Average Error: 0.4 → 0.3
Time: 5.2s
Precision: binary64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(d + \left(e + \left(b + c\right)\right)\right) + a\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(d + \left(e + \left(b + c\right)\right)\right) + a
double code(double a, double b, double c, double d, double e) {
	return ((double) (((double) (((double) (((double) (e + d)) + c)) + b)) + a));
}
↓
double code(double a, double b, double c, double d, double e) {
	return ((double) (((double) (d + ((double) (e + ((double) (b + c)))))) + a));
}

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. Taylor expanded around 0 0.4

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

  4. Applied associate-+l+0.4

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020148 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :precision binary64
  :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))