Average Error: 9.2 → 0.1
Time: 14.1s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{x}{y} + \frac{2}{t}\right) - \left(2 - \frac{\frac{2}{z}}{t}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{x}{y} + \frac{2}{t}\right) - \left(2 - \frac{\frac{2}{z}}{t}\right)
double f(double x, double y, double z, double t) {
        double r641078 = x;
        double r641079 = y;
        double r641080 = r641078 / r641079;
        double r641081 = 2.0;
        double r641082 = z;
        double r641083 = r641082 * r641081;
        double r641084 = 1.0;
        double r641085 = t;
        double r641086 = r641084 - r641085;
        double r641087 = r641083 * r641086;
        double r641088 = r641081 + r641087;
        double r641089 = r641085 * r641082;
        double r641090 = r641088 / r641089;
        double r641091 = r641080 + r641090;
        return r641091;
}
↓
double f(double x, double y, double z, double t) {
        double r641092 = x;
        double r641093 = y;
        double r641094 = r641092 / r641093;
        double r641095 = 2.0;
        double r641096 = t;
        double r641097 = r641095 / r641096;
        double r641098 = r641094 + r641097;
        double r641099 = z;
        double r641100 = r641095 / r641099;
        double r641101 = r641100 / r641096;
        double r641102 = r641095 - r641101;
        double r641103 = r641098 - r641102;
        return r641103;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 9.2

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

  3. Applied associate-/r*18.6

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

  4. Taylor expanded around 0 0.1

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

  5. Simplified0.1

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

  7. Applied associate-+l-0.1

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

  8. Applied associate-+r-0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 
(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))))