Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.7% → 96.1%

Time: 9.9s

Alternatives: 11

Speedup: 0.5×

• 32.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + (y * z)) + (t * a)) + ((a * z) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + (y * z)) + (t * a)) + ((a * z) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + (y * z)) + (t * a)) + ((a * z) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + (y * z)) + (t * a)) + ((a * z) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + (y * z)) + (t * a)) + ((a * z) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + (y * z)) + (t * a)) + ((a * z) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{\mathsf{fma}\left(a, \mathsf{fma}\left(b, z, t\right), \mathsf{fma}\left(z, y, x\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* b (* a z)) (+ (* a t) (+ (* z y) x)))))
   (if (<= t_1 5e+275) t_1 (/ 1.0 (/ 1.0 (fma a (fma b z t) (fma z y x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * (a * z)) + ((a * t) + ((z * y) + x));
	double tmp;
	if (t_1 <= 5e+275) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (1.0 / fma(a, fma(b, z, t), fma(z, y, x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(a * z)) + Float64(Float64(a * t) + Float64(Float64(z * y) + x)))
	tmp = 0.0
	if (t_1 <= 5e+275)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(1.0 / fma(a, fma(b, z, t), fma(z, y, x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+275], t$95$1, N[(1.0 / N[(1.0 / N[(a * N[(b * z + t), $MachinePrecision] + N[(z * y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 5.0000000000000003e275

   1. Initial program 98.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   if 5.0000000000000003e275 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 65.8%

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

      1. lift-+.f64 N/A

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

      2. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x + y \cdot z\right) + t \cdot a\right)}^{3} + {\left(\left(a \cdot z\right) \cdot b\right)}^{3}}{\left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(\left(a \cdot z\right) \cdot b\right) \cdot \left(\left(a \cdot z\right) \cdot b\right) - \left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(a \cdot z\right) \cdot b\right)\right)}} \]

      3. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(\left(a \cdot z\right) \cdot b\right) \cdot \left(\left(a \cdot z\right) \cdot b\right) - \left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(a \cdot z\right) \cdot b\right)\right)}{{\left(\left(x + y \cdot z\right) + t \cdot a\right)}^{3} + {\left(\left(a \cdot z\right) \cdot b\right)}^{3}}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(\left(a \cdot z\right) \cdot b\right) \cdot \left(\left(a \cdot z\right) \cdot b\right) - \left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(a \cdot z\right) \cdot b\right)\right)}{{\left(\left(x + y \cdot z\right) + t \cdot a\right)}^{3} + {\left(\left(a \cdot z\right) \cdot b\right)}^{3}}}} \]

      5. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x + y \cdot z\right) + t \cdot a\right)}^{3} + {\left(\left(a \cdot z\right) \cdot b\right)}^{3}}{\left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(\left(a \cdot z\right) \cdot b\right) \cdot \left(\left(a \cdot z\right) \cdot b\right) - \left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(a \cdot z\right) \cdot b\right)\right)}}}} \]

   4. Applied rewrites 93.4%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{\mathsf{fma}\left(a, \mathsf{fma}\left(b, z, t\right), \mathsf{fma}\left(z, y, x\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{1}{\mathsf{fma}\left(b, z, t\right)}}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* b (* a z)) (+ (* a t) (+ (* z y) x)))))
   (if (<= t_1 INFINITY) t_1 (/ 1.0 (/ (/ 1.0 (fma b z t)) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * (a * z)) + ((a * t) + ((z * y) + x));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((1.0 / fma(b, z, t)) / a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(a * z)) + Float64(Float64(a * t) + Float64(Float64(z * y) + x)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(Float64(1.0 / fma(b, z, t)) / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(1.0 / N[(N[(1.0 / N[(b * z + t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < +inf.0

   1. Initial program 97.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 0.0%

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

      1. lift-+.f64 N/A

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

      2. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(\left(x + y \cdot z\right) + t \cdot a\right)}^{3} + {\left(\left(a \cdot z\right) \cdot b\right)}^{3}}{\left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(\left(a \cdot z\right) \cdot b\right) \cdot \left(\left(a \cdot z\right) \cdot b\right) - \left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(a \cdot z\right) \cdot b\right)\right)}} \]

      3. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(\left(a \cdot z\right) \cdot b\right) \cdot \left(\left(a \cdot z\right) \cdot b\right) - \left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(a \cdot z\right) \cdot b\right)\right)}{{\left(\left(x + y \cdot z\right) + t \cdot a\right)}^{3} + {\left(\left(a \cdot z\right) \cdot b\right)}^{3}}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(\left(a \cdot z\right) \cdot b\right) \cdot \left(\left(a \cdot z\right) \cdot b\right) - \left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(a \cdot z\right) \cdot b\right)\right)}{{\left(\left(x + y \cdot z\right) + t \cdot a\right)}^{3} + {\left(\left(a \cdot z\right) \cdot b\right)}^{3}}}} \]

      5. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(\left(x + y \cdot z\right) + t \cdot a\right)}^{3} + {\left(\left(a \cdot z\right) \cdot b\right)}^{3}}{\left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(\left(a \cdot z\right) \cdot b\right) \cdot \left(\left(a \cdot z\right) \cdot b\right) - \left(\left(x + y \cdot z\right) + t \cdot a\right) \cdot \left(\left(a \cdot z\right) \cdot b\right)\right)}}}} \]

   4. Applied rewrites 77.8%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(a, \mathsf{fma}\left(b, z, t\right), \mathsf{fma}\left(z, y, x\right)\right)}}} \]

   5. Taylor expanded in a around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{a \cdot \left(t + b \cdot z\right)}}} \]
   6. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{t + b \cdot z}}{a}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{t + b \cdot z}}{a}}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{\frac{1}{t + b \cdot z}}}{a}} \]

      4. +-commutative N/A

         \[\leadsto \frac{1}{\frac{\frac{1}{\color{blue}{b \cdot z + t}}}{a}} \]

      5. lower-fma.f64 72.2

         \[\leadsto \frac{1}{\frac{\frac{1}{\color{blue}{\mathsf{fma}\left(b, z, t\right)}}}{a}} \]

   7. Applied rewrites 72.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{\mathsf{fma}\left(b, z, t\right)}}{a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right) \leq \infty:\\ \;\;\;\;b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{1}{\mathsf{fma}\left(b, z, t\right)}}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* b (* a z)) (+ (* a t) (+ (* z y) x)))))
   (if (<= t_1 INFINITY) t_1 (fma (fma b z t) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * (a * z)) + ((a * t) + ((z * y) + x));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(fma(b, z, t), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(a * z)) + Float64(Float64(a * t) + Float64(Float64(z * y) + x)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(fma(b, z, t), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(b * z + t), $MachinePrecision] * a + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < +inf.0

   1. Initial program 97.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 0.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. distribute-lft-in N/A

         \[\leadsto x + \color{blue}{a \cdot \left(t + b \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot \left(t + b \cdot z\right) + x} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(t + b \cdot z\right) \cdot a} + x \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t + b \cdot z, a, x\right)} \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot z + t}, a, x\right) \]

      6. lower-fma.f64 72.2

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(b, z, t\right)}, a, x\right) \]

   5. Applied rewrites 72.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right) \leq \infty:\\ \;\;\;\;b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, z, t\right) \cdot a\\ \mathbf{if}\;a \leq -120000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-112}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (fma b z t) a)))
   (if (<= a -120000.0)
     t_1
     (if (<= a 2.6e-112) (fma z y x) (if (<= a 2.8e+48) (fma t a x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, z, t) * a;
	double tmp;
	if (a <= -120000.0) {
		tmp = t_1;
	} else if (a <= 2.6e-112) {
		tmp = fma(z, y, x);
	} else if (a <= 2.8e+48) {
		tmp = fma(t, a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(b, z, t) * a)
	tmp = 0.0
	if (a <= -120000.0)
		tmp = t_1;
	elseif (a <= 2.6e-112)
		tmp = fma(z, y, x);
	elseif (a <= 2.8e+48)
		tmp = fma(t, a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * z + t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -120000.0], t$95$1, If[LessEqual[a, 2.6e-112], N[(z * y + x), $MachinePrecision], If[LessEqual[a, 2.8e+48], N[(t * a + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2e5 or 2.80000000000000012e48 < a

   1. Initial program 81.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(t + b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(t + b \cdot z\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(t + b \cdot z\right) \cdot a} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot z + t\right)} \cdot a \]

      4. lower-fma.f64 76.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, z, t\right)} \cdot a \]

   5. Applied rewrites 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, z, t\right) \cdot a} \]

   if -1.2e5 < a < 2.59999999999999992e-112

   1. Initial program 100.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 84.7

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

   5. Applied rewrites 84.7%

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

   if 2.59999999999999992e-112 < a < 2.80000000000000012e48

   1. Initial program 99.9%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot t + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot a} + x \]

      3. lower-fma.f64 80.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]

   5. Applied rewrites 80.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 86.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, y, \mathsf{fma}\left(t, a, x\right)\right)\\ \mathbf{if}\;y \leq -3.65 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z y (fma t a x))))
   (if (<= y -3.65e-37) t_1 (if (<= y 2.75e+20) (fma (fma b z t) a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, y, fma(t, a, x));
	double tmp;
	if (y <= -3.65e-37) {
		tmp = t_1;
	} else if (y <= 2.75e+20) {
		tmp = fma(fma(b, z, t), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, y, fma(t, a, x))
	tmp = 0.0
	if (y <= -3.65e-37)
		tmp = t_1;
	elseif (y <= 2.75e+20)
		tmp = fma(fma(b, z, t), a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * y + N[(t * a + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.65e-37], t$95$1, If[LessEqual[y, 2.75e+20], N[(N[(b * z + t), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6499999999999998e-37 or 2.75e20 < y

   1. Initial program 88.7%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 91.3

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

   5. Applied rewrites 91.3%

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

   if -3.6499999999999998e-37 < y < 2.75e20

   1. Initial program 92.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. distribute-lft-in N/A

         \[\leadsto x + \color{blue}{a \cdot \left(t + b \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot \left(t + b \cdot z\right) + x} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(t + b \cdot z\right) \cdot a} + x \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t + b \cdot z, a, x\right)} \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot z + t}, a, x\right) \]

      6. lower-fma.f64 93.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(b, z, t\right)}, a, x\right) \]

   5. Applied rewrites 93.7%

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

Alternative 6: 82.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, y\right) \cdot z\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(z, y, \mathsf{fma}\left(t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (fma b a y) z)))
   (if (<= z -1.85e+174) t_1 (if (<= z 1.45e+53) (fma z y (fma t a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, a, y) * z;
	double tmp;
	if (z <= -1.85e+174) {
		tmp = t_1;
	} else if (z <= 1.45e+53) {
		tmp = fma(z, y, fma(t, a, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(b, a, y) * z)
	tmp = 0.0
	if (z <= -1.85e+174)
		tmp = t_1;
	elseif (z <= 1.45e+53)
		tmp = fma(z, y, fma(t, a, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * a + y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.85e+174], t$95$1, If[LessEqual[z, 1.45e+53], N[(z * y + N[(t * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e174 or 1.4500000000000001e53 < z

   1. Initial program 78.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y + a \cdot b\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y + a \cdot b\right) \cdot z} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b + y\right)} \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{b \cdot a} + y\right) \cdot z \]

      5. lower-fma.f64 83.3

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, y\right)} \cdot z \]

   5. Applied rewrites 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, y\right) \cdot z} \]

   if -1.8500000000000001e174 < z < 1.4500000000000001e53

   1. Initial program 97.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 88.8

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

   5. Applied rewrites 88.8%

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

Alternative 7: 74.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, y\right) \cdot z\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (fma b a y) z)))
   (if (<= z -2.7e+71) t_1 (if (<= z 1.7e-55) (fma t a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, a, y) * z;
	double tmp;
	if (z <= -2.7e+71) {
		tmp = t_1;
	} else if (z <= 1.7e-55) {
		tmp = fma(t, a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(b, a, y) * z)
	tmp = 0.0
	if (z <= -2.7e+71)
		tmp = t_1;
	elseif (z <= 1.7e-55)
		tmp = fma(t, a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * a + y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.7e+71], t$95$1, If[LessEqual[z, 1.7e-55], N[(t * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999997e71 or 1.69999999999999986e-55 < z

   1. Initial program 82.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y + a \cdot b\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y + a \cdot b\right) \cdot z} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b + y\right)} \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{b \cdot a} + y\right) \cdot z \]

      5. lower-fma.f64 76.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, y\right)} \cdot z \]

   5. Applied rewrites 76.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, y\right) \cdot z} \]

   if -2.69999999999999997e71 < z < 1.69999999999999986e-55

   1. Initial program 98.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot t + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot a} + x \]

      3. lower-fma.f64 77.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]

   5. Applied rewrites 77.5%

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

Alternative 8: 63.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -150000:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -150000.0) (fma z y x) (if (<= y 1.6e+34) (fma t a x) (fma z y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -150000.0) {
		tmp = fma(z, y, x);
	} else if (y <= 1.6e+34) {
		tmp = fma(t, a, x);
	} else {
		tmp = fma(z, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -150000.0)
		tmp = fma(z, y, x);
	elseif (y <= 1.6e+34)
		tmp = fma(t, a, x);
	else
		tmp = fma(z, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -150000.0], N[(z * y + x), $MachinePrecision], If[LessEqual[y, 1.6e+34], N[(t * a + x), $MachinePrecision], N[(z * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e5 or 1.5999999999999999e34 < y

   1. Initial program 89.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 75.1

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

   5. Applied rewrites 75.1%

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

   if -1.5e5 < y < 1.5999999999999999e34

   1. Initial program 91.7%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot t + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot a} + x \]

      3. lower-fma.f64 69.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]

   5. Applied rewrites 69.5%

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

Alternative 9: 58.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+128}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.2e+128) (* z y) (if (<= y 1.65e+34) (fma t a x) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e+128) {
		tmp = z * y;
	} else if (y <= 1.65e+34) {
		tmp = fma(t, a, x);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.2e+128)
		tmp = Float64(z * y);
	elseif (y <= 1.65e+34)
		tmp = fma(t, a, x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.2e+128], N[(z * y), $MachinePrecision], If[LessEqual[y, 1.65e+34], N[(t * a + x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000008e128 or 1.64999999999999994e34 < y

   1. Initial program 89.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 62.1

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

   5. Applied rewrites 62.1%

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

   if -6.20000000000000008e128 < y < 1.64999999999999994e34

   1. Initial program 91.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot t + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot a} + x \]

      3. lower-fma.f64 67.3

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]

   5. Applied rewrites 67.3%

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

Alternative 10: 38.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0056:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+34}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -0.0056) (* z y) (if (<= y 1.6e+34) (* a t) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.0056) {
		tmp = z * y;
	} else if (y <= 1.6e+34) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-0.0056d0)) then
        tmp = z * y
    else if (y <= 1.6d+34) then
        tmp = a * t
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.0056) {
		tmp = z * y;
	} else if (y <= 1.6e+34) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -0.0056:
		tmp = z * y
	elif y <= 1.6e+34:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -0.0056)
		tmp = Float64(z * y);
	elseif (y <= 1.6e+34)
		tmp = Float64(a * t);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -0.0056)
		tmp = z * y;
	elseif (y <= 1.6e+34)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -0.0056], N[(z * y), $MachinePrecision], If[LessEqual[y, 1.6e+34], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00559999999999999994 or 1.5999999999999999e34 < y

   1. Initial program 89.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 56.4

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

   5. Applied rewrites 56.4%

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

   if -0.00559999999999999994 < y < 1.5999999999999999e34

   1. Initial program 91.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a \cdot t} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot a} \]

      2. lower-*.f64 37.3

         \[\leadsto \color{blue}{t \cdot a} \]

   5. Applied rewrites 37.3%

      \[\leadsto \color{blue}{t \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0056:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+34}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 27.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ a \cdot t \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* a t))

C

double code(double x, double y, double z, double t, double a, double b) {
	return a * t;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a * t
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a * t;
}

Python

def code(x, y, z, t, a, b):
	return a * t

Julia

function code(x, y, z, t, a, b)
	return Float64(a * t)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a * t;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a * t), $MachinePrecision]

Derivation

1. Initial program 90.7%

   \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{a \cdot t} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{t \cdot a} \]

   2. lower-*.f64 29.1

      \[\leadsto \color{blue}{t \cdot a} \]

5. Applied rewrites 29.1%

   \[\leadsto \color{blue}{t \cdot a} \]

6. Final simplification 29.1%

   \[\leadsto a \cdot t \]
7. Add Preprocessing

Developer Target 1: 97.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024257 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))