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

Percentage Accurate: 99.9% → 99.9%

Time: 9.9s

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, 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]

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0052 \lor \neg \left(x \leq 7 \cdot 10^{-5}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0052) (not (<= x 7e-5)))
   (+ x (cos y))
   (- (cos y) (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0052) || !(x <= 7e-5)) {
		tmp = x + cos(y);
	} else {
		tmp = cos(y) - (z * sin(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 <= (-0.0052d0)) .or. (.not. (x <= 7d-5))) then
        tmp = x + cos(y)
    else
        tmp = cos(y) - (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0052) || !(x <= 7e-5)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = Math.cos(y) - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0052) or not (x <= 7e-5):
		tmp = x + math.cos(y)
	else:
		tmp = math.cos(y) - (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0052) || !(x <= 7e-5))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.0052) || ~((x <= 7e-5)))
		tmp = x + cos(y);
	else
		tmp = cos(y) - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0052], N[Not[LessEqual[x, 7e-5]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0051999999999999998 or 6.9999999999999994e-5 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 83.7%

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

      1. +-commutative 83.7%

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

   4. Simplified 83.7%

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

   if -0.0051999999999999998 < x < 6.9999999999999994e-5

   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. Recombined 2 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0052 \lor \neg \left(x \leq 7 \cdot 10^{-5}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]

Alternative 3: 81.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+131} \lor \neg \left(z \leq 1.7 \cdot 10^{+220}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.6e+131) (not (<= z 1.7e+220)))
   (* z (- (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.6e+131) || !(z <= 1.7e+220)) {
		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 <= (-9.6d+131)) .or. (.not. (z <= 1.7d+220))) 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 <= -9.6e+131) || !(z <= 1.7e+220)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.6e+131) or not (z <= 1.7e+220):
		tmp = z * -math.sin(y)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.6e+131) || !(z <= 1.7e+220))
		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 <= -9.6e+131) || ~((z <= 1.7e+220)))
		tmp = z * -sin(y);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.6e+131], N[Not[LessEqual[z, 1.7e+220]], $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 < -9.5999999999999998e131 or 1.7e220 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-rgt-neg-in 74.3%

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

   4. Simplified 74.3%

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

   if -9.5999999999999998e131 < z < 1.7e220

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 85.6%

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

      1. +-commutative 85.6%

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

   4. Simplified 85.6%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+131} \lor \neg \left(z \leq 1.7 \cdot 10^{+220}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 4: 81.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -260 \lor \neg \left(y \leq 50000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -260.0) (not (<= y 50000.0)))
   (+ x (cos y))
   (+ x (+ 1.0 (* y (- (* y -0.5) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -260.0) || !(y <= 50000.0)) {
		tmp = x + cos(y);
	} else {
		tmp = x + (1.0 + (y * ((y * -0.5) - 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 <= (-260.0d0)) .or. (.not. (y <= 50000.0d0))) then
        tmp = x + cos(y)
    else
        tmp = x + (1.0d0 + (y * ((y * (-0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -260.0) || !(y <= 50000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 + (y * ((y * -0.5) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -260.0) or not (y <= 50000.0):
		tmp = x + math.cos(y)
	else:
		tmp = x + (1.0 + (y * ((y * -0.5) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -260.0) || !(y <= 50000.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(x + Float64(1.0 + Float64(y * Float64(Float64(y * -0.5) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -260.0) || ~((y <= 50000.0)))
		tmp = x + cos(y);
	else
		tmp = x + (1.0 + (y * ((y * -0.5) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -260.0], N[Not[LessEqual[y, 50000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -260 or 5e4 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 64.1%

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

      1. +-commutative 64.1%

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

   4. Simplified 64.1%

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

   if -260 < y < 5e4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.8%

      \[\leadsto \color{blue}{1 + \left(x + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ 97.8%

         \[\leadsto \color{blue}{\left(1 + x\right) + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)} \]

      2. +-commutative 97.8%

         \[\leadsto \color{blue}{\left(x + 1\right)} + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right) \]

      3. associate-+l+ 97.8%

         \[\leadsto \color{blue}{x + \left(1 + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)\right)} \]

      4. +-commutative 97.8%

         \[\leadsto x + \left(1 + \color{blue}{\left(-0.5 \cdot {y}^{2} + -1 \cdot \left(y \cdot z\right)\right)}\right) \]

      5. mul-1-neg 97.8%

         \[\leadsto x + \left(1 + \left(-0.5 \cdot {y}^{2} + \color{blue}{\left(-y \cdot z\right)}\right)\right) \]

      6. unsub-neg 97.8%

         \[\leadsto x + \left(1 + \color{blue}{\left(-0.5 \cdot {y}^{2} - y \cdot z\right)}\right) \]

      7. *-commutative 97.8%

         \[\leadsto x + \left(1 + \left(\color{blue}{{y}^{2} \cdot -0.5} - y \cdot z\right)\right) \]

      8. unpow2 97.8%

         \[\leadsto x + \left(1 + \left(\color{blue}{\left(y \cdot y\right)} \cdot -0.5 - y \cdot z\right)\right) \]

      9. associate-*l* 97.8%

         \[\leadsto x + \left(1 + \left(\color{blue}{y \cdot \left(y \cdot -0.5\right)} - y \cdot z\right)\right) \]

      10. distribute-lft-out-- 97.8%

          \[\leadsto x + \left(1 + \color{blue}{y \cdot \left(y \cdot -0.5 - z\right)}\right) \]

   4. Simplified 97.8%

      \[\leadsto \color{blue}{x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -260 \lor \neg \left(y \leq 50000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \]

Alternative 5: 70.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-35}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-153}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+124}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.4e-35)
   (+ x 1.0)
   (if (<= x 7.8e-153)
     (cos y)
     (if (<= x 1.35e+124) (- (+ x 1.0) (* y z)) (+ x 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e-35) {
		tmp = x + 1.0;
	} else if (x <= 7.8e-153) {
		tmp = cos(y);
	} else if (x <= 1.35e+124) {
		tmp = (x + 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 <= (-6.4d-35)) then
        tmp = x + 1.0d0
    else if (x <= 7.8d-153) then
        tmp = cos(y)
    else if (x <= 1.35d+124) then
        tmp = (x + 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 <= -6.4e-35) {
		tmp = x + 1.0;
	} else if (x <= 7.8e-153) {
		tmp = Math.cos(y);
	} else if (x <= 1.35e+124) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.4e-35:
		tmp = x + 1.0
	elif x <= 7.8e-153:
		tmp = math.cos(y)
	elif x <= 1.35e+124:
		tmp = (x + 1.0) - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.4e-35)
		tmp = Float64(x + 1.0);
	elseif (x <= 7.8e-153)
		tmp = cos(y);
	elseif (x <= 1.35e+124)
		tmp = Float64(Float64(x + 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 <= -6.4e-35)
		tmp = x + 1.0;
	elseif (x <= 7.8e-153)
		tmp = cos(y);
	elseif (x <= 1.35e+124)
		tmp = (x + 1.0) - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.4e-35], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 7.8e-153], N[Cos[y], $MachinePrecision], If[LessEqual[x, 1.35e+124], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.3999999999999996e-35 or 1.34999999999999989e124 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.3%

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

      1. +-commutative 83.3%

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

   4. Simplified 83.3%

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

   if -6.3999999999999996e-35 < x < 7.8000000000000004e-153

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 66.7%

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

      2. pow2 66.7%

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

      3. associate--l+ 66.7%

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

   3. Applied egg-rr 66.7%

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

   4. Taylor expanded in x around 0 66.7%

      \[\leadsto {\color{blue}{\left(\sqrt{\cos y - z \cdot \sin y}\right)}}^{2} \]
   5. Step-by-step derivation

      1. *-commutative 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in z around 0 66.2%

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

   if 7.8000000000000004e-153 < x < 1.34999999999999989e124

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.8%

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

      1. associate-+r+ 63.8%

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

      2. mul-1-neg 63.8%

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

      3. unsub-neg 63.8%

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

      4. +-commutative 63.8%

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

   4. Simplified 63.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-35}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-153}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+124}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 6: 66.9% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-10}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+122}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.5e-10)
   (+ x 1.0)
   (if (<= x 5.8e+122) (- (+ x 1.0) (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e-10) {
		tmp = x + 1.0;
	} else if (x <= 5.8e+122) {
		tmp = (x + 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 <= (-9.5d-10)) then
        tmp = x + 1.0d0
    else if (x <= 5.8d+122) then
        tmp = (x + 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 <= -9.5e-10) {
		tmp = x + 1.0;
	} else if (x <= 5.8e+122) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.5e-10:
		tmp = x + 1.0
	elif x <= 5.8e+122:
		tmp = (x + 1.0) - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.5e-10)
		tmp = Float64(x + 1.0);
	elseif (x <= 5.8e+122)
		tmp = Float64(Float64(x + 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 <= -9.5e-10)
		tmp = x + 1.0;
	elseif (x <= 5.8e+122)
		tmp = (x + 1.0) - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.5e-10], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 5.8e+122], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000028e-10 or 5.8000000000000002e122 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 84.0%

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

      1. +-commutative 84.0%

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

   4. Simplified 84.0%

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

   if -9.50000000000000028e-10 < x < 5.8000000000000002e122

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 54.7%

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

      1. associate-+r+ 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. +-commutative 54.7%

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

   4. Simplified 54.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-10}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+122}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 7: 66.9% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-25}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e-13) (+ x 1.0) (if (<= x 3e-25) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e-13) {
		tmp = x + 1.0;
	} else if (x <= 3e-25) {
		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 <= (-3.5d-13)) then
        tmp = x + 1.0d0
    else if (x <= 3d-25) 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 <= -3.5e-13) {
		tmp = x + 1.0;
	} else if (x <= 3e-25) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.5e-13:
		tmp = x + 1.0
	elif x <= 3e-25:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e-13)
		tmp = Float64(x + 1.0);
	elseif (x <= 3e-25)
		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 <= -3.5e-13)
		tmp = x + 1.0;
	elseif (x <= 3e-25)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e-13], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 3e-25], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000002e-13 or 2.9999999999999998e-25 < 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 -3.5000000000000002e-13 < x < 2.9999999999999998e-25

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 67.0%

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

      2. pow2 67.0%

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

      3. associate--l+ 67.0%

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

   3. Applied egg-rr 67.0%

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

   4. Taylor expanded in x around 0 67.0%

      \[\leadsto {\color{blue}{\left(\sqrt{\cos y - z \cdot \sin y}\right)}}^{2} \]
   5. Step-by-step derivation

      1. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   7. Taylor expanded in y around 0 50.6%

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

      1. mul-1-neg 50.6%

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

   9. Simplified 50.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-25}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8: 60.4% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.00016:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.5e-10) x (if (<= x 0.00016) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e-10) {
		tmp = x;
	} else if (x <= 0.00016) {
		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 <= (-9.5d-10)) then
        tmp = x
    else if (x <= 0.00016d0) 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 <= -9.5e-10) {
		tmp = x;
	} else if (x <= 0.00016) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.5e-10:
		tmp = x
	elif x <= 0.00016:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.5e-10)
		tmp = x;
	elseif (x <= 0.00016)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.5e-10)
		tmp = x;
	elseif (x <= 0.00016)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.5e-10], x, If[LessEqual[x, 0.00016], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000028e-10 or 1.60000000000000013e-4 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 81.6%

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

   if -9.50000000000000028e-10 < x < 1.60000000000000013e-4

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 68.6%

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

      2. pow2 68.6%

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

      3. associate--l+ 68.6%

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

   3. Applied egg-rr 68.6%

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

   4. Taylor expanded in x around 0 67.6%

      \[\leadsto {\color{blue}{\left(\sqrt{\cos y - z \cdot \sin y}\right)}}^{2} \]
   5. Step-by-step derivation

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in y around 0 37.4%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.00016:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 61.4% 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 59.4%

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

   1. +-commutative 59.4%

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

4. Simplified 59.4%

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

5. Final simplification 59.4%

   \[\leadsto x + 1 \]

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. Step-by-step derivation

   1. add-sqr-sqrt 56.7%

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

   2. pow2 56.7%

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

   3. associate--l+ 56.7%

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

3. Applied egg-rr 56.7%

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

4. Taylor expanded in x around 0 38.4%

   \[\leadsto {\color{blue}{\left(\sqrt{\cos y - z \cdot \sin y}\right)}}^{2} \]
5. Step-by-step derivation

   1. *-commutative 38.4%

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

6. Simplified 38.4%

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

7. Taylor expanded in y around 0 20.6%

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

8. Final simplification 20.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023277 
(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))))