Average Error: 9.2 → 0.8
Time: 3.4s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{1}{t} \cdot \left(\sqrt[3]{\frac{2}{z} + 2} \cdot \sqrt[3]{\frac{2}{z} + 2}\right)\right) \cdot \sqrt[3]{\frac{2}{z} + 2} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{1}{t} \cdot \left(\sqrt[3]{\frac{2}{z} + 2} \cdot \sqrt[3]{\frac{2}{z} + 2}\right)\right) \cdot \sqrt[3]{\frac{2}{z} + 2} - 2\right)
double f(double x, double y, double z, double t) {
        double r753180 = x;
        double r753181 = y;
        double r753182 = r753180 / r753181;
        double r753183 = 2.0;
        double r753184 = z;
        double r753185 = r753184 * r753183;
        double r753186 = 1.0;
        double r753187 = t;
        double r753188 = r753186 - r753187;
        double r753189 = r753185 * r753188;
        double r753190 = r753183 + r753189;
        double r753191 = r753187 * r753184;
        double r753192 = r753190 / r753191;
        double r753193 = r753182 + r753192;
        return r753193;
}
↓
double f(double x, double y, double z, double t) {
        double r753194 = x;
        double r753195 = y;
        double r753196 = r753194 / r753195;
        double r753197 = 1.0;
        double r753198 = t;
        double r753199 = r753197 / r753198;
        double r753200 = 2.0;
        double r753201 = z;
        double r753202 = r753200 / r753201;
        double r753203 = r753202 + r753200;
        double r753204 = cbrt(r753203);
        double r753205 = r753204 * r753204;
        double r753206 = r753199 * r753205;
        double r753207 = r753206 * r753204;
        double r753208 = r753207 - r753200;
        double r753209 = r753196 + r753208;
        return r753209;
}

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

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 add-cube-cbrt0.7

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

  6. Applied associate-*r*0.8

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

  7. Final simplification0.8

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

Reproduce

herbie shell --seed 2020049 
(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))))