Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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 + cos(y)) - (z * sin(y))
end function

Java

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

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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 + cos(y)) - (z * sin(y))
end function

Java

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

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. *-commutative 99.9%

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

   4. distribute-rgt-neg-in 99.9%

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

   5. fma-def 99.9%

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

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (sin(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 + cos(y)) - (sin(y) * z)
end function

Java

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

Python

def code(x, y, z):
	return (x + math.cos(y)) - (math.sin(y) * z)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 3: 99.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -25000000000 \lor \neg \left(z \leq 3 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x - -1\right) - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -25000000000.0) (not (<= z 3e-12)))
   (- (- x -1.0) (* (sin y) z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -25000000000.0) || !(z <= 3e-12)) {
		tmp = (x - -1.0) - (sin(y) * z);
	} else {
		tmp = x + cos(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 <= (-25000000000.0d0)) .or. (.not. (z <= 3d-12))) then
        tmp = (x - (-1.0d0)) - (sin(y) * z)
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -25000000000.0) || !(z <= 3e-12)) {
		tmp = (x - -1.0) - (Math.sin(y) * z);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -25000000000.0) or not (z <= 3e-12):
		tmp = (x - -1.0) - (math.sin(y) * z)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -25000000000.0) || !(z <= 3e-12))
		tmp = Float64(Float64(x - -1.0) - Float64(sin(y) * z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -25000000000.0) || ~((z <= 3e-12)))
		tmp = (x - -1.0) - (sin(y) * z);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -25000000000.0], N[Not[LessEqual[z, 3e-12]], $MachinePrecision]], N[(N[(x - -1.0), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e10 or 3.0000000000000001e-12 < z

   1. Initial program 99.9%

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

      1. flip-+ 79.0%

         \[\leadsto \color{blue}{\frac{x \cdot x - \cos y \cdot \cos y}{x - \cos y}} - z \cdot \sin y \]

      2. div-inv 79.0%

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

      3. fma-neg 79.0%

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

      4. pow2 79.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{x}^{2}} - \cos y \cdot \cos y, \frac{1}{x - \cos y}, -z \cdot \sin y\right) \]

      5. pow2 79.0%

         \[\leadsto \mathsf{fma}\left({x}^{2} - \color{blue}{{\cos y}^{2}}, \frac{1}{x - \cos y}, -z \cdot \sin y\right) \]

      6. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left({x}^{2} - {\cos y}^{2}, \frac{1}{x - \cos y}, -\color{blue}{\sin y \cdot z}\right) \]

      7. distribute-rgt-neg-in 79.0%

         \[\leadsto \mathsf{fma}\left({x}^{2} - {\cos y}^{2}, \frac{1}{x - \cos y}, \color{blue}{\sin y \cdot \left(-z\right)}\right) \]

   4. Applied egg-rr 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left({x}^{2} - {\cos y}^{2}, \frac{1}{x - \cos y}, \sin y \cdot \left(-z\right)\right)} \]
   5. Step-by-step derivation

      1. fma-udef 79.0%

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

      2. *-commutative 79.0%

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

      3. cancel-sign-sub-inv 79.0%

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

      4. associate-*r/ 79.0%

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

      5. *-rgt-identity 79.0%

         \[\leadsto \frac{\color{blue}{{x}^{2} - {\cos y}^{2}}}{x - \cos y} - z \cdot \sin y \]

   6. Simplified 79.0%

      \[\leadsto \color{blue}{\frac{{x}^{2} - {\cos y}^{2}}{x - \cos y} - z \cdot \sin y} \]

   7. Taylor expanded in y around 0 78.9%

      \[\leadsto \color{blue}{\frac{{x}^{2} - 1}{x - 1}} - z \cdot \sin y \]
   8. Step-by-step derivation

      1. unpow2 78.9%

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

      2. fma-neg 78.9%

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

      3. metadata-eval 78.9%

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

      4. sub-neg 78.9%

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

      5. metadata-eval 78.9%

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

   9. Simplified 78.9%

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

       1. metadata-eval 78.9%

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

       2. fma-neg 78.9%

          \[\leadsto \frac{\color{blue}{x \cdot x - 1}}{x + -1} - z \cdot \sin y \]

       3. metadata-eval 78.9%

          \[\leadsto \frac{x \cdot x - \color{blue}{-1 \cdot -1}}{x + -1} - z \cdot \sin y \]

       4. flip-- 99.7%

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

   11. Applied egg-rr 99.7%

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

   if -2.5e10 < z < 3.0000000000000001e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -25000000000 \lor \neg \left(z \leq 3 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x - -1\right) - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-129}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-10}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.7e+27)
   x
   (if (<= x -6.8e-129)
     (+ x (- 1.0 (* y z)))
     (if (<= x 6.2e-10) (cos y) (+ x 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.7e+27) {
		tmp = x;
	} else if (x <= -6.8e-129) {
		tmp = x + (1.0 - (y * z));
	} else if (x <= 6.2e-10) {
		tmp = cos(y);
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (x <= (-3.7d+27)) then
        tmp = x
    else if (x <= (-6.8d-129)) then
        tmp = x + (1.0d0 - (y * z))
    else if (x <= 6.2d-10) then
        tmp = cos(y)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.7e+27) {
		tmp = x;
	} else if (x <= -6.8e-129) {
		tmp = x + (1.0 - (y * z));
	} else if (x <= 6.2e-10) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.7e+27:
		tmp = x
	elif x <= -6.8e-129:
		tmp = x + (1.0 - (y * z))
	elif x <= 6.2e-10:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.7e+27)
		tmp = x;
	elseif (x <= -6.8e-129)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	elseif (x <= 6.2e-10)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.7e+27)
		tmp = x;
	elseif (x <= -6.8e-129)
		tmp = x + (1.0 - (y * z));
	elseif (x <= 6.2e-10)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.7e+27], x, If[LessEqual[x, -6.8e-129], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e-10], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.70000000000000002e27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.3%

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

   if -3.70000000000000002e27 < x < -6.80000000000000026e-129

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 67.3%

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

      1. associate-+r+ 67.3%

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

      2. +-commutative 67.3%

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

      3. associate-+l+ 67.3%

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

      4. mul-1-neg 67.3%

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

      5. unsub-neg 67.3%

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

   5. Simplified 67.3%

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

   if -6.80000000000000026e-129 < x < 6.2000000000000003e-10

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 80.1%

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

      2. pow2 80.1%

         \[\leadsto \color{blue}{{\left(\sqrt{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{2}} \]

      3. associate--l+ 80.1%

         \[\leadsto {\left(\sqrt{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{2} \]

   4. Applied egg-rr 80.1%

      \[\leadsto \color{blue}{{\left(\sqrt{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{2}} \]

   5. Taylor expanded in x around 0 80.1%

      \[\leadsto {\color{blue}{\left(\sqrt{\cos y - z \cdot \sin y}\right)}}^{2} \]

   6. Taylor expanded in z around 0 71.8%

      \[\leadsto \color{blue}{\cos y} \]

   if 6.2000000000000003e-10 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.5%

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative 89.5%

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 89.5%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-129}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-10}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0034 \lor \neg \left(y \leq 6.4 \cdot 10^{-35}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0034) (not (<= y 6.4e-35)))
   (+ x (cos y))
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0034) || !(y <= 6.4e-35)) {
		tmp = x + cos(y);
	} else {
		tmp = x + (1.0 - (y * 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 <= (-0.0034d0)) .or. (.not. (y <= 6.4d-35))) then
        tmp = x + cos(y)
    else
        tmp = x + (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0034) || !(y <= 6.4e-35)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0034) or not (y <= 6.4e-35):
		tmp = x + math.cos(y)
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0034) || !(y <= 6.4e-35))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0034) || ~((y <= 6.4e-35)))
		tmp = x + cos(y);
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0034], N[Not[LessEqual[y, 6.4e-35]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00339999999999999981 or 6.3999999999999996e-35 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.4%

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

      1. +-commutative 72.4%

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

   5. Simplified 72.4%

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

   if -0.00339999999999999981 < y < 6.3999999999999996e-35

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0034 \lor \neg \left(y \leq 6.4 \cdot 10^{-35}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.4% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+98} \lor \neg \left(y \leq 1.45 \cdot 10^{+29}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.6e+98) (not (<= y 1.45e+29)))
   (+ x 1.0)
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.6e+98) || !(y <= 1.45e+29)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (y * 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 <= (-7.6d+98)) .or. (.not. (y <= 1.45d+29))) then
        tmp = x + 1.0d0
    else
        tmp = x + (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.6e+98) || !(y <= 1.45e+29)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.6e+98) or not (y <= 1.45e+29):
		tmp = x + 1.0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.6e+98) || !(y <= 1.45e+29))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.6e+98) || ~((y <= 1.45e+29)))
		tmp = x + 1.0;
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.6e+98], N[Not[LessEqual[y, 1.45e+29]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5999999999999998e98 or 1.45e29 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 47.3%

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{x + 1} \]

   if -7.5999999999999998e98 < y < 1.45e29

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.8%

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

      1. associate-+r+ 92.8%

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

      2. +-commutative 92.8%

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

      3. associate-+l+ 92.8%

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

      4. mul-1-neg 92.8%

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

      5. unsub-neg 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+98} \lor \neg \left(y \leq 1.45 \cdot 10^{+29}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-7} \lor \neg \left(x \leq 1.45 \cdot 10^{-12}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.9e-7) (not (<= x 1.45e-12))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.9e-7) || !(x <= 1.45e-12)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * 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 <= (-3.9d-7)) .or. (.not. (x <= 1.45d-12))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.9e-7) || !(x <= 1.45e-12)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.9e-7) or not (x <= 1.45e-12):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.9e-7) || !(x <= 1.45e-12))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.9e-7) || ~((x <= 1.45e-12)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.9e-7], N[Not[LessEqual[x, 1.45e-12]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.90000000000000025e-7 or 1.4500000000000001e-12 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.4%

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative 88.4%

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 88.4%

      \[\leadsto \color{blue}{x + 1} \]

   if -3.90000000000000025e-7 < x < 1.4500000000000001e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 57.7%

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

      1. associate-+r+ 57.7%

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

      2. +-commutative 57.7%

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

      3. associate-+l+ 57.7%

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

      4. mul-1-neg 57.7%

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

      5. unsub-neg 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in x around 0 57.6%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-7} \lor \neg \left(x \leq 1.45 \cdot 10^{-12}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.5% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -1.0) x (if (<= x 1.45) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x;
	} else if (x <= 1.45) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	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 <= (-1.0d0)) then
        tmp = x
    else if (x <= 1.45d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x;
	} else if (x <= 1.45) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = x
	elif x <= 1.45:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 1.45)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 1.45)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], x, If[LessEqual[x, 1.45], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.44999999999999996 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.4%

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

   if -1 < x < 1.44999999999999996

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 76.9%

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

      2. pow2 76.9%

         \[\leadsto \color{blue}{{\left(\sqrt{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{2}} \]

      3. associate--l+ 76.9%

         \[\leadsto {\left(\sqrt{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{2} \]

   4. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{{\left(\sqrt{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{2}} \]

   5. Taylor expanded in x around 0 74.4%

      \[\leadsto {\color{blue}{\left(\sqrt{\cos y - z \cdot \sin y}\right)}}^{2} \]

   6. Taylor expanded in y around 0 45.1%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.3% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

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

C

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

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 + 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 68.9%

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. +-commutative 68.9%

      \[\leadsto \color{blue}{x + 1} \]

5. Simplified 68.9%

   \[\leadsto \color{blue}{x + 1} \]

6. Final simplification 68.9%

   \[\leadsto x + 1 \]
7. Add Preprocessing

Alternative 10: 21.1% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

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

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
end function

Java

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

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

   1. add-sqr-sqrt 61.8%

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

   2. pow2 61.8%

      \[\leadsto \color{blue}{{\left(\sqrt{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{2}} \]

   3. associate--l+ 61.8%

      \[\leadsto {\left(\sqrt{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{2} \]

4. Applied egg-rr 61.8%

   \[\leadsto \color{blue}{{\left(\sqrt{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{2}} \]

5. Taylor expanded in x around 0 38.7%

   \[\leadsto {\color{blue}{\left(\sqrt{\cos y - z \cdot \sin y}\right)}}^{2} \]

6. Taylor expanded in y around 0 23.4%

   \[\leadsto \color{blue}{1} \]

7. Final simplification 23.4%

   \[\leadsto 1 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))