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

Percentage Accurate: 99.9% → 99.9%

Time: 7.7s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

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: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\cos y + x\right) - \sin y \cdot z\\ t_1 := x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{if}\;t\_0 \leq -40:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.9995:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -40.0) t_1 (if (<= t_0 0.9995) (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 <= -40.0) {
		tmp = t_1;
	} else if (t_0 <= 0.9995) {
		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 <= -40.0)
		tmp = t_1;
	elseif (t_0 <= 0.9995)
		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, -40.0], t$95$1, If[LessEqual[t$95$0, 0.9995], 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))) < -40 or 0.99950000000000006 < (-.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 71.1

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

   5. Applied rewrites 71.1%

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

   if -40 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.99950000000000006

   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 92.0

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

   5. Applied rewrites 92.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 86.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\cos y + x\right) - \sin y \cdot z \leq -40:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{elif}\;\left(\cos y + x\right) - \sin y \cdot z \leq 0.9995:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ t_1 := \left(1 + x\right) - t\_0\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-7}:\\ \;\;\;\;\cos y - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z)) (t_1 (- (+ 1.0 x) t_0)))
   (if (<= x -8.5e-16) t_1 (if (<= x 1.65e-7) (- (cos y) t_0) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double t_1 = (1.0 + x) - t_0;
	double tmp;
	if (x <= -8.5e-16) {
		tmp = t_1;
	} else if (x <= 1.65e-7) {
		tmp = cos(y) - t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sin(y) * z
    t_1 = (1.0d0 + x) - t_0
    if (x <= (-8.5d-16)) then
        tmp = t_1
    else if (x <= 1.65d-7) then
        tmp = cos(y) - t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * z;
	double t_1 = (1.0 + x) - t_0;
	double tmp;
	if (x <= -8.5e-16) {
		tmp = t_1;
	} else if (x <= 1.65e-7) {
		tmp = Math.cos(y) - t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * z
	t_1 = (1.0 + x) - t_0
	tmp = 0
	if x <= -8.5e-16:
		tmp = t_1
	elif x <= 1.65e-7:
		tmp = math.cos(y) - t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	t_1 = Float64(Float64(1.0 + x) - t_0)
	tmp = 0.0
	if (x <= -8.5e-16)
		tmp = t_1;
	elseif (x <= 1.65e-7)
		tmp = Float64(cos(y) - t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * z;
	t_1 = (1.0 + x) - t_0;
	tmp = 0.0;
	if (x <= -8.5e-16)
		tmp = t_1;
	elseif (x <= 1.65e-7)
		tmp = cos(y) - t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 + x), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[x, -8.5e-16], t$95$1, If[LessEqual[x, 1.65e-7], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000001e-16 or 1.6500000000000001e-7 < 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

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

   5. Applied rewrites 98.8%

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

   if -8.5000000000000001e-16 < x < 1.6500000000000001e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-cos.f64 99.5

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

   5. Applied rewrites 99.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-7}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + x\right) - \sin y \cdot z\\ \mathbf{if}\;z \leq -12:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ 1.0 x) (* (sin y) z))))
   (if (<= z -12.0) t_0 (if (<= z 1.05e-10) (+ (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 <= -12.0) {
		tmp = t_0;
	} else if (z <= 1.05e-10) {
		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 <= (-12.0d0)) then
        tmp = t_0
    else if (z <= 1.05d-10) 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 <= -12.0) {
		tmp = t_0;
	} else if (z <= 1.05e-10) {
		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 <= -12.0:
		tmp = t_0
	elif z <= 1.05e-10:
		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 <= -12.0)
		tmp = t_0;
	elseif (z <= 1.05e-10)
		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 <= -12.0)
		tmp = t_0;
	elseif (z <= 1.05e-10)
		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, -12.0], t$95$0, If[LessEqual[z, 1.05e-10], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -12 or 1.05e-10 < 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 99.5%

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

   if -12 < z < 1.05e-10

   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 98.1

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

   5. Applied rewrites 98.1%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot \sin y\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+117}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+47}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) (sin y))))
   (if (<= z -3.1e+117) t_0 (if (<= z 6.8e+47) (+ (cos y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -z * sin(y);
	double tmp;
	if (z <= -3.1e+117) {
		tmp = t_0;
	} else if (z <= 6.8e+47) {
		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 <= (-3.1d+117)) then
        tmp = t_0
    else if (z <= 6.8d+47) 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 <= -3.1e+117) {
		tmp = t_0;
	} else if (z <= 6.8e+47) {
		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 <= -3.1e+117:
		tmp = t_0
	elif z <= 6.8e+47:
		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 <= -3.1e+117)
		tmp = t_0;
	elseif (z <= 6.8e+47)
		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 <= -3.1e+117)
		tmp = t_0;
	elseif (z <= 6.8e+47)
		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, -3.1e+117], t$95$0, If[LessEqual[z, 6.8e+47], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999975e117 or 6.7999999999999996e47 < 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

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

      5. lower-sin.f64 65.3

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

   5. Applied rewrites 65.3%

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

   if -3.09999999999999975e117 < z < 6.7999999999999996e47

   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 94.3

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

   5. Applied rewrites 94.3%

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

Alternative 6: 80.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y + x\\ \mathbf{if}\;y \leq -950:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.9:\\ \;\;\;\;\left(1 + x\right) - \mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (cos y) x)))
   (if (<= y -950.0)
     t_0
     (if (<= y 0.9)
       (-
        (+ 1.0 x)
        (*
         (fma
          (* (fma 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 <= -950.0) {
		tmp = t_0;
	} else if (y <= 0.9) {
		tmp = (1.0 + x) - (fma((fma(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 <= -950.0)
		tmp = t_0;
	elseif (y <= 0.9)
		tmp = Float64(Float64(1.0 + x) - Float64(fma(Float64(fma(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, -950.0], t$95$0, If[LessEqual[y, 0.9], N[(N[(1.0 + x), $MachinePrecision] - N[(N[(N[(N[(0.008333333333333333 * 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 < -950 or 0.900000000000000022 < 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 61.7

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

   5. Applied rewrites 61.7%

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

   if -950 < y < 0.900000000000000022

   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

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

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

   8. Applied rewrites 99.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -950:\\ \;\;\;\;\cos y + x\\ \mathbf{elif}\;y \leq 0.9:\\ \;\;\;\;\left(1 + x\right) - \mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.5% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+24}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 3.15:\\ \;\;\;\;\left(1 + x\right) - \mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+24)
   (+ 1.0 x)
   (if (<= y 3.15)
     (-
      (+ 1.0 x)
      (*
       (fma
        (* (fma 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 <= -1.25e+24) {
		tmp = 1.0 + x;
	} else if (y <= 3.15) {
		tmp = (1.0 + x) - (fma((fma(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 <= -1.25e+24)
		tmp = Float64(1.0 + x);
	elseif (y <= 3.15)
		tmp = Float64(Float64(1.0 + x) - Float64(fma(Float64(fma(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, -1.25e+24], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 3.15], N[(N[(1.0 + x), $MachinePrecision] - N[(N[(N[(N[(0.008333333333333333 * 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 < -1.25000000000000011e24 or 3.14999999999999991 < 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 42.6

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

   5. Applied rewrites 42.6%

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

   if -1.25000000000000011e24 < y < 3.14999999999999991

   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 99.4%

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

   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

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

   8. Applied rewrites 97.3%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+24}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 3.15:\\ \;\;\;\;\left(1 + x\right) - \mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.6% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 11:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z \cdot y, -0.5\right) \cdot y - z, y, 1 + x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.6)
   (+ 1.0 x)
   (if (<= y 11.0)
     (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 <= -4.6) {
		tmp = 1.0 + x;
	} else if (y <= 11.0) {
		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 <= -4.6)
		tmp = Float64(1.0 + x);
	elseif (y <= 11.0)
		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, -4.6], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 11.0], 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 < -4.5999999999999996 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 42.4

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

   5. Applied rewrites 42.4%

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

   if -4.5999999999999996 < 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

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)} \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

Alternative 9: 69.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+44}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 3.15:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e+44)
   (+ 1.0 x)
   (if (<= y 3.15) (- x (fma z y -1.0)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+44) {
		tmp = 1.0 + x;
	} else if (y <= 3.15) {
		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 <= -5.5e+44)
		tmp = Float64(1.0 + x);
	elseif (y <= 3.15)
		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, -5.5e+44], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 3.15], N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000001e44 or 3.14999999999999991 < 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 42.9

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

   5. Applied rewrites 42.9%

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

   if -5.5000000000000001e44 < y < 3.14999999999999991

   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 96.4

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

   5. Applied rewrites 96.4%

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

Alternative 10: 61.9% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+272}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.26e+272) (* (- z) y) (+ 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.26e+272) {
		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 <= (-1.26d+272)) 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 <= -1.26e+272) {
		tmp = -z * y;
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.26e+272:
		tmp = -z * y
	else:
		tmp = 1.0 + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.26e+272)
		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 <= -1.26e+272)
		tmp = -z * y;
	else
		tmp = 1.0 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.26e+272], N[((-z) * y), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.26e272

   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 61.2

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

   5. Applied rewrites 61.2%

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

   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 52.8%

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

   if -1.26e272 < 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 62.2

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

   5. Applied rewrites 62.2%

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

Alternative 11: 61.3% 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 60.0

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

5. Applied rewrites 60.0%

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

Alternative 12: 21.8% 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 60.0

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

5. Applied rewrites 60.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 20.0%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024276 
(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))))