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

↓

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

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 code(double x, double y, double z) {
	return (x * (1.0 - ((1.0 - y) * z)));
}

↓

double code(double x, double y, double z) {
	return ((x * 1.0) + ((x * z) * (y - 1.0)));
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	3.5
Target	0.2
Herbie	1.7

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

Derivation

Initial program 3.5
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
Using strategy rm
Applied sub-neg3.5
\[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(1 - y\right) \cdot z\right)\right)}\]
Applied distribute-lft-in3.5
\[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-\left(1 - y\right) \cdot z\right)}\]
Simplified1.7
\[\leadsto x \cdot 1 + \color{blue}{\left(x \cdot z\right) \cdot \left(y - 1\right)}\]
Final simplification1.7
\[\leadsto x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\]

Reproduce

herbie shell --seed 2020091 
(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))))