Average Error: 8.8 → 0.1
Time: 6.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t \cdot z} + \frac{2}{t}\right) - 2\right)\]
\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 \cdot z} + \frac{2}{t}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r494531 = x;
        double r494532 = y;
        double r494533 = r494531 / r494532;
        double r494534 = 2.0;
        double r494535 = z;
        double r494536 = r494535 * r494534;
        double r494537 = 1.0;
        double r494538 = t;
        double r494539 = r494537 - r494538;
        double r494540 = r494536 * r494539;
        double r494541 = r494534 + r494540;
        double r494542 = r494538 * r494535;
        double r494543 = r494541 / r494542;
        double r494544 = r494533 + r494543;
        return r494544;
}
↓
double f(double x, double y, double z, double t) {
        double r494545 = x;
        double r494546 = y;
        double r494547 = r494545 / r494546;
        double r494548 = 2.0;
        double r494549 = t;
        double r494550 = z;
        double r494551 = r494549 * r494550;
        double r494552 = r494548 / r494551;
        double r494553 = r494548 / r494549;
        double r494554 = r494552 + r494553;
        double r494555 = r494554 - r494548;
        double r494556 = r494547 + r494555;
        return r494556;
}

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

Original8.8
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 8.8

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

  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 distribute-lft-in0.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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))))