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

Percentage Accurate: 99.9% → 99.9%

Time: 9.9s

Alternatives: 11

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[Cos[y], $MachinePrecision] + N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. distribute-lft-neg-out 99.9%

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

   6. distribute-rgt-neg-in 99.9%

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

   7. sin-neg 99.9%

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

   8. fma-define 99.9%

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

   9. sin-neg 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 99.9%

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

   1. neg-mul-1 99.9%

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

   2. sub-neg 99.9%

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

7. Simplified 99.9%

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

Alternative 2: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -32000000:\\ \;\;\;\;1 + x \cdot \left(1 - \sin y \cdot \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -32000000.0)
   (+ 1.0 (* x (- 1.0 (* (sin y) (/ z x)))))
   (if (<= x 1.15e-10)
     (- (cos y) (* z (sin y)))
     (+ 1.0 (* x (- 1.0 (* z (/ (sin y) x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -32000000.0) {
		tmp = 1.0 + (x * (1.0 - (sin(y) * (z / x))));
	} else if (x <= 1.15e-10) {
		tmp = cos(y) - (z * sin(y));
	} else {
		tmp = 1.0 + (x * (1.0 - (z * (sin(y) / 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 <= (-32000000.0d0)) then
        tmp = 1.0d0 + (x * (1.0d0 - (sin(y) * (z / x))))
    else if (x <= 1.15d-10) then
        tmp = cos(y) - (z * sin(y))
    else
        tmp = 1.0d0 + (x * (1.0d0 - (z * (sin(y) / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -32000000.0) {
		tmp = 1.0 + (x * (1.0 - (Math.sin(y) * (z / x))));
	} else if (x <= 1.15e-10) {
		tmp = Math.cos(y) - (z * Math.sin(y));
	} else {
		tmp = 1.0 + (x * (1.0 - (z * (Math.sin(y) / x))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -32000000.0:
		tmp = 1.0 + (x * (1.0 - (math.sin(y) * (z / x))))
	elif x <= 1.15e-10:
		tmp = math.cos(y) - (z * math.sin(y))
	else:
		tmp = 1.0 + (x * (1.0 - (z * (math.sin(y) / x))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -32000000.0)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 - Float64(sin(y) * Float64(z / x)))));
	elseif (x <= 1.15e-10)
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 - Float64(z * Float64(sin(y) / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -32000000.0)
		tmp = 1.0 + (x * (1.0 - (sin(y) * (z / x))));
	elseif (x <= 1.15e-10)
		tmp = cos(y) - (z * sin(y));
	else
		tmp = 1.0 + (x * (1.0 - (z * (sin(y) / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -32000000.0], N[(1.0 + N[(x * N[(1.0 - N[(N[Sin[y], $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-10], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 - N[(z * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2e7

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/l* 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 99.4%

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

   if -3.2e7 < x < 1.15000000000000004e-10

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.5%

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

      1. neg-mul-1 99.5%

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

      2. sub-neg 99.5%

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

   7. Simplified 99.5%

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

   if 1.15000000000000004e-10 < x

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 99.9%

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

      1. associate-/l* 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in y around 0 99.9%

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

Alternative 3: 92.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ t_1 := 1 + x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+202}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -28000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85:\\ \;\;\;\;\cos y + x\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z)))
        (t_1 (+ 1.0 (* x (- 1.0 (* z (/ (sin y) x)))))))
   (if (<= z -6.4e+202)
     t_0
     (if (<= z -28000000000000.0)
       t_1
       (if (<= z 1.85) (+ (cos y) x) (if (<= z 7.3e+248) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double t_1 = 1.0 + (x * (1.0 - (z * (sin(y) / x))));
	double tmp;
	if (z <= -6.4e+202) {
		tmp = t_0;
	} else if (z <= -28000000000000.0) {
		tmp = t_1;
	} else if (z <= 1.85) {
		tmp = cos(y) + x;
	} else if (z <= 7.3e+248) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_0 = sin(y) * -z
    t_1 = 1.0d0 + (x * (1.0d0 - (z * (sin(y) / x))))
    if (z <= (-6.4d+202)) then
        tmp = t_0
    else if (z <= (-28000000000000.0d0)) then
        tmp = t_1
    else if (z <= 1.85d0) then
        tmp = cos(y) + x
    else if (z <= 7.3d+248) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double t_1 = 1.0 + (x * (1.0 - (z * (Math.sin(y) / x))));
	double tmp;
	if (z <= -6.4e+202) {
		tmp = t_0;
	} else if (z <= -28000000000000.0) {
		tmp = t_1;
	} else if (z <= 1.85) {
		tmp = Math.cos(y) + x;
	} else if (z <= 7.3e+248) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	t_1 = 1.0 + (x * (1.0 - (z * (math.sin(y) / x))))
	tmp = 0
	if z <= -6.4e+202:
		tmp = t_0
	elif z <= -28000000000000.0:
		tmp = t_1
	elif z <= 1.85:
		tmp = math.cos(y) + x
	elif z <= 7.3e+248:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	t_1 = Float64(1.0 + Float64(x * Float64(1.0 - Float64(z * Float64(sin(y) / x)))))
	tmp = 0.0
	if (z <= -6.4e+202)
		tmp = t_0;
	elseif (z <= -28000000000000.0)
		tmp = t_1;
	elseif (z <= 1.85)
		tmp = Float64(cos(y) + x);
	elseif (z <= 7.3e+248)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	t_1 = 1.0 + (x * (1.0 - (z * (sin(y) / x))));
	tmp = 0.0;
	if (z <= -6.4e+202)
		tmp = t_0;
	elseif (z <= -28000000000000.0)
		tmp = t_1;
	elseif (z <= 1.85)
		tmp = cos(y) + x;
	elseif (z <= 7.3e+248)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x * N[(1.0 - N[(z * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+202], t$95$0, If[LessEqual[z, -28000000000000.0], t$95$1, If[LessEqual[z, 1.85], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 7.3e+248], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.40000000000000024e202 or 7.2999999999999998e248 < z

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sin-neg 99.8%

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

      8. fma-define 99.8%

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

      9. sin-neg 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 91.5%

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

      1. neg-mul-1 91.5%

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

      2. *-commutative 91.5%

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

      3. distribute-rgt-neg-in 91.5%

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

   7. Simplified 91.5%

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

   if -6.40000000000000024e202 < z < -2.8e13 or 1.8500000000000001 < z < 7.2999999999999998e248

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 89.4%

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

      1. mul-1-neg 89.4%

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

      2. unsub-neg 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-/l* 80.8%

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

   7. Simplified 80.8%

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

   8. Taylor expanded in y around inf 89.4%

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

      1. associate-/l* 89.3%

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

   10. Simplified 89.3%

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

   11. Taylor expanded in y around 0 88.6%

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

   if -2.8e13 < z < 1.8500000000000001

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 97.8%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+202}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -28000000000000:\\ \;\;\;\;1 + x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{elif}\;z \leq 1.85:\\ \;\;\;\;\cos y + x\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{+248}:\\ \;\;\;\;1 + x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+120} \lor \neg \left(z \leq 6.5 \cdot 10^{+111}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e+120) (not (<= z 6.5e+111)))
   (* (sin y) (- z))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+120) || !(z <= 6.5e+111)) {
		tmp = sin(y) * -z;
	} else {
		tmp = cos(y) + 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 ((z <= (-1.8d+120)) .or. (.not. (z <= 6.5d+111))) then
        tmp = sin(y) * -z
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+120) || !(z <= 6.5e+111)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e+120) or not (z <= 6.5e+111):
		tmp = math.sin(y) * -z
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e+120) || !(z <= 6.5e+111))
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e+120) || ~((z <= 6.5e+111)))
		tmp = sin(y) * -z;
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e+120], N[Not[LessEqual[z, 6.5e+111]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000008e120 or 6.5000000000000002e111 < z

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sin-neg 99.8%

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

      8. fma-define 99.8%

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

      9. sin-neg 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 73.8%

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

      1. neg-mul-1 73.8%

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

      2. *-commutative 73.8%

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

      3. distribute-rgt-neg-in 73.8%

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

   7. Simplified 73.8%

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

   if -1.80000000000000008e120 < z < 6.5000000000000002e111

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 91.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+120} \lor \neg \left(z \leq 6.5 \cdot 10^{+111}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0064 \lor \neg \left(y \leq 0.25\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0064) (not (<= y 0.25)))
   (+ (cos y) x)
   (+ 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 <= -0.0064) || !(y <= 0.25)) {
		tmp = cos(y) + x;
	} 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 <= (-0.0064d0)) .or. (.not. (y <= 0.25d0))) then
        tmp = cos(y) + x
    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 <= -0.0064) || !(y <= 0.25)) {
		tmp = Math.cos(y) + x;
	} 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 <= -0.0064) or not (y <= 0.25):
		tmp = math.cos(y) + x
	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 <= -0.0064) || !(y <= 0.25))
		tmp = Float64(cos(y) + x);
	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 <= -0.0064) || ~((y <= 0.25)))
		tmp = cos(y) + x;
	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, -0.0064], N[Not[LessEqual[y, 0.25]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] + x), $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 < -0.00640000000000000031 or 0.25 < y

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 58.4%

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

   if -0.00640000000000000031 < y < 0.25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.5%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0064 \lor \neg \left(y \leq 0.25\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.3% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+16} \lor \neg \left(y \leq 30.5\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e+16) (not (<= y 30.5)))
   (+ x 1.0)
   (+ 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 <= -2.9e+16) || !(y <= 30.5)) {
		tmp = x + 1.0;
	} 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 <= (-2.9d+16)) .or. (.not. (y <= 30.5d0))) then
        tmp = x + 1.0d0
    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 <= -2.9e+16) || !(y <= 30.5)) {
		tmp = x + 1.0;
	} 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 <= -2.9e+16) or not (y <= 30.5):
		tmp = x + 1.0
	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 <= -2.9e+16) || !(y <= 30.5))
		tmp = Float64(x + 1.0);
	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 <= -2.9e+16) || ~((y <= 30.5)))
		tmp = x + 1.0;
	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, -2.9e+16], N[Not[LessEqual[y, 30.5]], $MachinePrecision]], N[(x + 1.0), $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 < -2.9e16 or 30.5 < y

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sin-neg 99.8%

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

      8. fma-define 99.8%

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

      9. sin-neg 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 29.6%

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

   if -2.9e16 < y < 30.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.1%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+16} \lor \neg \left(y \leq 30.5\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.5% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+88} \lor \neg \left(y \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8e+88) (not (<= y 5e+118))) (+ x 1.0) (- (+ x 1.0) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+88) || !(y <= 5e+118)) {
		tmp = x + 1.0;
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.8d+88)) .or. (.not. (y <= 5d+118))) then
        tmp = x + 1.0d0
    else
        tmp = (x + 1.0d0) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+88) || !(y <= 5e+118)) {
		tmp = x + 1.0;
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.8e+88) or not (y <= 5e+118):
		tmp = x + 1.0
	else:
		tmp = (x + 1.0) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.8e+88) || !(y <= 5e+118))
		tmp = Float64(x + 1.0);
	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 <= -4.8e+88) || ~((y <= 5e+118)))
		tmp = x + 1.0;
	else
		tmp = (x + 1.0) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.8e+88], N[Not[LessEqual[y, 5e+118]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7999999999999998e88 or 4.99999999999999972e118 < y

   1. Initial program 99.7%

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

      1. cancel-sign-sub-inv 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sin-neg 99.8%

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

      8. fma-define 99.8%

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

      9. sin-neg 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 30.6%

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

   if -4.7999999999999998e88 < y < 4.99999999999999972e118

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.1%

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

      1. associate-+r+ 80.1%

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

      2. associate-*r* 80.1%

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

      3. mul-1-neg 80.1%

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

   7. Simplified 80.1%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+88} \lor \neg \left(y \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.9% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-32}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.15e+16) x (if (<= x 3e-32) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.15e+16) {
		tmp = x;
	} else if (x <= 3e-32) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.15d+16)) then
        tmp = x
    else if (x <= 3d-32) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.15e+16) {
		tmp = x;
	} else if (x <= 3e-32) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.15e+16:
		tmp = x
	elif x <= 3e-32:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.15e+16)
		tmp = x;
	elseif (x <= 3e-32)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.15e+16)
		tmp = x;
	elseif (x <= 3e-32)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.15e+16], x, If[LessEqual[x, 3e-32], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15e16

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sin-neg 100.0%

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

      8. fma-define 100.0%

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

      9. sin-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.3%

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

   if -1.15e16 < x < 3e-32

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.1%

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

      1. neg-mul-1 99.1%

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

      2. sub-neg 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in y around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. unsub-neg 49.2%

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

   10. Simplified 49.2%

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

   if 3e-32 < x

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 76.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-32}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.4% accurate, 14.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+205} \lor \neg \left(z \leq 4.3 \cdot 10^{+243}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e+205) (not (<= z 4.3e+243))) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+205) || !(z <= 4.3e+243)) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.8d+205)) .or. (.not. (z <= 4.3d+243))) then
        tmp = y * -z
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+205) || !(z <= 4.3e+243)) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e+205) or not (z <= 4.3e+243):
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e+205) || !(z <= 4.3e+243))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e+205) || ~((z <= 4.3e+243)))
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e+205], N[Not[LessEqual[z, 4.3e+243]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000001e205 or 4.29999999999999964e243 < z

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sin-neg 99.8%

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

      8. fma-define 99.8%

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

      9. sin-neg 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 94.7%

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

      1. neg-mul-1 94.7%

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

      2. sub-neg 94.7%

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

   7. Simplified 94.7%

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

   8. Taylor expanded in y around 0 44.1%

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

      1. mul-1-neg 44.1%

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

      2. unsub-neg 44.1%

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

   10. Simplified 44.1%

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

   11. Taylor expanded in y around inf 40.6%

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

       1. mul-1-neg 40.6%

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

       2. *-commutative 40.6%

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

       3. distribute-rgt-neg-in 40.6%

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

   13. Simplified 40.6%

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

   if -1.80000000000000001e205 < z < 4.29999999999999964e243

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. sin-neg 99.9%

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

      8. fma-define 99.9%

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

      9. sin-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+205} \lor \neg \left(z \leq 4.3 \cdot 10^{+243}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.1% 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. Step-by-step derivation

   1. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. distribute-lft-neg-out 99.9%

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

   6. distribute-rgt-neg-in 99.9%

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

   7. sin-neg 99.9%

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

   8. fma-define 99.9%

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

   9. sin-neg 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 55.0%

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

6. Final simplification 55.0%

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

Alternative 11: 42.7% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

   1. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. distribute-lft-neg-out 99.9%

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

   6. distribute-rgt-neg-in 99.9%

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

   7. sin-neg 99.9%

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

   8. fma-define 99.9%

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

   9. sin-neg 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\cos y + \mathsf{fma}\left(z, -\sin y, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 35.2%

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

Reproduce

herbie shell --seed 2024170 
(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))))