Average Error: 3.5 → 1.7
Time: 27.8s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\left(y - 1\right) \cdot \left(z \cdot x\right) + x \cdot 1\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\left(y - 1\right) \cdot \left(z \cdot x\right) + x \cdot 1
double f(double x, double y, double z) {
        double r39398493 = x;
        double r39398494 = 1.0;
        double r39398495 = y;
        double r39398496 = r39398494 - r39398495;
        double r39398497 = z;
        double r39398498 = r39398496 * r39398497;
        double r39398499 = r39398494 - r39398498;
        double r39398500 = r39398493 * r39398499;
        return r39398500;
}
↓
double f(double x, double y, double z) {
        double r39398501 = y;
        double r39398502 = 1.0;
        double r39398503 = r39398501 - r39398502;
        double r39398504 = z;
        double r39398505 = x;
        double r39398506 = r39398504 * r39398505;
        double r39398507 = r39398503 * r39398506;
        double r39398508 = r39398505 * r39398502;
        double r39398509 = r39398507 + r39398508;
        return r39398509;
}

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
Target0.2
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.892237649663902900973248011051357504727 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Initial program 3.5

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

  3. Applied sub-neg3.5

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

  4. Applied distribute-lft-in3.5

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

  5. Taylor expanded around inf 3.5

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

  6. Simplified1.7

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

  7. Final simplification1.7

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))