Average Error: 9.5 → 0.1
Time: 2.9s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t \cdot z} + \frac{2}{t}\right) - 2\right)\]
\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 r822571 = x;
        double r822572 = y;
        double r822573 = r822571 / r822572;
        double r822574 = 2.0;
        double r822575 = z;
        double r822576 = r822575 * r822574;
        double r822577 = 1.0;
        double r822578 = t;
        double r822579 = r822577 - r822578;
        double r822580 = r822576 * r822579;
        double r822581 = r822574 + r822580;
        double r822582 = r822578 * r822575;
        double r822583 = r822581 / r822582;
        double r822584 = r822573 + r822583;
        return r822584;
}
↓
double f(double x, double y, double z, double t) {
        double r822585 = x;
        double r822586 = y;
        double r822587 = r822585 / r822586;
        double r822588 = 2.0;
        double r822589 = t;
        double r822590 = z;
        double r822591 = r822589 * r822590;
        double r822592 = r822588 / r822591;
        double r822593 = r822588 / r822589;
        double r822594 = r822592 + r822593;
        double r822595 = r822594 - r822588;
        double r822596 = r822587 + r822595;
        return r822596;
}

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

Original9.5
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.5

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

  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 2020056 
(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))))