(+ (+ (* (* a t) t) (* s t)) p)

Average Error: 0.1 → 0.1

Time: 1.5s

Precision: binary64

Math

\[\left(\left(a \cdot t\right) \cdot t + s \cdot t\right) + p\]

↓

\[p + t \cdot \left(a \cdot t + s\right)\]

C

double code(double a, double t, double s, double p) {
	return ((double) (((double) (((double) (((double) (a * t)) * t)) + ((double) (s * t)))) + p));
}

↓

double code(double a, double t, double s, double p) {
	return ((double) (p + ((double) (t * ((double) (((double) (a * t)) + s))))));
}

Error

Bits error versus a

Bits error versus t

Bits error versus s

Bits error versus p

Derivation

1. Initial program 0.1

   \[\left(\left(a \cdot t\right) \cdot t + s \cdot t\right) + p\]

2. Simplified 0.1

   \[\leadsto \color{blue}{p + t \cdot \left(a \cdot t + s\right)}\]

3. Final simplification 0.1

   \[\leadsto p + t \cdot \left(a \cdot t + s\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a t s p)
  :name "(+ (+ (* (* a t) t) (* s t)) p)"
  :precision binary64
  (+ (+ (* (* a t) t) (* s t)) p))