Average Error: 9.8 → 0.1
Time: 16.2s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \left(\frac{\frac{2}{z}}{t} - 2\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} + \left(\frac{\frac{2}{z}}{t} - 2\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r34849226 = x;
        double r34849227 = y;
        double r34849228 = r34849226 / r34849227;
        double r34849229 = 2.0;
        double r34849230 = z;
        double r34849231 = r34849230 * r34849229;
        double r34849232 = 1.0;
        double r34849233 = t;
        double r34849234 = r34849232 - r34849233;
        double r34849235 = r34849231 * r34849234;
        double r34849236 = r34849229 + r34849235;
        double r34849237 = r34849233 * r34849230;
        double r34849238 = r34849236 / r34849237;
        double r34849239 = r34849228 + r34849238;
        return r34849239;
}
↓
double f(double x, double y, double z, double t) {
        double r34849240 = 2.0;
        double r34849241 = t;
        double r34849242 = r34849240 / r34849241;
        double r34849243 = z;
        double r34849244 = r34849240 / r34849243;
        double r34849245 = r34849244 / r34849241;
        double r34849246 = r34849245 - r34849240;
        double r34849247 = r34849242 + r34849246;
        double r34849248 = x;
        double r34849249 = y;
        double r34849250 = r34849248 / r34849249;
        double r34849251 = r34849247 + r34849250;
        return r34849251;
}

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

Original9.8
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.8

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

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Taylor expanded around 0 0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(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))))