Expression 1, p15

Average Error: 0.4 → 0.3

Time: 19.4s

Precision: 64

\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]

Math

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

↓

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

C

double f(double a, double b, double c, double d, double e) {
        double r5005079 = e;
        double r5005080 = d;
        double r5005081 = r5005079 + r5005080;
        double r5005082 = c;
        double r5005083 = r5005081 + r5005082;
        double r5005084 = b;
        double r5005085 = r5005083 + r5005084;
        double r5005086 = a;
        double r5005087 = r5005085 + r5005086;
        return r5005087;
}

↓

double f(double a, double b, double c, double d, double e) {
        double r5005088 = b;
        double r5005089 = a;
        double r5005090 = r5005088 + r5005089;
        double r5005091 = c;
        double r5005092 = d;
        double r5005093 = e;
        double r5005094 = r5005092 + r5005093;
        double r5005095 = r5005091 + r5005094;
        double r5005096 = r5005090 + r5005095;
        return r5005096;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Target

Original	0.4
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 0.4

   \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
2. Using strategy rm

3. Applied associate-+l+ 0.3

   \[\leadsto \color{blue}{\left(\left(e + d\right) + c\right) + \left(b + a\right)}\]

4. Final simplification 0.3

   \[\leadsto \left(b + a\right) + \left(c + \left(d + e\right)\right)\]

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))