Average Error: 3.4 → 3.4
Time: 5.4s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[x \cdot \left(z \cdot \left(y - 1\right) + 1\right)\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
x \cdot \left(z \cdot \left(y - 1\right) + 1\right)
double f(double x, double y, double z) {
        double r649351 = x;
        double r649352 = 1.0;
        double r649353 = y;
        double r649354 = r649352 - r649353;
        double r649355 = z;
        double r649356 = r649354 * r649355;
        double r649357 = r649352 - r649356;
        double r649358 = r649351 * r649357;
        return r649358;
}
↓
double f(double x, double y, double z) {
        double r649359 = x;
        double r649360 = z;
        double r649361 = y;
        double r649362 = 1.0;
        double r649363 = r649361 - r649362;
        double r649364 = r649360 * r649363;
        double r649365 = r649364 + r649362;
        double r649366 = r649359 * r649365;
        return r649366;
}

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
Herbie3.4
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.892237649663902900973248011051357504727 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- 1.0 y) z) < -5.3226877608325174e+225 or 2.518193337981877e+209 < (* (- 1.0 y) z)

    1. Initial program 20.6

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

    3. Applied sub-neg20.6

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

    4. Applied distribute-lft-in20.6

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

    5. Simplified0.6

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

    if -5.3226877608325174e+225 < (* (- 1.0 y) z) < 2.518193337981877e+209

    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 simplification3.4

    \[\leadsto x \cdot \left(z \cdot \left(y - 1\right) + 1\right)\]

Reproduce

herbie shell --seed 1978988140 
(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))) -1.618195973607049e50) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 3.8922376496639029e134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x)))))

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