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

Percentage Accurate: 99.9% → 99.9%

Time: 11.3s

Alternatives: 13

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: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ t_1 := z \cdot \sin y\\ t_2 := t\_0 - t\_1\\ t_3 := x - t\_1\\ \mathbf{if}\;t\_2 \leq -20000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 50000000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y)))
        (t_1 (* z (sin y)))
        (t_2 (- t_0 t_1))
        (t_3 (- x t_1)))
   (if (<= t_2 -20000000.0) t_3 (if (<= t_2 50000000.0) t_0 t_3))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double t_1 = z * sin(y);
	double t_2 = t_0 - t_1;
	double t_3 = x - t_1;
	double tmp;
	if (t_2 <= -20000000.0) {
		tmp = t_3;
	} else if (t_2 <= 50000000.0) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x + cos(y)
    t_1 = z * sin(y)
    t_2 = t_0 - t_1
    t_3 = x - t_1
    if (t_2 <= (-20000000.0d0)) then
        tmp = t_3
    else if (t_2 <= 50000000.0d0) then
        tmp = t_0
    else
        tmp = t_3
    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 t_1 = z * Math.sin(y);
	double t_2 = t_0 - t_1;
	double t_3 = x - t_1;
	double tmp;
	if (t_2 <= -20000000.0) {
		tmp = t_3;
	} else if (t_2 <= 50000000.0) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	t_1 = z * math.sin(y)
	t_2 = t_0 - t_1
	t_3 = x - t_1
	tmp = 0
	if t_2 <= -20000000.0:
		tmp = t_3
	elif t_2 <= 50000000.0:
		tmp = t_0
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	t_1 = Float64(z * sin(y))
	t_2 = Float64(t_0 - t_1)
	t_3 = Float64(x - t_1)
	tmp = 0.0
	if (t_2 <= -20000000.0)
		tmp = t_3;
	elseif (t_2 <= 50000000.0)
		tmp = t_0;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	t_1 = z * sin(y);
	t_2 = t_0 - t_1;
	t_3 = x - t_1;
	tmp = 0.0;
	if (t_2 <= -20000000.0)
		tmp = t_3;
	elseif (t_2 <= 50000000.0)
		tmp = t_0;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -20000000.0], t$95$3, If[LessEqual[t$95$2, 50000000.0], t$95$0, t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -2e7 or 5e7 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 99.5%

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

   if -2e7 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 5e7

   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

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

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

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

      3. cos-lowering-cos.f64 100.0

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

   5. Simplified 100.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - z \cdot \sin y \leq -20000000:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{elif}\;\left(x + \cos y\right) - z \cdot \sin y \leq 50000000:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -z \cdot \sin y\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+204}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+126}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* z (sin y)))))
   (if (<= z -7.2e+204) t_0 (if (<= z 1.35e+126) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -(z * sin(y));
	double tmp;
	if (z <= -7.2e+204) {
		tmp = t_0;
	} else if (z <= 1.35e+126) {
		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 = -(z * sin(y))
    if (z <= (-7.2d+204)) then
        tmp = t_0
    else if (z <= 1.35d+126) 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 = -(z * Math.sin(y));
	double tmp;
	if (z <= -7.2e+204) {
		tmp = t_0;
	} else if (z <= 1.35e+126) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(z * math.sin(y))
	tmp = 0
	if z <= -7.2e+204:
		tmp = t_0
	elif z <= 1.35e+126:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -7.2e+204)
		tmp = t_0;
	elseif (z <= 1.35e+126)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -(z * sin(y));
	tmp = 0.0;
	if (z <= -7.2e+204)
		tmp = t_0;
	elseif (z <= 1.35e+126)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -7.2e+204], t$95$0, If[LessEqual[z, 1.35e+126], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000005e204 or 1.35000000000000001e126 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

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

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

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

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

      4. sin-lowering-sin.f64 72.5

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

   5. Simplified 72.5%

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

   if -7.2000000000000005e204 < z < 1.35000000000000001e126

   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

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

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

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

      3. cos-lowering-cos.f64 89.5

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

   5. Simplified 89.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+204}:\\ \;\;\;\;-z \cdot \sin y\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+126}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -76000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.116:\\ \;\;\;\;1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \left(y \cdot z\right) \cdot 0.16666666666666666, -z\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (<= y -76000.0)
     t_0
     (if (<= y 0.116)
       (+ 1.0 (fma y (fma y (* (* y z) 0.16666666666666666) (- z)) x))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if (y <= -76000.0) {
		tmp = t_0;
	} else if (y <= 0.116) {
		tmp = 1.0 + fma(y, fma(y, ((y * z) * 0.16666666666666666), -z), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if (y <= -76000.0)
		tmp = t_0;
	elseif (y <= 0.116)
		tmp = Float64(1.0 + fma(y, fma(y, Float64(Float64(y * z) * 0.16666666666666666), Float64(-z)), x));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -76000.0], t$95$0, If[LessEqual[y, 0.116], N[(1.0 + N[(y * N[(y * N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + (-z)), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -76000 or 0.116000000000000006 < 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

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

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

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

      3. cos-lowering-cos.f64 64.3

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

   5. Simplified 64.3%

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

   if -76000 < y < 0.116000000000000006

   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. +-lowering-+.f64 N/A

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

      2. +-commutative N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. sub-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. neg-lowering-neg.f64 99.0

          \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot 0.16666666666666666, -0.5\right), \color{blue}{-z}\right), x\right) \]

   5. Simplified 99.0%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot 0.16666666666666666, -0.5\right), -z\right), x\right)} \]

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\left(y \cdot z\right) \cdot \frac{1}{6}}, \mathsf{neg}\left(z\right)\right), x\right) \]

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

         \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\left(y \cdot z\right) \cdot \frac{1}{6}}, \mathsf{neg}\left(z\right)\right), x\right) \]

      3. *-lowering-*.f64 99.0

         \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\left(y \cdot z\right)} \cdot 0.16666666666666666, -z\right), x\right) \]

   8. Simplified 99.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -76000:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq 0.116:\\ \;\;\;\;1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \left(y \cdot z\right) \cdot 0.16666666666666666, -z\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.6% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+16}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+27}:\\ \;\;\;\;1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot 0.16666666666666666, -0.5\right), -z\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.1e+16)
   (+ x 1.0)
   (if (<= y 6e+27)
     (+ 1.0 (fma y (fma y (fma y (* z 0.16666666666666666) -0.5) (- z)) x))
     (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e+16) {
		tmp = x + 1.0;
	} else if (y <= 6e+27) {
		tmp = 1.0 + fma(y, fma(y, fma(y, (z * 0.16666666666666666), -0.5), -z), x);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.1e+16)
		tmp = Float64(x + 1.0);
	elseif (y <= 6e+27)
		tmp = Float64(1.0 + fma(y, fma(y, fma(y, Float64(z * 0.16666666666666666), -0.5), Float64(-z)), x));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.1e+16], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 6e+27], N[(1.0 + N[(y * N[(y * N[(y * N[(z * 0.16666666666666666), $MachinePrecision] + -0.5), $MachinePrecision] + (-z)), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1e16 or 5.99999999999999953e27 < 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

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

      2. +-lowering-+.f64 49.7

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

   5. Simplified 49.7%

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

   if -2.1e16 < y < 5.99999999999999953e27

   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. +-lowering-+.f64 N/A

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

      2. +-commutative N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. sub-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. neg-lowering-neg.f64 96.0

          \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot 0.16666666666666666, -0.5\right), \color{blue}{-z}\right), x\right) \]

   5. Simplified 96.0%

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

Alternative 6: 70.2% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+43}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.1e+43)
   (+ x 1.0)
   (if (<= y 1.18e+52) (fma y (- (* y -0.5) z) (+ x 1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.1e+43) {
		tmp = x + 1.0;
	} else if (y <= 1.18e+52) {
		tmp = fma(y, ((y * -0.5) - z), (x + 1.0));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.1e+43)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.18e+52)
		tmp = fma(y, Float64(Float64(y * -0.5) - z), Float64(x + 1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.1e+43], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.18e+52], N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e43 or 1.17999999999999997e52 < 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

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

      2. +-lowering-+.f64 49.6

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

   5. Simplified 49.6%

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

   if -1.1e43 < y < 1.17999999999999997e52

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 94.1

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

   5. Simplified 94.1%

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

Alternative 7: 70.3% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+83}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+52}:\\ \;\;\;\;\left(x - y \cdot z\right) - -1\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+83)
   (+ x 1.0)
   (if (<= y 1.2e+52) (- (- x (* y z)) -1.0) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+83) {
		tmp = x + 1.0;
	} else if (y <= 1.2e+52) {
		tmp = (x - (y * z)) - -1.0;
	} 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 <= (-1.05d+83)) then
        tmp = x + 1.0d0
    else if (y <= 1.2d+52) then
        tmp = (x - (y * z)) - (-1.0d0)
    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 <= -1.05e+83) {
		tmp = x + 1.0;
	} else if (y <= 1.2e+52) {
		tmp = (x - (y * z)) - -1.0;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+83:
		tmp = x + 1.0
	elif y <= 1.2e+52:
		tmp = (x - (y * z)) - -1.0
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+83)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.2e+52)
		tmp = Float64(Float64(x - Float64(y * z)) - -1.0);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e+83)
		tmp = x + 1.0;
	elseif (y <= 1.2e+52)
		tmp = (x - (y * z)) - -1.0;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+83], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.2e+52], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000001e83 or 1.2e52 < 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

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

      2. +-lowering-+.f64 48.5

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

   5. Simplified 48.5%

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

   if -1.05000000000000001e83 < y < 1.2e52

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 92.1

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

   5. Simplified 92.1%

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

      1. associate--r+ N/A

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

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

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

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

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

      4. *-lowering-*.f64 92.1

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

   7. Applied egg-rr 92.1%

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

Alternative 8: 70.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+83}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+52}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e+83)
   (+ x 1.0)
   (if (<= y 1.2e+52) (- x (fma y z -1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+83) {
		tmp = x + 1.0;
	} else if (y <= 1.2e+52) {
		tmp = x - fma(y, z, -1.0);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e+83)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.2e+52)
		tmp = Float64(x - fma(y, z, -1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e+83], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.2e+52], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999992e83 or 1.2e52 < 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

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

      2. +-lowering-+.f64 48.5

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

   5. Simplified 48.5%

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

   if -1.64999999999999992e83 < y < 1.2e52

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 92.1

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

   5. Simplified 92.1%

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

Alternative 9: 67.5% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-14}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 0.41:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.9e-14) (+ x 1.0) (if (<= x 0.41) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.9e-14) {
		tmp = x + 1.0;
	} else if (x <= 0.41) {
		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 <= (-3.9d-14)) then
        tmp = x + 1.0d0
    else if (x <= 0.41d0) 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 <= -3.9e-14) {
		tmp = x + 1.0;
	} else if (x <= 0.41) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.9e-14:
		tmp = x + 1.0
	elif x <= 0.41:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.9e-14)
		tmp = Float64(x + 1.0);
	elseif (x <= 0.41)
		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 <= -3.9e-14)
		tmp = x + 1.0;
	elseif (x <= 0.41)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.9e-14], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 0.41], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8999999999999998e-14 or 0.409999999999999976 < 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

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

      2. +-lowering-+.f64 82.0

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

   5. Simplified 82.0%

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

   if -3.8999999999999998e-14 < x < 0.409999999999999976

   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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 64.1

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

   5. Simplified 64.1%

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

   6. Taylor expanded in x around 0

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

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

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

      2. *-lowering-*.f64 64.1

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

   8. Simplified 64.1%

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

Alternative 10: 62.6% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.65 \cdot 10^{+197}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.65e+197) (+ x 1.0) (- (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.65e+197) {
		tmp = x + 1.0;
	} else {
		tmp = -(y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 1.65d+197) then
        tmp = x + 1.0d0
    else
        tmp = -(y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.65e+197) {
		tmp = x + 1.0;
	} else {
		tmp = -(y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.65e+197:
		tmp = x + 1.0
	else:
		tmp = -(y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.65e+197)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(-Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.65e+197)
		tmp = x + 1.0;
	else
		tmp = -(y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.65e+197], N[(x + 1.0), $MachinePrecision], (-N[(y * z), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if z < 1.6499999999999998e197

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 73.3

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

   5. Simplified 73.3%

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

   if 1.6499999999999998e197 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 50.7

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

   5. Simplified 50.7%

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

   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

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. neg-lowering-neg.f64 35.2

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

   8. Simplified 35.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.65 \cdot 10^{+197}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.3% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3600:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.00052:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3600.0) x (if (<= x 0.00052) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3600.0) {
		tmp = x;
	} else if (x <= 0.00052) {
		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 <= (-3600.0d0)) then
        tmp = x
    else if (x <= 0.00052d0) 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 <= -3600.0) {
		tmp = x;
	} else if (x <= 0.00052) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3600.0:
		tmp = x
	elif x <= 0.00052:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3600.0)
		tmp = x;
	elseif (x <= 0.00052)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3600.0)
		tmp = x;
	elseif (x <= 0.00052)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3600.0], x, If[LessEqual[x, 0.00052], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3600 or 5.19999999999999954e-4 < 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 83.7%

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

   if -3600 < x < 5.19999999999999954e-4

   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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 61.8

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

   5. Simplified 61.8%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 49.8%

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

   9. Taylor expanded in x around 0

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

   11. Simplified 49.3%

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

Alternative 12: 61.9% accurate, 53.0× 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

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

   2. +-lowering-+.f64 67.1

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

5. Simplified 67.1%

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

Alternative 13: 22.3% accurate, 212.0× 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

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. unsub-neg N/A

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

   4. associate-+l- N/A

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

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

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

   6. sub-neg N/A

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

   7. metadata-eval N/A

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

   8. accelerator-lowering-fma.f64 67.5

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

5. Simplified 67.5%

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

6. Taylor expanded in y around 0

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

8. Simplified 67.1%

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

9. Taylor expanded in x around 0

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

11. Simplified 26.0%

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

Reproduce

herbie shell --seed 2024199 
(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))))