Average Error: 11.6 → 0.9
Time: 14.4s
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 r22889562 = x;
        double r22889563 = y;
        double r22889564 = 2.0;
        double r22889565 = r22889563 * r22889564;
        double r22889566 = z;
        double r22889567 = r22889565 * r22889566;
        double r22889568 = r22889566 * r22889564;
        double r22889569 = r22889568 * r22889566;
        double r22889570 = t;
        double r22889571 = r22889563 * r22889570;
        double r22889572 = r22889569 - r22889571;
        double r22889573 = r22889567 / r22889572;
        double r22889574 = r22889562 - r22889573;
        return r22889574;
}
↓
double f(double x, double y, double z, double t) {
        double r22889575 = x;
        double r22889576 = 2.0;
        double r22889577 = y;
        double r22889578 = z;
        double r22889579 = r22889576 * r22889578;
        double r22889580 = t;
        double r22889581 = r22889578 / r22889580;
        double r22889582 = r22889577 / r22889581;
        double r22889583 = r22889579 - r22889582;
        double r22889584 = r22889577 / r22889583;
        double r22889585 = r22889576 * r22889584;
        double r22889586 = r22889575 - r22889585;
        return r22889586;
}

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)))))