Average Error: 0.4 → 0.3
Time: 3.6s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(\left(e + c\right) + b\right) + a\right) + d\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(\left(e + c\right) + b\right) + a\right) + d
double f(double a, double b, double c, double d, double e) {
        double r109938 = e;
        double r109939 = d;
        double r109940 = r109938 + r109939;
        double r109941 = c;
        double r109942 = r109940 + r109941;
        double r109943 = b;
        double r109944 = r109942 + r109943;
        double r109945 = a;
        double r109946 = r109944 + r109945;
        return r109946;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r109947 = e;
        double r109948 = c;
        double r109949 = r109947 + r109948;
        double r109950 = b;
        double r109951 = r109949 + r109950;
        double r109952 = a;
        double r109953 = r109951 + r109952;
        double r109954 = d;
        double r109955 = r109953 + r109954;
        return r109955;
}

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 *-un-lft-identity0.4

    \[\leadsto \left(\left(\left(e + d\right) + \color{blue}{1 \cdot c}\right) + b\right) + a\]

  4. Applied *-un-lft-identity0.4

    \[\leadsto \left(\left(\color{blue}{1 \cdot \left(e + d\right)} + 1 \cdot c\right) + b\right) + a\]

  5. Applied distribute-lft-out0.4

    \[\leadsto \left(\color{blue}{1 \cdot \left(\left(e + d\right) + c\right)} + b\right) + a\]

  6. Simplified0.4

    \[\leadsto \left(1 \cdot \color{blue}{\left(d + \left(e + c\right)\right)} + b\right) + a\]
  7. Using strategy rm

  8. Applied associate-+l+0.3

    \[\leadsto \color{blue}{1 \cdot \left(d + \left(e + c\right)\right) + \left(b + a\right)}\]
  9. Using strategy rm

  10. Applied distribute-rgt-in0.3

    \[\leadsto \color{blue}{\left(d \cdot 1 + \left(e + c\right) \cdot 1\right)} + \left(b + a\right)\]

  11. Applied associate-+l+0.3

    \[\leadsto \color{blue}{d \cdot 1 + \left(\left(e + c\right) \cdot 1 + \left(b + a\right)\right)}\]

  12. Simplified0.3

    \[\leadsto d \cdot 1 + \color{blue}{\left(\left(\left(e + c\right) + b\right) + a\right)}\]

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2020001 
(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))