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

Percentage Accurate: 99.9% → 99.9%

Time: 11.0s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 98.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ t_1 := z \cdot \sin y\\ t_2 := t\_0 - t\_1\\ t_3 := x - t\_1\\ \mathbf{if}\;t\_2 \leq -100000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 40000000000000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y)))
        (t_1 (* z (sin y)))
        (t_2 (- t_0 t_1))
        (t_3 (- x t_1)))
   (if (<= t_2 -100000000000.0) t_3 (if (<= t_2 40000000000000.0) t_0 t_3))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double t_1 = z * sin(y);
	double t_2 = t_0 - t_1;
	double t_3 = x - t_1;
	double tmp;
	if (t_2 <= -100000000000.0) {
		tmp = t_3;
	} else if (t_2 <= 40000000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x + cos(y)
    t_1 = z * sin(y)
    t_2 = t_0 - t_1
    t_3 = x - t_1
    if (t_2 <= (-100000000000.0d0)) then
        tmp = t_3
    else if (t_2 <= 40000000000000.0d0) then
        tmp = t_0
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.cos(y);
	double t_1 = z * Math.sin(y);
	double t_2 = t_0 - t_1;
	double t_3 = x - t_1;
	double tmp;
	if (t_2 <= -100000000000.0) {
		tmp = t_3;
	} else if (t_2 <= 40000000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	t_1 = z * math.sin(y)
	t_2 = t_0 - t_1
	t_3 = x - t_1
	tmp = 0
	if t_2 <= -100000000000.0:
		tmp = t_3
	elif t_2 <= 40000000000000.0:
		tmp = t_0
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	t_1 = Float64(z * sin(y))
	t_2 = Float64(t_0 - t_1)
	t_3 = Float64(x - t_1)
	tmp = 0.0
	if (t_2 <= -100000000000.0)
		tmp = t_3;
	elseif (t_2 <= 40000000000000.0)
		tmp = t_0;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	t_1 = z * sin(y);
	t_2 = t_0 - t_1;
	t_3 = x - t_1;
	tmp = 0.0;
	if (t_2 <= -100000000000.0)
		tmp = t_3;
	elseif (t_2 <= 40000000000000.0)
		tmp = t_0;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -100000000000.0], t$95$3, If[LessEqual[t$95$2, 40000000000000.0], t$95$0, t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -1e11 or 4e13 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 99.8%

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

   if -1e11 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 4e13

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 98.2

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

   5. Simplified 98.2%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - z \cdot \sin y \leq -100000000000:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{elif}\;\left(x + \cos y\right) - z \cdot \sin y \leq 40000000000000:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+181}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+66}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -3.6e+181) t_0 (if (<= z 8e+66) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -3.6e+181) {
		tmp = t_0;
	} else if (z <= 8e+66) {
		tmp = x + cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(y) * -z
    if (z <= (-3.6d+181)) then
        tmp = t_0
    else if (z <= 8d+66) then
        tmp = x + cos(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double tmp;
	if (z <= -3.6e+181) {
		tmp = t_0;
	} else if (z <= 8e+66) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -3.6e+181:
		tmp = t_0
	elif z <= 8e+66:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -3.6e+181)
		tmp = t_0;
	elseif (z <= 8e+66)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -3.6e+181)
		tmp = t_0;
	elseif (z <= 8e+66)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -3.6e+181], t$95$0, If[LessEqual[z, 8e+66], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999985e181 or 7.99999999999999956e66 < 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. neg-lowering-neg.f64 N/A

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

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

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

      4. sin-lowering-sin.f64 73.0

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

   5. Simplified 73.0%

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

   if -3.59999999999999985e181 < z < 7.99999999999999956e66

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 90.7

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

   5. Simplified 90.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+181}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+66}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -0.023:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 19000:\\ \;\;\;\;1 + \mathsf{fma}\left(y, -z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (<= y -0.023) t_0 (if (<= y 19000.0) (+ 1.0 (fma y (- z) x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if (y <= -0.023) {
		tmp = t_0;
	} else if (y <= 19000.0) {
		tmp = 1.0 + fma(y, -z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if (y <= -0.023)
		tmp = t_0;
	elseif (y <= 19000.0)
		tmp = Float64(1.0 + fma(y, Float64(-z), x));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.023], t$95$0, If[LessEqual[y, 19000.0], N[(1.0 + N[(y * (-z) + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.023 or 19000 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

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

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

      3. cos-lowering-cos.f64 63.9

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

   5. Simplified 63.9%

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

   if -0.023 < y < 19000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. sub-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. neg-lowering-neg.f64 99.1

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

   5. Simplified 99.1%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 99.2

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

   8. Simplified 99.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.023:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq 19000:\\ \;\;\;\;1 + \mathsf{fma}\left(y, -z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.3% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+44}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+71}:\\ \;\;\;\;1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, y \cdot \left(z \cdot 0.16666666666666666\right), -z\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+44)
   (+ x 1.0)
   (if (<= y 6e+71)
     (+ 1.0 (fma y (fma y (* y (* z 0.16666666666666666)) (- z)) x))
     (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+44) {
		tmp = x + 1.0;
	} else if (y <= 6e+71) {
		tmp = 1.0 + fma(y, fma(y, (y * (z * 0.16666666666666666)), -z), x);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+44)
		tmp = Float64(x + 1.0);
	elseif (y <= 6e+71)
		tmp = Float64(1.0 + fma(y, fma(y, Float64(y * Float64(z * 0.16666666666666666)), Float64(-z)), x));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+44], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 6e+71], N[(1.0 + N[(y * N[(y * N[(y * N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] + (-z)), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000018e44 or 6.00000000000000025e71 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 43.2

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

   5. Simplified 43.2%

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

   if -6.50000000000000018e44 < y < 6.00000000000000025e71

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. sub-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. neg-lowering-neg.f64 84.5

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

   5. Simplified 84.5%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 86.3

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

   8. Simplified 86.3%

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

Alternative 6: 69.0% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -47:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 300000000:\\ \;\;\;\;\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -47.0)
   (+ x 1.0)
   (if (<= y 300000000.0) (fma y (- (* y -0.5) z) (+ x 1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -47.0) {
		tmp = x + 1.0;
	} else if (y <= 300000000.0) {
		tmp = fma(y, ((y * -0.5) - z), (x + 1.0));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -47.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 300000000.0)
		tmp = fma(y, Float64(Float64(y * -0.5) - z), Float64(x + 1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -47.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 300000000.0], N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -47 or 3e8 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 41.1

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

   5. Simplified 41.1%

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

   if -47 < y < 3e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 97.8

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

   5. Simplified 97.8%

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

Alternative 7: 68.9% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+40}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+60}:\\ \;\;\;\;1 + \mathsf{fma}\left(y, -z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e+40)
   (+ x 1.0)
   (if (<= y 2.7e+60) (+ 1.0 (fma y (- z) x)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+40) {
		tmp = x + 1.0;
	} else if (y <= 2.7e+60) {
		tmp = 1.0 + fma(y, -z, x);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e+40)
		tmp = Float64(x + 1.0);
	elseif (y <= 2.7e+60)
		tmp = Float64(1.0 + fma(y, Float64(-z), x));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e+40], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 2.7e+60], N[(1.0 + N[(y * (-z) + x), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999999e40 or 2.6999999999999999e60 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 41.5

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

   5. Simplified 41.5%

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

   if -3.4999999999999999e40 < y < 2.6999999999999999e60

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. sub-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. neg-lowering-neg.f64 87.4

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

   5. Simplified 87.4%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 89.3

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

   8. Simplified 89.3%

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

Alternative 8: 68.9% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+40}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+60}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.4e+40)
   (+ x 1.0)
   (if (<= y 2.7e+60) (- x (fma y z -1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.4e+40) {
		tmp = x + 1.0;
	} else if (y <= 2.7e+60) {
		tmp = x - fma(y, z, -1.0);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.4e+40)
		tmp = Float64(x + 1.0);
	elseif (y <= 2.7e+60)
		tmp = Float64(x - fma(y, z, -1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.4e+40], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 2.7e+60], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e40 or 2.6999999999999999e60 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 41.5

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

   5. Simplified 41.5%

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

   if -4.3999999999999998e40 < y < 2.6999999999999999e60

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 89.3

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

   5. Simplified 89.3%

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

Alternative 9: 64.1% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - y \cdot z\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+181}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+234}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (* y z))))
   (if (<= z -2.2e+181) t_0 (if (<= z 4.7e+234) (+ x 1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (y * z);
	double tmp;
	if (z <= -2.2e+181) {
		tmp = t_0;
	} else if (z <= 4.7e+234) {
		tmp = x + 1.0;
	} 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 - (y * z)
    if (z <= (-2.2d+181)) then
        tmp = t_0
    else if (z <= 4.7d+234) then
        tmp = x + 1.0d0
    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 - (y * z);
	double tmp;
	if (z <= -2.2e+181) {
		tmp = t_0;
	} else if (z <= 4.7e+234) {
		tmp = x + 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (y * z)
	tmp = 0
	if z <= -2.2e+181:
		tmp = t_0
	elif z <= 4.7e+234:
		tmp = x + 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (z <= -2.2e+181)
		tmp = t_0;
	elseif (z <= 4.7e+234)
		tmp = Float64(x + 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (y * z);
	tmp = 0.0;
	if (z <= -2.2e+181)
		tmp = t_0;
	elseif (z <= 4.7e+234)
		tmp = x + 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+181], t$95$0, If[LessEqual[z, 4.7e+234], N[(x + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e181 or 4.6999999999999999e234 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 52.8

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 50.6

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

   8. Simplified 50.6%

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

   if -2.2000000000000001e181 < z < 4.6999999999999999e234

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 66.8

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

   5. Simplified 66.8%

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

Alternative 10: 65.8% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-5}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-54}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4e-5) (+ x 1.0) (if (<= x 1.25e-54) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4e-5) {
		tmp = x + 1.0;
	} else if (x <= 1.25e-54) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4d-5)) then
        tmp = x + 1.0d0
    else if (x <= 1.25d-54) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4e-5) {
		tmp = x + 1.0;
	} else if (x <= 1.25e-54) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4e-5:
		tmp = x + 1.0
	elif x <= 1.25e-54:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4e-5)
		tmp = Float64(x + 1.0);
	elseif (x <= 1.25e-54)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4e-5)
		tmp = x + 1.0;
	elseif (x <= 1.25e-54)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4e-5], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 1.25e-54], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000033e-5 or 1.25000000000000004e-54 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 76.6

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

   5. Simplified 76.6%

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

   if -4.00000000000000033e-5 < x < 1.25000000000000004e-54

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 45.9

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

   5. Simplified 45.9%

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

   6. Taylor expanded in x around 0

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

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

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

      2. *-lowering-*.f64 45.9

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

   8. Simplified 45.9%

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

Alternative 11: 61.5% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+196}:\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z -6e+196) (- (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6e+196) {
		tmp = -(y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-6d+196)) then
        tmp = -(y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6e+196) {
		tmp = -(y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6e+196:
		tmp = -(y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6e+196)
		tmp = Float64(-Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6e+196)
		tmp = -(y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6e+196], (-N[(y * z), $MachinePrecision]), N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999997e196

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 50.5

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

   5. Simplified 50.5%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

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

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

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

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

      4. neg-lowering-neg.f64 45.4

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

   8. Simplified 45.4%

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

   if -5.9999999999999997e196 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 62.7

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

   5. Simplified 62.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+196}:\\ \;\;\;\;-y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.1% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -150:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -150.0) x (if (<= x 1.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -150.0) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-150.0d0)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -150.0) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -150.0:
		tmp = x
	elif x <= 1.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -150.0)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -150.0)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -150.0], x, If[LessEqual[x, 1.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -150 or 1 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 78.5%

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

   if -150 < x < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 45.6

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

   5. Simplified 45.6%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 33.7%

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

   9. Taylor expanded in x around 0

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

   11. Simplified 32.3%

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

Alternative 13: 60.8% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 57.7

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

5. Simplified 57.7%

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

Alternative 14: 21.6% accurate, 212.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. unsub-neg N/A

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

   4. associate-+l- N/A

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

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

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

   6. sub-neg N/A

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

   7. metadata-eval N/A

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

   8. accelerator-lowering-fma.f64 61.3

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

5. Simplified 61.3%

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

6. Taylor expanded in y around 0

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

8. Simplified 57.7%

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

9. Taylor expanded in x around 0

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

11. Simplified 17.0%

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

Reproduce

herbie shell --seed 2024205 
(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))))