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

      4. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. fma-define 83.5%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -1, -1 \cdot \frac{y \cdot z}{x}\right)} \]

      3. mul-1-neg 83.5%

         \[\leadsto x \cdot \mathsf{fma}\left(z, -1, \color{blue}{-\frac{y \cdot z}{x}}\right) \]

      4. fma-neg 83.5%

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

      5. *-commutative 83.5%

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

      6. associate-/l* 85.2%

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

      7. distribute-lft-out-- 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in x around 0 57.1%

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

       1. mul-1-neg 57.1%

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

       2. distribute-lft-neg-out 57.1%

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

       3. *-commutative 57.1%

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

   11. Simplified 57.1%

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

   if -4e5 < (-.f64 #s(literal 1 binary64) z) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.5%

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

      1. +-commutative 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -5 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;1 - z \leq -400000:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 2 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -400000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -400000.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- x) y))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -400000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-x - y);
	} 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) <= (-400000.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = z * (-x - y)
    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) <= -400000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-x - y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -400000.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-x - y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -400000.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(z * Float64(Float64(-x) - y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -400000.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-x - y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -400000.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -4e5 or 2 < (-.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 98.4%

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

      1. mul-1-neg 98.4%

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

      2. distribute-lft-neg-out 98.4%

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

      3. *-commutative 98.4%

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

      4. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   if -4e5 < (-.f64 #s(literal 1 binary64) z) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.5%

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

      1. +-commutative 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -400000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -620000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -620000000000.0) (not (<= z 1.0))) (* z (- y)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -620000000000.0) || !(z <= 1.0)) {
		tmp = z * -y;
	} 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 <= (-620000000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -y
    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 <= -620000000000.0) || !(z <= 1.0)) {
		tmp = z * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -620000000000.0) or not (z <= 1.0):
		tmp = z * -y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -620000000000.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -620000000000.0) || ~((z <= 1.0)))
		tmp = z * -y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -620000000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e11 or 1 < 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 99.0%

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

      1. mul-1-neg 99.0%

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

      2. distribute-lft-neg-out 99.0%

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

      3. *-commutative 99.0%

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

      4. +-commutative 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in x around inf 80.1%

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

      1. *-commutative 80.1%

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

      2. fma-define 80.1%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -1, -1 \cdot \frac{y \cdot z}{x}\right)} \]

      3. mul-1-neg 80.1%

         \[\leadsto x \cdot \mathsf{fma}\left(z, -1, \color{blue}{-\frac{y \cdot z}{x}}\right) \]

      4. fma-neg 80.1%

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

      5. *-commutative 80.1%

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

      6. associate-/l* 82.4%

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

      7. distribute-lft-out-- 82.4%

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

   8. Simplified 82.4%

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

   9. Taylor expanded in x around 0 59.7%

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

       1. mul-1-neg 59.7%

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

       2. distribute-lft-neg-out 59.7%

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

       3. *-commutative 59.7%

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

   11. Simplified 59.7%

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

   if -6.2e11 < 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 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -620000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{+32}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1e+32) (* x (- 1.0 z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e+32) {
		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 (y <= 1d+32) 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 (y <= 1e+32) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1e+32:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1e+32)
		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 (y <= 1e+32)
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1e+32], 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 y < 1.00000000000000005e32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 55.4%

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

      1. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   if 1.00000000000000005e32 < 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 81.2%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{+32}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.3% 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 48.5%

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

   1. +-commutative 48.5%

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

5. Simplified 48.5%

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

6. Final simplification 48.5%

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

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))