Average Error: 3.4 → 3.4
Time: 11.8s
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 r592926 = x;
        double r592927 = 1.0;
        double r592928 = y;
        double r592929 = r592927 - r592928;
        double r592930 = z;
        double r592931 = r592929 * r592930;
        double r592932 = r592927 - r592931;
        double r592933 = r592926 * r592932;
        return r592933;
}
↓
double f(double x, double y, double z) {
        double r592934 = x;
        double r592935 = z;
        double r592936 = y;
        double r592937 = 1.0;
        double r592938 = r592936 - r592937;
        double r592939 = r592935 * r592938;
        double r592940 = r592939 + r592937;
        double r592941 = r592934 * r592940;
        return r592941;
}

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. 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. Simplified1.7

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

  6. Final simplification3.4

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

Reproduce

herbie shell --seed 2019297 
(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))))