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

Percentage Accurate: 99.9% → 99.9%

Time: 10.9s

Alternatives: 9

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

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

FPCore

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

C

double code(double x, double y, double z) {
	return (z * cos(y)) + (x + 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 = (z * cos(y)) + (x + sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + 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. Final simplification 99.9%

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

Alternative 2: 80.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y + \left(x + \sin y\right)\\ \mathbf{if}\;t\_0 \leq -5:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t\_0 \leq -0.15:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (cos y)) (+ x (sin y)))))
   (if (<= t_0 -5.0)
     (+ x z)
     (if (<= t_0 -0.15)
       (sin y)
       (if (<= t_0 2e-5) (+ y (+ x 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 <= -5.0) {
		tmp = x + z;
	} else if (t_0 <= -0.15) {
		tmp = sin(y);
	} else if (t_0 <= 2e-5) {
		tmp = y + (x + 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 <= (-5.0d0)) then
        tmp = x + z
    else if (t_0 <= (-0.15d0)) then
        tmp = sin(y)
    else if (t_0 <= 2d-5) then
        tmp = y + (x + 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 <= -5.0) {
		tmp = x + z;
	} else if (t_0 <= -0.15) {
		tmp = Math.sin(y);
	} else if (t_0 <= 2e-5) {
		tmp = y + (x + 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 <= -5.0:
		tmp = x + z
	elif t_0 <= -0.15:
		tmp = math.sin(y)
	elif t_0 <= 2e-5:
		tmp = y + (x + 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 <= -5.0)
		tmp = Float64(x + z);
	elseif (t_0 <= -0.15)
		tmp = sin(y);
	elseif (t_0 <= 2e-5)
		tmp = Float64(y + Float64(x + 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 <= -5.0)
		tmp = x + z;
	elseif (t_0 <= -0.15)
		tmp = sin(y);
	elseif (t_0 <= 2e-5)
		tmp = y + (x + 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, -5.0], N[(x + z), $MachinePrecision], If[LessEqual[t$95$0, -0.15], N[Sin[y], $MachinePrecision], If[LessEqual[t$95$0, 2e-5], N[(y + N[(x + z), $MachinePrecision]), $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))) < -5 or 1 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 76.6

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

   5. Simplified 76.6%

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

   if -5 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -0.149999999999999994 or 2.00000000000000016e-5 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 1

   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. +-lowering-+.f64 N/A

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

      3. sin-lowering-sin.f64 98.5

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x around 0

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

      1. sin-lowering-sin.f64 96.6

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

   8. Simplified 96.6%

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

   if -0.149999999999999994 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 2.00000000000000016e-5

   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. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 100.0

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

   5. Simplified 100.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \cos y + \left(x + \sin y\right) \leq -5:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \cdot \cos y + \left(x + \sin y\right) \leq -0.15:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \cdot \cos y + \left(x + \sin y\right) \leq 2 \cdot 10^{-5}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;z \cdot \cos y + \left(x + \sin y\right) \leq 1:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (cos y) z x)))
   (if (<= x -3.4e-5) t_0 (if (<= x 4.5e-20) (fma z (cos y) (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(cos(y), z, x);
	double tmp;
	if (x <= -3.4e-5) {
		tmp = t_0;
	} else if (x <= 4.5e-20) {
		tmp = fma(z, cos(y), sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(cos(y), z, x)
	tmp = 0.0
	if (x <= -3.4e-5)
		tmp = t_0;
	elseif (x <= 4.5e-20)
		tmp = fma(z, cos(y), sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[x, -3.4e-5], t$95$0, If[LessEqual[x, 4.5e-20], N[(z * N[Cos[y], $MachinePrecision] + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4e-5 or 4.5000000000000001e-20 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 99.9%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

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

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

      4. cos-lowering-cos.f64 99.9

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

   7. Applied egg-rr 99.9%

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

   if -3.4e-5 < x < 4.5000000000000001e-20

   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. accelerator-lowering-fma.f64 N/A

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

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

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

      4. sin-lowering-sin.f64 94.5

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

   5. Simplified 94.5%

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

Alternative 4: 95.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-18}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (cos y) z x)))
   (if (<= z -8.6e-9) t_0 (if (<= z 4.1e-18) (+ x (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(cos(y), z, x);
	double tmp;
	if (z <= -8.6e-9) {
		tmp = t_0;
	} else if (z <= 4.1e-18) {
		tmp = x + sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(cos(y), z, x)
	tmp = 0.0
	if (z <= -8.6e-9)
		tmp = t_0;
	elseif (z <= 4.1e-18)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[z, -8.6e-9], t$95$0, If[LessEqual[z, 4.1e-18], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.59999999999999925e-9 or 4.0999999999999998e-18 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 99.9%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

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

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

      4. cos-lowering-cos.f64 99.9

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

   7. Applied egg-rr 99.9%

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

   if -8.59999999999999925e-9 < z < 4.0999999999999998e-18

   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. +-lowering-+.f64 N/A

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

      3. sin-lowering-sin.f64 94.7

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

   5. Simplified 94.7%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-18}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+23}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.1e+30) t_0 (if (<= z 2.95e+23) (+ x (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.1e+30) {
		tmp = t_0;
	} else if (z <= 2.95e+23) {
		tmp = 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 <= (-2.1d+30)) then
        tmp = t_0
    else if (z <= 2.95d+23) then
        tmp = 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 <= -2.1e+30) {
		tmp = t_0;
	} else if (z <= 2.95e+23) {
		tmp = 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 <= -2.1e+30:
		tmp = t_0
	elif z <= 2.95e+23:
		tmp = 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 <= -2.1e+30)
		tmp = t_0;
	elseif (z <= 2.95e+23)
		tmp = 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 <= -2.1e+30)
		tmp = t_0;
	elseif (z <= 2.95e+23)
		tmp = 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, -2.1e+30], t$95$0, If[LessEqual[z, 2.95e+23], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e30 or 2.94999999999999994e23 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

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

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

      2. cos-lowering-cos.f64 78.5

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

   5. Simplified 78.5%

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

   if -2.1e30 < z < 2.94999999999999994e23

   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. +-lowering-+.f64 N/A

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

      3. sin-lowering-sin.f64 91.1

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

   5. Simplified 91.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+23}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -0.0295:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 19000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot -0.16666666666666666, y \cdot y, y\right) + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -0.0295)
     t_0
     (if (<= y 19000.0)
       (+ (fma (* y -0.16666666666666666) (* y y) y) (+ x z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -0.0295) {
		tmp = t_0;
	} else if (y <= 19000.0) {
		tmp = fma((y * -0.16666666666666666), (y * y), y) + (x + z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (y <= -0.0295)
		tmp = t_0;
	elseif (y <= 19000.0)
		tmp = Float64(fma(Float64(y * -0.16666666666666666), Float64(y * y), y) + Float64(x + z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0295], t$95$0, If[LessEqual[y, 19000.0], N[(N[(N[(y * -0.16666666666666666), $MachinePrecision] * N[(y * y), $MachinePrecision] + y), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.029499999999999998 or 19000 < y

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   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. +-lowering-+.f64 N/A

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

      3. sin-lowering-sin.f64 64.1

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

   5. Simplified 64.1%

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

   if -0.029499999999999998 < y < 19000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

      4. +-commutative N/A

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

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

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 99.1

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

   5. Simplified 99.1%

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

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

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

      4. distribute-rgt-in N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-lft-identity N/A

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

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

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

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

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

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

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

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

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

      12. +-lowering-+.f64 99.1

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

   7. Applied egg-rr 99.1%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 99.3

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

   10. Simplified 99.3%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0295:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq 19000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot -0.16666666666666666, y \cdot y, y\right) + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.1% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-13}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.65e-84) x (if (<= x 2.5e-13) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.65e-84) {
		tmp = x;
	} else if (x <= 2.5e-13) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.65d-84)) then
        tmp = x
    else if (x <= 2.5d-13) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.65e-84) {
		tmp = x;
	} else if (x <= 2.5e-13) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.65e-84:
		tmp = x
	elif x <= 2.5e-13:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.65e-84)
		tmp = x;
	elseif (x <= 2.5e-13)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.65e-84)
		tmp = x;
	elseif (x <= 2.5e-13)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.65e-84], x, If[LessEqual[x, 2.5e-13], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.64999999999999992e-84 or 2.49999999999999995e-13 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 68.9%

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

   if -1.64999999999999992e-84 < x < 2.49999999999999995e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 42.9

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

   5. Simplified 42.9%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 41.3%

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

Alternative 8: 64.8% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 66.2

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

5. Simplified 66.2%

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

6. Final simplification 66.2%

   \[\leadsto x + z \]
7. Add Preprocessing

Alternative 9: 41.5% accurate, 212.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf

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

5. Simplified 43.2%

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

Reproduce

herbie shell --seed 2024205 
(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))))