Average Error: 9.3 → 0.1
Time: 3.5s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{\sqrt{1}}{1} \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{\sqrt{1}}{1} \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)
double f(double x, double y, double z, double t) {
        double r728925 = x;
        double r728926 = y;
        double r728927 = r728925 / r728926;
        double r728928 = 2.0;
        double r728929 = z;
        double r728930 = r728929 * r728928;
        double r728931 = 1.0;
        double r728932 = t;
        double r728933 = r728931 - r728932;
        double r728934 = r728930 * r728933;
        double r728935 = r728928 + r728934;
        double r728936 = r728932 * r728929;
        double r728937 = r728935 / r728936;
        double r728938 = r728927 + r728937;
        return r728938;
}
↓
double f(double x, double y, double z, double t) {
        double r728939 = x;
        double r728940 = y;
        double r728941 = r728939 / r728940;
        double r728942 = 1.0;
        double r728943 = sqrt(r728942);
        double r728944 = r728943 / r728942;
        double r728945 = 2.0;
        double r728946 = z;
        double r728947 = r728945 / r728946;
        double r728948 = r728947 + r728945;
        double r728949 = t;
        double r728950 = r728948 / r728949;
        double r728951 = r728944 * r728950;
        double r728952 = r728951 - r728945;
        double r728953 = r728941 + r728952;
        return r728953;
}

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

Original9.3
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.3

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

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  5. Applied *-un-lft-identity0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Applied times-frac0.1

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

  8. Applied associate-*l*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020064 
(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))))