Average Error: 9.6 → 0.1
Time: 4.8s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r881585 = x;
        double r881586 = y;
        double r881587 = r881585 / r881586;
        double r881588 = 2.0;
        double r881589 = z;
        double r881590 = r881589 * r881588;
        double r881591 = 1.0;
        double r881592 = t;
        double r881593 = r881591 - r881592;
        double r881594 = r881590 * r881593;
        double r881595 = r881588 + r881594;
        double r881596 = r881592 * r881589;
        double r881597 = r881595 / r881596;
        double r881598 = r881587 + r881597;
        return r881598;
}
↓
double f(double x, double y, double z, double t) {
        double r881599 = x;
        double r881600 = y;
        double r881601 = r881599 / r881600;
        double r881602 = 1.0;
        double r881603 = t;
        double r881604 = r881602 / r881603;
        double r881605 = 2.0;
        double r881606 = z;
        double r881607 = r881605 / r881606;
        double r881608 = r881607 + r881605;
        double r881609 = r881604 * r881608;
        double r881610 = r881609 - r881605;
        double r881611 = r881601 + r881610;
        return r881611;
}

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

Original9.6
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.6

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

  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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))))