Average Error: 9.3 → 0.1
Time: 22.0s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \left(\frac{x}{y} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \left(\frac{x}{y} - 2\right)
double f(double x, double y, double z, double t) {
        double r527092 = x;
        double r527093 = y;
        double r527094 = r527092 / r527093;
        double r527095 = 2.0;
        double r527096 = z;
        double r527097 = r527096 * r527095;
        double r527098 = 1.0;
        double r527099 = t;
        double r527100 = r527098 - r527099;
        double r527101 = r527097 * r527100;
        double r527102 = r527095 + r527101;
        double r527103 = r527099 * r527096;
        double r527104 = r527102 / r527103;
        double r527105 = r527094 + r527104;
        return r527105;
}
↓
double f(double x, double y, double z, double t) {
        double r527106 = 2.0;
        double r527107 = t;
        double r527108 = r527106 / r527107;
        double r527109 = z;
        double r527110 = r527108 / r527109;
        double r527111 = r527108 + r527110;
        double r527112 = x;
        double r527113 = y;
        double r527114 = r527112 / r527113;
        double r527115 = r527114 - r527106;
        double r527116 = r527111 + r527115;
        return r527116;
}

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. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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))))