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

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 8

Speedup: 1.0×

• 20.7% 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. Final simplification 100.0%

   \[\leadsto \left(1 - z\right) \cdot \left(x + y\right) \]

Alternative 2: 75.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - z\right)\\ t_1 := y \cdot \left(-z\right)\\ t_2 := x \cdot \left(-z\right)\\ \mathbf{if}\;1 - z \leq -2 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;1 - z \leq -1 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;1 - z \leq 0.999995:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 10^{+180} \lor \neg \left(1 - z \leq 2 \cdot 10^{+226}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 z))) (t_1 (* y (- z))) (t_2 (* x (- z))))
   (if (<= (- 1.0 z) -2e+206)
     t_1
     (if (<= (- 1.0 z) -5e+131)
       t_2
       (if (<= (- 1.0 z) -1e+43)
         t_1
         (if (<= (- 1.0 z) 0.999995)
           t_0
           (if (<= (- 1.0 z) 2.0)
             (+ x y)
             (if (<= (- 1.0 z) 1e+125)
               t_0
               (if (or (<= (- 1.0 z) 1e+180) (not (<= (- 1.0 z) 2e+226)))
                 t_1
                 t_2)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - z);
	double t_1 = y * -z;
	double t_2 = x * -z;
	double tmp;
	if ((1.0 - z) <= -2e+206) {
		tmp = t_1;
	} else if ((1.0 - z) <= -5e+131) {
		tmp = t_2;
	} else if ((1.0 - z) <= -1e+43) {
		tmp = t_1;
	} else if ((1.0 - z) <= 0.999995) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 1e+125) {
		tmp = t_0;
	} else if (((1.0 - z) <= 1e+180) || !((1.0 - z) <= 2e+226)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = x * (1.0d0 - z)
    t_1 = y * -z
    t_2 = x * -z
    if ((1.0d0 - z) <= (-2d+206)) then
        tmp = t_1
    else if ((1.0d0 - z) <= (-5d+131)) then
        tmp = t_2
    else if ((1.0d0 - z) <= (-1d+43)) then
        tmp = t_1
    else if ((1.0d0 - z) <= 0.999995d0) then
        tmp = t_0
    else if ((1.0d0 - z) <= 2.0d0) then
        tmp = x + y
    else if ((1.0d0 - z) <= 1d+125) then
        tmp = t_0
    else if (((1.0d0 - z) <= 1d+180) .or. (.not. ((1.0d0 - z) <= 2d+226))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - z);
	double t_1 = y * -z;
	double t_2 = x * -z;
	double tmp;
	if ((1.0 - z) <= -2e+206) {
		tmp = t_1;
	} else if ((1.0 - z) <= -5e+131) {
		tmp = t_2;
	} else if ((1.0 - z) <= -1e+43) {
		tmp = t_1;
	} else if ((1.0 - z) <= 0.999995) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 1e+125) {
		tmp = t_0;
	} else if (((1.0 - z) <= 1e+180) || !((1.0 - z) <= 2e+226)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - z)
	t_1 = y * -z
	t_2 = x * -z
	tmp = 0
	if (1.0 - z) <= -2e+206:
		tmp = t_1
	elif (1.0 - z) <= -5e+131:
		tmp = t_2
	elif (1.0 - z) <= -1e+43:
		tmp = t_1
	elif (1.0 - z) <= 0.999995:
		tmp = t_0
	elif (1.0 - z) <= 2.0:
		tmp = x + y
	elif (1.0 - z) <= 1e+125:
		tmp = t_0
	elif ((1.0 - z) <= 1e+180) or not ((1.0 - z) <= 2e+226):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - z))
	t_1 = Float64(y * Float64(-z))
	t_2 = Float64(x * Float64(-z))
	tmp = 0.0
	if (Float64(1.0 - z) <= -2e+206)
		tmp = t_1;
	elseif (Float64(1.0 - z) <= -5e+131)
		tmp = t_2;
	elseif (Float64(1.0 - z) <= -1e+43)
		tmp = t_1;
	elseif (Float64(1.0 - z) <= 0.999995)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 2.0)
		tmp = Float64(x + y);
	elseif (Float64(1.0 - z) <= 1e+125)
		tmp = t_0;
	elseif ((Float64(1.0 - z) <= 1e+180) || !(Float64(1.0 - z) <= 2e+226))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - z);
	t_1 = y * -z;
	t_2 = x * -z;
	tmp = 0.0;
	if ((1.0 - z) <= -2e+206)
		tmp = t_1;
	elseif ((1.0 - z) <= -5e+131)
		tmp = t_2;
	elseif ((1.0 - z) <= -1e+43)
		tmp = t_1;
	elseif ((1.0 - z) <= 0.999995)
		tmp = t_0;
	elseif ((1.0 - z) <= 2.0)
		tmp = x + y;
	elseif ((1.0 - z) <= 1e+125)
		tmp = t_0;
	elseif (((1.0 - z) <= 1e+180) || ~(((1.0 - z) <= 2e+226)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -2e+206], t$95$1, If[LessEqual[N[(1.0 - z), $MachinePrecision], -5e+131], t$95$2, If[LessEqual[N[(1.0 - z), $MachinePrecision], -1e+43], t$95$1, If[LessEqual[N[(1.0 - z), $MachinePrecision], 0.999995], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(x + y), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 1e+125], t$95$0, If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], 1e+180], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2e+226]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 1 z) < -2.0000000000000001e206 or -4.99999999999999995e131 < (-.f64 1 z) < -1.00000000000000001e43 or 9.9999999999999992e124 < (-.f64 1 z) < 1e180 or 1.99999999999999992e226 < (-.f64 1 z)

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 93.0%

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

      3. fma-def 96.5%

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

   3. Applied egg-rr 96.5%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 52.8%

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

      1. associate-*r* 52.8%

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

      2. mul-1-neg 52.8%

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

   9. Simplified 52.8%

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

   if -2.0000000000000001e206 < (-.f64 1 z) < -4.99999999999999995e131 or 1e180 < (-.f64 1 z) < 1.99999999999999992e226

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 56.1%

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

   3. Taylor expanded in z around inf 56.1%

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

      1. associate-*r* 56.1%

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

      2. neg-mul-1 56.1%

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

      3. *-commutative 56.1%

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

   5. Simplified 56.1%

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

   if -1.00000000000000001e43 < (-.f64 1 z) < 0.99999499999999997 or 2 < (-.f64 1 z) < 9.9999999999999992e124

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 52.1%

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

   if 0.99999499999999997 < (-.f64 1 z) < 2

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.7%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -2 \cdot 10^{+206}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -5 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -1 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq 0.999995:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 10^{+125}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 10^{+180} \lor \neg \left(1 - z \leq 2 \cdot 10^{+226}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+230}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+124}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -28:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 10^{+43} \lor \neg \left(z \leq 1.4 \cdot 10^{+130}\right) \land \left(z \leq 4.2 \cdot 10^{+204} \lor \neg \left(z \leq 2.8 \cdot 10^{+257}\right) \land z \leq 6 \cdot 10^{+294}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))) (t_1 (* x (- z))))
   (if (<= z -1.4e+230)
     t_0
     (if (<= z -7e+180)
       t_1
       (if (<= z -7.5e+124)
         t_0
         (if (<= z -28.0)
           t_1
           (if (<= z 1.0)
             (+ x y)
             (if (or (<= z 1e+43)
                     (and (not (<= z 1.4e+130))
                          (or (<= z 4.2e+204)
                              (and (not (<= z 2.8e+257)) (<= z 6e+294)))))
               t_1
               t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double t_1 = x * -z;
	double tmp;
	if (z <= -1.4e+230) {
		tmp = t_0;
	} else if (z <= -7e+180) {
		tmp = t_1;
	} else if (z <= -7.5e+124) {
		tmp = t_0;
	} else if (z <= -28.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 1e+43) || (!(z <= 1.4e+130) && ((z <= 4.2e+204) || (!(z <= 2.8e+257) && (z <= 6e+294))))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = y * -z
    t_1 = x * -z
    if (z <= (-1.4d+230)) then
        tmp = t_0
    else if (z <= (-7d+180)) then
        tmp = t_1
    else if (z <= (-7.5d+124)) then
        tmp = t_0
    else if (z <= (-28.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x + y
    else if ((z <= 1d+43) .or. (.not. (z <= 1.4d+130)) .and. (z <= 4.2d+204) .or. (.not. (z <= 2.8d+257)) .and. (z <= 6d+294)) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -z;
	double t_1 = x * -z;
	double tmp;
	if (z <= -1.4e+230) {
		tmp = t_0;
	} else if (z <= -7e+180) {
		tmp = t_1;
	} else if (z <= -7.5e+124) {
		tmp = t_0;
	} else if (z <= -28.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 1e+43) || (!(z <= 1.4e+130) && ((z <= 4.2e+204) || (!(z <= 2.8e+257) && (z <= 6e+294))))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	t_1 = x * -z
	tmp = 0
	if z <= -1.4e+230:
		tmp = t_0
	elif z <= -7e+180:
		tmp = t_1
	elif z <= -7.5e+124:
		tmp = t_0
	elif z <= -28.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = x + y
	elif (z <= 1e+43) or (not (z <= 1.4e+130) and ((z <= 4.2e+204) or (not (z <= 2.8e+257) and (z <= 6e+294)))):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	t_1 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -1.4e+230)
		tmp = t_0;
	elseif (z <= -7e+180)
		tmp = t_1;
	elseif (z <= -7.5e+124)
		tmp = t_0;
	elseif (z <= -28.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif ((z <= 1e+43) || (!(z <= 1.4e+130) && ((z <= 4.2e+204) || (!(z <= 2.8e+257) && (z <= 6e+294)))))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	t_1 = x * -z;
	tmp = 0.0;
	if (z <= -1.4e+230)
		tmp = t_0;
	elseif (z <= -7e+180)
		tmp = t_1;
	elseif (z <= -7.5e+124)
		tmp = t_0;
	elseif (z <= -28.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif ((z <= 1e+43) || (~((z <= 1.4e+130)) && ((z <= 4.2e+204) || (~((z <= 2.8e+257)) && (z <= 6e+294)))))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.4e+230], t$95$0, If[LessEqual[z, -7e+180], t$95$1, If[LessEqual[z, -7.5e+124], t$95$0, If[LessEqual[z, -28.0], t$95$1, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 1e+43], And[N[Not[LessEqual[z, 1.4e+130]], $MachinePrecision], Or[LessEqual[z, 4.2e+204], And[N[Not[LessEqual[z, 2.8e+257]], $MachinePrecision], LessEqual[z, 6e+294]]]]], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4000000000000001e230 or -6.9999999999999996e180 < z < -7.50000000000000038e124 or 1.00000000000000001e43 < z < 1.3999999999999999e130 or 4.2000000000000001e204 < z < 2.7999999999999998e257 or 6.00000000000000011e294 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 96.2%

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

      3. fma-def 96.2%

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

   3. Applied egg-rr 96.2%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 50.1%

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

      1. associate-*r* 50.1%

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

      2. mul-1-neg 50.1%

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

   9. Simplified 50.1%

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

   if -1.4000000000000001e230 < z < -6.9999999999999996e180 or -7.50000000000000038e124 < z < -28 or 1 < z < 1.00000000000000001e43 or 1.3999999999999999e130 < z < 4.2000000000000001e204 or 2.7999999999999998e257 < z < 6.00000000000000011e294

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 50.5%

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

   3. Taylor expanded in z around inf 48.9%

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

      1. associate-*r* 48.9%

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

      2. neg-mul-1 48.9%

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

      3. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   if -28 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+230}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+180}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -28:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 10^{+43} \lor \neg \left(z \leq 1.4 \cdot 10^{+130}\right) \land \left(z \leq 4.2 \cdot 10^{+204} \lor \neg \left(z \leq 2.8 \cdot 10^{+257}\right) \land z \leq 6 \cdot 10^{+294}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -1000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -1000.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- y) x))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -1000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} 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) <= (-1000.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = z * (-y - x)
    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) <= -1000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -1000.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-y - x)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -1000.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(z * Float64(Float64(-y) - x));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -1000.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-y - x);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -1000.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -1e3 or 2 < (-.f64 1 z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around inf 97.7%

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

      1. mul-1-neg 97.7%

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

      2. +-commutative 97.7%

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

      3. distribute-rgt-neg-out 97.7%

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

      4. +-commutative 97.7%

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

   4. Simplified 97.7%

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

   if -1e3 < (-.f64 1 z) < 2

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -1000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 63.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-30}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-111} \lor \neg \left(x \leq -2.2 \cdot 10^{-129}\right):\\ \;\;\;\;y - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.8e-30)
   (- x (* x z))
   (if (or (<= x -1.62e-111) (not (<= x -2.2e-129)))
     (- y (* y z))
     (* x (- 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e-30) {
		tmp = x - (x * z);
	} else if ((x <= -1.62e-111) || !(x <= -2.2e-129)) {
		tmp = y - (y * z);
	} else {
		tmp = x * (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 <= (-2.8d-30)) then
        tmp = x - (x * z)
    else if ((x <= (-1.62d-111)) .or. (.not. (x <= (-2.2d-129)))) then
        tmp = y - (y * z)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e-30) {
		tmp = x - (x * z);
	} else if ((x <= -1.62e-111) || !(x <= -2.2e-129)) {
		tmp = y - (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.8e-30:
		tmp = x - (x * z)
	elif (x <= -1.62e-111) or not (x <= -2.2e-129):
		tmp = y - (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8e-30)
		tmp = Float64(x - Float64(x * z));
	elseif ((x <= -1.62e-111) || !(x <= -2.2e-129))
		tmp = Float64(y - Float64(y * z));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.8e-30)
		tmp = x - (x * z);
	elseif ((x <= -1.62e-111) || ~((x <= -2.2e-129)))
		tmp = y - (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8e-30], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.62e-111], N[Not[LessEqual[x, -2.2e-129]], $MachinePrecision]], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.79999999999999988e-30

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 74.5%

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

      1. sub-neg 74.5%

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

      2. +-commutative 74.5%

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

      3. distribute-rgt1-in 74.5%

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

      4. distribute-lft-neg-out 74.5%

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

      5. unsub-neg 74.5%

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

   4. Simplified 74.5%

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

   if -2.79999999999999988e-30 < x < -1.62000000000000004e-111 or -2.20000000000000003e-129 < x

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around 0 57.2%

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

      1. sub-neg 57.2%

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

      2. distribute-lft-in 57.2%

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

      3. distribute-rgt-neg-out 57.2%

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

      4. unsub-neg 57.2%

         \[\leadsto \color{blue}{y \cdot 1 - y \cdot z} \]

      5. *-rgt-identity 57.2%

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

   4. Simplified 57.2%

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

   if -1.62000000000000004e-111 < x < -2.20000000000000003e-129

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 80.8%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-30}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-111} \lor \neg \left(x \leq -2.2 \cdot 10^{-129}\right):\\ \;\;\;\;y - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 6: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -28 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -28.0) (not (<= z 1.0))) (* x (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -28.0) || !(z <= 1.0)) {
		tmp = 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 ((z <= (-28.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = 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 ((z <= -28.0) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -28.0) or not (z <= 1.0):
		tmp = x * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -28.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -28.0) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -28.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -28 or 1 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 51.8%

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

   3. Taylor expanded in z around inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

      3. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   if -28 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -28 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 51.0% 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. Taylor expanded in z around 0 55.2%

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

3. Final simplification 55.2%

   \[\leadsto x + y \]

Alternative 8: 26.1% 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. Taylor expanded in x around inf 53.5%

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

3. Taylor expanded in z around 0 31.0%

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

4. Final simplification 31.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))