Average Error: 2.4 → 0.8
Time: 4.0s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -2.2442947297478706 \cdot 10^{79} \lor \neg \left(b \le 1.3998214706111869 \cdot 10^{-169}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + \frac{a}{\frac{1}{t + z \cdot b}}\right)\\ \end{array}\]
\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 -2.2442947297478706 \cdot 10^{79} \lor \neg \left(b \le 1.3998214706111869 \cdot 10^{-169}\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 + \frac{a}{\frac{1}{t + z \cdot b}}\right)\\

\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 (((b <= -2.2442947297478706e+79) || !(b <= 1.399821470611187e-169))) {
		VAR = (((x + (y * z)) + (t * a)) + ((a * z) * b));
	} else {
		VAR = ((y * z) + (x + (a / (1.0 / (t + (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

Original2.4
Target0.3
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -2.2442947297478706e+79 or 1.399821470611187e-169 < b

    1. Initial program 1.2

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

    if -2.2442947297478706e+79 < b < 1.399821470611187e-169

    1. Initial program 3.7

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

    2. Simplified0.3

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

    4. Applied flip-+15.8

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

    5. Applied associate-*r/18.9

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

    7. Applied associate-/l*15.9

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

    9. Applied clear-num15.8

      \[\leadsto y \cdot z + \left(x + \frac{a}{\color{blue}{\frac{1}{\frac{t \cdot t - \left(z \cdot b\right) \cdot \left(z \cdot b\right)}{t - z \cdot b}}}}\right)\]

    10. Simplified0.4

      \[\leadsto y \cdot z + \left(x + \frac{a}{\frac{1}{\color{blue}{t + z \cdot b}}}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.2442947297478706 \cdot 10^{79} \lor \neg \left(b \le 1.3998214706111869 \cdot 10^{-169}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + \frac{a}{\frac{1}{t + z \cdot b}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020103 
(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)))