Average Error: 2.1 → 0.7
Time: 4.2s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le -4.2133560858925846 \cdot 10^{307}:\\ \;\;\;\;y \cdot z + \left(x + \left(a \cdot \left(\sqrt[3]{t + z \cdot b} \cdot \sqrt[3]{t + z \cdot b}\right)\right) \cdot \sqrt[3]{t + z \cdot b}\right)\\ \mathbf{elif}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 2.3942825002580448 \cdot 10^{261}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le -4.2133560858925846 \cdot 10^{307}:\\
\;\;\;\;y \cdot z + \left(x + \left(a \cdot \left(\sqrt[3]{t + z \cdot b} \cdot \sqrt[3]{t + z \cdot b}\right)\right) \cdot \sqrt[3]{t + z \cdot b}\right)\\

\mathbf{elif}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 2.3942825002580448 \cdot 10^{261}:\\
\;\;\;\;\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 + a \cdot \left(t + z \cdot 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 ((((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b)))) <= -4.2133560858925846e+307)) {
		VAR = ((double) (((double) (y * z)) + ((double) (x + ((double) (((double) (a * ((double) (((double) cbrt(((double) (t + ((double) (z * b)))))) * ((double) cbrt(((double) (t + ((double) (z * b)))))))))) * ((double) cbrt(((double) (t + ((double) (z * b))))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b)))) <= 2.3942825002580448e+261)) {
			VAR_1 = ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b))));
		} else {
			VAR_1 = ((double) (((double) (y * z)) + ((double) (x + ((double) (a * ((double) (t + ((double) (z * 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

Original2.1
Target0.4
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < -4.2133560858925846e+307

    1. Initial program 59.8

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

    2. Simplified1.2

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

    4. Applied add-cube-cbrt1.8

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

    5. Applied associate-*r*1.8

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

    if -4.2133560858925846e+307 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < 2.3942825002580448e+261

    1. Initial program 0.3

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

    if 2.3942825002580448e+261 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))

    1. Initial program 9.3

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

    2. Simplified4.0

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le -4.2133560858925846 \cdot 10^{307}:\\ \;\;\;\;y \cdot z + \left(x + \left(a \cdot \left(\sqrt[3]{t + z \cdot b} \cdot \sqrt[3]{t + z \cdot b}\right)\right) \cdot \sqrt[3]{t + z \cdot b}\right)\\ \mathbf{elif}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 2.3942825002580448 \cdot 10^{261}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020120 
(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)))