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

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

Alternatives: 11

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. 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%

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

3. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 90.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -410000000 \lor \neg \left(x \leq 135000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -410000000.0) (not (<= x 135000.0)))
   (+ x (cos y))
   (- (cos y) (* (sin y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -410000000.0) || !(x <= 135000.0)) {
		tmp = x + cos(y);
	} else {
		tmp = cos(y) - (sin(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 <= (-410000000.0d0)) .or. (.not. (x <= 135000.0d0))) then
        tmp = x + cos(y)
    else
        tmp = cos(y) - (sin(y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -410000000.0) || !(x <= 135000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = Math.cos(y) - (Math.sin(y) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -410000000.0) or not (x <= 135000.0):
		tmp = x + math.cos(y)
	else:
		tmp = math.cos(y) - (math.sin(y) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -410000000.0) || !(x <= 135000.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(cos(y) - Float64(sin(y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -410000000.0) || ~((x <= 135000.0)))
		tmp = x + cos(y);
	else
		tmp = cos(y) - (sin(y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -410000000.0], N[Not[LessEqual[x, 135000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1e8 or 135000 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 79.8%

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

   if -4.1e8 < x < 135000

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 98.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -410000000 \lor \neg \left(x \leq 135000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \end{array} \]

Alternative 3: 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. Final simplification 99.9%

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

Alternative 4: 82.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+138} \lor \neg \left(z \leq 9.5 \cdot 10^{+141}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e+138) (not (<= z 9.5e+141)))
   (* (sin y) (- z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e+138) || !(z <= 9.5e+141)) {
		tmp = 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 <= (-2.4d+138)) .or. (.not. (z <= 9.5d+141))) then
        tmp = 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 <= -2.4e+138) || !(z <= 9.5e+141)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e+138) or not (z <= 9.5e+141):
		tmp = math.sin(y) * -z
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e+138) || !(z <= 9.5e+141))
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.4e+138) || ~((z <= 9.5e+141)))
		tmp = sin(y) * -z;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e+138], N[Not[LessEqual[z, 9.5e+141]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e138 or 9.49999999999999974e141 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 79.6%

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

      1. associate-*r* 79.6%

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

      2. neg-mul-1 79.6%

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

      3. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   if -2.4000000000000001e138 < z < 9.49999999999999974e141

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 87.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+138} \lor \neg \left(z \leq 9.5 \cdot 10^{+141}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 71.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -15200000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-127}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;x \leq 0.092:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -15200000000.0)
   (+ x 1.0)
   (if (<= x -2.8e-127)
     (+ 1.0 (- x (* y z)))
     (if (<= x 0.092) (cos y) (+ x 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -15200000000.0) {
		tmp = x + 1.0;
	} else if (x <= -2.8e-127) {
		tmp = 1.0 + (x - (y * z));
	} else if (x <= 0.092) {
		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 <= (-15200000000.0d0)) then
        tmp = x + 1.0d0
    else if (x <= (-2.8d-127)) then
        tmp = 1.0d0 + (x - (y * z))
    else if (x <= 0.092d0) 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 <= -15200000000.0) {
		tmp = x + 1.0;
	} else if (x <= -2.8e-127) {
		tmp = 1.0 + (x - (y * z));
	} else if (x <= 0.092) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -15200000000.0:
		tmp = x + 1.0
	elif x <= -2.8e-127:
		tmp = 1.0 + (x - (y * z))
	elif x <= 0.092:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -15200000000.0)
		tmp = Float64(x + 1.0);
	elseif (x <= -2.8e-127)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	elseif (x <= 0.092)
		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 <= -15200000000.0)
		tmp = x + 1.0;
	elseif (x <= -2.8e-127)
		tmp = 1.0 + (x - (y * z));
	elseif (x <= 0.092)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -15200000000.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, -2.8e-127], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.092], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.52e10 or 0.091999999999999998 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.5%

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

      1. +-commutative 79.5%

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

   4. Simplified 79.5%

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

   if -1.52e10 < x < -2.8e-127

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around 0 64.5%

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

      1. +-commutative 64.5%

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

      2. mul-1-neg 64.5%

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

      3. unsub-neg 64.5%

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

   6. Simplified 64.5%

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

   if -2.8e-127 < x < 0.091999999999999998

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   3. Step-by-step derivation

      1. add-cube-cbrt 99.2%

         \[\leadsto \cos y - \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}} \]

      2. pow3 99.2%

         \[\leadsto \cos y - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

   4. Applied egg-rr 99.2%

      \[\leadsto \cos y - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]
   5. Step-by-step derivation

      1. rem-cube-cbrt 99.9%

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

      2. *-commutative 99.9%

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

      3. add-sqr-sqrt 53.3%

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

      4. associate-*r* 53.3%

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

   6. Applied egg-rr 53.3%

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

   7. Taylor expanded in z around 0 62.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -15200000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-127}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;x \leq 0.092:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 6: 80.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-8} \lor \neg \left(y \leq 0.34\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.55e-8) (not (<= y 0.34)))
   (+ x (cos y))
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.55e-8) || !(y <= 0.34)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x - (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 <= (-2.55d-8)) .or. (.not. (y <= 0.34d0))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.55e-8) || !(y <= 0.34)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.55e-8) or not (y <= 0.34):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.55e-8) || !(y <= 0.34))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.55e-8) || ~((y <= 0.34)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.55e-8], N[Not[LessEqual[y, 0.34]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55e-8 or 0.340000000000000024 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 52.9%

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

   if -2.55e-8 < y < 0.340000000000000024

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 99.5%

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

      1. +-commutative 99.5%

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

      2. mul-1-neg 99.5%

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

      3. unsub-neg 99.5%

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

   6. Simplified 99.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-8} \lor \neg \left(y \leq 0.34\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 7: 69.1% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+94}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+91}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.55e+94)
   (+ x 1.0)
   (if (<= y 5.3e+91) (+ 1.0 (- x (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+94) {
		tmp = x + 1.0;
	} else if (y <= 5.3e+91) {
		tmp = 1.0 + (x - (y * z));
	} 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 (y <= (-1.55d+94)) then
        tmp = x + 1.0d0
    else if (y <= 5.3d+91) then
        tmp = 1.0d0 + (x - (y * z))
    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 (y <= -1.55e+94) {
		tmp = x + 1.0;
	} else if (y <= 5.3e+91) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.55e+94:
		tmp = x + 1.0
	elif y <= 5.3e+91:
		tmp = 1.0 + (x - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.55e+94)
		tmp = Float64(x + 1.0);
	elseif (y <= 5.3e+91)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.55e+94)
		tmp = x + 1.0;
	elseif (y <= 5.3e+91)
		tmp = 1.0 + (x - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.55e+94], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 5.3e+91], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.54999999999999996e94 or 5.29999999999999997e91 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 32.9%

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

      1. +-commutative 32.9%

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

   4. Simplified 32.9%

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

   if -1.54999999999999996e94 < y < 5.29999999999999997e91

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. mul-1-neg 85.3%

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

      3. unsub-neg 85.3%

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

   6. Simplified 85.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+94}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+91}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8: 67.0% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-10}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.2e-12) (+ x 1.0) (if (<= x 1.25e-10) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.2e-12) {
		tmp = x + 1.0;
	} else if (x <= 1.25e-10) {
		tmp = 1.0 - (y * z);
	} 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 <= (-2.2d-12)) then
        tmp = x + 1.0d0
    else if (x <= 1.25d-10) then
        tmp = 1.0d0 - (y * z)
    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 <= -2.2e-12) {
		tmp = x + 1.0;
	} else if (x <= 1.25e-10) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.2e-12:
		tmp = x + 1.0
	elif x <= 1.25e-10:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.2e-12)
		tmp = Float64(x + 1.0);
	elseif (x <= 1.25e-10)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.2e-12)
		tmp = x + 1.0;
	elseif (x <= 1.25e-10)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.2e-12], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 1.25e-10], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999992e-12 or 1.25000000000000008e-10 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.2%

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

      1. +-commutative 77.2%

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

   4. Simplified 77.2%

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

   if -2.19999999999999992e-12 < x < 1.25000000000000008e-10

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   3. Step-by-step derivation

      1. add-cube-cbrt 99.2%

         \[\leadsto \cos y - \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}} \]

      2. pow3 99.2%

         \[\leadsto \cos y - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

   4. Applied egg-rr 99.2%

      \[\leadsto \cos y - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]
   5. Step-by-step derivation

      1. rem-cube-cbrt 99.9%

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

      2. *-commutative 99.9%

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

      3. add-sqr-sqrt 53.1%

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

      4. associate-*r* 53.1%

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

   6. Applied egg-rr 53.1%

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

   7. Taylor expanded in y around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

   9. Simplified 54.6%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-10}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9: 60.2% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.28:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.28) x (if (<= x 3.9e-35) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.28) {
		tmp = x;
	} else if (x <= 3.9e-35) {
		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 <= (-0.28d0)) then
        tmp = x
    else if (x <= 3.9d-35) 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 <= -0.28) {
		tmp = x;
	} else if (x <= 3.9e-35) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.28:
		tmp = x
	elif x <= 3.9e-35:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.28)
		tmp = x;
	elseif (x <= 3.9e-35)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.28)
		tmp = x;
	elseif (x <= 3.9e-35)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.28], x, If[LessEqual[x, 3.9e-35], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.28000000000000003 or 3.8999999999999998e-35 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.2%

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

   if -0.28000000000000003 < x < 3.8999999999999998e-35

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 98.9%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   3. Step-by-step derivation

      1. add-cube-cbrt 98.2%

         \[\leadsto \cos y - \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}} \]

      2. pow3 98.2%

         \[\leadsto \cos y - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

   4. Applied egg-rr 98.2%

      \[\leadsto \cos y - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]
   5. Step-by-step derivation

      1. rem-cube-cbrt 98.9%

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

      2. *-commutative 98.9%

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

      3. add-sqr-sqrt 53.2%

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

      4. associate-*r* 53.3%

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

   6. Applied egg-rr 53.3%

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

   7. Taylor expanded in y around 0 43.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.28:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 61.6% 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. Taylor expanded in y around 0 60.3%

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

   1. +-commutative 60.3%

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

4. Simplified 60.3%

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

5. Final simplification 60.3%

   \[\leadsto x + 1 \]

Alternative 11: 22.1% 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. Taylor expanded in x around 0 61.1%

   \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
3. Step-by-step derivation

   1. add-cube-cbrt 60.6%

      \[\leadsto \cos y - \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}} \]

   2. pow3 60.5%

      \[\leadsto \cos y - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

4. Applied egg-rr 60.5%

   \[\leadsto \cos y - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]
5. Step-by-step derivation

   1. rem-cube-cbrt 61.1%

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

   2. *-commutative 61.1%

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

   3. add-sqr-sqrt 31.2%

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

   4. associate-*r* 31.2%

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

6. Applied egg-rr 31.2%

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

7. Taylor expanded in y around 0 22.2%

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

8. Final simplification 22.2%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023200 
(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))))