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

Percentage Accurate: 99.9% → 99.9%

Time: 8.8s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\cos y + x\right) - \sin y \cdot z\\ t_1 := x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{if}\;t\_0 \leq -500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.995:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (cos y) x) (* (sin y) z))) (t_1 (- x (fma z y -1.0))))
   (if (<= t_0 -500000000000.0) t_1 (if (<= t_0 0.995) (cos y) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (cos(y) + x) - (sin(y) * z);
	double t_1 = x - fma(z, y, -1.0);
	double tmp;
	if (t_0 <= -500000000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.995) {
		tmp = cos(y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cos(y) + x) - Float64(sin(y) * z))
	t_1 = Float64(x - fma(z, y, -1.0))
	tmp = 0.0
	if (t_0 <= -500000000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.995)
		tmp = cos(y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -500000000000.0], t$95$1, If[LessEqual[t$95$0, 0.995], N[Cos[y], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -5e11 or 0.994999999999999996 < (-.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 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. lower--.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. *-commutative N/A

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

      8. metadata-eval N/A

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

      9. lower-fma.f64 69.7

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

   5. Applied rewrites 69.7%

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

   if -5e11 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.994999999999999996

   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. lower-+.f64 N/A

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

      3. lower-cos.f64 94.5

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

   5. Applied rewrites 94.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \cos y \]
   7. Step-by-step derivation

   8. Applied rewrites 92.1%

      \[\leadsto \cos y \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\cos y + x\right) - \sin y \cdot z \leq -500000000000:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{elif}\;\left(\cos y + x\right) - \sin y \cdot z \leq 0.995:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + x\right) - \sin y \cdot z\\ \mathbf{if}\;z \leq -580000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.22:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ 1.0 x) (* (sin y) z))))
   (if (<= z -580000.0) t_0 (if (<= z 1.22) (+ (cos y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 + x) - (sin(y) * z);
	double tmp;
	if (z <= -580000.0) {
		tmp = t_0;
	} else if (z <= 1.22) {
		tmp = cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 + x) - (sin(y) * z)
    if (z <= (-580000.0d0)) then
        tmp = t_0
    else if (z <= 1.22d0) then
        tmp = cos(y) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 + x) - (Math.sin(y) * z);
	double tmp;
	if (z <= -580000.0) {
		tmp = t_0;
	} else if (z <= 1.22) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 + x) - (math.sin(y) * z)
	tmp = 0
	if z <= -580000.0:
		tmp = t_0
	elif z <= 1.22:
		tmp = math.cos(y) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 + x) - Float64(sin(y) * z))
	tmp = 0.0
	if (z <= -580000.0)
		tmp = t_0;
	elseif (z <= 1.22)
		tmp = Float64(cos(y) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 + x) - (sin(y) * z);
	tmp = 0.0;
	if (z <= -580000.0)
		tmp = t_0;
	elseif (z <= 1.22)
		tmp = cos(y) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 + x), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -580000.0], t$95$0, If[LessEqual[z, 1.22], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e5 or 1.21999999999999997 < 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

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

   5. Applied rewrites 99.3%

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

   if -5.8e5 < z < 1.21999999999999997

   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. lower-+.f64 N/A

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

      3. lower-cos.f64 99.7

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

   5. Applied rewrites 99.7%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -580000:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \mathbf{elif}\;z \leq 1.22:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot \sin y\\ \mathbf{if}\;z \leq -8000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 10^{+178}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) (sin y))))
   (if (<= z -8000000000.0) t_0 (if (<= z 1e+178) (+ (cos y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -z * sin(y);
	double tmp;
	if (z <= -8000000000.0) {
		tmp = t_0;
	} else if (z <= 1e+178) {
		tmp = cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -z * sin(y)
    if (z <= (-8000000000.0d0)) then
        tmp = t_0
    else if (z <= 1d+178) then
        tmp = cos(y) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z * Math.sin(y);
	double tmp;
	if (z <= -8000000000.0) {
		tmp = t_0;
	} else if (z <= 1e+178) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z * math.sin(y)
	tmp = 0
	if z <= -8000000000.0:
		tmp = t_0
	elif z <= 1e+178:
		tmp = math.cos(y) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) * sin(y))
	tmp = 0.0
	if (z <= -8000000000.0)
		tmp = t_0;
	elseif (z <= 1e+178)
		tmp = Float64(cos(y) + x);
	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 <= -8000000000.0)
		tmp = t_0;
	elseif (z <= 1e+178)
		tmp = cos(y) + x;
	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, -8000000000.0], t$95$0, If[LessEqual[z, 1e+178], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8e9 or 1.0000000000000001e178 < z

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   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. distribute-lft-neg-in N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-sin.f64 67.0

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

   5. Applied rewrites 67.0%

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

   if -8e9 < z < 1.0000000000000001e178

   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. lower-+.f64 N/A

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

      3. lower-cos.f64 89.6

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

   5. Applied rewrites 89.6%

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

Alternative 5: 80.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y + x\\ \mathbf{if}\;y \leq -1.12:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 30:\\ \;\;\;\;\left(1 + x\right) - \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.0001984126984126984, y \cdot y, 0.008333333333333333\right), y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (cos y) x)))
   (if (<= y -1.12)
     t_0
     (if (<= y 30.0)
       (-
        (+ 1.0 x)
        (*
         (fma
          (*
           (fma
            (fma -0.0001984126984126984 (* y y) 0.008333333333333333)
            (* y y)
            -0.16666666666666666)
           z)
          (* y y)
          z)
         y))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) + x;
	double tmp;
	if (y <= -1.12) {
		tmp = t_0;
	} else if (y <= 30.0) {
		tmp = (1.0 + x) - (fma((fma(fma(-0.0001984126984126984, (y * y), 0.008333333333333333), (y * y), -0.16666666666666666) * z), (y * y), z) * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) + x)
	tmp = 0.0
	if (y <= -1.12)
		tmp = t_0;
	elseif (y <= 30.0)
		tmp = Float64(Float64(1.0 + x) - Float64(fma(Float64(fma(fma(-0.0001984126984126984, Float64(y * y), 0.008333333333333333), Float64(y * y), -0.16666666666666666) * z), Float64(y * y), z) * y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -1.12], t$95$0, If[LessEqual[y, 30.0], N[(N[(1.0 + x), $MachinePrecision] - N[(N[(N[(N[(N[(-0.0001984126984126984 * N[(y * y), $MachinePrecision] + 0.008333333333333333), $MachinePrecision] * N[(y * y), $MachinePrecision] + -0.16666666666666666), $MachinePrecision] * z), $MachinePrecision] * N[(y * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1200000000000001 or 30 < 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. lower-+.f64 N/A

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

      3. lower-cos.f64 59.9

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

   5. Applied rewrites 59.9%

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

   if -1.1200000000000001 < y < 30

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + {y}^{2} \cdot \left(\frac{-1}{5040} \cdot \left({y}^{2} \cdot z\right) + \frac{1}{120} \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + {y}^{2} \cdot \left(\frac{-1}{5040} \cdot \left({y}^{2} \cdot z\right) + \frac{1}{120} \cdot z\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + {y}^{2} \cdot \left(\frac{-1}{5040} \cdot \left({y}^{2} \cdot z\right) + \frac{1}{120} \cdot z\right)\right)\right) \cdot y} \]

   8. Applied rewrites 99.0%

      \[\leadsto \left(x + 1\right) - \color{blue}{\mathsf{fma}\left(z \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0001984126984126984, y \cdot y, 0.008333333333333333\right), y \cdot y, -0.16666666666666666\right), y \cdot y, z\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12:\\ \;\;\;\;\cos y + x\\ \mathbf{elif}\;y \leq 30:\\ \;\;\;\;\left(1 + x\right) - \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.0001984126984126984, y \cdot y, 0.008333333333333333\right), y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6500000:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 7800:\\ \;\;\;\;\left(1 + x\right) - \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.0001984126984126984, y \cdot y, 0.008333333333333333\right), y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6500000.0)
   (+ 1.0 x)
   (if (<= y 7800.0)
     (-
      (+ 1.0 x)
      (*
       (fma
        (*
         (fma
          (fma -0.0001984126984126984 (* y y) 0.008333333333333333)
          (* y y)
          -0.16666666666666666)
         z)
        (* y y)
        z)
       y))
     (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6500000.0) {
		tmp = 1.0 + x;
	} else if (y <= 7800.0) {
		tmp = (1.0 + x) - (fma((fma(fma(-0.0001984126984126984, (y * y), 0.008333333333333333), (y * y), -0.16666666666666666) * z), (y * y), z) * y);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6500000.0)
		tmp = Float64(1.0 + x);
	elseif (y <= 7800.0)
		tmp = Float64(Float64(1.0 + x) - Float64(fma(Float64(fma(fma(-0.0001984126984126984, Float64(y * y), 0.008333333333333333), Float64(y * y), -0.16666666666666666) * z), Float64(y * y), z) * y));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6500000.0], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 7800.0], N[(N[(1.0 + x), $MachinePrecision] - N[(N[(N[(N[(N[(-0.0001984126984126984 * N[(y * y), $MachinePrecision] + 0.008333333333333333), $MachinePrecision] * N[(y * y), $MachinePrecision] + -0.16666666666666666), $MachinePrecision] * z), $MachinePrecision] * N[(y * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e6 or 7800 < 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. lower-+.f64 35.7

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

   5. Applied rewrites 35.7%

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

   if -6.5e6 < y < 7800

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + {y}^{2} \cdot \left(\frac{-1}{5040} \cdot \left({y}^{2} \cdot z\right) + \frac{1}{120} \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + {y}^{2} \cdot \left(\frac{-1}{5040} \cdot \left({y}^{2} \cdot z\right) + \frac{1}{120} \cdot z\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + {y}^{2} \cdot \left(\frac{-1}{5040} \cdot \left({y}^{2} \cdot z\right) + \frac{1}{120} \cdot z\right)\right)\right) \cdot y} \]

   8. Applied rewrites 97.7%

      \[\leadsto \left(x + 1\right) - \color{blue}{\mathsf{fma}\left(z \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0001984126984126984, y \cdot y, 0.008333333333333333\right), y \cdot y, -0.16666666666666666\right), y \cdot y, z\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6500000:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 7800:\\ \;\;\;\;\left(1 + x\right) - \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.0001984126984126984, y \cdot y, 0.008333333333333333\right), y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.3% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1720000:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 30:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z \cdot y, -0.5\right) \cdot y - z, y, 1 + x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1720000.0)
   (+ 1.0 x)
   (if (<= y 30.0)
     (fma (- (* (fma 0.16666666666666666 (* z y) -0.5) y) z) y (+ 1.0 x))
     (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1720000.0) {
		tmp = 1.0 + x;
	} else if (y <= 30.0) {
		tmp = fma(((fma(0.16666666666666666, (z * y), -0.5) * y) - z), y, (1.0 + x));
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1720000.0)
		tmp = Float64(1.0 + x);
	elseif (y <= 30.0)
		tmp = fma(Float64(Float64(fma(0.16666666666666666, Float64(z * y), -0.5) * y) - z), y, Float64(1.0 + x));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1720000.0], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 30.0], N[(N[(N[(N[(0.16666666666666666 * N[(z * y), $MachinePrecision] + -0.5), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.72e6 or 30 < 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. lower-+.f64 35.6

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

   5. Applied rewrites 35.6%

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

   if -1.72e6 < y < 30

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-+.f64 98.2

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

   5. Applied rewrites 98.2%

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

Alternative 8: 69.0% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+49}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 8500:\\ \;\;\;\;\left(1 + x\right) - \left(\mathsf{fma}\left(-0.16666666666666666, y \cdot y, 1\right) \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e+49)
   (+ 1.0 x)
   (if (<= y 8500.0)
     (- (+ 1.0 x) (* (* (fma -0.16666666666666666 (* y y) 1.0) z) y))
     (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e+49) {
		tmp = 1.0 + x;
	} else if (y <= 8500.0) {
		tmp = (1.0 + x) - ((fma(-0.16666666666666666, (y * y), 1.0) * z) * y);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e+49)
		tmp = Float64(1.0 + x);
	elseif (y <= 8500.0)
		tmp = Float64(Float64(1.0 + x) - Float64(Float64(fma(-0.16666666666666666, Float64(y * y), 1.0) * z) * y));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.9e+49], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 8500.0], N[(N[(1.0 + x), $MachinePrecision] - N[(N[(N[(-0.16666666666666666 * N[(y * y), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e49 or 8500 < 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. lower-+.f64 35.1

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

   5. Applied rewrites 35.1%

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

   if -2.9e49 < y < 8500

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right) \cdot y} \]

      3. +-commutative N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left({y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right) + z\right)} \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(x + 1\right) - \left(\color{blue}{\left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right) \cdot {y}^{2}} + z\right) \cdot y \]

      5. +-commutative N/A

         \[\leadsto \left(x + 1\right) - \left(\color{blue}{\left(\frac{1}{120} \cdot \left({y}^{2} \cdot z\right) + \frac{-1}{6} \cdot z\right)} \cdot {y}^{2} + z\right) \cdot y \]

      6. associate-*r* N/A

         \[\leadsto \left(x + 1\right) - \left(\left(\color{blue}{\left(\frac{1}{120} \cdot {y}^{2}\right) \cdot z} + \frac{-1}{6} \cdot z\right) \cdot {y}^{2} + z\right) \cdot y \]

      7. distribute-rgt-out N/A

         \[\leadsto \left(x + 1\right) - \left(\color{blue}{\left(z \cdot \left(\frac{1}{120} \cdot {y}^{2} + \frac{-1}{6}\right)\right)} \cdot {y}^{2} + z\right) \cdot y \]

      8. associate-*l* N/A

         \[\leadsto \left(x + 1\right) - \left(\color{blue}{z \cdot \left(\left(\frac{1}{120} \cdot {y}^{2} + \frac{-1}{6}\right) \cdot {y}^{2}\right)} + z\right) \cdot y \]

      9. *-rgt-identity N/A

         \[\leadsto \left(x + 1\right) - \left(z \cdot \left(\left(\frac{1}{120} \cdot {y}^{2} + \frac{-1}{6}\right) \cdot {y}^{2}\right) + \color{blue}{z \cdot 1}\right) \cdot y \]

      10. distribute-lft-out N/A

          \[\leadsto \left(x + 1\right) - \color{blue}{\left(z \cdot \left(\left(\frac{1}{120} \cdot {y}^{2} + \frac{-1}{6}\right) \cdot {y}^{2} + 1\right)\right)} \cdot y \]

      11. lower-*.f64 N/A

          \[\leadsto \left(x + 1\right) - \color{blue}{\left(z \cdot \left(\left(\frac{1}{120} \cdot {y}^{2} + \frac{-1}{6}\right) \cdot {y}^{2} + 1\right)\right)} \cdot y \]

      12. lower-fma.f64 N/A

          \[\leadsto \left(x + 1\right) - \left(z \cdot \color{blue}{\mathsf{fma}\left(\frac{1}{120} \cdot {y}^{2} + \frac{-1}{6}, {y}^{2}, 1\right)}\right) \cdot y \]

      13. lower-fma.f64 N/A

          \[\leadsto \left(x + 1\right) - \left(z \cdot \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{1}{120}, {y}^{2}, \frac{-1}{6}\right)}, {y}^{2}, 1\right)\right) \cdot y \]

      14. unpow2 N/A

          \[\leadsto \left(x + 1\right) - \left(z \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{120}, \color{blue}{y \cdot y}, \frac{-1}{6}\right), {y}^{2}, 1\right)\right) \cdot y \]

      15. lower-*.f64 N/A

          \[\leadsto \left(x + 1\right) - \left(z \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{120}, \color{blue}{y \cdot y}, \frac{-1}{6}\right), {y}^{2}, 1\right)\right) \cdot y \]

      16. unpow2 N/A

          \[\leadsto \left(x + 1\right) - \left(z \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{120}, y \cdot y, \frac{-1}{6}\right), \color{blue}{y \cdot y}, 1\right)\right) \cdot y \]

      17. lower-*.f64 93.9

          \[\leadsto \left(x + 1\right) - \left(z \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right), \color{blue}{y \cdot y}, 1\right)\right) \cdot y \]

   8. Applied rewrites 93.9%

      \[\leadsto \left(x + 1\right) - \color{blue}{\left(z \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right), y \cdot y, 1\right)\right) \cdot y} \]

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 94.8%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+49}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 8500:\\ \;\;\;\;\left(1 + x\right) - \left(\mathsf{fma}\left(-0.16666666666666666, y \cdot y, 1\right) \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.0% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+49}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 180:\\ \;\;\;\;\left(1 + x\right) - \left(\mathsf{fma}\left(-0.16666666666666666, y \cdot y, 1\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e+49)
   (+ 1.0 x)
   (if (<= y 180.0)
     (- (+ 1.0 x) (* (* (fma -0.16666666666666666 (* y y) 1.0) y) z))
     (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e+49) {
		tmp = 1.0 + x;
	} else if (y <= 180.0) {
		tmp = (1.0 + x) - ((fma(-0.16666666666666666, (y * y), 1.0) * y) * z);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e+49)
		tmp = Float64(1.0 + x);
	elseif (y <= 180.0)
		tmp = Float64(Float64(1.0 + x) - Float64(Float64(fma(-0.16666666666666666, Float64(y * y), 1.0) * y) * z));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.9e+49], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 180.0], N[(N[(1.0 + x), $MachinePrecision] - N[(N[(N[(-0.16666666666666666 * N[(y * y), $MachinePrecision] + 1.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e49 or 180 < 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. lower-+.f64 35.1

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

   5. Applied rewrites 35.1%

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

   if -2.9e49 < y < 180

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. distribute-rgt1-in N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 95.3

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

   8. Applied rewrites 95.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+49}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 180:\\ \;\;\;\;\left(1 + x\right) - \left(\mathsf{fma}\left(-0.16666666666666666, y \cdot y, 1\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.2% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1100000000000:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 11:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot y - z, y, 1 + x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1100000000000.0)
   (+ 1.0 x)
   (if (<= y 11.0) (fma (- (* -0.5 y) z) y (+ 1.0 x)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1100000000000.0) {
		tmp = 1.0 + x;
	} else if (y <= 11.0) {
		tmp = fma(((-0.5 * y) - z), y, (1.0 + x));
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1100000000000.0)
		tmp = Float64(1.0 + x);
	elseif (y <= 11.0)
		tmp = fma(Float64(Float64(-0.5 * y) - z), y, Float64(1.0 + x));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1100000000000.0], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 11.0], N[(N[(N[(-0.5 * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e12 or 11 < 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. lower-+.f64 35.1

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

   5. Applied rewrites 35.1%

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

   if -1.1e12 < y < 11

   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 98.1

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

   5. Applied rewrites 98.1%

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

Alternative 11: 69.1% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -360000000000:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 9.5:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -360000000000.0)
   (+ 1.0 x)
   (if (<= y 9.5) (- x (fma z y -1.0)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -360000000000.0) {
		tmp = 1.0 + x;
	} else if (y <= 9.5) {
		tmp = x - fma(z, y, -1.0);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -360000000000.0)
		tmp = Float64(1.0 + x);
	elseif (y <= 9.5)
		tmp = Float64(x - fma(z, y, -1.0));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -360000000000.0], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 9.5], N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e11 or 9.5 < 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. lower-+.f64 35.1

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

   5. Applied rewrites 35.1%

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

   if -3.6e11 < y < 9.5

   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. lower--.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. *-commutative N/A

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

      8. metadata-eval N/A

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

      9. lower-fma.f64 97.9

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

   5. Applied rewrites 97.9%

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

Alternative 12: 66.2% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-12}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;x \leq 0.72:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.4e-12) (+ 1.0 x) (if (<= x 0.72) (fma (- z) y 1.0) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e-12) {
		tmp = 1.0 + x;
	} else if (x <= 0.72) {
		tmp = fma(-z, y, 1.0);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.4e-12)
		tmp = Float64(1.0 + x);
	elseif (x <= 0.72)
		tmp = fma(Float64(-z), y, 1.0);
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.4e-12], N[(1.0 + x), $MachinePrecision], If[LessEqual[x, 0.72], N[((-z) * y + 1.0), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4000000000000002e-12 or 0.71999999999999997 < x

   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. lower-+.f64 82.6

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

   5. Applied rewrites 82.6%

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

   if -6.4000000000000002e-12 < x < 0.71999999999999997

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(\frac{-1}{2} \cdot y - z\right)\right)} \]
   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 43.3

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

   5. Applied rewrites 43.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1}{2} \cdot y - z, y, 1\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 43.0%

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

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot z, y, 1\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 44.8%

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

Alternative 13: 61.5% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+217}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.4e+217) (* (- z) y) (+ 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.4e+217) {
		tmp = -z * y;
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-6.4d+217)) then
        tmp = -z * y
    else
        tmp = 1.0d0 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.4e+217) {
		tmp = -z * y;
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.4e+217:
		tmp = -z * y
	else:
		tmp = 1.0 + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.4e+217)
		tmp = Float64(Float64(-z) * y);
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.4e+217)
		tmp = -z * y;
	else
		tmp = 1.0 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.4e+217], N[((-z) * y), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4000000000000001e217

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(\frac{-1}{2} \cdot y - z\right)\right)} \]
   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 62.7

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

   5. Applied rewrites 62.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.7%

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

   if -6.4000000000000001e217 < 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

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

      1. lower-+.f64 61.9

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

   5. Applied rewrites 61.9%

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

Alternative 14: 61.1% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(1.0 + x), $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. lower-+.f64 58.4

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

5. Applied rewrites 58.4%

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

Alternative 15: 21.2% 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

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

   1. lower-+.f64 58.4

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

5. Applied rewrites 58.4%

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

6. Taylor expanded in x around 0

   \[\leadsto 1 \]
7. Step-by-step derivation

8. Applied rewrites 18.8%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024236 
(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))))