Average Error: 0.4 → 0.3
Time: 5.5s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \left(c + \left(b + a\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + d\right) + \left(c + \left(b + a\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r100342 = e;
        double r100343 = d;
        double r100344 = r100342 + r100343;
        double r100345 = c;
        double r100346 = r100344 + r100345;
        double r100347 = b;
        double r100348 = r100346 + r100347;
        double r100349 = a;
        double r100350 = r100348 + r100349;
        return r100350;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r100351 = e;
        double r100352 = d;
        double r100353 = r100351 + r100352;
        double r100354 = c;
        double r100355 = b;
        double r100356 = a;
        double r100357 = r100355 + r100356;
        double r100358 = r100354 + r100357;
        double r100359 = r100353 + r100358;
        return r100359;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.3
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

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. Using strategy rm

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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))