Average Error: 9.4 → 0.1
Time: 6.8s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{1}{t} \cdot \frac{2}{z}\right) - 2\right)\]
\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{1}{t} \cdot \frac{2}{z}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r786546 = x;
        double r786547 = y;
        double r786548 = r786546 / r786547;
        double r786549 = 2.0;
        double r786550 = z;
        double r786551 = r786550 * r786549;
        double r786552 = 1.0;
        double r786553 = t;
        double r786554 = r786552 - r786553;
        double r786555 = r786551 * r786554;
        double r786556 = r786549 + r786555;
        double r786557 = r786553 * r786550;
        double r786558 = r786556 / r786557;
        double r786559 = r786548 + r786558;
        return r786559;
}
↓
double f(double x, double y, double z, double t) {
        double r786560 = x;
        double r786561 = y;
        double r786562 = r786560 / r786561;
        double r786563 = 2.0;
        double r786564 = t;
        double r786565 = r786563 / r786564;
        double r786566 = 1.0;
        double r786567 = r786566 / r786564;
        double r786568 = z;
        double r786569 = r786563 / r786568;
        double r786570 = r786567 * r786569;
        double r786571 = r786565 + r786570;
        double r786572 = r786571 - r786563;
        double r786573 = r786562 + r786572;
        return r786573;
}

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

Original9.4
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.4

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

  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 *-un-lft-identity0.1

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

  6. Applied times-frac0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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))))