Average Error: 11.5 → 1.1
Time: 16.2s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{1}{z - \frac{\frac{t}{z} \cdot y}{2}} \cdot y\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - \frac{1}{z - \frac{\frac{t}{z} \cdot y}{2}} \cdot y
double f(double x, double y, double z, double t) {
        double r26912634 = x;
        double r26912635 = y;
        double r26912636 = 2.0;
        double r26912637 = r26912635 * r26912636;
        double r26912638 = z;
        double r26912639 = r26912637 * r26912638;
        double r26912640 = r26912638 * r26912636;
        double r26912641 = r26912640 * r26912638;
        double r26912642 = t;
        double r26912643 = r26912635 * r26912642;
        double r26912644 = r26912641 - r26912643;
        double r26912645 = r26912639 / r26912644;
        double r26912646 = r26912634 - r26912645;
        return r26912646;
}
↓
double f(double x, double y, double z, double t) {
        double r26912647 = x;
        double r26912648 = 1.0;
        double r26912649 = z;
        double r26912650 = t;
        double r26912651 = r26912650 / r26912649;
        double r26912652 = y;
        double r26912653 = r26912651 * r26912652;
        double r26912654 = 2.0;
        double r26912655 = r26912653 / r26912654;
        double r26912656 = r26912649 - r26912655;
        double r26912657 = r26912648 / r26912656;
        double r26912658 = r26912657 * r26912652;
        double r26912659 = r26912647 - r26912658;
        return r26912659;
}

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

Original11.5
Target0.1
Herbie1.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.5

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

  2. Simplified1.0

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

  4. Applied div-inv1.1

    \[\leadsto x - \color{blue}{y \cdot \frac{1}{z - \frac{\frac{t}{z} \cdot y}{2}}}\]

  5. Final simplification1.1

    \[\leadsto x - \frac{1}{z - \frac{\frac{t}{z} \cdot y}{2}} \cdot y\]

Reproduce

herbie shell --seed 2019172 
(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)))))