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

Percentage Accurate: 99.9% → 99.9%

Time: 13.1s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\cos y, \color{blue}{z}, \left(x + \sin y\right)\right) \]

   4. cos-lowering-cos.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(y\right), z, \left(x + \sin y\right)\right) \]

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(y\right), z, \mathsf{+.f64}\left(x, \sin y\right)\right) \]

   6. sin-lowering-sin.f64 99.9%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(y\right), z, \mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right)\right) \]

4. Applied egg-rr 99.9%

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

Alternative 2: 94.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{-35}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-53}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\cos y + \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.05e-35)
   (fma (cos y) z x)
   (if (<= z 2.1e-53) (+ x (sin y)) (* z (+ (cos y) (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.05e-35) {
		tmp = fma(cos(y), z, x);
	} else if (z <= 2.1e-53) {
		tmp = x + sin(y);
	} else {
		tmp = z * (cos(y) + (x / z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.05e-35)
		tmp = fma(cos(y), z, x);
	elseif (z <= 2.1e-53)
		tmp = Float64(x + sin(y));
	else
		tmp = Float64(z * Float64(cos(y) + Float64(x / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.05e-35], N[(N[Cos[y], $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[z, 2.1e-53], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z * N[(N[Cos[y], $MachinePrecision] + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.05e-35

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\cos y, \color{blue}{z}, \left(x + \sin y\right)\right) \]

      4. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(y\right), z, \left(x + \sin y\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(y\right), z, \mathsf{+.f64}\left(x, \sin y\right)\right) \]

      6. sin-lowering-sin.f64 99.9%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(y\right), z, \mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(y\right), z, \color{blue}{x}\right) \]
   6. Step-by-step derivation

   7. Simplified 97.4%

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

   if -3.05e-35 < z < 2.09999999999999977e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 97.9%

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

   if 2.09999999999999977e-53 < z

   1. Initial program 99.9%

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

      1. flip-+ N/A

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

      2. div-inv N/A

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

      3. difference-of-squares N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x + \sin y\right) + z \cdot \cos y\right), \color{blue}{\left(\left(\left(x + \sin y\right) - z \cdot \cos y\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)}\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(x + \sin y\right), \left(z \cdot \cos y\right)\right), \left(\color{blue}{\left(\left(x + \sin y\right) - z \cdot \cos y\right)} \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \sin y\right), \left(z \cdot \cos y\right)\right), \left(\left(\color{blue}{\left(x + \sin y\right)} - z \cdot \cos y\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      8. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \left(z \cdot \cos y\right)\right), \left(\left(\left(x + \color{blue}{\sin y}\right) - z \cdot \cos y\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \mathsf{*.f64}\left(z, \cos y\right)\right), \left(\left(\left(x + \sin y\right) - \color{blue}{z \cdot \cos y}\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      10. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right), \left(\left(\left(x + \sin y\right) - z \cdot \color{blue}{\cos y}\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right), \mathsf{*.f64}\left(\left(\left(x + \sin y\right) - z \cdot \cos y\right), \color{blue}{\left(\frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)}\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. distribute-lft-out N/A

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

      4. mul-1-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\cos y + \frac{x + \sin y}{z}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\cos y + \frac{x + \sin y}{z}\right)}\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\cos y, \color{blue}{\left(\frac{x + \sin y}{z}\right)}\right)\right) \]

      8. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \left(\frac{\color{blue}{x + \sin y}}{z}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\left(x + \sin y\right), \color{blue}{z}\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\left(\sin y + x\right), z\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\sin y, x\right), z\right)\right)\right) \]

      12. sin-lowering-sin.f64 99.9%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right), z\right)\right)\right) \]

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \color{blue}{\left(\frac{x}{z}\right)}\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 99.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{-35}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-53}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\cos y + \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 4: 84.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+200}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-35}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-73}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+125}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -9.2e+200)
     t_0
     (if (<= z -5e-35)
       (+ z x)
       (if (<= z 1.7e-73) (+ x (sin y)) (if (<= z 2e+125) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -9.2e+200) {
		tmp = t_0;
	} else if (z <= -5e-35) {
		tmp = z + x;
	} else if (z <= 1.7e-73) {
		tmp = x + sin(y);
	} else if (z <= 2e+125) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(y) * z
    if (z <= (-9.2d+200)) then
        tmp = t_0
    else if (z <= (-5d-35)) then
        tmp = z + x
    else if (z <= 1.7d-73) then
        tmp = x + sin(y)
    else if (z <= 2d+125) then
        tmp = z + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * z;
	double tmp;
	if (z <= -9.2e+200) {
		tmp = t_0;
	} else if (z <= -5e-35) {
		tmp = z + x;
	} else if (z <= 1.7e-73) {
		tmp = x + Math.sin(y);
	} else if (z <= 2e+125) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	tmp = 0
	if z <= -9.2e+200:
		tmp = t_0
	elif z <= -5e-35:
		tmp = z + x
	elif z <= 1.7e-73:
		tmp = x + math.sin(y)
	elif z <= 2e+125:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -9.2e+200)
		tmp = t_0;
	elseif (z <= -5e-35)
		tmp = Float64(z + x);
	elseif (z <= 1.7e-73)
		tmp = Float64(x + sin(y));
	elseif (z <= 2e+125)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	tmp = 0.0;
	if (z <= -9.2e+200)
		tmp = t_0;
	elseif (z <= -5e-35)
		tmp = z + x;
	elseif (z <= 1.7e-73)
		tmp = x + sin(y);
	elseif (z <= 2e+125)
		tmp = z + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -9.2e+200], t$95$0, If[LessEqual[z, -5e-35], N[(z + x), $MachinePrecision], If[LessEqual[z, 1.7e-73], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+125], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.20000000000000013e200 or 1.9999999999999998e125 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right) \]

      2. cos-lowering-cos.f64 96.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right) \]

   5. Simplified 96.2%

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

   if -9.20000000000000013e200 < z < -4.99999999999999964e-35 or 1.7000000000000001e-73 < z < 1.9999999999999998e125

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 83.7%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 83.7%

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

   if -4.99999999999999964e-35 < z < 1.7000000000000001e-73

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 97.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 97.8%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+200}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-35}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-73}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+125}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+197}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-98}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-169}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+125}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -1.9e+197)
     t_0
     (if (<= z -2.55e-98)
       (+ z x)
       (if (<= z -5e-169) (sin y) (if (<= z 1.26e+125) (+ y (+ z x)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -1.9e+197) {
		tmp = t_0;
	} else if (z <= -2.55e-98) {
		tmp = z + x;
	} else if (z <= -5e-169) {
		tmp = sin(y);
	} else if (z <= 1.26e+125) {
		tmp = y + (z + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(y) * z
    if (z <= (-1.9d+197)) then
        tmp = t_0
    else if (z <= (-2.55d-98)) then
        tmp = z + x
    else if (z <= (-5d-169)) then
        tmp = sin(y)
    else if (z <= 1.26d+125) then
        tmp = y + (z + x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * z;
	double tmp;
	if (z <= -1.9e+197) {
		tmp = t_0;
	} else if (z <= -2.55e-98) {
		tmp = z + x;
	} else if (z <= -5e-169) {
		tmp = Math.sin(y);
	} else if (z <= 1.26e+125) {
		tmp = y + (z + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	tmp = 0
	if z <= -1.9e+197:
		tmp = t_0
	elif z <= -2.55e-98:
		tmp = z + x
	elif z <= -5e-169:
		tmp = math.sin(y)
	elif z <= 1.26e+125:
		tmp = y + (z + x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -1.9e+197)
		tmp = t_0;
	elseif (z <= -2.55e-98)
		tmp = Float64(z + x);
	elseif (z <= -5e-169)
		tmp = sin(y);
	elseif (z <= 1.26e+125)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	tmp = 0.0;
	if (z <= -1.9e+197)
		tmp = t_0;
	elseif (z <= -2.55e-98)
		tmp = z + x;
	elseif (z <= -5e-169)
		tmp = sin(y);
	elseif (z <= 1.26e+125)
		tmp = y + (z + x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.9e+197], t$95$0, If[LessEqual[z, -2.55e-98], N[(z + x), $MachinePrecision], If[LessEqual[z, -5e-169], N[Sin[y], $MachinePrecision], If[LessEqual[z, 1.26e+125], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9000000000000001e197 or 1.25999999999999993e125 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right) \]

      2. cos-lowering-cos.f64 96.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right) \]

   5. Simplified 96.2%

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

   if -1.9000000000000001e197 < z < -2.55000000000000011e-98

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 80.1%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 80.1%

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

   if -2.55000000000000011e-98 < z < -5.0000000000000002e-169

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{\left(z \cdot \cos y\right)}\right) \]

      2. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \left(\color{blue}{z} \cdot \cos y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right)\right) \]

      4. cos-lowering-cos.f64 84.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 84.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\sin y} \]
   7. Step-by-step derivation

      1. sin-lowering-sin.f64 84.0%

         \[\leadsto \mathsf{sin.f64}\left(y\right) \]

   8. Simplified 84.0%

      \[\leadsto \color{blue}{\sin y} \]

   if -5.0000000000000002e-169 < z < 1.25999999999999993e125

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(x + z\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(z + \color{blue}{x}\right)\right) \]

      6. +-lowering-+.f64 69.9%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{+.f64}\left(z, \color{blue}{x}\right)\right) \]

   5. Simplified 69.9%

      \[\leadsto \color{blue}{y + \left(z + x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+197}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-98}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-169}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+125}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-37}:\\ \;\;\;\;x + \cos y \cdot z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-48}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\cos y + \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.9e-37)
   (+ x (* (cos y) z))
   (if (<= z 5.8e-48) (+ x (sin y)) (* z (+ (cos y) (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.9e-37) {
		tmp = x + (cos(y) * z);
	} else if (z <= 5.8e-48) {
		tmp = x + sin(y);
	} else {
		tmp = z * (cos(y) + (x / 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 <= (-2.9d-37)) then
        tmp = x + (cos(y) * z)
    else if (z <= 5.8d-48) then
        tmp = x + sin(y)
    else
        tmp = z * (cos(y) + (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.9e-37) {
		tmp = x + (Math.cos(y) * z);
	} else if (z <= 5.8e-48) {
		tmp = x + Math.sin(y);
	} else {
		tmp = z * (Math.cos(y) + (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.9e-37:
		tmp = x + (math.cos(y) * z)
	elif z <= 5.8e-48:
		tmp = x + math.sin(y)
	else:
		tmp = z * (math.cos(y) + (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.9e-37)
		tmp = Float64(x + Float64(cos(y) * z));
	elseif (z <= 5.8e-48)
		tmp = Float64(x + sin(y));
	else
		tmp = Float64(z * Float64(cos(y) + Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.9e-37)
		tmp = x + (cos(y) * z);
	elseif (z <= 5.8e-48)
		tmp = x + sin(y);
	else
		tmp = z * (cos(y) + (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.9e-37], N[(x + N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-48], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z * N[(N[Cos[y], $MachinePrecision] + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.90000000000000005e-37

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 97.4%

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

   if -2.90000000000000005e-37 < z < 5.8000000000000006e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 97.9%

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

   if 5.8000000000000006e-48 < z

   1. Initial program 99.9%

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

      1. flip-+ N/A

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

      2. div-inv N/A

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

      3. difference-of-squares N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x + \sin y\right) + z \cdot \cos y\right), \color{blue}{\left(\left(\left(x + \sin y\right) - z \cdot \cos y\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)}\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(x + \sin y\right), \left(z \cdot \cos y\right)\right), \left(\color{blue}{\left(\left(x + \sin y\right) - z \cdot \cos y\right)} \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \sin y\right), \left(z \cdot \cos y\right)\right), \left(\left(\color{blue}{\left(x + \sin y\right)} - z \cdot \cos y\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      8. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \left(z \cdot \cos y\right)\right), \left(\left(\left(x + \color{blue}{\sin y}\right) - z \cdot \cos y\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \mathsf{*.f64}\left(z, \cos y\right)\right), \left(\left(\left(x + \sin y\right) - \color{blue}{z \cdot \cos y}\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      10. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right), \left(\left(\left(x + \sin y\right) - z \cdot \color{blue}{\cos y}\right) \cdot \frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{sin.f64}\left(y\right)\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right), \mathsf{*.f64}\left(\left(\left(x + \sin y\right) - z \cdot \cos y\right), \color{blue}{\left(\frac{1}{\left(x + \sin y\right) - z \cdot \cos y}\right)}\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. distribute-lft-out N/A

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

      4. mul-1-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\cos y + \frac{x + \sin y}{z}\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\cos y + \frac{x + \sin y}{z}\right)}\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\cos y, \color{blue}{\left(\frac{x + \sin y}{z}\right)}\right)\right) \]

      8. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \left(\frac{\color{blue}{x + \sin y}}{z}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\left(x + \sin y\right), \color{blue}{z}\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\left(\sin y + x\right), z\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\sin y, x\right), z\right)\right)\right) \]

      12. sin-lowering-sin.f64 99.9%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right), z\right)\right)\right) \]

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \color{blue}{\left(\frac{x}{z}\right)}\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 99.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-37}:\\ \;\;\;\;x + \cos y \cdot z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-48}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\cos y + \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y \cdot z\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-34}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-71}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* (cos y) z))))
   (if (<= z -4.1e-34) t_0 (if (<= z 3.2e-71) (+ x (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (cos(y) * z);
	double tmp;
	if (z <= -4.1e-34) {
		tmp = t_0;
	} else if (z <= 3.2e-71) {
		tmp = x + sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (cos(y) * z)
    if (z <= (-4.1d-34)) then
        tmp = t_0
    else if (z <= 3.2d-71) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (Math.cos(y) * z);
	double tmp;
	if (z <= -4.1e-34) {
		tmp = t_0;
	} else if (z <= 3.2e-71) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (math.cos(y) * z)
	tmp = 0
	if z <= -4.1e-34:
		tmp = t_0
	elif z <= 3.2e-71:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(cos(y) * z))
	tmp = 0.0
	if (z <= -4.1e-34)
		tmp = t_0;
	elseif (z <= 3.2e-71)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (cos(y) * z);
	tmp = 0.0;
	if (z <= -4.1e-34)
		tmp = t_0;
	elseif (z <= 3.2e-71)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e-34], t$95$0, If[LessEqual[z, 3.2e-71], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1000000000000004e-34 or 3.1999999999999999e-71 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 98.7%

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

   if -4.1000000000000004e-34 < z < 3.1999999999999999e-71

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 97.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 97.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-34}:\\ \;\;\;\;x + \cos y \cdot z\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-71}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+252}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+42}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+29}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(1 + y \cdot \left(z \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+252)
   (sin y)
   (if (<= y -1.2e+42)
     (+ z x)
     (if (<= y 2.15e+29) (+ (+ z x) (* y (+ 1.0 (* y (* z -0.5))))) (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+252) {
		tmp = sin(y);
	} else if (y <= -1.2e+42) {
		tmp = z + x;
	} else if (y <= 2.15e+29) {
		tmp = (z + x) + (y * (1.0 + (y * (z * -0.5))));
	} else {
		tmp = z + 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 (y <= (-3.4d+252)) then
        tmp = sin(y)
    else if (y <= (-1.2d+42)) then
        tmp = z + x
    else if (y <= 2.15d+29) then
        tmp = (z + x) + (y * (1.0d0 + (y * (z * (-0.5d0)))))
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+252) {
		tmp = Math.sin(y);
	} else if (y <= -1.2e+42) {
		tmp = z + x;
	} else if (y <= 2.15e+29) {
		tmp = (z + x) + (y * (1.0 + (y * (z * -0.5))));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e+252:
		tmp = math.sin(y)
	elif y <= -1.2e+42:
		tmp = z + x
	elif y <= 2.15e+29:
		tmp = (z + x) + (y * (1.0 + (y * (z * -0.5))))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+252)
		tmp = sin(y);
	elseif (y <= -1.2e+42)
		tmp = Float64(z + x);
	elseif (y <= 2.15e+29)
		tmp = Float64(Float64(z + x) + Float64(y * Float64(1.0 + Float64(y * Float64(z * -0.5)))));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+252)
		tmp = sin(y);
	elseif (y <= -1.2e+42)
		tmp = z + x;
	elseif (y <= 2.15e+29)
		tmp = (z + x) + (y * (1.0 + (y * (z * -0.5))));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e+252], N[Sin[y], $MachinePrecision], If[LessEqual[y, -1.2e+42], N[(z + x), $MachinePrecision], If[LessEqual[y, 2.15e+29], N[(N[(z + x), $MachinePrecision] + N[(y * N[(1.0 + N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e252

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{\left(z \cdot \cos y\right)}\right) \]

      2. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \left(\color{blue}{z} \cdot \cos y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right)\right) \]

      4. cos-lowering-cos.f64 89.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 89.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\sin y} \]
   7. Step-by-step derivation

      1. sin-lowering-sin.f64 54.5%

         \[\leadsto \mathsf{sin.f64}\left(y\right) \]

   8. Simplified 54.5%

      \[\leadsto \color{blue}{\sin y} \]

   if -3.4e252 < y < -1.1999999999999999e42 or 2.1500000000000001e29 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 39.6%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 39.6%

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

   if -1.1999999999999999e42 < y < 2.1500000000000001e29

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + z\right), \color{blue}{\left(y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z + x\right), \left(\color{blue}{y} \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\color{blue}{y} \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(y \cdot \left(1 + \left(y \cdot z\right) \cdot \color{blue}{\frac{-1}{2}}\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(y \cdot \left(1 + y \cdot \color{blue}{\left(z \cdot \frac{-1}{2}\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot \color{blue}{z}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \color{blue}{\left(1 + y \cdot \left(\frac{-1}{2} \cdot z\right)\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot z\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-1}{2} \cdot z\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(z \cdot \color{blue}{\frac{-1}{2}}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 95.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{2}}\right)\right)\right)\right)\right) \]

   5. Simplified 95.7%

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

Alternative 9: 69.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+42}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+27}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(1 + y \cdot \left(z \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e+42)
   (+ z x)
   (if (<= y 2.1e+27) (+ (+ z x) (* y (+ 1.0 (* y (* z -0.5))))) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+42) {
		tmp = z + x;
	} else if (y <= 2.1e+27) {
		tmp = (z + x) + (y * (1.0 + (y * (z * -0.5))));
	} else {
		tmp = z + 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 (y <= (-1.3d+42)) then
        tmp = z + x
    else if (y <= 2.1d+27) then
        tmp = (z + x) + (y * (1.0d0 + (y * (z * (-0.5d0)))))
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+42) {
		tmp = z + x;
	} else if (y <= 2.1e+27) {
		tmp = (z + x) + (y * (1.0 + (y * (z * -0.5))));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e+42:
		tmp = z + x
	elif y <= 2.1e+27:
		tmp = (z + x) + (y * (1.0 + (y * (z * -0.5))))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e+42)
		tmp = Float64(z + x);
	elseif (y <= 2.1e+27)
		tmp = Float64(Float64(z + x) + Float64(y * Float64(1.0 + Float64(y * Float64(z * -0.5)))));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3e+42)
		tmp = z + x;
	elseif (y <= 2.1e+27)
		tmp = (z + x) + (y * (1.0 + (y * (z * -0.5))));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e+42], N[(z + x), $MachinePrecision], If[LessEqual[y, 2.1e+27], N[(N[(z + x), $MachinePrecision] + N[(y * N[(1.0 + N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999995e42 or 2.09999999999999995e27 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 36.0%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 36.0%

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

   if -1.29999999999999995e42 < y < 2.09999999999999995e27

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + z\right), \color{blue}{\left(y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z + x\right), \left(\color{blue}{y} \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(\color{blue}{y} \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(y \cdot \left(1 + \left(y \cdot z\right) \cdot \color{blue}{\frac{-1}{2}}\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(y \cdot \left(1 + y \cdot \color{blue}{\left(z \cdot \frac{-1}{2}\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \left(y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot \color{blue}{z}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \color{blue}{\left(1 + y \cdot \left(\frac{-1}{2} \cdot z\right)\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(\frac{-1}{2} \cdot z\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-1}{2} \cdot z\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(z \cdot \color{blue}{\frac{-1}{2}}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 95.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{2}}\right)\right)\right)\right)\right) \]

   5. Simplified 95.7%

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

Alternative 10: 69.2% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+27}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+49) x (if (<= y 2e+27) (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+49) {
		tmp = x;
	} else if (y <= 2e+27) {
		tmp = y + (z + x);
	} else {
		tmp = z + 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 (y <= (-3.8d+49)) then
        tmp = x
    else if (y <= 2d+27) then
        tmp = y + (z + x)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+49) {
		tmp = x;
	} else if (y <= 2e+27) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+49:
		tmp = x
	elif y <= 2e+27:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+49)
		tmp = x;
	elseif (y <= 2e+27)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+49)
		tmp = x;
	elseif (y <= 2e+27)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+49], x, If[LessEqual[y, 2e+27], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999999e49

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 39.6%

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

   if -3.7999999999999999e49 < y < 2e27

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(x + z\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(z + \color{blue}{x}\right)\right) \]

      6. +-lowering-+.f64 95.1%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{+.f64}\left(z, \color{blue}{x}\right)\right) \]

   5. Simplified 95.1%

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

   if 2e27 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 31.8%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 31.8%

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

Alternative 11: 68.0% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-123}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-157}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e-123) (+ z x) (if (<= x 1.32e-157) (+ y z) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-123) {
		tmp = z + x;
	} else if (x <= 1.32e-157) {
		tmp = y + z;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.05d-123)) then
        tmp = z + x
    else if (x <= 1.32d-157) then
        tmp = y + z
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-123) {
		tmp = z + x;
	} else if (x <= 1.32e-157) {
		tmp = y + z;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e-123:
		tmp = z + x
	elif x <= 1.32e-157:
		tmp = y + z
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e-123)
		tmp = Float64(z + x);
	elseif (x <= 1.32e-157)
		tmp = Float64(y + z);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.05e-123)
		tmp = z + x;
	elseif (x <= 1.32e-157)
		tmp = y + z;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e-123], N[(z + x), $MachinePrecision], If[LessEqual[x, 1.32e-157], N[(y + z), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e-123 or 1.3200000000000001e-157 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 75.2%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 75.2%

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

   if -1.05e-123 < x < 1.3200000000000001e-157

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{\left(z \cdot \cos y\right)}\right) \]

      2. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \left(\color{blue}{z} \cdot \cos y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right)\right) \]

      4. cos-lowering-cos.f64 99.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 99.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y + z} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto z + \color{blue}{y} \]

      2. +-lowering-+.f64 58.1%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{y}\right) \]

   8. Simplified 58.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-123}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-157}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.5% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-132}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-224}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e-132) (+ z x) (if (<= z 3.4e-224) (+ y x) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e-132) {
		tmp = z + x;
	} else if (z <= 3.4e-224) {
		tmp = y + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-9d-132)) then
        tmp = z + x
    else if (z <= 3.4d-224) then
        tmp = y + x
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e-132) {
		tmp = z + x;
	} else if (z <= 3.4e-224) {
		tmp = y + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e-132:
		tmp = z + x
	elif z <= 3.4e-224:
		tmp = y + x
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e-132)
		tmp = Float64(z + x);
	elseif (z <= 3.4e-224)
		tmp = Float64(y + x);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e-132)
		tmp = z + x;
	elseif (z <= 3.4e-224)
		tmp = y + x;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e-132], N[(z + x), $MachinePrecision], If[LessEqual[z, 3.4e-224], N[(y + x), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.9999999999999999e-132 or 3.39999999999999992e-224 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 69.5%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   5. Simplified 69.5%

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

   if -8.9999999999999999e-132 < z < 3.39999999999999992e-224

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{x}\right) \]

      3. sin-lowering-sin.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), x\right) \]

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{y}, x\right) \]
   7. Step-by-step derivation

   8. Simplified 64.2%

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

Alternative 13: 54.5% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e-25) x (if (<= x 6.4e-19) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-25) {
		tmp = x;
	} else if (x <= 6.4e-19) {
		tmp = 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 <= (-1.4d-25)) then
        tmp = x
    else if (x <= 6.4d-19) then
        tmp = 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 <= -1.4e-25) {
		tmp = x;
	} else if (x <= 6.4e-19) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e-25:
		tmp = x
	elif x <= 6.4e-19:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e-25)
		tmp = x;
	elseif (x <= 6.4e-19)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4e-25)
		tmp = x;
	elseif (x <= 6.4e-19)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e-25], x, If[LessEqual[x, 6.4e-19], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999994e-25 or 6.39999999999999965e-19 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 69.1%

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

   if -1.39999999999999994e-25 < x < 6.39999999999999965e-19

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{\left(z \cdot \cos y\right)}\right) \]

      2. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \left(\color{blue}{z} \cdot \cos y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right)\right) \]

      4. cos-lowering-cos.f64 92.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 92.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 39.5%

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

Alternative 14: 44.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-158}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.16e-122) x (if (<= x 5.1e-158) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.16e-122) {
		tmp = x;
	} else if (x <= 5.1e-158) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.16d-122)) then
        tmp = x
    else if (x <= 5.1d-158) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.16e-122) {
		tmp = x;
	} else if (x <= 5.1e-158) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.16e-122:
		tmp = x
	elif x <= 5.1e-158:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.16e-122)
		tmp = x;
	elseif (x <= 5.1e-158)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.16e-122)
		tmp = x;
	elseif (x <= 5.1e-158)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.16e-122], x, If[LessEqual[x, 5.1e-158], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.16000000000000001e-122 or 5.1000000000000003e-158 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 54.5%

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

   if -1.16000000000000001e-122 < x < 5.1000000000000003e-158

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\sin y, \color{blue}{\left(z \cdot \cos y\right)}\right) \]

      2. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \left(\color{blue}{z} \cdot \cos y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \color{blue}{\cos y}\right)\right) \]

      4. cos-lowering-cos.f64 99.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(z, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   5. Simplified 99.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\sin y} \]
   7. Step-by-step derivation

      1. sin-lowering-sin.f64 43.4%

         \[\leadsto \mathsf{sin.f64}\left(y\right) \]

   8. Simplified 43.4%

      \[\leadsto \color{blue}{\sin y} \]

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y} \]
   10. Step-by-step derivation

   11. Simplified 21.4%

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

Alternative 15: 41.9% 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%

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

3. Taylor expanded in x around inf

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

5. Simplified 39.8%

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

Reproduce

herbie shell --seed 2024192 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))