Average Error: 1.9 → 0.5
Time: 4.0s
Precision: binary64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -6.54362694421427648 \cdot 10^{-28} \lor \neg \left(b \le 3.89335838121635307 \cdot 10^{-90}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;b \le -6.54362694421427648 \cdot 10^{-28} \lor \neg \left(b \le 3.89335838121635307 \cdot 10^{-90}\right):\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;y \cdot z + \left(x + \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\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 (((b <= -6.5436269442142765e-28) || !(b <= 3.893358381216353e-90))) {
		VAR = ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b))));
	} else {
		VAR = ((double) (((double) (y * z)) + ((double) (x + ((double) (((double) (((double) cbrt(a)) * ((double) cbrt(a)))) * ((double) (((double) cbrt(a)) * ((double) (t + ((double) (z * 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

Original1.9
Target0.3
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 b < -6.54362694421427648e-28 or 3.89335838121635307e-90 < b

    1. Initial program 0.6

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

    if -6.54362694421427648e-28 < b < 3.89335838121635307e-90

    1. Initial program 3.5

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

    2. Simplified0.0

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

    4. Applied add-cube-cbrt0.5

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

    5. Applied associate-*l*0.5

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -6.54362694421427648 \cdot 10^{-28} \lor \neg \left(b \le 3.89335838121635307 \cdot 10^{-90}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020161 
(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)))