Average Error: 9.1 → 0.1
Time: 4.3s
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 r689711 = x;
        double r689712 = y;
        double r689713 = r689711 / r689712;
        double r689714 = 2.0;
        double r689715 = z;
        double r689716 = r689715 * r689714;
        double r689717 = 1.0;
        double r689718 = t;
        double r689719 = r689717 - r689718;
        double r689720 = r689716 * r689719;
        double r689721 = r689714 + r689720;
        double r689722 = r689718 * r689715;
        double r689723 = r689721 / r689722;
        double r689724 = r689713 + r689723;
        return r689724;
}
↓
double f(double x, double y, double z, double t) {
        double r689725 = x;
        double r689726 = y;
        double r689727 = r689725 / r689726;
        double r689728 = 2.0;
        double r689729 = t;
        double r689730 = z;
        double r689731 = r689729 * r689730;
        double r689732 = r689728 / r689731;
        double r689733 = r689728 / r689729;
        double r689734 = r689732 + r689733;
        double r689735 = r689734 - r689728;
        double r689736 = r689727 + r689735;
        return r689736;
}

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

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

Derivation

  1. Initial program 9.1

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

  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 2019362 
(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))))