Average Error: 3.4 → 2.3
Time: 22.3s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[1 \cdot x + \left(x \cdot \left(z \cdot \left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right)\right)\right) \cdot \sqrt[3]{y - 1}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
1 \cdot x + \left(x \cdot \left(z \cdot \left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right)\right)\right) \cdot \sqrt[3]{y - 1}
double f(double x, double y, double z) {
        double r495940 = x;
        double r495941 = 1.0;
        double r495942 = y;
        double r495943 = r495941 - r495942;
        double r495944 = z;
        double r495945 = r495943 * r495944;
        double r495946 = r495941 - r495945;
        double r495947 = r495940 * r495946;
        return r495947;
}
↓
double f(double x, double y, double z) {
        double r495948 = 1.0;
        double r495949 = x;
        double r495950 = r495948 * r495949;
        double r495951 = z;
        double r495952 = y;
        double r495953 = r495952 - r495948;
        double r495954 = cbrt(r495953);
        double r495955 = r495954 * r495954;
        double r495956 = r495951 * r495955;
        double r495957 = r495949 * r495956;
        double r495958 = r495957 * r495954;
        double r495959 = r495950 + r495958;
        return r495959;
}

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

Original3.4
Target0.2
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.892237649663902900973248011051357504727 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Initial program 3.4

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

  3. Applied sub-neg3.4

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

  4. Applied distribute-lft-in3.4

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

  5. Simplified3.4

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

  6. Simplified1.7

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

  8. Applied add-cube-cbrt2.0

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

  9. Applied associate-*r*2.0

    \[\leadsto 1 \cdot x + \color{blue}{\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right)\right) \cdot \sqrt[3]{y - 1}}\]
  10. Using strategy rm

  11. Applied associate-*l*2.3

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

  12. Final simplification2.3

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1 (* (- 1 y) z))) -1.618195973607049e+50) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x)))))

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