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

Percentage Accurate: 99.9% → 99.9%

Time: 9.0s

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: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.95\right):\\ \;\;\;\;x - t_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -1.0) (not (<= x 0.95))) (- x t_0) (- (cos y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -1.0) || !(x <= 0.95)) {
		tmp = x - t_0;
	} else {
		tmp = cos(y) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * sin(y)
    if ((x <= (-1.0d0)) .or. (.not. (x <= 0.95d0))) then
        tmp = x - t_0
    else
        tmp = cos(y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -1.0) || !(x <= 0.95)) {
		tmp = x - t_0;
	} else {
		tmp = Math.cos(y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -1.0) or not (x <= 0.95):
		tmp = x - t_0
	else:
		tmp = math.cos(y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.95))
		tmp = Float64(x - t_0);
	else
		tmp = Float64(cos(y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 0.95)))
		tmp = x - t_0;
	else
		tmp = cos(y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 0.95]], $MachinePrecision]], N[(x - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.94999999999999996 < x

   1. Initial program 99.9%

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

      1. add-log-exp 6.2%

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

   3. Applied egg-rr 6.2%

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

   4. Taylor expanded in x around inf 98.7%

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

   if -1 < x < 0.94999999999999996

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.6%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.95\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]

Alternative 3: 93.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4000000000000 \lor \neg \left(z \leq 5.5 \cdot 10^{+72}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4000000000000.0) (not (<= z 5.5e+72)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4000000000000.0) || !(z <= 5.5e+72)) {
		tmp = x - (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 <= (-4000000000000.0d0)) .or. (.not. (z <= 5.5d+72))) then
        tmp = x - (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 <= -4000000000000.0) || !(z <= 5.5e+72)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4000000000000.0) or not (z <= 5.5e+72):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4000000000000.0) || !(z <= 5.5e+72))
		tmp = Float64(x - Float64(z * 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 <= -4000000000000.0) || ~((z <= 5.5e+72)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4000000000000.0], N[Not[LessEqual[z, 5.5e+72]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e12 or 5.5e72 < z

   1. Initial program 99.8%

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

      1. add-log-exp 56.7%

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

   3. Applied egg-rr 56.7%

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

   4. Taylor expanded in x around inf 93.0%

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

   if -4e12 < z < 5.5e72

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.6%

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

      1. +-commutative 97.6%

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

   4. Simplified 97.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4000000000000 \lor \neg \left(z \leq 5.5 \cdot 10^{+72}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 4: 82.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+121} \lor \neg \left(z \leq 6 \cdot 10^{+114}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e+121) (not (<= z 6e+114)))
   (* z (- (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e+121) || !(z <= 6e+114)) {
		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 <= (-2.4d+121)) .or. (.not. (z <= 6d+114))) 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 <= -2.4e+121) || !(z <= 6e+114)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e+121) or not (z <= 6e+114):
		tmp = z * -math.sin(y)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e+121) || !(z <= 6e+114))
		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 <= -2.4e+121) || ~((z <= 6e+114)))
		tmp = z * -sin(y);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e+121], N[Not[LessEqual[z, 6e+114]], $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 < -2.4e121 or 6.0000000000000001e114 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 76.8%

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

      1. associate-*r* 76.8%

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

      2. neg-mul-1 76.8%

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

      3. *-commutative 76.8%

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

   4. Simplified 76.8%

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

   if -2.4e121 < z < 6.0000000000000001e114

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 90.6%

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

      1. +-commutative 90.6%

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

   4. Simplified 90.6%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+121} \lor \neg \left(z \leq 6 \cdot 10^{+114}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.88 \lor \neg \left(y \leq 1.15 \cdot 10^{-10}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.88) (not (<= y 1.15e-10)))
   (+ x (cos y))
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.88) || !(y <= 1.15e-10)) {
		tmp = x + cos(y);
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-0.88d0)) .or. (.not. (y <= 1.15d-10))) then
        tmp = x + cos(y)
    else
        tmp = x + (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.88) || !(y <= 1.15e-10)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.88) or not (y <= 1.15e-10):
		tmp = x + math.cos(y)
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.88) || !(y <= 1.15e-10))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.88) || ~((y <= 1.15e-10)))
		tmp = x + cos(y);
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.88], N[Not[LessEqual[y, 1.15e-10]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.880000000000000004 or 1.15000000000000004e-10 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 56.4%

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

      1. +-commutative 56.4%

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

   4. Simplified 56.4%

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

   if -0.880000000000000004 < y < 1.15000000000000004e-10

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.3%

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

      1. associate-+r+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+l+ 99.3%

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

      4. mul-1-neg 99.3%

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

      5. unsub-neg 99.3%

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

   4. Simplified 99.3%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.88 \lor \neg \left(y \leq 1.15 \cdot 10^{-10}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 6: 69.8% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+55} \lor \neg \left(y \leq 0.015\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.5e+55) (not (<= y 0.015))) (+ x 1.0) (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+55) || !(y <= 0.015)) {
		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 <= (-4.5d+55)) .or. (.not. (y <= 0.015d0))) 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 <= -4.5e+55) || !(y <= 0.015)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.5e+55) or not (y <= 0.015):
		tmp = x + 1.0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.5e+55) || !(y <= 0.015))
		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 <= -4.5e+55) || ~((y <= 0.015)))
		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, -4.5e+55], N[Not[LessEqual[y, 0.015]], $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 < -4.49999999999999998e55 or 0.014999999999999999 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 31.4%

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

      1. +-commutative 31.4%

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

   4. Simplified 31.4%

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

   if -4.49999999999999998e55 < y < 0.014999999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.3%

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

      1. associate-+r+ 93.3%

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

      2. +-commutative 93.3%

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

      3. associate-+l+ 93.3%

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

      4. mul-1-neg 93.3%

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

      5. unsub-neg 93.3%

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

   4. Simplified 93.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+55} \lor \neg \left(y \leq 0.015\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 7: 67.0% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-15} \lor \neg \left(x \leq 9.8 \cdot 10^{-9}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e-15) (not (<= x 9.8e-9))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-15) || !(x <= 9.8e-9)) {
		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 <= (-6d-15)) .or. (.not. (x <= 9.8d-9))) 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 <= -6e-15) || !(x <= 9.8e-9)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e-15) or not (x <= 9.8e-9):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e-15) || !(x <= 9.8e-9))
		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 <= -6e-15) || ~((x <= 9.8e-9)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e-15], N[Not[LessEqual[x, 9.8e-9]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6e-15 or 9.80000000000000007e-9 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.9%

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

      1. +-commutative 77.9%

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

   4. Simplified 77.9%

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

   if -6e-15 < x < 9.80000000000000007e-9

   1. Initial program 99.9%

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

      1. add-log-exp 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around 0 99.7%

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

   5. Taylor expanded in y around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

   7. Simplified 50.6%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-15} \lor \neg \left(x \leq 9.8 \cdot 10^{-9}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]

Alternative 8: 62.3% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.5e+223) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.5e+223) {
		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 <= (-6.5d+223)) 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 <= -6.5e+223) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.5e+223:
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.5e+223)
		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 <= -6.5e+223)
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.5e+223], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000001e223

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 88.4%

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

      1. associate-*r* 88.4%

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

      2. neg-mul-1 88.4%

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

      3. *-commutative 88.4%

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

   4. Simplified 88.4%

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

   5. Taylor expanded in y around 0 35.4%

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

      1. mul-1-neg 35.4%

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

      2. distribute-rgt-neg-in 35.4%

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

   7. Simplified 35.4%

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

   if -6.5000000000000001e223 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 61.6%

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

      1. +-commutative 61.6%

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

   4. Simplified 61.6%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9: 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 57.7%

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

   1. +-commutative 57.7%

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

4. Simplified 57.7%

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

5. Final simplification 57.7%

   \[\leadsto x + 1 \]

Alternative 10: 42.8% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around inf 39.6%

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

3. Final simplification 39.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023320 
(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))))