Average Error: 3.5 → 3.5
Time: 12.5s
Precision: binary64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\left(x + x \cdot \left(z \cdot y\right)\right) - x \cdot z\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\left(x + x \cdot \left(z \cdot y\right)\right) - x \cdot z
(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))
↓
(FPCore (x y z) :precision binary64 (- (+ x (* x (* z y))) (* x z)))
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 + (x * (z * y))) - (x * z);
}

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
Target0.3
Herbie3.5
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Initial program 3.5

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

  2. Taylor expanded around 0 3.5

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

  3. Final simplification3.5

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

Reproduce

herbie shell --seed 2021098 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :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))))