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

Percentage Accurate: 99.9% → 99.9%

Time: 8.7s

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, 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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 2: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{-8} \lor \neg \left(x \leq 4.2 \cdot 10^{-7}\right):\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -6.6e-8) (not (<= x 4.2e-7)))
     (- (+ x 1.0) 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 <= -6.6e-8) || !(x <= 4.2e-7)) {
		tmp = (x + 1.0) - 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 <= (-6.6d-8)) .or. (.not. (x <= 4.2d-7))) then
        tmp = (x + 1.0d0) - 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 <= -6.6e-8) || !(x <= 4.2e-7)) {
		tmp = (x + 1.0) - 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 <= -6.6e-8) or not (x <= 4.2e-7):
		tmp = (x + 1.0) - 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 <= -6.6e-8) || !(x <= 4.2e-7))
		tmp = Float64(Float64(x + 1.0) - 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 <= -6.6e-8) || ~((x <= 4.2e-7)))
		tmp = (x + 1.0) - 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, -6.6e-8], N[Not[LessEqual[x, 4.2e-7]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.59999999999999954e-8 or 4.2e-7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.1%

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

      1. +-commutative 99.1%

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

   5. Simplified 99.1%

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

   if -6.59999999999999954e-8 < x < 4.2e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-8} \lor \neg \left(x \leq 4.2 \cdot 10^{-7}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-22} \lor \neg \left(z \leq 2.3 \cdot 10^{-39}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.95e-22) (not (<= z 2.3e-39)))
   (- (+ x 1.0) (* z (sin y)))
   (- (+ x (cos y)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95e-22) || !(z <= 2.3e-39)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = (x + cos(y)) - (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 ((z <= (-1.95d-22)) .or. (.not. (z <= 2.3d-39))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = (x + cos(y)) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95e-22) || !(z <= 2.3e-39)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = (x + Math.cos(y)) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.95e-22) or not (z <= 2.3e-39):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = (x + math.cos(y)) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.95e-22) || !(z <= 2.3e-39))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(Float64(x + cos(y)) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.95e-22) || ~((z <= 2.3e-39)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = (x + cos(y)) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.95e-22], N[Not[LessEqual[z, 2.3e-39]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999999e-22 or 2.30000000000000008e-39 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 97.6%

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

      1. +-commutative 97.6%

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

   5. Simplified 97.6%

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

   if -1.94999999999999999e-22 < z < 2.30000000000000008e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.3%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-22} \lor \neg \left(z \leq 2.3 \cdot 10^{-39}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -50 \lor \neg \left(x \leq 0.95\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -50.0) (not (<= x 0.95))) (+ x 1.0) (- 1.0 (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -50.0) || !(x <= 0.95)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (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 <= (-50.0d0)) .or. (.not. (x <= 0.95d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -50.0) || !(x <= 0.95)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -50.0) or not (x <= 0.95):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -50.0) || !(x <= 0.95))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -50.0) || ~((x <= 0.95)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -50.0], N[Not[LessEqual[x, 0.95]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -50 or 0.94999999999999996 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.3%

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

   4. Taylor expanded in y around 0 60.8%

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

      1. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   7. Taylor expanded in y around 0 81.9%

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

   if -50 < x < 0.94999999999999996

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.8%

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

   4. Taylor expanded in y around 0 77.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -50 \lor \neg \left(x \leq 0.95\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000000000000 \lor \neg \left(y \leq 0.00082\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4000000000000.0) (not (<= y 0.00082)))
   (- x (* z (sin y)))
   (- (+ x 1.0) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4000000000000.0) || !(y <= 0.00082)) {
		tmp = x - (z * sin(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 <= (-4000000000000.0d0)) .or. (.not. (y <= 0.00082d0))) then
        tmp = x - (z * sin(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 <= -4000000000000.0) || !(y <= 0.00082)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4000000000000.0) or not (y <= 0.00082):
		tmp = x - (z * math.sin(y))
	else:
		tmp = (x + 1.0) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4000000000000.0) || !(y <= 0.00082))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4000000000000.0) || ~((y <= 0.00082)))
		tmp = x - (z * sin(y));
	else
		tmp = (x + 1.0) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4000000000000.0], N[Not[LessEqual[y, 0.00082]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e12 or 8.1999999999999998e-4 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.4%

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

   if -4e12 < y < 8.1999999999999998e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.0%

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

      1. +-commutative 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in y around 0 98.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4000000000000 \lor \neg \left(y \leq 0.00082\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-11} \lor \neg \left(x \leq 8.8 \cdot 10^{-7}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e-11) (not (<= x 8.8e-7))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-11) || !(x <= 8.8e-7)) {
		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 <= (-5.8d-11)) .or. (.not. (x <= 8.8d-7))) 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 <= -5.8e-11) || !(x <= 8.8e-7)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e-11) or not (x <= 8.8e-7):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e-11) || !(x <= 8.8e-7))
		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 <= -5.8e-11) || ~((x <= 8.8e-7)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e-11], N[Not[LessEqual[x, 8.8e-7]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8e-11 or 8.8000000000000004e-7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.1%

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

   4. Taylor expanded in y around 0 60.2%

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

      1. *-commutative 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in y around 0 80.5%

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

   if -5.8e-11 < x < 8.8000000000000004e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.8%

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

   4. Taylor expanded in y around 0 66.7%

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

   5. Taylor expanded in z around 0 63.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-11} \lor \neg \left(x \leq 8.8 \cdot 10^{-7}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x 1.0) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + 1.0) - (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 + 1.0d0) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + 1.0) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + 1.0) - (z * math.sin(y))

Julia

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

MATLAB

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

Wolfram

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

3. Taylor expanded in y around 0 89.5%

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

   1. +-commutative 89.5%

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

5. Simplified 89.5%

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

6. Final simplification 89.5%

   \[\leadsto \left(x + 1\right) - z \cdot \sin y \]
7. Add Preprocessing

Alternative 8: 67.0% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-90} \lor \neg \left(x \leq 1.45 \cdot 10^{-48}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.4e-90) (not (<= x 1.45e-48))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.4e-90) || !(x <= 1.45e-48)) {
		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 <= (-4.4d-90)) .or. (.not. (x <= 1.45d-48))) 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 <= -4.4e-90) || !(x <= 1.45e-48)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.4e-90) or not (x <= 1.45e-48):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.4e-90) || !(x <= 1.45e-48))
		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 <= -4.4e-90) || ~((x <= 1.45e-48)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.4e-90], N[Not[LessEqual[x, 1.45e-48]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.39999999999999972e-90 or 1.4500000000000001e-48 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.3%

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

   4. Taylor expanded in y around 0 59.2%

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

      1. *-commutative 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in y around 0 76.2%

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

   if -4.39999999999999972e-90 < x < 1.4500000000000001e-48

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in y around 0 80.1%

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

   5. Taylor expanded in y around 0 56.2%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-90} \lor \neg \left(x \leq 1.45 \cdot 10^{-48}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.0% accurate, 17.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1050000000:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1050000000.0) (- (+ x 1.0) (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1050000000.0) {
		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 (y <= 1050000000.0d0) 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 (y <= 1050000000.0) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1050000000.0:
		tmp = (x + 1.0) - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1050000000.0)
		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 (y <= 1050000000.0)
		tmp = (x + 1.0) - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1050000000.0], 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 y < 1.05e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in y around 0 78.4%

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

   if 1.05e9 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 47.7%

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

   4. Taylor expanded in y around 0 12.6%

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

      1. *-commutative 12.6%

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

   6. Simplified 12.6%

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

   7. Taylor expanded in y around 0 49.9%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1050000000:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.5% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0074:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.46:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0074) x (if (<= x 0.46) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0074) {
		tmp = x;
	} else if (x <= 0.46) {
		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 <= (-0.0074d0)) then
        tmp = x
    else if (x <= 0.46d0) 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 <= -0.0074) {
		tmp = x;
	} else if (x <= 0.46) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0074:
		tmp = x
	elif x <= 0.46:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0074)
		tmp = x;
	elseif (x <= 0.46)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0074)
		tmp = x;
	elseif (x <= 0.46)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0074], x, If[LessEqual[x, 0.46], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0074000000000000003 or 0.46000000000000002 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.3%

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

   4. Taylor expanded in y around 0 60.0%

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

      1. *-commutative 60.0%

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

   6. Simplified 60.0%

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

   7. Taylor expanded in x around inf 78.7%

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

   if -0.0074000000000000003 < x < 0.46000000000000002

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.8%

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

   4. Taylor expanded in y around 0 65.7%

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

   5. Taylor expanded in y around 0 43.1%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0074:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.46:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.4% 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. Add Preprocessing

3. Taylor expanded in y around 0 72.8%

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

4. Taylor expanded in y around 0 57.8%

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

   1. *-commutative 57.8%

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

6. Simplified 57.8%

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

7. Taylor expanded in y around 0 63.7%

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

8. Final simplification 63.7%

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

Alternative 12: 21.4% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 56.6%

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

4. Taylor expanded in y around 0 34.7%

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

5. Taylor expanded in y around 0 21.8%

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

6. Final simplification 21.8%

   \[\leadsto 1 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024115 
(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))))