Average Error: 0.4 → 0.3
Time: 4.4s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(d + \left(b + c\right)\right) + a\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(d + \left(b + c\right)\right) + a\right)
double f(double a, double b, double c, double d, double e) {
        double r100487 = e;
        double r100488 = d;
        double r100489 = r100487 + r100488;
        double r100490 = c;
        double r100491 = r100489 + r100490;
        double r100492 = b;
        double r100493 = r100491 + r100492;
        double r100494 = a;
        double r100495 = r100493 + r100494;
        return r100495;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r100496 = e;
        double r100497 = d;
        double r100498 = b;
        double r100499 = c;
        double r100500 = r100498 + r100499;
        double r100501 = r100497 + r100500;
        double r100502 = a;
        double r100503 = r100501 + r100502;
        double r100504 = r100496 + r100503;
        return r100504;
}

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+0.4

    \[\leadsto \left(\color{blue}{\left(e + \left(d + c\right)\right)} + b\right) + a\]
  4. Using strategy rm

  5. Applied associate-+l+0.3

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

  6. Simplified0.3

    \[\leadsto \left(e + \color{blue}{\left(d + \left(b + c\right)\right)}\right) + a\]
  7. Using strategy rm

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020001 +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))