Average Error: 9.0 → 0.1
Time: 17.1s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r636041 = x;
        double r636042 = y;
        double r636043 = r636041 / r636042;
        double r636044 = 2.0;
        double r636045 = z;
        double r636046 = r636045 * r636044;
        double r636047 = 1.0;
        double r636048 = t;
        double r636049 = r636047 - r636048;
        double r636050 = r636046 * r636049;
        double r636051 = r636044 + r636050;
        double r636052 = r636048 * r636045;
        double r636053 = r636051 / r636052;
        double r636054 = r636043 + r636053;
        return r636054;
}
↓
double f(double x, double y, double z, double t) {
        double r636055 = 2.0;
        double r636056 = t;
        double r636057 = r636055 / r636056;
        double r636058 = z;
        double r636059 = r636057 / r636058;
        double r636060 = r636057 - r636055;
        double r636061 = r636059 + r636060;
        double r636062 = x;
        double r636063 = y;
        double r636064 = r636062 / r636063;
        double r636065 = r636061 + r636064;
        return r636065;
}

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

Original9.0
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.0

    \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{\left(1 - t\right) \cdot 2 + \frac{2}{z}}{t} + \frac{x}{y}}\]

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) - 2\right)} + \frac{x}{y}\]

  4. Simplified0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y)))

  (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 t))) (* t z))))