Average Error: 9.1 → 0.1
Time: 12.6s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{\frac{2}{z}}{t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{\frac{2}{z}}{t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r42068003 = x;
        double r42068004 = y;
        double r42068005 = r42068003 / r42068004;
        double r42068006 = 2.0;
        double r42068007 = z;
        double r42068008 = r42068007 * r42068006;
        double r42068009 = 1.0;
        double r42068010 = t;
        double r42068011 = r42068009 - r42068010;
        double r42068012 = r42068008 * r42068011;
        double r42068013 = r42068006 + r42068012;
        double r42068014 = r42068010 * r42068007;
        double r42068015 = r42068013 / r42068014;
        double r42068016 = r42068005 + r42068015;
        return r42068016;
}
↓
double f(double x, double y, double z, double t) {
        double r42068017 = 2.0;
        double r42068018 = z;
        double r42068019 = r42068017 / r42068018;
        double r42068020 = t;
        double r42068021 = r42068019 / r42068020;
        double r42068022 = r42068021 - r42068017;
        double r42068023 = r42068017 / r42068020;
        double r42068024 = r42068022 + r42068023;
        double r42068025 = x;
        double r42068026 = y;
        double r42068027 = r42068025 / r42068026;
        double r42068028 = r42068024 + r42068027;
        return r42068028;
}

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

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

  3. Simplified0.1

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

  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

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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))))