Average Error: 8.9 → 0.1
Time: 16.2s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2.0}{t \cdot z} - 2.0\right) + \frac{2.0}{t}\right) + \frac{x}{y}\]
\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 \cdot z} - 2.0\right) + \frac{2.0}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r42001210 = x;
        double r42001211 = y;
        double r42001212 = r42001210 / r42001211;
        double r42001213 = 2.0;
        double r42001214 = z;
        double r42001215 = r42001214 * r42001213;
        double r42001216 = 1.0;
        double r42001217 = t;
        double r42001218 = r42001216 - r42001217;
        double r42001219 = r42001215 * r42001218;
        double r42001220 = r42001213 + r42001219;
        double r42001221 = r42001217 * r42001214;
        double r42001222 = r42001220 / r42001221;
        double r42001223 = r42001212 + r42001222;
        return r42001223;
}
↓
double f(double x, double y, double z, double t) {
        double r42001224 = 2.0;
        double r42001225 = t;
        double r42001226 = z;
        double r42001227 = r42001225 * r42001226;
        double r42001228 = r42001224 / r42001227;
        double r42001229 = r42001228 - r42001224;
        double r42001230 = r42001224 / r42001225;
        double r42001231 = r42001229 + r42001230;
        double r42001232 = x;
        double r42001233 = y;
        double r42001234 = r42001232 / r42001233;
        double r42001235 = r42001231 + r42001234;
        return r42001235;
}

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

Original8.9
Target0.1
Herbie0.1
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 8.9

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

  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

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

  5. Applied div-inv0.1

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

  6. Applied associate-/l*0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 
(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))))