Expression 1, p15

Average Error: 0.4 → 0.3

Time: 5.8s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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

Math

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

↓

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

C

double f(double a, double b, double c, double d, double e) {
        double r71352 = e;
        double r71353 = d;
        double r71354 = r71352 + r71353;
        double r71355 = c;
        double r71356 = r71354 + r71355;
        double r71357 = b;
        double r71358 = r71356 + r71357;
        double r71359 = a;
        double r71360 = r71358 + r71359;
        return r71360;
}

↓

double f(double a, double b, double c, double d, double e) {
        double r71361 = e;
        double r71362 = d;
        double r71363 = r71361 + r71362;
        double r71364 = c;
        double r71365 = r71363 + r71364;
        double r71366 = b;
        double r71367 = a;
        double r71368 = r71366 + r71367;
        double r71369 = r71365 + r71368;
        return r71369;
}

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

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :precision binary64
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

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

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