Average Error: 11.4 → 1.0
Time: 19.3s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x + \frac{-y}{z - \frac{t}{z} \cdot \frac{y}{2}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x + \frac{-y}{z - \frac{t}{z} \cdot \frac{y}{2}}
double f(double x, double y, double z, double t) {
        double r21585515 = x;
        double r21585516 = y;
        double r21585517 = 2.0;
        double r21585518 = r21585516 * r21585517;
        double r21585519 = z;
        double r21585520 = r21585518 * r21585519;
        double r21585521 = r21585519 * r21585517;
        double r21585522 = r21585521 * r21585519;
        double r21585523 = t;
        double r21585524 = r21585516 * r21585523;
        double r21585525 = r21585522 - r21585524;
        double r21585526 = r21585520 / r21585525;
        double r21585527 = r21585515 - r21585526;
        return r21585527;
}
↓
double f(double x, double y, double z, double t) {
        double r21585528 = x;
        double r21585529 = y;
        double r21585530 = -r21585529;
        double r21585531 = z;
        double r21585532 = t;
        double r21585533 = r21585532 / r21585531;
        double r21585534 = 2.0;
        double r21585535 = r21585529 / r21585534;
        double r21585536 = r21585533 * r21585535;
        double r21585537 = r21585531 - r21585536;
        double r21585538 = r21585530 / r21585537;
        double r21585539 = r21585528 + r21585538;
        return r21585539;
}

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

Original11.4
Target0.1
Herbie1.0
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.4

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

  2. Simplified1.0

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

  4. Applied sub-neg1.0

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

  5. Final simplification1.0

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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)))))