Average Error: 0.0 → 0.0
Time: 3.8s
Precision: 64
Internal Precision: 128
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(b + a\right) \cdot \left(b + a\right)\]

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(b \cdot a + b \cdot b\right) + b \cdot a\right) + a \cdot a\]

Derivation

  1. Initial program 0.0

    \[\left(a + b\right) \cdot \left(a + b\right)\]

  2. Final simplification0.0

    \[\leadsto \left(b + a\right) \cdot \left(b + a\right)\]

Reproduce

herbie shell --seed 2019022 +o rules:numerics
(FPCore (a b)
  :name "Expression 4, p15"
  :pre (and (<= 5 a 10) (<= 0 b 0.001))

  :herbie-target
  (+ (+ (+ (* b a) (* b b)) (* b a)) (* a a))

  (* (+ a b) (+ a b)))

Details

Time bar (total: 3.5s)Debug log

sample21.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
6.0ms256×pre80true

simplify23.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
22.0ms
(* (+ a b) (+ a b))

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ a b) (+ a b))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
6×flip-+
6×flip3-+
6×pow1
4×frac-times
3×add-cube-cbrt
3×add-exp-log
3×associate-*l*
3×associate-*r*
3×add-cbrt-cube
3×*-un-lft-identity
3×add-sqr-sqrt
2×associate-*r/
2×associate-*l/
1×add-log-exp
1×log1p-expm1-u
1×cbrt-unprod
1×pow-prod-up
1×*-commutative
1×prod-exp
1×pow-prod-down
1×pow-plus
1×distribute-lft-in
1×expm1-log1p-u
1×distribute-rgt-in
1×pow2
Counts
1 → 32
Calls
1 calls:
Slowest
4.0ms
(* (+ a b) (+ a b))

series13.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
13.0ms
(* (+ a b) (+ a b))

simplify2.0s

Counts
28 → 35
Calls
28 calls:
Slowest
298.0ms
(* (- (* a a) (* b b)) (+ (pow a 3) (pow b 3)))
267.0ms
(* (+ (* a a) (- (* b b) (* a b))) (+ (* a a) (- (* b b) (* a b))))
206.0ms
(* (+ (pow a 3) (pow b 3)) (+ (pow a 3) (pow b 3)))
204.0ms
(* (+ (pow a 3) (pow b 3)) (+ a b))
176.0ms
(* (- a b) (+ (* a a) (- (* b b) (* a b))))

prune216.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma (fma 2 a b) b (* a a))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×add-log-exp
1×log1p-expm1-u
1×fma-udef
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×*-un-lft-identity
1×pow1
1×expm1-log1p-u
1×add-sqr-sqrt
Counts
1 → 10
Calls
1 calls:
Slowest
0.0ms
(fma (fma 2 a b) b (* a a))

series21.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
21.0ms
(fma (fma 2 a b) b (* a a))

simplify154.0ms

Counts
3 → 13
Calls
3 calls:
Slowest
54.0ms
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))
51.0ms
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))
48.0ms
(+ (pow a 2) (+ (pow b 2) (* 2 (* a b))))

prune101.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes123.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms

end0.0ms

sample762.0ms

Algorithm
intervals
Results
339.0ms8000×body80valid
292.0ms8000×pre80true