Average Error: 9.2 → 0.1
Time: 5.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t \cdot z} + \frac{2}{t}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2}{t \cdot z} + \frac{2}{t}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r804090 = x;
        double r804091 = y;
        double r804092 = r804090 / r804091;
        double r804093 = 2.0;
        double r804094 = z;
        double r804095 = r804094 * r804093;
        double r804096 = 1.0;
        double r804097 = t;
        double r804098 = r804096 - r804097;
        double r804099 = r804095 * r804098;
        double r804100 = r804093 + r804099;
        double r804101 = r804097 * r804094;
        double r804102 = r804100 / r804101;
        double r804103 = r804092 + r804102;
        return r804103;
}
↓
double f(double x, double y, double z, double t) {
        double r804104 = x;
        double r804105 = y;
        double r804106 = r804104 / r804105;
        double r804107 = 2.0;
        double r804108 = t;
        double r804109 = z;
        double r804110 = r804108 * r804109;
        double r804111 = r804107 / r804110;
        double r804112 = r804107 / r804108;
        double r804113 = r804111 + r804112;
        double r804114 = r804113 - r804107;
        double r804115 = r804106 + r804114;
        return r804115;
}

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

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

Derivation

  1. Initial program 9.2

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

  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(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))))