Average Error: 2.2 → 0.4
Time: 3.9s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.886177702795923 \cdot 10^{32} \lor \neg \left(z \le 1.48374886465327952 \cdot 10^{-141}\right):\\ \;\;\;\;\left(z \cdot \left(y + b \cdot a\right) + x\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.886177702795923 \cdot 10^{32} \lor \neg \left(z \le 1.48374886465327952 \cdot 10^{-141}\right):\\
\;\;\;\;\left(z \cdot \left(y + b \cdot a\right) + x\right) + a \cdot t\\

\mathbf{else}:\\
\;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\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 temp;
	if (((z <= -2.8861777027959232e+32) || !(z <= 1.4837488646532795e-141))) {
		temp = (((z * (y + (b * a))) + x) + (a * t));
	} else {
		temp = ((x + (y * z)) + (a * ((z * b) + t)));
	}
	return temp;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -2.8861777027959232e+32 or 1.4837488646532795e-141 < z

    1. Initial program 4.0

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

    3. Applied associate-+l+4.0

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

    4. Simplified5.8

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

    6. Applied distribute-lft-in5.8

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

    7. Applied associate-+r+5.8

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

    8. Simplified0.8

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

    if -2.8861777027959232e+32 < z < 1.4837488646532795e-141

    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 associate-+l+0.4

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

    4. Simplified0.1

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.886177702795923 \cdot 10^{32} \lor \neg \left(z \le 1.48374886465327952 \cdot 10^{-141}\right):\\ \;\;\;\;\left(z \cdot \left(y + b \cdot a\right) + x\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020058 
(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)))