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

Percentage Accurate: 99.9% → 99.9%

Time: 9.2s

Alternatives: 12

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: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.7e+79)
   x
   (if (<= x 1.05e-10) (- (cos y) (* (sin y) z)) (+ x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.7e+79) {
		tmp = x;
	} else if (x <= 1.05e-10) {
		tmp = cos(y) - (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 (x <= (-3.7d+79)) then
        tmp = x
    else if (x <= 1.05d-10) then
        tmp = cos(y) - (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 (x <= -3.7e+79) {
		tmp = x;
	} else if (x <= 1.05e-10) {
		tmp = Math.cos(y) - (Math.sin(y) * z);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.7e+79:
		tmp = x
	elif x <= 1.05e-10:
		tmp = math.cos(y) - (math.sin(y) * z)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.7e+79)
		tmp = x;
	elseif (x <= 1.05e-10)
		tmp = Float64(cos(y) - 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 (x <= -3.7e+79)
		tmp = x;
	elseif (x <= 1.05e-10)
		tmp = cos(y) - (sin(y) * z);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.7e+79], x, If[LessEqual[x, 1.05e-10], N[(N[Cos[y], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.70000000000000009e79

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 91.6%

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

   if -3.70000000000000009e79 < x < 1.05e-10

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 94.8%

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

   if 1.05e-10 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 88.8%

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

      1. +-commutative 88.8%

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

   4. Simplified 88.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

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: 81.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+91} \lor \neg \left(z \leq 2.65 \cdot 10^{+213}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e+91) (not (<= z 2.65e+213)))
   (* z (- (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e+91) || !(z <= 2.65e+213)) {
		tmp = z * -sin(y);
	} 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 <= (-1.7d+91)) .or. (.not. (z <= 2.65d+213))) then
        tmp = z * -sin(y)
    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 <= -1.7e+91) || !(z <= 2.65e+213)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e+91) or not (z <= 2.65e+213):
		tmp = z * -math.sin(y)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e+91) || !(z <= 2.65e+213))
		tmp = Float64(z * Float64(-sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e+91) || ~((z <= 2.65e+213)))
		tmp = z * -sin(y);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e+91], N[Not[LessEqual[z, 2.65e+213]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e91 or 2.6499999999999999e213 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 72.0%

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

      1. associate-*r* 72.0%

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

      2. neg-mul-1 72.0%

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

      3. *-commutative 72.0%

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

   4. Simplified 72.0%

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

   if -1.7e91 < z < 2.6499999999999999e213

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 89.2%

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

      1. +-commutative 89.2%

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

   4. Simplified 89.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+91} \lor \neg \left(z \leq 2.65 \cdot 10^{+213}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 80.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+19} \lor \neg \left(y \leq 9.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.9e+19) (not (<= y 9.5e-5)))
   (+ x (cos y))
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.9e+19) || !(y <= 9.5e-5)) {
		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 <= (-4.9d+19)) .or. (.not. (y <= 9.5d-5))) 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 <= -4.9e+19) || !(y <= 9.5e-5)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.9e+19) or not (y <= 9.5e-5):
		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 <= -4.9e+19) || !(y <= 9.5e-5))
		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 <= -4.9e+19) || ~((y <= 9.5e-5)))
		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, -4.9e+19], N[Not[LessEqual[y, 9.5e-5]], $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 < -4.9e19 or 9.5000000000000005e-5 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 64.2%

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

      1. +-commutative 64.2%

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

   4. Simplified 64.2%

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

   if -4.9e19 < y < 9.5000000000000005e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.9%

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

      1. associate-+r+ 97.9%

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

      2. +-commutative 97.9%

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

      3. associate-+l+ 97.9%

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

      4. mul-1-neg 97.9%

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

      5. unsub-neg 97.9%

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

   4. Simplified 97.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+19} \lor \neg \left(y \leq 9.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 6: 71.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-29} \lor \neg \left(x \leq 8.5 \cdot 10^{-15}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e-29) (not (<= x 8.5e-15))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-29) || !(x <= 8.5e-15)) {
		tmp = x + 1.0;
	} else {
		tmp = 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 ((x <= (-1d-29)) .or. (.not. (x <= 8.5d-15))) then
        tmp = x + 1.0d0
    else
        tmp = cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-29) || !(x <= 8.5e-15)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e-29) or not (x <= 8.5e-15):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e-29) || !(x <= 8.5e-15))
		tmp = Float64(x + 1.0);
	else
		tmp = cos(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1e-29) || ~((x <= 8.5e-15)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e-29], N[Not[LessEqual[x, 8.5e-15]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999943e-30 or 8.50000000000000007e-15 < x

   1. Initial program 99.9%

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

   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 -9.99999999999999943e-30 < x < 8.50000000000000007e-15

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 61.7%

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

      1. +-commutative 61.7%

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

   4. Simplified 61.7%

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

   5. Taylor expanded in x around 0 61.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-29} \lor \neg \left(x \leq 8.5 \cdot 10^{-15}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]

Alternative 7: 70.0% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+22} \lor \neg \left(y \leq 3.85 \cdot 10^{+62}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.25e+22) (not (<= y 3.85e+62)))
   (+ x 1.0)
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e+22) || !(y <= 3.85e+62)) {
		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 <= (-1.25d+22)) .or. (.not. (y <= 3.85d+62))) 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 <= -1.25e+22) || !(y <= 3.85e+62)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.25e+22) or not (y <= 3.85e+62):
		tmp = x + 1.0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.25e+22) || !(y <= 3.85e+62))
		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 <= -1.25e+22) || ~((y <= 3.85e+62)))
		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, -1.25e+22], N[Not[LessEqual[y, 3.85e+62]], $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 < -1.2499999999999999e22 or 3.8500000000000001e62 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 42.4%

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

      1. +-commutative 42.4%

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

   4. Simplified 42.4%

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

   if -1.2499999999999999e22 < y < 3.8500000000000001e62

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.8%

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

      1. associate-+r+ 90.8%

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

      2. +-commutative 90.8%

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

      3. associate-+l+ 90.8%

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

      4. mul-1-neg 90.8%

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

      5. unsub-neg 90.8%

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

   4. Simplified 90.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+22} \lor \neg \left(y \leq 3.85 \cdot 10^{+62}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 8: 67.2% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-12} \lor \neg \left(x \leq 5.8 \cdot 10^{-37}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e-12) (not (<= x 5.8e-37))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e-12) || !(x <= 5.8e-37)) {
		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 <= (-1.9d-12)) .or. (.not. (x <= 5.8d-37))) 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 <= -1.9e-12) || !(x <= 5.8e-37)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e-12) or not (x <= 5.8e-37):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e-12) || !(x <= 5.8e-37))
		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 <= -1.9e-12) || ~((x <= 5.8e-37)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e-12], N[Not[LessEqual[x, 5.8e-37]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.89999999999999998e-12 or 5.80000000000000009e-37 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.5%

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

      1. +-commutative 81.5%

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

   4. Simplified 81.5%

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

   if -1.89999999999999998e-12 < x < 5.80000000000000009e-37

   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. Taylor expanded in x around 0 99.9%

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

   5. Taylor expanded in y around 0 52.5%

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

      1. mul-1-neg 52.5%

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

      2. unsub-neg 52.5%

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

   7. Simplified 52.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-12} \lor \neg \left(x \leq 5.8 \cdot 10^{-37}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]

Alternative 9: 63.2% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+248} \lor \neg \left(z \leq 7 \cdot 10^{+215}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.45e+248) (not (<= z 7e+215))) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.45e+248) || !(z <= 7e+215)) {
		tmp = 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 ((z <= (-1.45d+248)) .or. (.not. (z <= 7d+215))) then
        tmp = 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 ((z <= -1.45e+248) || !(z <= 7e+215)) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.45e+248) or not (z <= 7e+215):
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.45e+248) || !(z <= 7e+215))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.45e+248) || ~((z <= 7e+215)))
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.45e+248], N[Not[LessEqual[z, 7e+215]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e248 or 6.99999999999999954e215 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 82.5%

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

      1. associate-*r* 82.5%

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

      2. neg-mul-1 82.5%

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

      3. *-commutative 82.5%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in y around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. *-commutative 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

   7. Simplified 51.4%

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

   if -1.45e248 < z < 6.99999999999999954e215

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 67.5%

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

      1. +-commutative 67.5%

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

   4. Simplified 67.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+248} \lor \neg \left(z \leq 7 \cdot 10^{+215}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 10: 61.0% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.56:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.77:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -0.56) x (if (<= x 0.77) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.56) {
		tmp = x;
	} else if (x <= 0.77) {
		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 <= (-0.56d0)) then
        tmp = x
    else if (x <= 0.77d0) 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 <= -0.56) {
		tmp = x;
	} else if (x <= 0.77) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.56:
		tmp = x
	elif x <= 0.77:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.56)
		tmp = x;
	elseif (x <= 0.77)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.56)
		tmp = x;
	elseif (x <= 0.77)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.56], x, If[LessEqual[x, 0.77], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.56000000000000005 or 0.77000000000000002 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 81.1%

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

   if -0.56000000000000005 < x < 0.77000000000000002

   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. Taylor expanded in y around 0 39.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.56:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.77:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 61.9% 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 60.4%

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

   1. +-commutative 60.4%

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

4. Simplified 60.4%

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

5. Final simplification 60.4%

   \[\leadsto x + 1 \]

Alternative 12: 21.7% 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 60.5%

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

3. Taylor expanded in y around 0 22.2%

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

4. Final simplification 22.2%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023312 
(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))))