Average Error: 0.4 → 0.3
Time: 12.7s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(\left(c + d\right) + \left(a + b\right)\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(\left(c + d\right) + \left(a + b\right)\right)
double f(double a, double b, double c, double d, double e) {
        double r7042153 = e;
        double r7042154 = d;
        double r7042155 = r7042153 + r7042154;
        double r7042156 = c;
        double r7042157 = r7042155 + r7042156;
        double r7042158 = b;
        double r7042159 = r7042157 + r7042158;
        double r7042160 = a;
        double r7042161 = r7042159 + r7042160;
        return r7042161;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r7042162 = e;
        double r7042163 = c;
        double r7042164 = d;
        double r7042165 = r7042163 + r7042164;
        double r7042166 = a;
        double r7042167 = b;
        double r7042168 = r7042166 + r7042167;
        double r7042169 = r7042165 + r7042168;
        double r7042170 = r7042162 + r7042169;
        return r7042170;
}

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. Taylor expanded around 0 0.3

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

  6. Applied associate-+l+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019170 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1.0 a 2.0 b 4.0 c 8.0 d 16.0 e 32.0)

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

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