Average Error: 2.0 → 0.8
Time: 5.6s
Precision: binary64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \leq -6.521478695897989 \cdot 10^{+120}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 4.868649893543251 \cdot 10^{-122}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + a \cdot t\right) + b \cdot \left(a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + a \cdot t\right) + \left(a \cdot \left(z \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{b}} \cdot \left(\sqrt[3]{\sqrt[3]{b}} \cdot \sqrt[3]{\sqrt[3]{b}}\right)\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;a \leq -6.521478695897989 \cdot 10^{+120}:\\
\;\;\;\;x + \left(y \cdot z + a \cdot \left(t + z \cdot b\right)\right)\\

\mathbf{elif}\;a \leq 4.868649893543251 \cdot 10^{-122}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + a \cdot t\right) + b \cdot \left(a \cdot z\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + a \cdot t\right) + \left(a \cdot \left(z \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{b}} \cdot \left(\sqrt[3]{\sqrt[3]{b}} \cdot \sqrt[3]{\sqrt[3]{b}}\right)\right)\\

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double VAR;
	if ((a <= -6.521478695897989e+120)) {
		VAR = ((double) (x + ((double) (((double) (y * z)) + ((double) (a * ((double) (t + ((double) (z * b))))))))));
	} else {
		double VAR_1;
		if ((a <= 4.868649893543251e-122)) {
			VAR_1 = ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (a * t)))) + ((double) (b * ((double) (a * z))))));
		} else {
			VAR_1 = ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (a * t)))) + ((double) (((double) (a * ((double) (z * ((double) (((double) cbrt(b)) * ((double) cbrt(b)))))))) * ((double) (((double) cbrt(((double) cbrt(b)))) * ((double) (((double) cbrt(((double) cbrt(b)))) * ((double) cbrt(((double) cbrt(b))))))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.0
Target0.4
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z < -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -6.5214786958979887e120

    1. Initial program 7.9

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

    2. Simplified0.1

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

    if -6.5214786958979887e120 < a < 4.8686498935432509e-122

    1. Initial program 0.7

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

    if 4.8686498935432509e-122 < a

    1. Initial program 2.9

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
    2. Using strategy rm

    3. Applied add-cube-cbrt3.2

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

    4. Applied associate-*r*3.2

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

    5. Simplified1.1

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(a \cdot \left(z \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\right)} \cdot \sqrt[3]{b}\]
    6. Using strategy rm

    7. Applied add-cube-cbrt1.2

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.521478695897989 \cdot 10^{+120}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 4.868649893543251 \cdot 10^{-122}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + a \cdot t\right) + b \cdot \left(a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + a \cdot t\right) + \left(a \cdot \left(z \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{b}} \cdot \left(\sqrt[3]{\sqrt[3]{b}} \cdot \sqrt[3]{\sqrt[3]{b}}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -1.1820553527347888e+19) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

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