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

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 99.9

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. lower-+.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 81.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y + \left(x + \sin y\right)\\ \mathbf{if}\;t\_0 \leq -5000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t\_0 \leq -0.05:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-21}:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (cos y)) (+ x (sin y)))))
   (if (<= t_0 -5000000.0)
     (+ x z)
     (if (<= t_0 -0.05)
       (sin y)
       (if (<= t_0 5e-21) (+ (+ x y) z) (if (<= t_0 1.0) (sin y) (+ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * cos(y)) + (x + sin(y));
	double tmp;
	if (t_0 <= -5000000.0) {
		tmp = x + z;
	} else if (t_0 <= -0.05) {
		tmp = sin(y);
	} else if (t_0 <= 5e-21) {
		tmp = (x + y) + z;
	} else if (t_0 <= 1.0) {
		tmp = sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * cos(y)) + (x + sin(y))
    if (t_0 <= (-5000000.0d0)) then
        tmp = x + z
    else if (t_0 <= (-0.05d0)) then
        tmp = sin(y)
    else if (t_0 <= 5d-21) then
        tmp = (x + y) + z
    else if (t_0 <= 1.0d0) then
        tmp = sin(y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * Math.cos(y)) + (x + Math.sin(y));
	double tmp;
	if (t_0 <= -5000000.0) {
		tmp = x + z;
	} else if (t_0 <= -0.05) {
		tmp = Math.sin(y);
	} else if (t_0 <= 5e-21) {
		tmp = (x + y) + z;
	} else if (t_0 <= 1.0) {
		tmp = Math.sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * math.cos(y)) + (x + math.sin(y))
	tmp = 0
	if t_0 <= -5000000.0:
		tmp = x + z
	elif t_0 <= -0.05:
		tmp = math.sin(y)
	elif t_0 <= 5e-21:
		tmp = (x + y) + z
	elif t_0 <= 1.0:
		tmp = math.sin(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * cos(y)) + Float64(x + sin(y)))
	tmp = 0.0
	if (t_0 <= -5000000.0)
		tmp = Float64(x + z);
	elseif (t_0 <= -0.05)
		tmp = sin(y);
	elseif (t_0 <= 5e-21)
		tmp = Float64(Float64(x + y) + z);
	elseif (t_0 <= 1.0)
		tmp = sin(y);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * cos(y)) + (x + sin(y));
	tmp = 0.0;
	if (t_0 <= -5000000.0)
		tmp = x + z;
	elseif (t_0 <= -0.05)
		tmp = sin(y);
	elseif (t_0 <= 5e-21)
		tmp = (x + y) + z;
	elseif (t_0 <= 1.0)
		tmp = sin(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5000000.0], N[(x + z), $MachinePrecision], If[LessEqual[t$95$0, -0.05], N[Sin[y], $MachinePrecision], If[LessEqual[t$95$0, 5e-21], N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[Sin[y], $MachinePrecision], N[(x + z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -5e6 or 1 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 73.4

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

   5. Applied rewrites 73.4%

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

   if -5e6 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -0.050000000000000003 or 4.99999999999999973e-21 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-sin.f64 97.7

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.6%

      \[\leadsto \sin y \]

   if -0.050000000000000003 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 4.99999999999999973e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \cos y + \left(x + \sin y\right) \leq -5000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \cdot \cos y + \left(x + \sin y\right) \leq -0.05:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \cdot \cos y + \left(x + \sin y\right) \leq 5 \cdot 10^{-21}:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{elif}\;z \cdot \cos y + \left(x + \sin y\right) \leq 1:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y + \left(x + \sin y\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-45}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-111}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (cos y)) (+ x (sin y)))))
   (if (<= t_0 -1e-45) (+ x z) (if (<= t_0 2e-111) (+ x y) (+ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = (z * cos(y)) + (x + sin(y));
	double tmp;
	if (t_0 <= -1e-45) {
		tmp = x + z;
	} else if (t_0 <= 2e-111) {
		tmp = x + y;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * cos(y)) + (x + sin(y))
    if (t_0 <= (-1d-45)) then
        tmp = x + z
    else if (t_0 <= 2d-111) then
        tmp = x + y
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * Math.cos(y)) + (x + Math.sin(y));
	double tmp;
	if (t_0 <= -1e-45) {
		tmp = x + z;
	} else if (t_0 <= 2e-111) {
		tmp = x + y;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * math.cos(y)) + (x + math.sin(y))
	tmp = 0
	if t_0 <= -1e-45:
		tmp = x + z
	elif t_0 <= 2e-111:
		tmp = x + y
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * cos(y)) + Float64(x + sin(y)))
	tmp = 0.0
	if (t_0 <= -1e-45)
		tmp = Float64(x + z);
	elseif (t_0 <= 2e-111)
		tmp = Float64(x + y);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * cos(y)) + (x + sin(y));
	tmp = 0.0;
	if (t_0 <= -1e-45)
		tmp = x + z;
	elseif (t_0 <= 2e-111)
		tmp = x + y;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-45], N[(x + z), $MachinePrecision], If[LessEqual[t$95$0, 2e-111], N[(x + y), $MachinePrecision], N[(x + z), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -9.99999999999999984e-46 or 2.00000000000000018e-111 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 65.9

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

   5. Applied rewrites 65.9%

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

   if -9.99999999999999984e-46 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 2.00000000000000018e-111

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 87.2

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 87.2%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \cos y + \left(x + \sin y\right) \leq -1 \cdot 10^{-45}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \cdot \cos y + \left(x + \sin y\right) \leq 2 \cdot 10^{-111}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{z \cdot \cos y}{x} - -1\right) \cdot x\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- (/ (* z (cos y)) x) -1.0) x)))
   (if (<= x -1.8e-43) t_0 (if (<= x 1.9e-21) (fma (cos y) z (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (((z * cos(y)) / x) - -1.0) * x;
	double tmp;
	if (x <= -1.8e-43) {
		tmp = t_0;
	} else if (x <= 1.9e-21) {
		tmp = fma(cos(y), z, sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(z * cos(y)) / x) - -1.0) * x)
	tmp = 0.0
	if (x <= -1.8e-43)
		tmp = t_0;
	elseif (x <= 1.9e-21)
		tmp = fma(cos(y), z, sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -1.0), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.8e-43], t$95$0, If[LessEqual[x, 1.9e-21], N[(N[Cos[y], $MachinePrecision] * z + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e-43 or 1.8999999999999999e-21 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 69.2

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

   5. Applied rewrites 69.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 52.7%

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

   9. Taylor expanded in x around -inf

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

       1. associate-*r* N/A

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

       2. lower-*.f64 N/A

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

       3. mul-1-neg N/A

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

       4. lower-neg.f64 N/A

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

       5. sub-neg N/A

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

       6. metadata-eval N/A

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

       7. +-commutative N/A

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

       8. mul-1-neg N/A

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

       9. unsub-neg N/A

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

       10. lower--.f64 N/A

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

       11. lower-/.f64 N/A

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

       12. +-commutative N/A

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

       13. *-commutative N/A

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

       14. lower-fma.f64 N/A

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

       15. lower-cos.f64 N/A

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

       16. lower-sin.f64 99.8

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

   11. Applied rewrites 99.8%

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

   12. Taylor expanded in z around inf

       \[\leadsto \left(-x\right) \cdot \left(-1 - \frac{z \cdot \cos y}{x}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 98.5%

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

   if -1.7999999999999999e-43 < x < 1.8999999999999999e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-sin.f64 95.8

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

   5. Applied rewrites 95.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;\left(\frac{z \cdot \cos y}{x} - -1\right) \cdot x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z \cdot \cos y}{x} - -1\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-94}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+129}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -5.4e+17)
     t_0
     (if (<= z 2e-94) (+ x (sin y)) (if (<= z 3e+129) (+ x z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -5.4e+17) {
		tmp = t_0;
	} else if (z <= 2e-94) {
		tmp = x + sin(y);
	} else if (z <= 3e+129) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-5.4d+17)) then
        tmp = t_0
    else if (z <= 2d-94) then
        tmp = x + sin(y)
    else if (z <= 3d+129) then
        tmp = x + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -5.4e+17) {
		tmp = t_0;
	} else if (z <= 2e-94) {
		tmp = x + Math.sin(y);
	} else if (z <= 3e+129) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -5.4e+17:
		tmp = t_0
	elif z <= 2e-94:
		tmp = x + math.sin(y)
	elif z <= 3e+129:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -5.4e+17)
		tmp = t_0;
	elseif (z <= 2e-94)
		tmp = Float64(x + sin(y));
	elseif (z <= 3e+129)
		tmp = Float64(x + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -5.4e+17)
		tmp = t_0;
	elseif (z <= 2e-94)
		tmp = x + sin(y);
	elseif (z <= 3e+129)
		tmp = x + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+17], t$95$0, If[LessEqual[z, 2e-94], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+129], N[(x + z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4e17 or 3.0000000000000003e129 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if -5.4e17 < z < 1.9999999999999999e-94

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 94.2

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

   5. Applied rewrites 94.2%

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

   if 1.9999999999999999e-94 < z < 3.0000000000000003e129

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 80.0

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

   5. Applied rewrites 80.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-94}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+129}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+129}:\\ \;\;\;\;1 \cdot z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.95e+19)
     t_0
     (if (<= z 3e+129) (+ (* 1.0 z) (+ x (sin y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.95e+19) {
		tmp = t_0;
	} else if (z <= 3e+129) {
		tmp = (1.0 * z) + (x + sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1.95d+19)) then
        tmp = t_0
    else if (z <= 3d+129) then
        tmp = (1.0d0 * z) + (x + sin(y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -1.95e+19) {
		tmp = t_0;
	} else if (z <= 3e+129) {
		tmp = (1.0 * z) + (x + Math.sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.95e+19:
		tmp = t_0
	elif z <= 3e+129:
		tmp = (1.0 * z) + (x + math.sin(y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.95e+19)
		tmp = t_0;
	elseif (z <= 3e+129)
		tmp = Float64(Float64(1.0 * z) + Float64(x + sin(y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1.95e+19)
		tmp = t_0;
	elseif (z <= 3e+129)
		tmp = (1.0 * z) + (x + sin(y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+19], t$95$0, If[LessEqual[z, 3e+129], N[(N[(1.0 * z), $MachinePrecision] + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e19 or 3.0000000000000003e129 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 85.4

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

   5. Applied rewrites 85.4%

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

   if -1.95e19 < z < 3.0000000000000003e129

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 95.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+129}:\\ \;\;\;\;1 \cdot z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -48000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 25500:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -48000000.0) t_0 (if (<= y 25500.0) (+ (+ x y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -48000000.0) {
		tmp = t_0;
	} else if (y <= 25500.0) {
		tmp = (x + y) + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + sin(y)
    if (y <= (-48000000.0d0)) then
        tmp = t_0
    else if (y <= 25500.0d0) then
        tmp = (x + y) + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.sin(y);
	double tmp;
	if (y <= -48000000.0) {
		tmp = t_0;
	} else if (y <= 25500.0) {
		tmp = (x + y) + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.sin(y)
	tmp = 0
	if y <= -48000000.0:
		tmp = t_0
	elif y <= 25500.0:
		tmp = (x + y) + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (y <= -48000000.0)
		tmp = t_0;
	elseif (y <= 25500.0)
		tmp = Float64(Float64(x + y) + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + sin(y);
	tmp = 0.0;
	if (y <= -48000000.0)
		tmp = t_0;
	elseif (y <= 25500.0)
		tmp = (x + y) + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -48000000.0], t$95$0, If[LessEqual[y, 25500.0], N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e7 or 25500 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 58.1

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

   5. Applied rewrites 58.1%

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

   if -4.8e7 < y < 25500

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 97.3

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

   5. Applied rewrites 97.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -48000000:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq 25500:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.1% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -22000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 280:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z, 1\right), y, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -22000000.0)
   (+ x z)
   (if (<= y 280.0) (fma (fma (* -0.5 y) z 1.0) y (+ x z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -22000000.0) {
		tmp = x + z;
	} else if (y <= 280.0) {
		tmp = fma(fma((-0.5 * y), z, 1.0), y, (x + z));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -22000000.0)
		tmp = Float64(x + z);
	elseif (y <= 280.0)
		tmp = fma(fma(Float64(-0.5 * y), z, 1.0), y, Float64(x + z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -22000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 280.0], N[(N[(N[(-0.5 * y), $MachinePrecision] * z + 1.0), $MachinePrecision] * y + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e7 or 280 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 37.2

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

   5. Applied rewrites 37.2%

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

   if -2.2e7 < y < 280

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 99.3

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

   5. Applied rewrites 99.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -22000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 280:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z, 1\right), y, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.9% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -27000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -27000000.0) (+ x z) (if (<= y 1.3e+67) (+ (+ x y) z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -27000000.0) {
		tmp = x + z;
	} else if (y <= 1.3e+67) {
		tmp = (x + y) + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-27000000.0d0)) then
        tmp = x + z
    else if (y <= 1.3d+67) then
        tmp = (x + y) + z
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -27000000.0) {
		tmp = x + z;
	} else if (y <= 1.3e+67) {
		tmp = (x + y) + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -27000000.0:
		tmp = x + z
	elif y <= 1.3e+67:
		tmp = (x + y) + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -27000000.0)
		tmp = Float64(x + z);
	elseif (y <= 1.3e+67)
		tmp = Float64(Float64(x + y) + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -27000000.0)
		tmp = x + z;
	elseif (y <= 1.3e+67)
		tmp = (x + y) + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -27000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.3e+67], N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e7 or 1.3e67 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 36.2

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

   5. Applied rewrites 36.2%

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

   if -2.7e7 < y < 1.3e67

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 94.8

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

   5. Applied rewrites 94.8%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -27000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.9% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+149}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-22}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.7e+149) (+ x y) (if (<= x 1.5e-22) (+ z y) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e+149) {
		tmp = x + y;
	} else if (x <= 1.5e-22) {
		tmp = z + y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.7d+149)) then
        tmp = x + y
    else if (x <= 1.5d-22) then
        tmp = z + y
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e+149) {
		tmp = x + y;
	} else if (x <= 1.5e-22) {
		tmp = z + y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.7e+149:
		tmp = x + y
	elif x <= 1.5e-22:
		tmp = z + y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.7e+149)
		tmp = Float64(x + y);
	elseif (x <= 1.5e-22)
		tmp = Float64(z + y);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.7e+149)
		tmp = x + y;
	elseif (x <= 1.5e-22)
		tmp = z + y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.7e+149], N[(x + y), $MachinePrecision], If[LessEqual[x, 1.5e-22], N[(z + y), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6999999999999999e149 or 1.5e-22 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 79.1

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 64.4%

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

   if -1.6999999999999999e149 < x < 1.5e-22

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-sin.f64 87.3

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 41.3%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+149}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-22}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.4% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. lower-sin.f64 56.1

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

5. Applied rewrites 56.1%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 36.2%

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

9. Final simplification 36.2%

   \[\leadsto x + y \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024243 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))