Average Error: 9.6 → 0.1
Time: 4.9s
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 r757593 = x;
        double r757594 = y;
        double r757595 = r757593 / r757594;
        double r757596 = 2.0;
        double r757597 = z;
        double r757598 = r757597 * r757596;
        double r757599 = 1.0;
        double r757600 = t;
        double r757601 = r757599 - r757600;
        double r757602 = r757598 * r757601;
        double r757603 = r757596 + r757602;
        double r757604 = r757600 * r757597;
        double r757605 = r757603 / r757604;
        double r757606 = r757595 + r757605;
        return r757606;
}
↓
double f(double x, double y, double z, double t) {
        double r757607 = x;
        double r757608 = y;
        double r757609 = r757607 / r757608;
        double r757610 = 1.0;
        double r757611 = t;
        double r757612 = r757610 / r757611;
        double r757613 = 2.0;
        double r757614 = z;
        double r757615 = r757613 / r757614;
        double r757616 = r757615 + r757613;
        double r757617 = r757612 * r757616;
        double r757618 = r757617 - r757613;
        double r757619 = r757609 + r757618;
        return r757619;
}

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 2020081 
(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))))