Error

The X axis uses an exponential scale — Bits error versus `a`

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.4
Target	0.2
Herbie	0.3

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

Derivation

Initial program 0.4
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
Initial simplification0.2
\[\leadsto \left(\left(a + d\right) + \left(c + b\right)\right) + e\]
Using strategy rm
Applied add-sqr-sqrt0.3
\[\leadsto \left(\color{blue}{\sqrt{a + d} \cdot \sqrt{a + d}} + \left(c + b\right)\right) + e\]
Applied fma-def0.3
\[\leadsto \color{blue}{(\left(\sqrt{a + d}\right) \cdot \left(\sqrt{a + d}\right) + \left(c + b\right))_*} + e\]
Using strategy rm
Applied fma-udef0.3
\[\leadsto \color{blue}{\left(\sqrt{a + d} \cdot \sqrt{a + d} + \left(c + b\right)\right)} + e\]
Applied associate-+l+0.3
\[\leadsto \color{blue}{\sqrt{a + d} \cdot \sqrt{a + d} + \left(\left(c + b\right) + e\right)}\]
Simplified0.3
\[\leadsto \color{blue}{\left(d + a\right)} + \left(\left(c + b\right) + e\right)\]
Final simplification0.3
\[\leadsto \left(\left(c + b\right) + e\right) + \left(a + d\right)\]

Runtime

herbie shell --seed 2018349 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

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

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