Average Error: 9.9 → 1.3
Time: 18.7s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\frac{\sqrt[3]{\left(y - z\right) + 1} \cdot \sqrt[3]{\left(y - z\right) + 1}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{\left(y - z\right) + 1}}}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\frac{\sqrt[3]{\left(y - z\right) + 1} \cdot \sqrt[3]{\left(y - z\right) + 1}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{\left(y - z\right) + 1}}}
double f(double x, double y, double z) {
        double r382252 = x;
        double r382253 = y;
        double r382254 = z;
        double r382255 = r382253 - r382254;
        double r382256 = 1.0;
        double r382257 = r382255 + r382256;
        double r382258 = r382252 * r382257;
        double r382259 = r382258 / r382254;
        return r382259;
}
↓
double f(double x, double y, double z) {
        double r382260 = y;
        double r382261 = z;
        double r382262 = r382260 - r382261;
        double r382263 = 1.0;
        double r382264 = r382262 + r382263;
        double r382265 = cbrt(r382264);
        double r382266 = r382265 * r382265;
        double r382267 = cbrt(r382261);
        double r382268 = r382267 * r382267;
        double r382269 = r382266 / r382268;
        double r382270 = x;
        double r382271 = r382267 / r382265;
        double r382272 = r382270 / r382271;
        double r382273 = r382269 * r382272;
        return r382273;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.9
Target0.4
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Initial program 9.9

    \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
  2. Using strategy rm

  3. Applied associate-/l*3.4

    \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt4.3

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

  6. Applied add-cube-cbrt4.1

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

  7. Applied times-frac4.1

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

  8. Applied *-un-lft-identity4.1

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

  9. Applied times-frac1.3

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

  10. Simplified1.3

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

  11. Final simplification1.3

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))