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

Percentage Accurate: 99.9% → 99.9%

Time: 9.2s

Alternatives: 15

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. Add Preprocessing

Alternative 2: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{-8} \lor \neg \left(x \leq 6 \cdot 10^{-9}\right):\\ \;\;\;\;1 + \left(x - t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -1.65e-8) (not (<= x 6e-9)))
     (+ 1.0 (- 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 <= -1.65e-8) || !(x <= 6e-9)) {
		tmp = 1.0 + (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 <= (-1.65d-8)) .or. (.not. (x <= 6d-9))) then
        tmp = 1.0d0 + (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 <= -1.65e-8) || !(x <= 6e-9)) {
		tmp = 1.0 + (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 <= -1.65e-8) or not (x <= 6e-9):
		tmp = 1.0 + (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 <= -1.65e-8) || !(x <= 6e-9))
		tmp = Float64(1.0 + 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 <= -1.65e-8) || ~((x <= 6e-9)))
		tmp = 1.0 + (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, -1.65e-8], N[Not[LessEqual[x, 6e-9]], $MachinePrecision]], N[(1.0 + N[(x - t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.64999999999999989e-8 or 5.99999999999999996e-9 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. distribute-rgt-neg-in 82.4%

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

      3. distribute-lft-out-- 82.4%

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

      4. mul-1-neg 82.4%

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

      5. remove-double-neg 82.4%

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

      6. +-commutative 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in y around 0 81.9%

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

   7. Taylor expanded in z around 0 99.3%

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

      1. neg-mul-1 99.3%

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

      2. unsub-neg 99.3%

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

   9. Simplified 99.3%

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

   if -1.64999999999999989e-8 < x < 5.99999999999999996e-9

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.4%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-8} \lor \neg \left(x \leq 6 \cdot 10^{-9}\right):\\ \;\;\;\;1 + \left(x - z \cdot \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.52 \lor \neg \left(z \leq 0.0026\right):\\ \;\;\;\;1 + \left(x - z \cdot \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.52) (not (<= z 0.0026)))
   (+ 1.0 (- x (* z (sin y))))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.52) || !(z <= 0.0026)) {
		tmp = 1.0 + (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 <= (-0.52d0)) .or. (.not. (z <= 0.0026d0))) then
        tmp = 1.0d0 + (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 <= -0.52) || !(z <= 0.0026)) {
		tmp = 1.0 + (x - (z * Math.sin(y)));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.52) or not (z <= 0.0026):
		tmp = 1.0 + (x - (z * math.sin(y)))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.52) || !(z <= 0.0026))
		tmp = Float64(1.0 + 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 <= -0.52) || ~((z <= 0.0026)))
		tmp = 1.0 + (x - (z * sin(y)));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.52], N[Not[LessEqual[z, 0.0026]], $MachinePrecision]], N[(1.0 + N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.52000000000000002 or 0.0025999999999999999 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-in 99.7%

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

      3. distribute-lft-out-- 99.7%

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

      4. mul-1-neg 99.7%

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

      5. remove-double-neg 99.7%

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

      6. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 98.3%

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

   7. Taylor expanded in z around 0 98.4%

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

      1. neg-mul-1 98.4%

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

      2. unsub-neg 98.4%

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

   9. Simplified 98.4%

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

   if -0.52000000000000002 < z < 0.0025999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.52 \lor \neg \left(z \leq 0.0026\right):\\ \;\;\;\;1 + \left(x - z \cdot \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -82000000000000 \lor \neg \left(z \leq 29500\right):\\ \;\;\;\;z \cdot \left(\frac{x}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -82000000000000.0) (not (<= z 29500.0)))
   (* z (- (/ x z) (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -82000000000000.0) || !(z <= 29500.0)) {
		tmp = z * ((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 <= (-82000000000000.0d0)) .or. (.not. (z <= 29500.0d0))) then
        tmp = z * ((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 <= -82000000000000.0) || !(z <= 29500.0)) {
		tmp = z * ((x / z) - Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -82000000000000.0) or not (z <= 29500.0):
		tmp = z * ((x / z) - math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -82000000000000.0) || !(z <= 29500.0))
		tmp = Float64(z * Float64(Float64(x / 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 <= -82000000000000.0) || ~((z <= 29500.0)))
		tmp = z * ((x / z) - sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -82000000000000.0], N[Not[LessEqual[z, 29500.0]], $MachinePrecision]], N[(z * N[(N[(x / z), $MachinePrecision] - N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e13 or 29500 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-in 99.7%

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

      3. distribute-lft-out-- 99.7%

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

      4. mul-1-neg 99.7%

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

      5. remove-double-neg 99.7%

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

      6. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 90.7%

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

   if -8.2e13 < z < 29500

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -82000000000000 \lor \neg \left(z \leq 29500\right):\\ \;\;\;\;z \cdot \left(\frac{x}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+26} \lor \neg \left(z \leq 62000000\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.15e+26) (not (<= z 62000000.0)))
   (- 1.0 (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.15e+26) || !(z <= 62000000.0)) {
		tmp = 1.0 - (z * sin(y));
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.15d+26)) .or. (.not. (z <= 62000000.0d0))) then
        tmp = 1.0d0 - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.15e+26) || !(z <= 62000000.0)) {
		tmp = 1.0 - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.15e+26) or not (z <= 62000000.0):
		tmp = 1.0 - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.15e+26) || !(z <= 62000000.0))
		tmp = Float64(1.0 - 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 <= -1.15e+26) || ~((z <= 62000000.0)))
		tmp = 1.0 - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.15e+26], N[Not[LessEqual[z, 62000000.0]], $MachinePrecision]], N[(1.0 - 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 < -1.15e26 or 6.2e7 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-in 99.7%

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

      3. distribute-lft-out-- 99.7%

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

      4. mul-1-neg 99.7%

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

      5. remove-double-neg 99.7%

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

      6. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 99.3%

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

   7. Taylor expanded in x around 0 76.7%

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

      1. sub-neg 76.7%

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

      2. distribute-lft-in 76.7%

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

      3. rgt-mult-inverse 76.7%

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

      4. distribute-rgt-neg-in 76.7%

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

      5. unsub-neg 76.7%

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

   9. Simplified 76.7%

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

   if -1.15e26 < z < 6.2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.7%

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

      1. +-commutative 97.7%

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

   5. Simplified 97.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+26} \lor \neg \left(z \leq 62000000\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+119} \lor \neg \left(z \leq 1.3 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e+119) (not (<= z 1.3e+105)))
   (* z (- (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e+119) || !(z <= 1.3e+105)) {
		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 <= (-3.5d+119)) .or. (.not. (z <= 1.3d+105))) 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 <= -3.5e+119) || !(z <= 1.3e+105)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e+119) or not (z <= 1.3e+105):
		tmp = z * -math.sin(y)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.5e+119) || !(z <= 1.3e+105))
		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 <= -3.5e+119) || ~((z <= 1.3e+105)))
		tmp = z * -sin(y);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e+119], N[Not[LessEqual[z, 1.3e+105]], $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 < -3.5000000000000001e119 or 1.3000000000000001e105 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 76.7%

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

      1. associate-*r* 76.7%

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

      2. neg-mul-1 76.7%

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

      3. *-commutative 76.7%

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

   5. Simplified 76.7%

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

   if -3.5000000000000001e119 < z < 1.3000000000000001e105

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 88.8%

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

      1. +-commutative 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+119} \lor \neg \left(z \leq 1.3 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+29} \lor \neg \left(y \leq 3.4 \cdot 10^{-10}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.6e+29) (not (<= y 3.4e-10)))
   (+ x (cos y))
   (+ 1.0 (+ x (* y (- (* y (- (* 0.16666666666666666 (* y z)) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.6e+29) || !(y <= 3.4e-10)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 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 <= (-1.6d+29)) .or. (.not. (y <= 3.4d-10))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x + (y * ((y * ((0.16666666666666666d0 * (y * z)) - 0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.6e+29) || !(y <= 3.4e-10)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.6e+29) or not (y <= 3.4e-10):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.6e+29) || !(y <= 3.4e-10))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * z)) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.6e+29) || ~((y <= 3.4e-10)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.6e+29], N[Not[LessEqual[y, 3.4e-10]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999993e29 or 3.40000000000000015e-10 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 57.4%

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

      1. +-commutative 57.4%

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

   5. Simplified 57.4%

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

   if -1.59999999999999993e29 < y < 3.40000000000000015e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 94.6%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+29} \lor \neg \left(y \leq 3.4 \cdot 10^{-10}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-9} \lor \neg \left(x \leq 1.35 \cdot 10^{-8}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45e-9) (not (<= x 1.35e-8))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e-9) || !(x <= 1.35e-8)) {
		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 <= (-1.45d-9)) .or. (.not. (x <= 1.35d-8))) 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 <= -1.45e-9) || !(x <= 1.35e-8)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45e-9) or not (x <= 1.35e-8):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45e-9) || !(x <= 1.35e-8))
		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 <= -1.45e-9) || ~((x <= 1.35e-8)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45e-9], N[Not[LessEqual[x, 1.35e-8]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996e-9 or 1.35000000000000001e-8 < 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 80.6%

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

      1. +-commutative 80.6%

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

   5. Simplified 80.6%

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

   if -1.44999999999999996e-9 < x < 1.35000000000000001e-8

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

      4. add-cube-cbrt 99.1%

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

      5. associate-*r* 99.1%

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

      6. fma-define 99.1%

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

      7. pow2 99.1%

         \[\leadsto \mathsf{fma}\left(\left(-z\right) \cdot \color{blue}{{\left(\sqrt[3]{\sin y}\right)}^{2}}, \sqrt[3]{\sin y}, x + \cos y\right) \]

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(-z\right) \cdot {\left(\sqrt[3]{\sin y}\right)}^{2}, \sqrt[3]{\sin y}, x + \cos y\right)} \]

   5. Taylor expanded in x around 0 99.4%

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

      1. mul-1-neg 99.4%

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

      2. sub-neg 99.4%

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

      3. *-commutative 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in z around 0 54.6%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-9} \lor \neg \left(x \leq 1.35 \cdot 10^{-8}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \mathbf{elif}\;y \leq 45:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.15e+17)
   (* x (+ 1.0 (/ 1.0 x)))
   (if (<= y 45.0)
     (+ 1.0 (+ x (* y (- (* y (- (* 0.16666666666666666 (* y z)) 0.5)) z))))
     (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e+17) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 45.0) {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.15d+17)) then
        tmp = x * (1.0d0 + (1.0d0 / x))
    else if (y <= 45.0d0) then
        tmp = 1.0d0 + (x + (y * ((y * ((0.16666666666666666d0 * (y * z)) - 0.5d0)) - z)))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e+17) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 45.0) {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.15e+17:
		tmp = x * (1.0 + (1.0 / x))
	elif y <= 45.0:
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.15e+17)
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	elseif (y <= 45.0)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * z)) - 0.5)) - z))));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.15e+17)
		tmp = x * (1.0 + (1.0 / x));
	elseif (y <= 45.0)
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.15e+17], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 45.0], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e17

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 87.7%

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

      1. associate--l+ 87.7%

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

      2. div-sub 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in y around 0 34.9%

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

   if -1.15e17 < y < 45

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)} \]

   if 45 < 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 32.8%

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

      1. +-commutative 32.8%

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

   5. Simplified 32.8%

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

Alternative 10: 69.2% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \mathbf{elif}\;y \leq 42:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+27)
   (* x (+ 1.0 (/ 1.0 x)))
   (if (<= y 42.0) (+ 1.0 (+ x (* y (- (* y -0.5) z)))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+27) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 42.0) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - 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 <= (-6.5d+27)) then
        tmp = x * (1.0d0 + (1.0d0 / x))
    else if (y <= 42.0d0) then
        tmp = 1.0d0 + (x + (y * ((y * (-0.5d0)) - 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 <= -6.5e+27) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 42.0) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e+27:
		tmp = x * (1.0 + (1.0 / x))
	elif y <= 42.0:
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+27)
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	elseif (y <= 42.0)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * -0.5) - z))));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e+27)
		tmp = x * (1.0 + (1.0 / x));
	elseif (y <= 42.0)
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+27], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 42.0], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000005e27

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 88.8%

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

      1. associate--l+ 88.8%

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

      2. div-sub 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in y around 0 36.0%

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

   if -6.5000000000000005e27 < y < 42

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.9%

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

   if 42 < 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 32.8%

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

      1. +-commutative 32.8%

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

   5. Simplified 32.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \mathbf{elif}\;y \leq 42:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.1% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-10}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.3e+42)
   (* x (+ 1.0 (/ 1.0 x)))
   (if (<= y 3.4e-10) (+ x (- 1.0 (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.3e+42) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 3.4e-10) {
		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 <= (-5.3d+42)) then
        tmp = x * (1.0d0 + (1.0d0 / x))
    else if (y <= 3.4d-10) 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 <= -5.3e+42) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 3.4e-10) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.3e+42:
		tmp = x * (1.0 + (1.0 / x))
	elif y <= 3.4e-10:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.3e+42)
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	elseif (y <= 3.4e-10)
		tmp = Float64(x + 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 (y <= -5.3e+42)
		tmp = x * (1.0 + (1.0 / x));
	elseif (y <= 3.4e-10)
		tmp = x + (1.0 - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.3e+42], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-10], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.30000000000000028e42

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 89.2%

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

      1. associate--l+ 89.2%

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

      2. div-sub 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around 0 37.1%

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

   if -5.30000000000000028e42 < y < 3.40000000000000015e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 92.0%

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

      1. associate-+r+ 92.0%

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

      2. +-commutative 92.0%

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

      3. associate-+l+ 92.0%

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

      4. mul-1-neg 92.0%

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

      5. unsub-neg 92.0%

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

   5. Simplified 92.0%

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

   if 3.40000000000000015e-10 < 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 35.5%

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

      1. +-commutative 35.5%

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

   5. Simplified 35.5%

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

Alternative 12: 66.1% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-13} \lor \neg \left(x \leq 4.8 \cdot 10^{-17}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e-13) (not (<= x 4.8e-17))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-13) || !(x <= 4.8e-17)) {
		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 <= (-2.8d-13)) .or. (.not. (x <= 4.8d-17))) 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 <= -2.8e-13) || !(x <= 4.8e-17)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e-13) or not (x <= 4.8e-17):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e-13) || !(x <= 4.8e-17))
		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 <= -2.8e-13) || ~((x <= 4.8e-17)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e-13], N[Not[LessEqual[x, 4.8e-17]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000002e-13 or 4.79999999999999973e-17 < 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 79.1%

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

      1. +-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -2.8000000000000002e-13 < x < 4.79999999999999973e-17

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

      4. add-cube-cbrt 99.1%

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

      5. associate-*r* 99.1%

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

      6. fma-define 99.1%

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

      7. pow2 99.1%

         \[\leadsto \mathsf{fma}\left(\left(-z\right) \cdot \color{blue}{{\left(\sqrt[3]{\sin y}\right)}^{2}}, \sqrt[3]{\sin y}, x + \cos y\right) \]

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(-z\right) \cdot {\left(\sqrt[3]{\sin y}\right)}^{2}, \sqrt[3]{\sin y}, x + \cos y\right)} \]

   5. Taylor expanded in x around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

   10. Simplified 48.0%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-13} \lor \neg \left(x \leq 4.8 \cdot 10^{-17}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.9% accurate, 18.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 79.9%

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

   if -1 < x < 1

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

      4. add-cube-cbrt 99.1%

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

      5. associate-*r* 99.2%

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

      6. fma-define 99.2%

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

      7. pow2 99.2%

         \[\leadsto \mathsf{fma}\left(\left(-z\right) \cdot \color{blue}{{\left(\sqrt[3]{\sin y}\right)}^{2}}, \sqrt[3]{\sin y}, x + \cos y\right) \]

   4. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(-z\right) \cdot {\left(\sqrt[3]{\sin y}\right)}^{2}, \sqrt[3]{\sin y}, x + \cos y\right)} \]

   5. Taylor expanded in x around 0 98.3%

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

      1. mul-1-neg 98.3%

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

      2. sub-neg 98.3%

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

      3. *-commutative 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in y around 0 34.8%

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

Alternative 14: 60.8% 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 55.2%

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

   1. +-commutative 55.2%

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

5. Simplified 55.2%

   \[\leadsto \color{blue}{x + 1} \]
6. Add Preprocessing

Alternative 15: 21.5% 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. Step-by-step derivation

   1. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. distribute-lft-neg-in 99.9%

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

   4. add-cube-cbrt 99.4%

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

   5. associate-*r* 99.3%

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

   6. fma-define 99.3%

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

   7. pow2 99.3%

      \[\leadsto \mathsf{fma}\left(\left(-z\right) \cdot \color{blue}{{\left(\sqrt[3]{\sin y}\right)}^{2}}, \sqrt[3]{\sin y}, x + \cos y\right) \]

4. Applied egg-rr 99.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\left(-z\right) \cdot {\left(\sqrt[3]{\sin y}\right)}^{2}, \sqrt[3]{\sin y}, x + \cos y\right)} \]

5. Taylor expanded in x around 0 64.7%

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

   1. mul-1-neg 64.7%

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

   2. sub-neg 64.7%

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

   3. *-commutative 64.7%

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

7. Simplified 64.7%

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

8. Taylor expanded in y around 0 20.9%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024091 
(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))))