Average Error: 0.0 → 0.0
Time: 6.7s
Precision: binary64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(b \cdot \left(1 \cdot t - 2\right) + 1 \cdot \left(y \cdot b\right)\right)\]
\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(b \cdot \left(1 \cdot t - 2\right) + 1 \cdot \left(y \cdot b\right)\right)
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (x - ((double) (((double) (y - 1.0)) * z)))) - ((double) (((double) (t - 1.0)) * a)))) + ((double) (((double) (((double) (y + t)) - 2.0)) * b))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (x - ((double) (((double) (y - 1.0)) * z)))) - ((double) (((double) (t - 1.0)) * a)))) + ((double) (((double) (b * ((double) (((double) (1.0 * t)) - 2.0)))) + ((double) (1.0 * ((double) (y * b))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied flip--15.4

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\frac{\left(y + t\right) \cdot \left(y + t\right) - 2 \cdot 2}{\left(y + t\right) + 2}} \cdot b\]

  4. Applied associate-*l/18.8

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\frac{\left(\left(y + t\right) \cdot \left(y + t\right) - 2 \cdot 2\right) \cdot b}{\left(y + t\right) + 2}}\]

  5. Taylor expanded around 0 0.0

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(1 \cdot \left(y \cdot b\right) + 1 \cdot \left(t \cdot b\right)\right) - 2 \cdot b\right)}\]

  6. Simplified0.0

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(b \cdot \left(1 \cdot t - 2\right) + 1 \cdot \left(y \cdot b\right)\right)}\]

  7. Final simplification0.0

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(b \cdot \left(1 \cdot t - 2\right) + 1 \cdot \left(y \cdot b\right)\right)\]

Reproduce

herbie shell --seed 2020148 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))