Average Error: 11.3 → 1.0
Time: 29.5s
Precision: 64
\[x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{y}{z - \frac{\frac{y}{\frac{z}{t}}}{2.0}}\]
x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}
↓
x - \frac{y}{z - \frac{\frac{y}{\frac{z}{t}}}{2.0}}
double f(double x, double y, double z, double t) {
        double r24461197 = x;
        double r24461198 = y;
        double r24461199 = 2.0;
        double r24461200 = r24461198 * r24461199;
        double r24461201 = z;
        double r24461202 = r24461200 * r24461201;
        double r24461203 = r24461201 * r24461199;
        double r24461204 = r24461203 * r24461201;
        double r24461205 = t;
        double r24461206 = r24461198 * r24461205;
        double r24461207 = r24461204 - r24461206;
        double r24461208 = r24461202 / r24461207;
        double r24461209 = r24461197 - r24461208;
        return r24461209;
}
↓
double f(double x, double y, double z, double t) {
        double r24461210 = x;
        double r24461211 = y;
        double r24461212 = z;
        double r24461213 = t;
        double r24461214 = r24461212 / r24461213;
        double r24461215 = r24461211 / r24461214;
        double r24461216 = 2.0;
        double r24461217 = r24461215 / r24461216;
        double r24461218 = r24461212 - r24461217;
        double r24461219 = r24461211 / r24461218;
        double r24461220 = r24461210 - r24461219;
        return r24461220;
}

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

Original11.3
Target0.1
Herbie1.0
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2.0}}{z}}\]

Derivation

  1. Initial program 11.3

    \[x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}\]

  2. Simplified1.1

    \[\leadsto \color{blue}{x - \frac{y}{z - \frac{\frac{t}{z} \cdot y}{2.0}}}\]
  3. Using strategy rm

  4. Applied clear-num1.1

    \[\leadsto x - \frac{y}{z - \frac{\color{blue}{\frac{1}{\frac{z}{t}}} \cdot y}{2.0}}\]

  5. Applied associate-*l/1.0

    \[\leadsto x - \frac{y}{z - \frac{\color{blue}{\frac{1 \cdot y}{\frac{z}{t}}}}{2.0}}\]

  6. Simplified1.0

    \[\leadsto x - \frac{y}{z - \frac{\frac{\color{blue}{y}}{\frac{z}{t}}}{2.0}}\]

  7. Final simplification1.0

    \[\leadsto x - \frac{y}{z - \frac{\frac{y}{\frac{z}{t}}}{2.0}}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"

  :herbie-target
  (- x (/ 1 (- (/ z y) (/ (/ t 2.0) z))))

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