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

Percentage Accurate: 99.9% → 99.9%

Time: 9.2s

Alternatives: 14

Speedup: 1.0×

• could not determine a ground truth

  1. x = -0.24720922009284302
  2. y = -7.156955405889217e-295
  3. z = 9.349012676000357e+238

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+24} \lor \neg \left(x \leq 0.88\right):\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e+24) (not (<= x 0.88)))
   (* x (- 1.0 (* z (/ (sin y) x))))
   (- (cos y) (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e+24) || !(x <= 0.88)) {
		tmp = x * (1.0 - (z * (sin(y) / x)));
	} 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 <= (-6d+24)) .or. (.not. (x <= 0.88d0))) then
        tmp = x * (1.0d0 - (z * (sin(y) / x)))
    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 <= -6e+24) || !(x <= 0.88)) {
		tmp = x * (1.0 - (z * (Math.sin(y) / x)));
	} else {
		tmp = Math.cos(y) - (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e+24) or not (x <= 0.88):
		tmp = x * (1.0 - (z * (math.sin(y) / x)))
	else:
		tmp = math.cos(y) - (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e+24) || !(x <= 0.88))
		tmp = Float64(x * Float64(1.0 - Float64(z * Float64(sin(y) / x))));
	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 <= -6e+24) || ~((x <= 0.88)))
		tmp = x * (1.0 - (z * (sin(y) / x)));
	else
		tmp = cos(y) - (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e+24], N[Not[LessEqual[x, 0.88]], $MachinePrecision]], N[(x * N[(1.0 - N[(z * N[(N[Sin[y], $MachinePrecision] / x), $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 < -5.9999999999999999e24 or 0.880000000000000004 < x

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

      4. add-cube-cbrt 99.5%

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

      5. associate-*r* 99.6%

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

      6. fma-define 99.6%

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

      7. pow2 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. associate-/l* 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

      4. distribute-neg-frac2 99.5%

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

   10. Simplified 99.5%

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

   if -5.9999999999999999e24 < x < 0.880000000000000004

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+24} \lor \neg \left(x \leq 0.88\right):\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+202}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+54} \lor \neg \left(z \leq 4.6 \cdot 10^{+70}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (sin y)))))
   (if (<= z -7e+202)
     t_0
     (if (<= z -7.8e+64)
       (+ x (- 1.0 (* y z)))
       (if (or (<= z -1.6e+54) (not (<= z 4.6e+70))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -sin(y);
	double tmp;
	if (z <= -7e+202) {
		tmp = t_0;
	} else if (z <= -7.8e+64) {
		tmp = x + (1.0 - (y * z));
	} else if ((z <= -1.6e+54) || !(z <= 4.6e+70)) {
		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 <= (-7d+202)) then
        tmp = t_0
    else if (z <= (-7.8d+64)) then
        tmp = x + (1.0d0 - (y * z))
    else if ((z <= (-1.6d+54)) .or. (.not. (z <= 4.6d+70))) 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 <= -7e+202) {
		tmp = t_0;
	} else if (z <= -7.8e+64) {
		tmp = x + (1.0 - (y * z));
	} else if ((z <= -1.6e+54) || !(z <= 4.6e+70)) {
		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 <= -7e+202:
		tmp = t_0
	elif z <= -7.8e+64:
		tmp = x + (1.0 - (y * z))
	elif (z <= -1.6e+54) or not (z <= 4.6e+70):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (z <= -7e+202)
		tmp = t_0;
	elseif (z <= -7.8e+64)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	elseif ((z <= -1.6e+54) || !(z <= 4.6e+70))
		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 <= -7e+202)
		tmp = t_0;
	elseif (z <= -7.8e+64)
		tmp = x + (1.0 - (y * z));
	elseif ((z <= -1.6e+54) || ~((z <= 4.6e+70)))
		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, -7e+202], t$95$0, If[LessEqual[z, -7.8e+64], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.6e+54], N[Not[LessEqual[z, 4.6e+70]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999975e202 or -7.7999999999999996e64 < z < -1.6e54 or 4.59999999999999987e70 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 81.2%

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

      1. associate-*r* 81.2%

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

      2. neg-mul-1 81.2%

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

      3. *-commutative 81.2%

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

   5. Simplified 81.2%

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

   if -6.99999999999999975e202 < z < -7.7999999999999996e64

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 65.2%

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

      1. associate-+r+ 65.2%

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

      2. +-commutative 65.2%

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

      3. associate-+l+ 65.2%

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

      4. mul-1-neg 65.2%

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

      5. unsub-neg 65.2%

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

   5. Simplified 65.2%

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

   if -1.6e54 < z < 4.59999999999999987e70

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.2%

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

      1. +-commutative 95.2%

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

   5. Simplified 95.2%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+202}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+54} \lor \neg \left(z \leq 4.6 \cdot 10^{+70}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00325 \lor \neg \left(y \leq 4.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(y, y \cdot -0.5 - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00325) (not (<= y 4.1e-8)))
   (* x (- 1.0 (* z (/ (sin y) x))))
   (+ 1.0 (fma y (- (* y -0.5) z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00325) || !(y <= 4.1e-8)) {
		tmp = x * (1.0 - (z * (sin(y) / x)));
	} else {
		tmp = 1.0 + fma(y, ((y * -0.5) - z), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00325) || !(y <= 4.1e-8))
		tmp = Float64(x * Float64(1.0 - Float64(z * Float64(sin(y) / x))));
	else
		tmp = Float64(1.0 + fma(y, Float64(Float64(y * -0.5) - z), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00325], N[Not[LessEqual[y, 4.1e-8]], $MachinePrecision]], N[(x * N[(1.0 - N[(z * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00324999999999999985 or 4.10000000000000032e-8 < y

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

      4. add-cube-cbrt 99.0%

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

      5. associate-*r* 99.0%

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

      6. fma-define 99.0%

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

      7. pow2 99.0%

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

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in x around inf 88.1%

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

      1. +-commutative 88.1%

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

      2. mul-1-neg 88.1%

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

      3. sub-neg 88.1%

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

      4. *-commutative 88.1%

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

      5. div-sub 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in z around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. associate-/l* 69.6%

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

      3. distribute-rgt-neg-in 69.6%

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

      4. distribute-neg-frac2 69.6%

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

   10. Simplified 69.6%

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

   if -0.00324999999999999985 < y < 4.10000000000000032e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00325 \lor \neg \left(y \leq 4.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(y, y \cdot -0.5 - z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0035:\\ \;\;\;\;x \cdot \left(1 - \sin y \cdot \frac{z}{x}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-8}:\\ \;\;\;\;1 + \mathsf{fma}\left(y, y \cdot -0.5 - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.0035)
   (* x (- 1.0 (* (sin y) (/ z x))))
   (if (<= y 4.1e-8)
     (+ 1.0 (fma y (- (* y -0.5) z) x))
     (* x (- 1.0 (* z (/ (sin y) x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0035) {
		tmp = x * (1.0 - (sin(y) * (z / x)));
	} else if (y <= 4.1e-8) {
		tmp = 1.0 + fma(y, ((y * -0.5) - z), x);
	} else {
		tmp = x * (1.0 - (z * (sin(y) / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.0035)
		tmp = Float64(x * Float64(1.0 - Float64(sin(y) * Float64(z / x))));
	elseif (y <= 4.1e-8)
		tmp = Float64(1.0 + fma(y, Float64(Float64(y * -0.5) - z), x));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z * Float64(sin(y) / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.0035], N[(x * N[(1.0 - N[(N[Sin[y], $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-8], N[(1.0 + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00350000000000000007

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. distribute-lft-neg-in 99.7%

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

      4. add-cube-cbrt 98.8%

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

      5. associate-*r* 98.9%

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

      6. fma-define 98.9%

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

      7. pow2 98.9%

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

   4. Applied egg-rr 98.9%

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

   5. Taylor expanded in x around inf 88.3%

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

      1. +-commutative 88.3%

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

      2. mul-1-neg 88.3%

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

      3. sub-neg 88.3%

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

      4. *-commutative 88.3%

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

      5. div-sub 88.3%

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

   7. Simplified 88.3%

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

   8. Taylor expanded in z around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. associate-*r/ 76.7%

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

      3. neg-mul-1 76.7%

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

      4. distribute-rgt-neg-in 76.7%

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

      5. distribute-frac-neg 76.7%

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

   10. Simplified 76.7%

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

   if -0.00350000000000000007 < y < 4.10000000000000032e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 4.10000000000000032e-8 < y

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

      4. add-cube-cbrt 99.2%

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

      5. associate-*r* 99.2%

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

      6. fma-define 99.2%

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

      7. pow2 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in x around inf 87.9%

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

      1. +-commutative 87.9%

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

      2. mul-1-neg 87.9%

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

      3. sub-neg 87.9%

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

      4. *-commutative 87.9%

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

      5. div-sub 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in z around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. associate-/l* 61.0%

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

      3. distribute-rgt-neg-in 61.0%

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

      4. distribute-neg-frac2 61.0%

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

   10. Simplified 61.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0035:\\ \;\;\;\;x \cdot \left(1 - \sin y \cdot \frac{z}{x}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-8}:\\ \;\;\;\;1 + \mathsf{fma}\left(y, y \cdot -0.5 - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+19} \lor \neg \left(y \leq 11000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.15e+19) (not (<= y 11000000.0)))
   (+ x (cos y))
   (+ 1.0 (+ x (* y (- (* y (- (* (* y z) 0.16666666666666666) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.15e+19) || !(y <= 11000000.0)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 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 <= (-3.15d+19)) .or. (.not. (y <= 11000000.0d0))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x + (y * ((y * (((y * z) * 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 <= -3.15e+19) || !(y <= 11000000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.15e+19) or not (y <= 11000000.0):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.15e+19) || !(y <= 11000000.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(Float64(y * z) * 0.16666666666666666) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.15e+19) || ~((y <= 11000000.0)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.15e+19], N[Not[LessEqual[y, 11000000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.15e19 or 1.1e7 < 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 52.7%

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

      1. +-commutative 52.7%

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

   5. Simplified 52.7%

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

   if -3.15e19 < y < 1.1e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+19} \lor \neg \left(y \leq 11000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.7% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+112} \lor \neg \left(z \leq 1.05 \cdot 10^{+61}\right):\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e+112) (not (<= z 1.05e+61)))
   (+ 1.0 (+ x (* y (- (* y -0.5) z))))
   (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e+112) || !(z <= 1.05e+61)) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.3d+112)) .or. (.not. (z <= 1.05d+61))) then
        tmp = 1.0d0 + (x + (y * ((y * (-0.5d0)) - z)))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e+112) || !(z <= 1.05e+61)) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e+112) or not (z <= 1.05e+61):
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e+112) || !(z <= 1.05e+61))
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * -0.5) - z))));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.3e+112) || ~((z <= 1.05e+61)))
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e+112], N[Not[LessEqual[z, 1.05e+61]], $MachinePrecision]], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e112 or 1.0500000000000001e61 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.4%

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

   if -1.3e112 < z < 1.0500000000000001e61

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.1%

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

      1. +-commutative 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+112} \lor \neg \left(z \leq 1.05 \cdot 10^{+61}\right):\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.7% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+112}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+60}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x + 1}{z} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e+112)
   (+ x (- 1.0 (* y z)))
   (if (<= z 1.9e+60) (+ x 1.0) (* z (- (/ (+ x 1.0) z) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+112) {
		tmp = x + (1.0 - (y * z));
	} else if (z <= 1.9e+60) {
		tmp = x + 1.0;
	} else {
		tmp = z * (((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 (z <= (-1.8d+112)) then
        tmp = x + (1.0d0 - (y * z))
    else if (z <= 1.9d+60) then
        tmp = x + 1.0d0
    else
        tmp = z * (((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 (z <= -1.8e+112) {
		tmp = x + (1.0 - (y * z));
	} else if (z <= 1.9e+60) {
		tmp = x + 1.0;
	} else {
		tmp = z * (((x + 1.0) / z) - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e+112:
		tmp = x + (1.0 - (y * z))
	elif z <= 1.9e+60:
		tmp = x + 1.0
	else:
		tmp = z * (((x + 1.0) / z) - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e+112)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	elseif (z <= 1.9e+60)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(z * Float64(Float64(Float64(x + 1.0) / z) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.8e+112)
		tmp = x + (1.0 - (y * z));
	elseif (z <= 1.9e+60)
		tmp = x + 1.0;
	else
		tmp = z * (((x + 1.0) / z) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e+112], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+60], N[(x + 1.0), $MachinePrecision], N[(z * N[(N[(N[(x + 1.0), $MachinePrecision] / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e112

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.8%

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

      1. associate-+r+ 49.8%

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

      2. +-commutative 49.8%

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

      3. associate-+l+ 49.8%

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

      4. mul-1-neg 49.8%

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

      5. unsub-neg 49.8%

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

   5. Simplified 49.8%

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

   if -1.8e112 < z < 1.90000000000000005e60

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.1%

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

      1. +-commutative 80.1%

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

   5. Simplified 80.1%

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

   if 1.90000000000000005e60 < z

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

      4. add-cube-cbrt 98.2%

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

      5. associate-*r* 98.3%

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

      6. fma-define 98.3%

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

      7. pow2 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in x around inf 82.7%

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

      1. +-commutative 82.7%

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

      2. mul-1-neg 82.7%

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

      3. sub-neg 82.7%

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

      4. *-commutative 82.7%

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

      5. div-sub 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in y around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. unsub-neg 43.0%

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

   10. Simplified 43.0%

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

   11. Taylor expanded in z around inf 49.0%

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

       1. +-commutative 49.0%

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

       2. mul-1-neg 49.0%

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

       3. unsub-neg 49.0%

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

       4. +-commutative 49.0%

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

       5. distribute-lft-in 49.0%

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

       6. rgt-mult-inverse 49.0%

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

       7. *-rgt-identity 49.0%

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

   13. Simplified 49.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+112}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+60}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x + 1}{z} - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.8% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+113} \lor \neg \left(z \leq 9 \cdot 10^{+60}\right):\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e+113) (not (<= z 9e+60))) (+ x (- 1.0 (* y z))) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e+113) || !(z <= 9e+60)) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.8d+113)) .or. (.not. (z <= 9d+60))) then
        tmp = x + (1.0d0 - (y * z))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e+113) || !(z <= 9e+60)) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e+113) or not (z <= 9e+60):
		tmp = x + (1.0 - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e+113) || !(z <= 9e+60))
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e+113) || ~((z <= 9e+60)))
		tmp = x + (1.0 - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e+113], N[Not[LessEqual[z, 9e+60]], $MachinePrecision]], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999966e113 or 9.00000000000000026e60 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.3%

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

      1. associate-+r+ 49.3%

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

      2. +-commutative 49.3%

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

      3. associate-+l+ 49.3%

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

      4. mul-1-neg 49.3%

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

      5. unsub-neg 49.3%

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

   5. Simplified 49.3%

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

   if -4.79999999999999966e113 < z < 9.00000000000000026e60

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.1%

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

      1. +-commutative 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+113} \lor \neg \left(z \leq 9 \cdot 10^{+60}\right):\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.4% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.9e+23) x (if (<= x 2.55e+38) (- 1.0 (* y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.9e+23) {
		tmp = x;
	} else if (x <= 2.55e+38) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.9d+23)) then
        tmp = x
    else if (x <= 2.55d+38) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.9e+23) {
		tmp = x;
	} else if (x <= 2.55e+38) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.9e+23:
		tmp = x
	elif x <= 2.55e+38:
		tmp = 1.0 - (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.9e+23)
		tmp = x;
	elseif (x <= 2.55e+38)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.9e+23)
		tmp = x;
	elseif (x <= 2.55e+38)
		tmp = 1.0 - (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.9e+23], x, If[LessEqual[x, 2.55e+38], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.90000000000000013e23 or 2.5500000000000001e38 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.0%

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

   if -2.90000000000000013e23 < x < 2.5500000000000001e38

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.5%

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

   4. Taylor expanded in y around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

   6. Simplified 56.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.0% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00115:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.00115) x (if (<= x 4.6e-10) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.00115) {
		tmp = x;
	} else if (x <= 4.6e-10) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.00115d0)) then
        tmp = x
    else if (x <= 4.6d-10) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.00115) {
		tmp = x;
	} else if (x <= 4.6e-10) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.00115:
		tmp = x
	elif x <= 4.6e-10:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.00115)
		tmp = x;
	elseif (x <= 4.6e-10)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.00115)
		tmp = x;
	elseif (x <= 4.6e-10)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.00115], x, If[LessEqual[x, 4.6e-10], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00115 or 4.60000000000000014e-10 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 73.9%

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

   if -0.00115 < x < 4.60000000000000014e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.3%

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

   4. Taylor expanded in y around 0 44.9%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00115:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.2% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+204}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 5e+204) (+ x 1.0) (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e+204) {
		tmp = x + 1.0;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 5d+204) then
        tmp = x + 1.0d0
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e+204) {
		tmp = x + 1.0;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 5e+204:
		tmp = x + 1.0
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5e+204)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 5e+204)
		tmp = x + 1.0;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5e+204], N[(x + 1.0), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.00000000000000008e204

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 66.0%

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

      1. +-commutative 66.0%

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

   5. Simplified 66.0%

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

   if 5.00000000000000008e204 < 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 85.3%

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

      1. associate-*r* 85.3%

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

      2. neg-mul-1 85.3%

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

      3. *-commutative 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in y around 0 34.7%

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

      1. mul-1-neg 34.7%

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

      2. distribute-rgt-neg-in 34.7%

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

   8. Simplified 34.7%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+204}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.9% 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 60.6%

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

   1. +-commutative 60.6%

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

5. Simplified 60.6%

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

6. Final simplification 60.6%

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

Alternative 14: 21.8% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 60.8%

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

4. Taylor expanded in y around 0 22.4%

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

5. Final simplification 22.4%

   \[\leadsto 1 \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(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))))