Average Error: 3.5 → 0.1
Time: 3.9s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -4.4945677410742948 \cdot 10^{274} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 7.298284657353298 \cdot 10^{202}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -4.4945677410742948 \cdot 10^{274} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 7.298284657353298 \cdot 10^{202}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\

\end{array}
double f(double x, double y, double z) {
        double r837940 = x;
        double r837941 = 1.0;
        double r837942 = y;
        double r837943 = r837941 - r837942;
        double r837944 = z;
        double r837945 = r837943 * r837944;
        double r837946 = r837941 - r837945;
        double r837947 = r837940 * r837946;
        return r837947;
}
↓
double f(double x, double y, double z) {
        double r837948 = x;
        double r837949 = 1.0;
        double r837950 = y;
        double r837951 = r837949 - r837950;
        double r837952 = z;
        double r837953 = r837951 * r837952;
        double r837954 = r837949 - r837953;
        double r837955 = r837948 * r837954;
        double r837956 = -4.494567741074295e+274;
        bool r837957 = r837955 <= r837956;
        double r837958 = 7.298284657353298e+202;
        bool r837959 = r837955 <= r837958;
        double r837960 = !r837959;
        bool r837961 = r837957 || r837960;
        double r837962 = r837948 * r837949;
        double r837963 = r837948 * r837952;
        double r837964 = r837950 - r837949;
        double r837965 = r837963 * r837964;
        double r837966 = r837962 + r837965;
        double r837967 = r837961 ? r837966 : r837955;
        return r837967;
}

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

Original3.5
Target0.3
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (- 1.0 (* (- 1.0 y) z))) < -4.494567741074295e+274 or 7.298284657353298e+202 < (* x (- 1.0 (* (- 1.0 y) z)))

    1. Initial program 19.7

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

    3. Applied sub-neg19.7

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

    4. Applied distribute-lft-in19.7

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

    5. Simplified0.1

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

    if -4.494567741074295e+274 < (* x (- 1.0 (* (- 1.0 y) z))) < 7.298284657353298e+202

    1. Initial program 0.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -4.4945677410742948 \cdot 10^{274} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 7.298284657353298 \cdot 10^{202}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 
(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))))