Average Error: 11.6 → 0.9
Time: 11.9s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - 2 \cdot \frac{y}{2 \cdot z - \frac{y}{\frac{z}{t}}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - 2 \cdot \frac{y}{2 \cdot z - \frac{y}{\frac{z}{t}}}
double f(double x, double y, double z, double t) {
        double r441473 = x;
        double r441474 = y;
        double r441475 = 2.0;
        double r441476 = r441474 * r441475;
        double r441477 = z;
        double r441478 = r441476 * r441477;
        double r441479 = r441477 * r441475;
        double r441480 = r441479 * r441477;
        double r441481 = t;
        double r441482 = r441474 * r441481;
        double r441483 = r441480 - r441482;
        double r441484 = r441478 / r441483;
        double r441485 = r441473 - r441484;
        return r441485;
}
↓
double f(double x, double y, double z, double t) {
        double r441486 = x;
        double r441487 = 2.0;
        double r441488 = y;
        double r441489 = z;
        double r441490 = r441487 * r441489;
        double r441491 = t;
        double r441492 = r441489 / r441491;
        double r441493 = r441488 / r441492;
        double r441494 = r441490 - r441493;
        double r441495 = r441488 / r441494;
        double r441496 = r441487 * r441495;
        double r441497 = r441486 - r441496;
        return r441497;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.6
Target0.1
Herbie0.9
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.6

    \[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]

  2. Simplified2.8

    \[\leadsto \color{blue}{x - \frac{y}{2 \cdot z - \frac{y \cdot t}{z}} \cdot 2}\]
  3. Using strategy rm

  4. Applied associate-/l*0.9

    \[\leadsto x - \frac{y}{2 \cdot z - \color{blue}{\frac{y}{\frac{z}{t}}}} \cdot 2\]

  5. Final simplification0.9

    \[\leadsto x - 2 \cdot \frac{y}{2 \cdot z - \frac{y}{\frac{z}{t}}}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"

  :herbie-target
  (- x (/ 1.0 (- (/ z y) (/ (/ t 2.0) z))))

  (- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))))