Average Error: 9.4 → 0.1
Time: 2.7s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r889076 = x;
        double r889077 = y;
        double r889078 = r889076 / r889077;
        double r889079 = 2.0;
        double r889080 = z;
        double r889081 = r889080 * r889079;
        double r889082 = 1.0;
        double r889083 = t;
        double r889084 = r889082 - r889083;
        double r889085 = r889081 * r889084;
        double r889086 = r889079 + r889085;
        double r889087 = r889083 * r889080;
        double r889088 = r889086 / r889087;
        double r889089 = r889078 + r889088;
        return r889089;
}
↓
double f(double x, double y, double z, double t) {
        double r889090 = 2.0;
        double r889091 = z;
        double r889092 = r889090 / r889091;
        double r889093 = r889092 + r889090;
        double r889094 = t;
        double r889095 = r889093 / r889094;
        double r889096 = x;
        double r889097 = y;
        double r889098 = r889096 / r889097;
        double r889099 = r889090 - r889098;
        double r889100 = r889095 - r889099;
        return r889100;
}

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

Original9.4
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.4

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

  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

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

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

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

  7. Applied distribute-lft-out0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(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))))