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

Percentage Accurate: 99.9% → 99.9%

Time: 9.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := x - t\_0\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.9:\\ \;\;\;\;\cos y - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))) (t_1 (- x t_0)))
   (if (<= x -1.0) t_1 (if (<= x 0.9) (- (cos y) t_0) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double t_1 = x - t_0;
	double tmp;
	if (x <= -1.0) {
		tmp = t_1;
	} else if (x <= 0.9) {
		tmp = cos(y) - t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * sin(y)
    t_1 = x - t_0
    if (x <= (-1.0d0)) then
        tmp = t_1
    else if (x <= 0.9d0) then
        tmp = cos(y) - t_0
    else
        tmp = t_1
    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 t_1 = x - t_0;
	double tmp;
	if (x <= -1.0) {
		tmp = t_1;
	} else if (x <= 0.9) {
		tmp = Math.cos(y) - t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	t_1 = x - t_0
	tmp = 0
	if x <= -1.0:
		tmp = t_1
	elif x <= 0.9:
		tmp = math.cos(y) - t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	t_1 = Float64(x - t_0)
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_1;
	elseif (x <= 0.9)
		tmp = Float64(cos(y) - t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	t_1 = x - t_0;
	tmp = 0.0;
	if (x <= -1.0)
		tmp = t_1;
	elseif (x <= 0.9)
		tmp = cos(y) - t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x - t$95$0), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$1, If[LessEqual[x, 0.9], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.900000000000000022 < 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

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

   5. Simplified 97.9%

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

   if -1 < x < 0.900000000000000022

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. sin-lowering-sin.f64 99.2%

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

   5. Simplified 99.2%

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

Alternative 3: 93.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - z \cdot \sin y\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8500:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (* z (sin y)))))
   (if (<= z -5.9e+32) t_0 (if (<= z 8500.0) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (z * sin(y));
	double tmp;
	if (z <= -5.9e+32) {
		tmp = t_0;
	} else if (z <= 8500.0) {
		tmp = x + cos(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 - (z * sin(y))
    if (z <= (-5.9d+32)) then
        tmp = t_0
    else if (z <= 8500.0d0) then
        tmp = x + cos(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 - (z * Math.sin(y));
	double tmp;
	if (z <= -5.9e+32) {
		tmp = t_0;
	} else if (z <= 8500.0) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (z * math.sin(y))
	tmp = 0
	if z <= -5.9e+32:
		tmp = t_0
	elif z <= 8500.0:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -5.9e+32)
		tmp = t_0;
	elseif (z <= 8500.0)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (z * sin(y));
	tmp = 0.0;
	if (z <= -5.9e+32)
		tmp = t_0;
	elseif (z <= 8500.0)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.9e+32], t$95$0, If[LessEqual[z, 8500.0], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.89999999999999965e32 or 8500 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 87.5%

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

   if -5.89999999999999965e32 < z < 8500

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{elif}\;z \leq 8500:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2700:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot \left(-0.5 + \left(y \cdot z\right) \cdot 0.16666666666666666\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (<= y -0.58)
     t_0
     (if (<= y 2700.0)
       (+ x (+ 1.0 (* y (- (* y (+ -0.5 (* (* y z) 0.16666666666666666))) z))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if (y <= -0.58) {
		tmp = t_0;
	} else if (y <= 2700.0) {
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)));
	} 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)
    if (y <= (-0.58d0)) then
        tmp = t_0
    else if (y <= 2700.0d0) then
        tmp = x + (1.0d0 + (y * ((y * ((-0.5d0) + ((y * z) * 0.16666666666666666d0))) - z)))
    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);
	double tmp;
	if (y <= -0.58) {
		tmp = t_0;
	} else if (y <= 2700.0) {
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	tmp = 0
	if y <= -0.58:
		tmp = t_0
	elif y <= 2700.0:
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if (y <= -0.58)
		tmp = t_0;
	elseif (y <= 2700.0)
		tmp = Float64(x + Float64(1.0 + Float64(y * Float64(Float64(y * Float64(-0.5 + Float64(Float64(y * z) * 0.16666666666666666))) - z))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	tmp = 0.0;
	if (y <= -0.58)
		tmp = t_0;
	elseif (y <= 2700.0)
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.58], t$95$0, If[LessEqual[y, 2700.0], N[(x + N[(1.0 + N[(y * N[(N[(y * N[(-0.5 + N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.57999999999999996 or 2700 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 59.7%

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

   5. Simplified 59.7%

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

   if -0.57999999999999996 < y < 2700

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right) + \color{blue}{1} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + 1\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + 1\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(1 + \color{blue}{y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right)\right), \color{blue}{z}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right)\right), z\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), z\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{-1}{2}\right)\right), z\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-1}{2} + \frac{1}{6} \cdot \left(y \cdot z\right)\right)\right), z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(\left(y \cdot z\right) \cdot \frac{1}{6}\right)\right)\right), z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(\left(y \cdot z\right), \frac{1}{6}\right)\right)\right), z\right)\right)\right)\right) \]

      15. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \frac{1}{6}\right)\right)\right), z\right)\right)\right)\right) \]

   5. Simplified 99.3%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.58:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq 2700:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot \left(-0.5 + \left(y \cdot z\right) \cdot 0.16666666666666666\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+71}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq -3:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+45}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot \left(-0.5 + \left(y \cdot z\right) \cdot 0.16666666666666666\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.08e+71)
   (+ x 1.0)
   (if (<= y -3.0)
     (cos y)
     (if (<= y 4.5e+45)
       (+ x (+ 1.0 (* y (- (* y (+ -0.5 (* (* y z) 0.16666666666666666))) z))))
       (+ x 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.08e+71) {
		tmp = x + 1.0;
	} else if (y <= -3.0) {
		tmp = cos(y);
	} else if (y <= 4.5e+45) {
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.08d+71)) then
        tmp = x + 1.0d0
    else if (y <= (-3.0d0)) then
        tmp = cos(y)
    else if (y <= 4.5d+45) then
        tmp = x + (1.0d0 + (y * ((y * ((-0.5d0) + ((y * z) * 0.16666666666666666d0))) - z)))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.08e+71) {
		tmp = x + 1.0;
	} else if (y <= -3.0) {
		tmp = Math.cos(y);
	} else if (y <= 4.5e+45) {
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.08e+71:
		tmp = x + 1.0
	elif y <= -3.0:
		tmp = math.cos(y)
	elif y <= 4.5e+45:
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.08e+71)
		tmp = Float64(x + 1.0);
	elseif (y <= -3.0)
		tmp = cos(y);
	elseif (y <= 4.5e+45)
		tmp = Float64(x + Float64(1.0 + Float64(y * Float64(Float64(y * Float64(-0.5 + Float64(Float64(y * z) * 0.16666666666666666))) - z))));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.08e+71)
		tmp = x + 1.0;
	elseif (y <= -3.0)
		tmp = cos(y);
	elseif (y <= 4.5e+45)
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.08e+71], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, -3.0], N[Cos[y], $MachinePrecision], If[LessEqual[y, 4.5e+45], N[(x + N[(1.0 + N[(y * N[(N[(y * N[(-0.5 + N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08e71 or 4.4999999999999998e45 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 42.9%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 42.9%

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

   if -1.08e71 < y < -3

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in x around 0

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

      1. cos-lowering-cos.f64 55.8%

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

   8. Simplified 55.8%

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

   if -3 < y < 4.4999999999999998e45

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right) + \color{blue}{1} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + 1\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + 1\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(1 + \color{blue}{y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right)\right), \color{blue}{z}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right)\right), z\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), z\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{-1}{2}\right)\right), z\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-1}{2} + \frac{1}{6} \cdot \left(y \cdot z\right)\right)\right), z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(\left(y \cdot z\right) \cdot \frac{1}{6}\right)\right)\right), z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(\left(y \cdot z\right), \frac{1}{6}\right)\right)\right), z\right)\right)\right)\right) \]

      15. *-lowering-*.f64 97.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \frac{1}{6}\right)\right)\right), z\right)\right)\right)\right) \]

   5. Simplified 97.2%

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

Alternative 6: 69.2% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4200000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+45}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot \left(-0.5 + \left(y \cdot z\right) \cdot 0.16666666666666666\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4200000.0)
   (+ x 1.0)
   (if (<= y 4.5e+45)
     (+ x (+ 1.0 (* y (- (* y (+ -0.5 (* (* y z) 0.16666666666666666))) z))))
     (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4200000.0) {
		tmp = x + 1.0;
	} else if (y <= 4.5e+45) {
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4200000.0d0)) then
        tmp = x + 1.0d0
    else if (y <= 4.5d+45) then
        tmp = x + (1.0d0 + (y * ((y * ((-0.5d0) + ((y * z) * 0.16666666666666666d0))) - z)))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4200000.0) {
		tmp = x + 1.0;
	} else if (y <= 4.5e+45) {
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4200000.0:
		tmp = x + 1.0
	elif y <= 4.5e+45:
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4200000.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 4.5e+45)
		tmp = Float64(x + Float64(1.0 + Float64(y * Float64(Float64(y * Float64(-0.5 + Float64(Float64(y * z) * 0.16666666666666666))) - z))));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4200000.0)
		tmp = x + 1.0;
	elseif (y <= 4.5e+45)
		tmp = x + (1.0 + (y * ((y * (-0.5 + ((y * z) * 0.16666666666666666))) - z)));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4200000.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 4.5e+45], N[(x + N[(1.0 + N[(y * N[(N[(y * N[(-0.5 + N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e6 or 4.4999999999999998e45 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 39.5%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 39.5%

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

   if -4.2e6 < y < 4.4999999999999998e45

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right) + \color{blue}{1} \]

      2. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + 1\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + 1\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(1 + \color{blue}{y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right)\right), \color{blue}{z}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right)\right), z\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), z\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{-1}{2}\right)\right), z\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-1}{2} + \frac{1}{6} \cdot \left(y \cdot z\right)\right)\right), z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(\frac{1}{6} \cdot \left(y \cdot z\right)\right)\right)\right), z\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \left(\left(y \cdot z\right) \cdot \frac{1}{6}\right)\right)\right), z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(\left(y \cdot z\right), \frac{1}{6}\right)\right)\right), z\right)\right)\right)\right) \]

      15. *-lowering-*.f64 96.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \frac{1}{6}\right)\right)\right), z\right)\right)\right)\right) \]

   5. Simplified 96.0%

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

Alternative 7: 68.8% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+125}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+17}:\\ \;\;\;\;1 - \left(y \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+125)
   (+ x 1.0)
   (if (<= y 2.75e+17) (- 1.0 (- (* y z) x)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+125) {
		tmp = x + 1.0;
	} else if (y <= 2.75e+17) {
		tmp = 1.0 - ((y * z) - x);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.3d+125)) then
        tmp = x + 1.0d0
    else if (y <= 2.75d+17) then
        tmp = 1.0d0 - ((y * z) - x)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+125) {
		tmp = x + 1.0;
	} else if (y <= 2.75e+17) {
		tmp = 1.0 - ((y * z) - x);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+125:
		tmp = x + 1.0
	elif y <= 2.75e+17:
		tmp = 1.0 - ((y * z) - x)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+125)
		tmp = Float64(x + 1.0);
	elseif (y <= 2.75e+17)
		tmp = Float64(1.0 - Float64(Float64(y * z) - x));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+125)
		tmp = x + 1.0;
	elseif (y <= 2.75e+17)
		tmp = 1.0 - ((y * z) - x);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+125], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 2.75e+17], N[(1.0 - N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.30000000000000013e125 or 2.75e17 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 46.4%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 46.4%

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

   if -2.30000000000000013e125 < y < 2.75e17

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

         \[\leadsto \left(1 - y \cdot z\right) + x \]

      5. associate-+l- N/A

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

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

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

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

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

      8. *-lowering-*.f64 81.8%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), x\right)\right) \]

   5. Simplified 81.8%

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

Alternative 8: 65.9% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-51}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 820:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.2e-51) (+ x 1.0) (if (<= x 820.0) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e-51) {
		tmp = x + 1.0;
	} else if (x <= 820.0) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-6.2d-51)) then
        tmp = x + 1.0d0
    else if (x <= 820.0d0) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e-51) {
		tmp = x + 1.0;
	} else if (x <= 820.0) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.2e-51:
		tmp = x + 1.0
	elif x <= 820.0:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.2e-51)
		tmp = Float64(x + 1.0);
	elseif (x <= 820.0)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.2e-51)
		tmp = x + 1.0;
	elseif (x <= 820.0)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.2e-51], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 820.0], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999995e-51 or 820 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 80.7%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 80.7%

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

   if -6.1999999999999995e-51 < x < 820

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

         \[\leadsto \left(1 - y \cdot z\right) + x \]

      5. associate-+l- N/A

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

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

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

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

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

      8. *-lowering-*.f64 53.5%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), x\right)\right) \]

   5. Simplified 53.5%

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

   6. Taylor expanded in x around 0

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

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

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 53.5%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 53.5%

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

Alternative 9: 60.3% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e-11) x (if (<= x 2.2) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-11) {
		tmp = x;
	} else if (x <= 2.2) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.05d-11)) then
        tmp = x
    else if (x <= 2.2d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-11) {
		tmp = x;
	} else if (x <= 2.2) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e-11:
		tmp = x
	elif x <= 2.2:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e-11)
		tmp = x;
	elseif (x <= 2.2)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.05e-11)
		tmp = x;
	elseif (x <= 2.2)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e-11], x, If[LessEqual[x, 2.2], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0499999999999999e-11 or 2.2000000000000002 < 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

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

   5. Simplified 79.0%

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

   if -1.0499999999999999e-11 < x < 2.2000000000000002

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 40.9%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 40.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Simplified 40.8%

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

Alternative 10: 61.7% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.8 \cdot 10^{+251}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;0 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 4.8e+251) (+ x 1.0) (- 0.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.8e+251) {
		tmp = x + 1.0;
	} else {
		tmp = 0.0 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 4.8d+251) then
        tmp = x + 1.0d0
    else
        tmp = 0.0d0 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.8e+251) {
		tmp = x + 1.0;
	} else {
		tmp = 0.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 4.8e+251:
		tmp = x + 1.0
	else:
		tmp = 0.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 4.8e+251)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(0.0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 4.8e+251)
		tmp = x + 1.0;
	else
		tmp = 0.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 4.8e+251], N[(x + 1.0), $MachinePrecision], N[(0.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.79999999999999962e251

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 62.7%

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

   5. Simplified 62.7%

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

   if 4.79999999999999962e251 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

         \[\leadsto \left(1 - y \cdot z\right) + x \]

      5. associate-+l- N/A

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

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

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

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

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

      8. *-lowering-*.f64 57.9%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), x\right)\right) \]

   5. Simplified 57.9%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y \cdot z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y \cdot z} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y \cdot z\right)}\right) \]

      4. *-lowering-*.f64 57.9%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 57.9%

      \[\leadsto \color{blue}{0 - y \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 61.1% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 60.1%

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

5. Simplified 60.1%

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

Alternative 12: 20.9% 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 y around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 60.1%

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{1}\right) \]

5. Simplified 60.1%

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

6. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
7. Step-by-step derivation

8. Simplified 22.5%

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

Reproduce

herbie shell --seed 2024161 
(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))))