Average Error: 3.3 → 0.2
Time: 3.4s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -1.3495595828906216 \cdot 10^{192} \lor \neg \left(\left(1 - y\right) \cdot z \le 3.09952408847658801 \cdot 10^{180}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(1 - y\right) \cdot z \le -1.3495595828906216 \cdot 10^{192} \lor \neg \left(\left(1 - y\right) \cdot z \le 3.09952408847658801 \cdot 10^{180}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r765319 = x;
        double r765320 = 1.0;
        double r765321 = y;
        double r765322 = r765320 - r765321;
        double r765323 = z;
        double r765324 = r765322 * r765323;
        double r765325 = r765320 - r765324;
        double r765326 = r765319 * r765325;
        return r765326;
}
↓
double f(double x, double y, double z) {
        double r765327 = 1.0;
        double r765328 = y;
        double r765329 = r765327 - r765328;
        double r765330 = z;
        double r765331 = r765329 * r765330;
        double r765332 = -1.3495595828906216e+192;
        bool r765333 = r765331 <= r765332;
        double r765334 = 3.099524088476588e+180;
        bool r765335 = r765331 <= r765334;
        double r765336 = !r765335;
        bool r765337 = r765333 || r765336;
        double r765338 = x;
        double r765339 = r765338 * r765327;
        double r765340 = r765338 * r765330;
        double r765341 = r765328 - r765327;
        double r765342 = r765340 * r765341;
        double r765343 = r765339 + r765342;
        double r765344 = r765330 * r765328;
        double r765345 = r765338 * r765344;
        double r765346 = -r765327;
        double r765347 = r765340 * r765346;
        double r765348 = r765345 + r765347;
        double r765349 = r765339 + r765348;
        double r765350 = r765337 ? r765343 : r765349;
        return r765350;
}

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

Original3.3
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- 1.0 y) z) < -1.3495595828906216e+192 or 3.099524088476588e+180 < (* (- 1.0 y) z)

    1. Initial program 16.5

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

    3. Applied sub-neg16.5

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

    4. Applied distribute-lft-in16.5

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

    5. Simplified0.6

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

    if -1.3495595828906216e+192 < (* (- 1.0 y) z) < 3.099524088476588e+180

    1. Initial program 0.1

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

    3. Applied sub-neg0.1

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

    4. Applied distribute-lft-in0.1

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

    5. Simplified1.9

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

    7. Applied sub-neg1.9

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

    8. Applied distribute-lft-in1.9

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

    9. Simplified0.1

      \[\leadsto x \cdot 1 + \left(\color{blue}{x \cdot \left(z \cdot y\right)} + \left(x \cdot z\right) \cdot \left(-1\right)\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -1.3495595828906216 \cdot 10^{192} \lor \neg \left(\left(1 - y\right) \cdot z \le 3.09952408847658801 \cdot 10^{180}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(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))))