Average Error: 2.2 → 0.5
Time: 3.9s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -3.1193980571631084 \cdot 10^{-53} \lor \neg \left(a \le 2.07619091583006111 \cdot 10^{-104}\right):\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{\left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}}\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;a \le -3.1193980571631084 \cdot 10^{-53} \lor \neg \left(a \le 2.07619091583006111 \cdot 10^{-104}\right):\\
\;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\

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

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return (((x + (y * z)) + (t * a)) + ((a * z) * b));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double VAR;
	if (((a <= -3.1193980571631084e-53) || !(a <= 2.076190915830061e-104))) {
		VAR = ((y * z) + (x + (a * (t + (z * b)))));
	} else {
		VAR = (((x + (y * z)) + (t * a)) + ((cbrt(((a * z) * b)) * (cbrt((a * z)) * cbrt(b))) * cbrt((((a * z) * (cbrt(b) * cbrt(b))) * cbrt(b)))));
	}
	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

Original2.2
Target0.4
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -3.1193980571631084e-53 or 2.076190915830061e-104 < a

    1. Initial program 3.8

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

    2. Simplified0.5

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

    if -3.1193980571631084e-53 < a < 2.076190915830061e-104

    1. Initial program 0.4

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

    3. Applied add-cube-cbrt0.5

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

    5. Applied cbrt-prod0.5

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

    7. Applied add-cube-cbrt0.6

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

    8. Applied associate-*r*0.5

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -3.1193980571631084 \cdot 10^{-53} \lor \neg \left(a \le 2.07619091583006111 \cdot 10^{-104}\right):\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{\left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020091 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000) (+ (* 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)))