Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 91.9% → 97.2%

Time: 11.4s

Alternatives: 12

Speedup: 1.2×

• 32.1% 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: 91.9% 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: 97.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, \mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 5e+274) t_1 (fma z y (fma (fma z b t) a x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= 5e+274) {
		tmp = t_1;
	} else {
		tmp = fma(z, y, fma(fma(z, b, t), a, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 5e+274)
		tmp = t_1;
	else
		tmp = fma(z, y, fma(fma(z, b, t), a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+274], t$95$1, N[(z * y + N[(N[(z * b + t), $MachinePrecision] * a + x), $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)) < 4.9999999999999998e274

   1. Initial program 99.0%

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

   if 4.9999999999999998e274 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 68.3%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-+l+ N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. associate-*l* N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. distribute-lft-out N/A

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

      21. lower-*.f64 N/A

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

      22. lower-fma.f64 96.2

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

   4. Applied rewrites 96.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 96.2

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

   6. Applied rewrites 96.2%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, \mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, \mathsf{fma}\left(b, z, t\right), x\right)\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-200}:\\ \;\;\;\;\mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (fma b z t) x)))
   (if (<= a -8.8e+33)
     t_1
     (if (<= a 1.1e-200)
       (fma z (fma a b y) x)
       (if (<= a 5.5e+77) (fma a t (fma z y x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, fma(b, z, t), x);
	double tmp;
	if (a <= -8.8e+33) {
		tmp = t_1;
	} else if (a <= 1.1e-200) {
		tmp = fma(z, fma(a, b, y), x);
	} else if (a <= 5.5e+77) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, fma(b, z, t), x)
	tmp = 0.0
	if (a <= -8.8e+33)
		tmp = t_1;
	elseif (a <= 1.1e-200)
		tmp = fma(z, fma(a, b, y), x);
	elseif (a <= 5.5e+77)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b * z + t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -8.8e+33], t$95$1, If[LessEqual[a, 1.1e-200], N[(z * N[(a * b + y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 5.5e+77], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.79999999999999975e33 or 5.50000000000000036e77 < a

   1. Initial program 85.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 91.4

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

   5. Applied rewrites 91.4%

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

   if -8.79999999999999975e33 < a < 1.10000000000000007e-200

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 92.5

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

   5. Applied rewrites 92.5%

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

   if 1.10000000000000007e-200 < a < 5.50000000000000036e77

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 96.7%

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

Alternative 3: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+253}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8.8e+33)
   (fma a t x)
   (if (<= a 5.5e+77)
     (fma z y x)
     (if (<= a 5.7e+253) (fma a t x) (* (* z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.8e+33) {
		tmp = fma(a, t, x);
	} else if (a <= 5.5e+77) {
		tmp = fma(z, y, x);
	} else if (a <= 5.7e+253) {
		tmp = fma(a, t, x);
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8.8e+33)
		tmp = fma(a, t, x);
	elseif (a <= 5.5e+77)
		tmp = fma(z, y, x);
	elseif (a <= 5.7e+253)
		tmp = fma(a, t, x);
	else
		tmp = Float64(Float64(z * a) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8.8e+33], N[(a * t + x), $MachinePrecision], If[LessEqual[a, 5.5e+77], N[(z * y + x), $MachinePrecision], If[LessEqual[a, 5.7e+253], N[(a * t + x), $MachinePrecision], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.79999999999999975e33 or 5.50000000000000036e77 < a < 5.70000000000000016e253

   1. Initial program 84.9%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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. lower-fma.f64 57.5

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

   5. Applied rewrites 57.5%

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

   if -8.79999999999999975e33 < a < 5.50000000000000036e77

   1. Initial program 98.7%

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

   3. Taylor expanded in 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 74.5

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

   5. Applied rewrites 74.5%

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

   if 5.70000000000000016e253 < a

   1. Initial program 85.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 66.3

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

   5. Applied rewrites 66.3%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 79.3

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

   7. Applied rewrites 79.3%

      \[\leadsto \color{blue}{\left(z \cdot a\right) \cdot b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 86.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, \mathsf{fma}\left(b, z, t\right), x\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (fma b z t) x)))
   (if (<= a -2.8e-97) t_1 (if (<= a 5.5e+77) (fma a t (fma z y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, fma(b, z, t), x);
	double tmp;
	if (a <= -2.8e-97) {
		tmp = t_1;
	} else if (a <= 5.5e+77) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, fma(b, z, t), x)
	tmp = 0.0
	if (a <= -2.8e-97)
		tmp = t_1;
	elseif (a <= 5.5e+77)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b * z + t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.8e-97], t$95$1, If[LessEqual[a, 5.5e+77], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8000000000000002e-97 or 5.50000000000000036e77 < a

   1. Initial program 88.1%

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

   3. Taylor expanded in 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. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 88.3

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

   5. Applied rewrites 88.3%

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

   if -2.8000000000000002e-97 < a < 5.50000000000000036e77

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 90.1%

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

Alternative 5: 82.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z \cdot a, b, x\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* z a) b x)))
   (if (<= b -6e+191) t_1 (if (<= b 1.2e+101) (fma a t (fma z y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((z * a), b, x);
	double tmp;
	if (b <= -6e+191) {
		tmp = t_1;
	} else if (b <= 1.2e+101) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(z * a), b, x)
	tmp = 0.0
	if (b <= -6e+191)
		tmp = t_1;
	elseif (b <= 1.2e+101)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -6e+191], t$95$1, If[LessEqual[b, 1.2e+101], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.9999999999999995e191 or 1.19999999999999994e101 < b

   1. Initial program 94.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 89.8

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

   5. Applied rewrites 89.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 78.4

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

   8. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, b \cdot z, x\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lower-fma.f64 86.5

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 86.5

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

   10. Applied rewrites 86.5%

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

   if -5.9999999999999995e191 < b < 1.19999999999999994e101

   1. Initial program 92.2%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 87.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+191}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot a, b, x\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot a, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.6 \cdot 10^{+223}:\\ \;\;\;\;\mathsf{fma}\left(z, y, \mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 4.6e+223) (fma z y (fma (fma z b t) a x)) (fma z (fma a b y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 4.6e+223) {
		tmp = fma(z, y, fma(fma(z, b, t), a, x));
	} else {
		tmp = fma(z, fma(a, b, y), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 4.6e+223)
		tmp = fma(z, y, fma(fma(z, b, t), a, x));
	else
		tmp = fma(z, fma(a, b, y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 4.6e+223], N[(z * y + N[(N[(z * b + t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * b + y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.60000000000000009e223

   1. Initial program 94.5%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-+l+ N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. associate-*l* N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. distribute-lft-out N/A

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

      21. lower-*.f64 N/A

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

      22. lower-fma.f64 96.3

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

   4. Applied rewrites 96.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 96.3

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

   6. Applied rewrites 96.3%

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

   if 4.60000000000000009e223 < z

   1. Initial program 74.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 7: 95.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(z, b, t\right), \mathsf{fma}\left(y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.7e+101) (fma a (fma z b t) (fma y z x)) (fma z (fma a b y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.7e+101) {
		tmp = fma(a, fma(z, b, t), fma(y, z, x));
	} else {
		tmp = fma(z, fma(a, b, y), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.7e+101)
		tmp = fma(a, fma(z, b, t), fma(y, z, x));
	else
		tmp = fma(z, fma(a, b, y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.7e+101], N[(a * N[(z * b + t), $MachinePrecision] + N[(y * z + x), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * b + y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.70000000000000009e101

   1. Initial program 94.9%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. distribute-lft-out N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-fma.f64 96.8

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lower-fma.f64 96.8

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

   4. Applied rewrites 96.8%

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

   if 1.70000000000000009e101 < z

   1. Initial program 82.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 95.9

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

   5. Applied rewrites 95.9%

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

Alternative 8: 71.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(b, z, t\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (fma b z t))))
   (if (<= a -2.8e-97) t_1 (if (<= a 8.2e+77) (fma z y x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * fma(b, z, t);
	double tmp;
	if (a <= -2.8e-97) {
		tmp = t_1;
	} else if (a <= 8.2e+77) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * fma(b, z, t))
	tmp = 0.0
	if (a <= -2.8e-97)
		tmp = t_1;
	elseif (a <= 8.2e+77)
		tmp = fma(z, y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b * z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e-97], t$95$1, If[LessEqual[a, 8.2e+77], N[(z * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8000000000000002e-97 or 8.2000000000000002e77 < a

   1. Initial program 88.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 75.8

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

   5. Applied rewrites 75.8%

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

   if -2.8000000000000002e-97 < a < 8.2000000000000002e77

   1. Initial program 98.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 81.4

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

   5. Applied rewrites 81.4%

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

Alternative 9: 63.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.3e-25) (fma z y x) (if (<= y 2.7e-44) (fma a t x) (fma z y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.3e-25) {
		tmp = fma(z, y, x);
	} else if (y <= 2.7e-44) {
		tmp = fma(a, t, x);
	} else {
		tmp = fma(z, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.3e-25)
		tmp = fma(z, y, x);
	elseif (y <= 2.7e-44)
		tmp = fma(a, t, x);
	else
		tmp = fma(z, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.3e-25], N[(z * y + x), $MachinePrecision], If[LessEqual[y, 2.7e-44], N[(a * t + x), $MachinePrecision], N[(z * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.30000000000000045e-25 or 2.6999999999999999e-44 < y

   1. Initial program 93.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 69.8

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

   5. Applied rewrites 69.8%

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

   if -7.30000000000000045e-25 < y < 2.6999999999999999e-44

   1. Initial program 92.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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. lower-fma.f64 62.1

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

   5. Applied rewrites 62.1%

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

Alternative 10: 58.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+114}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.8e+114) (* y z) (if (<= y 6.3e+94) (fma a t x) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e+114) {
		tmp = y * z;
	} else if (y <= 6.3e+94) {
		tmp = fma(a, t, x);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.8e+114)
		tmp = Float64(y * z);
	elseif (y <= 6.3e+94)
		tmp = fma(a, t, x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.8e+114], N[(y * z), $MachinePrecision], If[LessEqual[y, 6.3e+94], N[(a * t + x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e114 or 6.3000000000000001e94 < y

   1. Initial program 93.2%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 64.2

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

   5. Applied rewrites 64.2%

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

   if -4.8e114 < y < 6.3000000000000001e94

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 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. lower-fma.f64 58.1

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

   5. Applied rewrites 58.1%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+114}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+77}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8.2e+30) (* t a) (if (<= a 5.5e+77) (* y z) (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.2e+30) {
		tmp = t * a;
	} else if (a <= 5.5e+77) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	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 (a <= (-8.2d+30)) then
        tmp = t * a
    else if (a <= 5.5d+77) then
        tmp = y * z
    else
        tmp = t * a
    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 (a <= -8.2e+30) {
		tmp = t * a;
	} else if (a <= 5.5e+77) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8.2e+30:
		tmp = t * a
	elif a <= 5.5e+77:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8.2e+30)
		tmp = Float64(t * a);
	elseif (a <= 5.5e+77)
		tmp = Float64(y * z);
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8.2e+30)
		tmp = t * a;
	elseif (a <= 5.5e+77)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8.2e+30], N[(t * a), $MachinePrecision], If[LessEqual[a, 5.5e+77], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.20000000000000011e30 or 5.50000000000000036e77 < a

   1. Initial program 85.1%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 45.0

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

   5. Applied rewrites 45.0%

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

   if -8.20000000000000011e30 < a < 5.50000000000000036e77

   1. Initial program 98.7%

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

   3. Taylor expanded in 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 40.9

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

   5. Applied rewrites 40.9%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+77}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 27.9% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

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 = t * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

3. Taylor expanded in t around inf

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

   1. lower-*.f64 26.1

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

5. Applied rewrites 26.1%

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

6. Final simplification 26.1%

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

Developer Target 1: 97.3% 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 2024214 
(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)))