Average Error: 8.8 → 0.1
Time: 17.2s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2.0}{z \cdot t} + \frac{2.0}{t}\right) + \frac{x}{y}\right) - 2.0\]
\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}{z \cdot t} + \frac{2.0}{t}\right) + \frac{x}{y}\right) - 2.0
double f(double x, double y, double z, double t) {
        double r37269508 = x;
        double r37269509 = y;
        double r37269510 = r37269508 / r37269509;
        double r37269511 = 2.0;
        double r37269512 = z;
        double r37269513 = r37269512 * r37269511;
        double r37269514 = 1.0;
        double r37269515 = t;
        double r37269516 = r37269514 - r37269515;
        double r37269517 = r37269513 * r37269516;
        double r37269518 = r37269511 + r37269517;
        double r37269519 = r37269515 * r37269512;
        double r37269520 = r37269518 / r37269519;
        double r37269521 = r37269510 + r37269520;
        return r37269521;
}
↓
double f(double x, double y, double z, double t) {
        double r37269522 = 2.0;
        double r37269523 = z;
        double r37269524 = t;
        double r37269525 = r37269523 * r37269524;
        double r37269526 = r37269522 / r37269525;
        double r37269527 = r37269522 / r37269524;
        double r37269528 = r37269526 + r37269527;
        double r37269529 = x;
        double r37269530 = y;
        double r37269531 = r37269529 / r37269530;
        double r37269532 = r37269528 + r37269531;
        double r37269533 = r37269532 - r37269522;
        return r37269533;
}

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

Derivation

  1. Initial program 8.8

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2.0}{t}, \frac{\mathsf{fma}\left(z, 1.0, 1\right)}{z}, \frac{x}{y}\right) - 2.0}\]

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied div-inv0.1

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

  7. Applied associate-/l*0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(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))))