Average Error: 9.2 → 0.1
Time: 3.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)
double f(double x, double y, double z, double t) {
        double r741013 = x;
        double r741014 = y;
        double r741015 = r741013 / r741014;
        double r741016 = 2.0;
        double r741017 = z;
        double r741018 = r741017 * r741016;
        double r741019 = 1.0;
        double r741020 = t;
        double r741021 = r741019 - r741020;
        double r741022 = r741018 * r741021;
        double r741023 = r741016 + r741022;
        double r741024 = r741020 * r741017;
        double r741025 = r741023 / r741024;
        double r741026 = r741015 + r741025;
        return r741026;
}
↓
double f(double x, double y, double z, double t) {
        double r741027 = x;
        double r741028 = y;
        double r741029 = r741027 / r741028;
        double r741030 = 1.0;
        double r741031 = cbrt(r741030);
        double r741032 = r741031 * r741031;
        double r741033 = r741032 / r741030;
        double r741034 = 2.0;
        double r741035 = z;
        double r741036 = r741034 / r741035;
        double r741037 = r741036 + r741034;
        double r741038 = t;
        double r741039 = r741037 / r741038;
        double r741040 = r741033 * r741039;
        double r741041 = r741040 - r741034;
        double r741042 = r741029 + r741041;
        return r741042;
}

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 *-un-lft-identity0.1

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

  6. Applied add-cube-cbrt0.1

    \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{1 \cdot t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]

  7. Applied times-frac0.1

    \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\sqrt[3]{1}}{t}\right)} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]

  8. Applied associate-*l*0.1

    \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \left(\frac{\sqrt[3]{1}}{t} \cdot \left(\frac{2}{z} + 2\right)\right)} - 2\right)\]

  9. Simplified0.1

    \[\leadsto \frac{x}{y} + \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \color{blue}{\frac{\frac{2}{z} + 2}{t}} - 2\right)\]

  10. Final simplification0.1

    \[\leadsto \frac{x}{y} + \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)\]

Reproduce

herbie shell --seed 2019356 
(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))))