Average Error: 0.4 → 0.3
Time: 8.2s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(e + d\right) + \left(c + b\right)\right) + a\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(e + d\right) + \left(c + b\right)\right) + a
double f(double a, double b, double c, double d, double e) {
        double r74151 = e;
        double r74152 = d;
        double r74153 = r74151 + r74152;
        double r74154 = c;
        double r74155 = r74153 + r74154;
        double r74156 = b;
        double r74157 = r74155 + r74156;
        double r74158 = a;
        double r74159 = r74157 + r74158;
        return r74159;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r74160 = e;
        double r74161 = d;
        double r74162 = r74160 + r74161;
        double r74163 = c;
        double r74164 = b;
        double r74165 = r74163 + r74164;
        double r74166 = r74162 + r74165;
        double r74167 = a;
        double r74168 = r74166 + r74167;
        return r74168;
}

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

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019306 +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))