Average Error: 9.3 → 0.1
Time: 10.2s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) - 2.0\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) - 2.0\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r16957642 = x;
        double r16957643 = y;
        double r16957644 = r16957642 / r16957643;
        double r16957645 = 2.0;
        double r16957646 = z;
        double r16957647 = r16957646 * r16957645;
        double r16957648 = 1.0;
        double r16957649 = t;
        double r16957650 = r16957648 - r16957649;
        double r16957651 = r16957647 * r16957650;
        double r16957652 = r16957645 + r16957651;
        double r16957653 = r16957649 * r16957646;
        double r16957654 = r16957652 / r16957653;
        double r16957655 = r16957644 + r16957654;
        return r16957655;
}
↓
double f(double x, double y, double z, double t) {
        double r16957656 = 2.0;
        double r16957657 = t;
        double r16957658 = r16957656 / r16957657;
        double r16957659 = z;
        double r16957660 = r16957658 / r16957659;
        double r16957661 = r16957658 + r16957660;
        double r16957662 = r16957661 - r16957656;
        double r16957663 = x;
        double r16957664 = y;
        double r16957665 = r16957663 / r16957664;
        double r16957666 = r16957662 + r16957665;
        return r16957666;
}

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

Original9.3
Target0.1
Herbie0.1
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.3

    \[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2.0 \cdot \frac{1}{t} + 2.0 \cdot \frac{1}{t \cdot z}\right) - 2.0\right)}\]

  3. Simplified0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2.0}{t} + \left(\frac{2.0}{z \cdot t} - 2.0\right)\right)}\]
  4. Using strategy rm

  5. Applied associate-+r-0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(\frac{2.0}{t} + \frac{2.0}{z \cdot t}\right) - 2.0\right)}\]

  6. Simplified0.1

    \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(\frac{\frac{2.0}{t}}{z} + \frac{2.0}{t}\right)} - 2.0\right)\]

  7. Final simplification0.1

    \[\leadsto \left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) - 2.0\right) + \frac{x}{y}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))