Average Error: 3.6 → 1.5
Time: 3.4s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)
double f(double x, double y, double z) {
        double r818167 = x;
        double r818168 = 1.0;
        double r818169 = y;
        double r818170 = r818168 - r818169;
        double r818171 = z;
        double r818172 = r818170 * r818171;
        double r818173 = r818168 - r818172;
        double r818174 = r818167 * r818173;
        return r818174;
}
↓
double f(double x, double y, double z) {
        double r818175 = x;
        double r818176 = 1.0;
        double r818177 = r818175 * r818176;
        double r818178 = z;
        double r818179 = r818175 * r818178;
        double r818180 = y;
        double r818181 = r818180 - r818176;
        double r818182 = r818179 * r818181;
        double r818183 = r818177 + r818182;
        return r818183;
}

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

Original3.6
Target0.3
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Initial program 3.6

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

  3. Applied sub-neg3.6

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

  4. Applied distribute-lft-in3.6

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

  5. Simplified1.5

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

  6. Final simplification1.5

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

Reproduce

herbie shell --seed 2020083 
(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))))