Average Error: 9.2 → 0.1
Time: 16.2s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r547473 = x;
        double r547474 = y;
        double r547475 = r547473 / r547474;
        double r547476 = 2.0;
        double r547477 = z;
        double r547478 = r547477 * r547476;
        double r547479 = 1.0;
        double r547480 = t;
        double r547481 = r547479 - r547480;
        double r547482 = r547478 * r547481;
        double r547483 = r547476 + r547482;
        double r547484 = r547480 * r547477;
        double r547485 = r547483 / r547484;
        double r547486 = r547475 + r547485;
        return r547486;
}
↓
double f(double x, double y, double z, double t) {
        double r547487 = x;
        double r547488 = y;
        double r547489 = r547487 / r547488;
        double r547490 = 2.0;
        double r547491 = t;
        double r547492 = r547490 / r547491;
        double r547493 = z;
        double r547494 = r547492 / r547493;
        double r547495 = r547492 + r547494;
        double r547496 = r547495 - r547490;
        double r547497 = r547489 + r547496;
        return r547497;
}

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

Original9.2
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. 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

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

  5. Applied associate-/r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 
(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))))