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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

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, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma(z, sin(-y), (x + cos(y)));
}

Julia

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

Wolfram

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

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

   3. distribute-lft-neg-out 99.9%

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

   4. distribute-rgt-neg-in 99.9%

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

   5. sin-neg 99.9%

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

   6. fma-define 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-12} \lor \neg \left(x \leq 7 \cdot 10^{-17}\right):\\ \;\;\;\;x + z \cdot \left(\frac{1}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e-12) (not (<= x 7e-17)))
   (+ x (* z (- (/ 1.0 z) (sin y))))
   (- (cos y) (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-12) || !(x <= 7e-17)) {
		tmp = x + (z * ((1.0 / z) - sin(y)));
	} else {
		tmp = cos(y) - (z * sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1d-12)) .or. (.not. (x <= 7d-17))) then
        tmp = x + (z * ((1.0d0 / z) - sin(y)))
    else
        tmp = cos(y) - (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-12) || !(x <= 7e-17)) {
		tmp = x + (z * ((1.0 / z) - Math.sin(y)));
	} else {
		tmp = Math.cos(y) - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e-12) or not (x <= 7e-17):
		tmp = x + (z * ((1.0 / z) - math.sin(y)))
	else:
		tmp = math.cos(y) - (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e-12) || !(x <= 7e-17))
		tmp = Float64(x + Float64(z * Float64(Float64(1.0 / z) - sin(y))));
	else
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1e-12) || ~((x <= 7e-17)))
		tmp = x + (z * ((1.0 / z) - sin(y)));
	else
		tmp = cos(y) - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e-12], N[Not[LessEqual[x, 7e-17]], $MachinePrecision]], N[(x + N[(z * N[(N[(1.0 / z), $MachinePrecision] - N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999998e-13 or 7.0000000000000003e-17 < 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 78.2%

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

      1. associate-*r* 78.2%

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

      2. *-commutative 78.2%

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

      3. sub-neg 78.2%

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

      4. distribute-rgt-neg-in 78.2%

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

      5. sin-neg 78.2%

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

      6. +-commutative 78.2%

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

      7. associate-*l* 78.2%

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

      8. neg-mul-1 78.2%

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

      9. distribute-lft-out 78.2%

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

      10. mul-1-neg 78.2%

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

      11. remove-double-neg 78.2%

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

      12. +-commutative 78.2%

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

      13. sin-neg 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in y around 0 77.1%

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

   7. Taylor expanded in x around 0 98.7%

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

   if -9.9999999999999998e-13 < x < 7.0000000000000003e-17

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-12} \lor \neg \left(x \leq 7 \cdot 10^{-17}\right):\\ \;\;\;\;x + z \cdot \left(\frac{1}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 4: 84.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - z \cdot \sin y\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+225}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+179}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+142} \lor \neg \left(z \leq 1.42 \cdot 10^{+88}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* z (sin y)))))
   (if (<= z -1.8e+225)
     t_0
     (if (<= z -7e+179)
       (- (+ x 1.0) (* z y))
       (if (or (<= z -1.15e+142) (not (<= z 1.42e+88))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (z * sin(y));
	double tmp;
	if (z <= -1.8e+225) {
		tmp = t_0;
	} else if (z <= -7e+179) {
		tmp = (x + 1.0) - (z * y);
	} else if ((z <= -1.15e+142) || !(z <= 1.42e+88)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (z * sin(y))
    if (z <= (-1.8d+225)) then
        tmp = t_0
    else if (z <= (-7d+179)) then
        tmp = (x + 1.0d0) - (z * y)
    else if ((z <= (-1.15d+142)) .or. (.not. (z <= 1.42d+88))) then
        tmp = t_0
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (z * Math.sin(y));
	double tmp;
	if (z <= -1.8e+225) {
		tmp = t_0;
	} else if (z <= -7e+179) {
		tmp = (x + 1.0) - (z * y);
	} else if ((z <= -1.15e+142) || !(z <= 1.42e+88)) {
		tmp = t_0;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (z * math.sin(y))
	tmp = 0
	if z <= -1.8e+225:
		tmp = t_0
	elif z <= -7e+179:
		tmp = (x + 1.0) - (z * y)
	elif (z <= -1.15e+142) or not (z <= 1.42e+88):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -1.8e+225)
		tmp = t_0;
	elseif (z <= -7e+179)
		tmp = Float64(Float64(x + 1.0) - Float64(z * y));
	elseif ((z <= -1.15e+142) || !(z <= 1.42e+88))
		tmp = t_0;
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (z * sin(y));
	tmp = 0.0;
	if (z <= -1.8e+225)
		tmp = t_0;
	elseif (z <= -7e+179)
		tmp = (x + 1.0) - (z * y);
	elseif ((z <= -1.15e+142) || ~((z <= 1.42e+88)))
		tmp = t_0;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+225], t$95$0, If[LessEqual[z, -7e+179], N[(N[(x + 1.0), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.15e+142], N[Not[LessEqual[z, 1.42e+88]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e225 or -7.0000000000000003e179 < z < -1.15000000000000001e142 or 1.41999999999999996e88 < 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 99.6%

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

      1. associate-*r* 99.6%

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

      2. *-commutative 99.6%

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

      3. sub-neg 99.6%

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

      4. distribute-rgt-neg-in 99.6%

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

      5. sin-neg 99.6%

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

      6. +-commutative 99.6%

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

      7. associate-*l* 99.6%

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

      8. neg-mul-1 99.6%

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

      9. distribute-lft-out 99.6%

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

      10. mul-1-neg 99.6%

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

      11. remove-double-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. sin-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in y around 0 99.6%

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

   7. Taylor expanded in x around 0 82.3%

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

      1. sub-neg 82.3%

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

      2. distribute-lft-in 82.4%

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

      3. rgt-mult-inverse 82.4%

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

   9. Simplified 82.4%

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

   if -1.7999999999999999e225 < z < -7.0000000000000003e179

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.5%

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

      1. associate-+r+ 89.5%

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

      2. mul-1-neg 89.5%

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

      3. unsub-neg 89.5%

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

      4. +-commutative 89.5%

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

   5. Simplified 89.5%

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

   if -1.15000000000000001e142 < z < 1.41999999999999996e88

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.6%

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

      1. +-commutative 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+225}:\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+179}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+142} \lor \neg \left(z \leq 1.42 \cdot 10^{+88}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin \left(-y\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+225}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.05 \cdot 10^{+183}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+142} \lor \neg \left(z \leq 1.2 \cdot 10^{+88}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin (- y)))))
   (if (<= z -1.8e+225)
     t_0
     (if (<= z -4.05e+183)
       (- (+ x 1.0) (* z y))
       (if (or (<= z -4.8e+142) (not (<= z 1.2e+88))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(-y);
	double tmp;
	if (z <= -1.8e+225) {
		tmp = t_0;
	} else if (z <= -4.05e+183) {
		tmp = (x + 1.0) - (z * y);
	} else if ((z <= -4.8e+142) || !(z <= 1.2e+88)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * sin(-y)
    if (z <= (-1.8d+225)) then
        tmp = t_0
    else if (z <= (-4.05d+183)) then
        tmp = (x + 1.0d0) - (z * y)
    else if ((z <= (-4.8d+142)) .or. (.not. (z <= 1.2d+88))) then
        tmp = t_0
    else
        tmp = x + cos(y)
    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 (z <= -1.8e+225) {
		tmp = t_0;
	} else if (z <= -4.05e+183) {
		tmp = (x + 1.0) - (z * y);
	} else if ((z <= -4.8e+142) || !(z <= 1.2e+88)) {
		tmp = t_0;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(-y)
	tmp = 0
	if z <= -1.8e+225:
		tmp = t_0
	elif z <= -4.05e+183:
		tmp = (x + 1.0) - (z * y)
	elif (z <= -4.8e+142) or not (z <= 1.2e+88):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(Float64(-y)))
	tmp = 0.0
	if (z <= -1.8e+225)
		tmp = t_0;
	elseif (z <= -4.05e+183)
		tmp = Float64(Float64(x + 1.0) - Float64(z * y));
	elseif ((z <= -4.8e+142) || !(z <= 1.2e+88))
		tmp = t_0;
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(-y);
	tmp = 0.0;
	if (z <= -1.8e+225)
		tmp = t_0;
	elseif (z <= -4.05e+183)
		tmp = (x + 1.0) - (z * y);
	elseif ((z <= -4.8e+142) || ~((z <= 1.2e+88)))
		tmp = t_0;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[(-y)], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+225], t$95$0, If[LessEqual[z, -4.05e+183], N[(N[(x + 1.0), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.8e+142], N[Not[LessEqual[z, 1.2e+88]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e225 or -4.04999999999999997e183 < z < -4.7999999999999998e142 or 1.2e88 < 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%

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

      3. distribute-lft-neg-out 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. sin-neg 99.8%

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

      6. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 68.8%

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

   if -1.7999999999999999e225 < z < -4.04999999999999997e183

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.5%

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

      1. associate-+r+ 89.5%

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

      2. mul-1-neg 89.5%

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

      3. unsub-neg 89.5%

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

      4. +-commutative 89.5%

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

   5. Simplified 89.5%

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

   if -4.7999999999999998e142 < z < 1.2e88

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.6%

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

      1. +-commutative 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+225}:\\ \;\;\;\;z \cdot \sin \left(-y\right)\\ \mathbf{elif}\;z \leq -4.05 \cdot 10^{+183}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+142} \lor \neg \left(z \leq 1.2 \cdot 10^{+88}\right):\\ \;\;\;\;z \cdot \sin \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \lor \neg \left(z \leq 3.5 \cdot 10^{-16}\right):\\ \;\;\;\;x + z \cdot \left(\frac{1}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.65) (not (<= z 3.5e-16)))
   (+ x (* z (- (/ 1.0 z) (sin y))))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.65) || !(z <= 3.5e-16)) {
		tmp = x + (z * ((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 <= (-1.65d0)) .or. (.not. (z <= 3.5d-16))) then
        tmp = x + (z * ((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 <= -1.65) || !(z <= 3.5e-16)) {
		tmp = x + (z * ((1.0 / z) - Math.sin(y)));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.65) or not (z <= 3.5e-16):
		tmp = x + (z * ((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 <= -1.65) || !(z <= 3.5e-16))
		tmp = Float64(x + Float64(z * Float64(Float64(1.0 / 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 <= -1.65) || ~((z <= 3.5e-16)))
		tmp = x + (z * ((1.0 / z) - sin(y)));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.65], N[Not[LessEqual[z, 3.5e-16]], $MachinePrecision]], N[(x + N[(z * N[(N[(1.0 / z), $MachinePrecision] - N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999 or 3.50000000000000017e-16 < 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. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. sub-neg 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. sin-neg 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-*l* 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-lft-out 99.7%

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

      10. mul-1-neg 99.7%

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

      11. remove-double-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. sin-neg 99.7%

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

   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 99.2%

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

   7. Taylor expanded in x around 0 99.3%

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

   if -1.6499999999999999 < z < 3.50000000000000017e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.2%

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

      1. +-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \lor \neg \left(z \leq 3.5 \cdot 10^{-16}\right):\\ \;\;\;\;x + z \cdot \left(\frac{1}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.82 \lor \neg \left(z \leq 3.5 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(\frac{x + 1}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.82) (not (<= z 3.5e-16)))
   (* z (- (/ (+ x 1.0) z) (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.82) || !(z <= 3.5e-16)) {
		tmp = z * (((x + 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 <= (-0.82d0)) .or. (.not. (z <= 3.5d-16))) then
        tmp = z * (((x + 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 <= -0.82) || !(z <= 3.5e-16)) {
		tmp = z * (((x + 1.0) / z) - Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.82) or not (z <= 3.5e-16):
		tmp = z * (((x + 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 <= -0.82) || !(z <= 3.5e-16))
		tmp = Float64(z * Float64(Float64(Float64(x + 1.0) / 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 <= -0.82) || ~((z <= 3.5e-16)))
		tmp = z * (((x + 1.0) / z) - sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.82], N[Not[LessEqual[z, 3.5e-16]], $MachinePrecision]], N[(z * N[(N[(N[(x + 1.0), $MachinePrecision] / 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 < -0.819999999999999951 or 3.50000000000000017e-16 < 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. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. sub-neg 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. sin-neg 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-*l* 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-lft-out 99.7%

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

      10. mul-1-neg 99.7%

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

      11. remove-double-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. sin-neg 99.7%

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

   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 99.2%

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

   if -0.819999999999999951 < z < 3.50000000000000017e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.2%

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

      1. +-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.82 \lor \neg \left(z \leq 3.5 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(\frac{x + 1}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+77} \lor \neg \left(z \leq 2.85 \cdot 10^{+69}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e+77) (not (<= z 2.85e+69)))
   (* z (- (/ x z) (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+77) || !(z <= 2.85e+69)) {
		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 <= (-2.5d+77)) .or. (.not. (z <= 2.85d+69))) 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 <= -2.5e+77) || !(z <= 2.85e+69)) {
		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 <= -2.5e+77) or not (z <= 2.85e+69):
		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 <= -2.5e+77) || !(z <= 2.85e+69))
		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 <= -2.5e+77) || ~((z <= 2.85e+69)))
		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, -2.5e+77], N[Not[LessEqual[z, 2.85e+69]], $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 < -2.50000000000000002e77 or 2.85e69 < 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 99.6%

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

      1. associate-*r* 99.6%

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

      2. *-commutative 99.6%

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

      3. sub-neg 99.6%

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

      4. distribute-rgt-neg-in 99.6%

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

      5. sin-neg 99.6%

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

      6. +-commutative 99.6%

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

      7. associate-*l* 99.6%

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

      8. neg-mul-1 99.6%

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

      9. distribute-lft-out 99.6%

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

      10. mul-1-neg 99.6%

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

      11. remove-double-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. sin-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf 86.4%

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

   if -2.50000000000000002e77 < z < 2.85e69

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.4%

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

      1. +-commutative 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+77} \lor \neg \left(z \leq 2.85 \cdot 10^{+69}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{z} - \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.62 \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(z \cdot y\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.62) (not (<= y 0.0072)))
   (+ x (cos y))
   (+ 1.0 (+ x (* y (- (* y (- (* (* z y) 0.16666666666666666) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.62) || !(y <= 0.0072)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * (((z * y) * 0.16666666666666666) - 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 <= (-0.62d0)) .or. (.not. (y <= 0.0072d0))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x + (y * ((y * (((z * y) * 0.16666666666666666d0) - 0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.62) || !(y <= 0.0072)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * (((z * y) * 0.16666666666666666) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.62) or not (y <= 0.0072):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x + (y * ((y * (((z * y) * 0.16666666666666666) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.62) || !(y <= 0.0072))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(Float64(z * y) * 0.16666666666666666) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.62) || ~((y <= 0.0072)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x + (y * ((y * (((z * y) * 0.16666666666666666) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.62], N[Not[LessEqual[y, 0.0072]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(N[(z * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.619999999999999996 or 0.0071999999999999998 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 58.2%

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

      1. +-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -0.619999999999999996 < y < 0.0071999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.9%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.62 \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(z \cdot y\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-12} \lor \neg \left(x \leq 1.6 \cdot 10^{-42}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e-12) (not (<= x 1.6e-42))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-12) || !(x <= 1.6e-42)) {
		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 <= (-3.8d-12)) .or. (.not. (x <= 1.6d-42))) 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 <= -3.8e-12) || !(x <= 1.6e-42)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e-12) or not (x <= 1.6e-42):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e-12) || !(x <= 1.6e-42))
		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 <= -3.8e-12) || ~((x <= 1.6e-42)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e-12], N[Not[LessEqual[x, 1.6e-42]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.79999999999999996e-12 or 1.60000000000000012e-42 < 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 75.8%

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

      1. +-commutative 75.8%

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

   5. Simplified 75.8%

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

   if -3.79999999999999996e-12 < x < 1.60000000000000012e-42

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 62.1%

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

      1. +-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in x around 0 62.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-12} \lor \neg \left(x \leq 1.6 \cdot 10^{-42}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.8% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+22} \lor \neg \left(y \leq 1.3 \cdot 10^{+68}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(z \cdot y\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e+22) (not (<= y 1.3e+68)))
   (+ x 1.0)
   (+ 1.0 (+ x (* y (- (* y (- (* (* z y) 0.16666666666666666) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+22) || !(y <= 1.3e+68)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * (((z * y) * 0.16666666666666666) - 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 <= (-2.7d+22)) .or. (.not. (y <= 1.3d+68))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x + (y * ((y * (((z * y) * 0.16666666666666666d0) - 0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+22) || !(y <= 1.3e+68)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * (((z * y) * 0.16666666666666666) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e+22) or not (y <= 1.3e+68):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x + (y * ((y * (((z * y) * 0.16666666666666666) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e+22) || !(y <= 1.3e+68))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(Float64(z * y) * 0.16666666666666666) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.7e+22) || ~((y <= 1.3e+68)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x + (y * ((y * (((z * y) * 0.16666666666666666) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e+22], N[Not[LessEqual[y, 1.3e+68]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(N[(z * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000002e22 or 1.2999999999999999e68 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 39.3%

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

      1. +-commutative 39.3%

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

   5. Simplified 39.3%

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

   if -2.7000000000000002e22 < y < 1.2999999999999999e68

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.3%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+22} \lor \neg \left(y \leq 1.3 \cdot 10^{+68}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(z \cdot y\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.9% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+24} \lor \neg \left(y \leq 1.8 \cdot 10^{+68}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.1e+24) (not (<= y 1.8e+68)))
   (+ x 1.0)
   (+ 1.0 (+ x (* y (- (* y -0.5) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.1e+24) || !(y <= 1.8e+68)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.1d+24)) .or. (.not. (y <= 1.8d+68))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x + (y * ((y * (-0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.1e+24) || !(y <= 1.8e+68)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.1e+24) or not (y <= 1.8e+68):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.1e+24) || !(y <= 1.8e+68))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * -0.5) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.1e+24) || ~((y <= 1.8e+68)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.1e+24], N[Not[LessEqual[y, 1.8e+68]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1000000000000001e24 or 1.7999999999999999e68 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 39.0%

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

      1. +-commutative 39.0%

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

   5. Simplified 39.0%

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

   if -4.1000000000000001e24 < y < 1.7999999999999999e68

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+24} \lor \neg \left(y \leq 1.8 \cdot 10^{+68}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.3% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+25} \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e+25) (not (<= y 0.0072))) (+ x 1.0) (- (+ x 1.0) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+25) || !(y <= 0.0072)) {
		tmp = x + 1.0;
	} else {
		tmp = (x + 1.0) - (z * 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 ((y <= (-6.5d+25)) .or. (.not. (y <= 0.0072d0))) then
        tmp = x + 1.0d0
    else
        tmp = (x + 1.0d0) - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+25) || !(y <= 0.0072)) {
		tmp = x + 1.0;
	} else {
		tmp = (x + 1.0) - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e+25) or not (y <= 0.0072):
		tmp = x + 1.0
	else:
		tmp = (x + 1.0) - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e+25) || !(y <= 0.0072))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(Float64(x + 1.0) - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e+25) || ~((y <= 0.0072)))
		tmp = x + 1.0;
	else
		tmp = (x + 1.0) - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e+25], N[Not[LessEqual[y, 0.0072]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000005e25 or 0.0071999999999999998 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 37.9%

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

      1. +-commutative 37.9%

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

   5. Simplified 37.9%

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

   if -6.50000000000000005e25 < y < 0.0071999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

      1. associate-+r+ 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

      4. +-commutative 97.3%

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

   5. Simplified 97.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+25} \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.9% 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 59.5%

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

   1. +-commutative 59.5%

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

5. Simplified 59.5%

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

Alternative 15: 42.2% 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. Add Preprocessing

3. Taylor expanded in x around inf 40.5%

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

Reproduce

herbie shell --seed 2024096 
(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))))