Average Error: 0.4 → 0.3
Time: 2.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + \left(d + \left(b + c\right)\right)\right) + a\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + \left(d + \left(b + c\right)\right)\right) + a
double f(double a, double b, double c, double d, double e) {
        double r124231 = e;
        double r124232 = d;
        double r124233 = r124231 + r124232;
        double r124234 = c;
        double r124235 = r124233 + r124234;
        double r124236 = b;
        double r124237 = r124235 + r124236;
        double r124238 = a;
        double r124239 = r124237 + r124238;
        return r124239;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r124240 = e;
        double r124241 = d;
        double r124242 = b;
        double r124243 = c;
        double r124244 = r124242 + r124243;
        double r124245 = r124241 + r124244;
        double r124246 = r124240 + r124245;
        double r124247 = a;
        double r124248 = r124246 + r124247;
        return r124248;
}

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

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

  5. Applied associate-+l+0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020056 +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))