Average Error: 3.7 → 0
Time: 1.6s
Precision: binary64
\[\left(\left(\left(-14 \leq a \land a \leq -13\right) \land \left(-3 \leq b \land b \leq -2\right)\right) \land \left(3 \leq c \land c \leq 3.5\right)\right) \land \left(12.5 \leq d \land d \leq 13.5\right)\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]
↓
\[\mathsf{fma}\left(1, b + c, d + a\right) \cdot 2 \]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\mathsf{fma}\left(1, b + c, d + a\right) \cdot 2

(FPCore (a b c d) :precision binary64 (* (+ a (+ b (+ c d))) 2.0))
↓
(FPCore (a b c d) :precision binary64 (* (fma 1.0 (+ b c) (+ d a)) 2.0))
double code(double a, double b, double c, double d) {
	return (a + (b + (c + d))) * 2.0;
}
↓
double code(double a, double b, double c, double d) {
	return fma(1.0, (b + c), (d + a)) * 2.0;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original3.7
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2 \]

Derivation

  1. Initial program 3.7

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2 \]

  2. Applied egg-rr0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1, b + c, d + a\right)} \cdot 2 \]

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(1, b + c, d + a\right) \cdot 2 \]

Reproduce

herbie shell --seed 2022130 
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (and (and (and (<= -14.0 a) (<= a -13.0)) (and (<= -3.0 b) (<= b -2.0))) (and (<= 3.0 c) (<= c 3.5))) (and (<= 12.5 d) (<= d 13.5)))

  :herbie-target
  (+ (* (+ a b) 2.0) (* (+ c d) 2.0))

  (* (+ a (+ b (+ c d))) 2.0))