Average Error: 9.1 → 0.1
Time: 3.2s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{\frac{2}{t}}{z} + \frac{2}{t}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{\frac{2}{t}}{z} + \frac{2}{t}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r871052 = x;
        double r871053 = y;
        double r871054 = r871052 / r871053;
        double r871055 = 2.0;
        double r871056 = z;
        double r871057 = r871056 * r871055;
        double r871058 = 1.0;
        double r871059 = t;
        double r871060 = r871058 - r871059;
        double r871061 = r871057 * r871060;
        double r871062 = r871055 + r871061;
        double r871063 = r871059 * r871056;
        double r871064 = r871062 / r871063;
        double r871065 = r871054 + r871064;
        return r871065;
}
↓
double f(double x, double y, double z, double t) {
        double r871066 = x;
        double r871067 = y;
        double r871068 = r871066 / r871067;
        double r871069 = 2.0;
        double r871070 = t;
        double r871071 = r871069 / r871070;
        double r871072 = z;
        double r871073 = r871071 / r871072;
        double r871074 = r871073 + r871071;
        double r871075 = r871074 - r871069;
        double r871076 = r871068 + r871075;
        return r871076;
}

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. Using strategy rm

  9. Applied associate-/r*0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 
(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))))