Average Error: 0.0 → 0.0
Time: 19.6s
Precision: 64
Internal Precision: 128
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot \left(b + a\right) + \left(b + a\right) \cdot b\]

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. Using strategy rm

  3. Applied distribute-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 +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: 19.0s)Debug log

sample34.0ms

Algorithm
intervals

simplify37.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

37.0ms
(* (+ a b) (+ a b))

prune4.0ms

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
Counts
1 → 32
Calls

1 calls. Slowest were:

4.0ms
(* (+ a b) (+ a b))

series10.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

10.0ms
(* (+ a b) (+ a b))

simplify2.8s

Counts
28 → 35
Calls

28 calls. Slowest were:

728.0ms
(* (- (* a a) (* b b)) (+ (pow a 3) (pow b 3)))
382.0ms
(* (+ (* a a) (- (* b b) (* a b))) (+ (* a a) (- (* b b) (* a b))))
280.0ms
(* (+ (pow a 3) (pow b 3)) (+ (pow a 3) (pow b 3)))

prune244.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
3 → 57
Calls

3 calls. Slowest were:

7.0ms
(+ (* a (+ a b)) (* b (+ a b)))
2.0ms
(* b (+ a b))
2.0ms
(* a (+ a b))

series78.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

27.0ms
(* b (+ a b))
26.0ms
(+ (* a (+ a b)) (* b (+ a b)))
25.0ms
(* a (+ a b))

simplify1.7s

Counts
38 → 66
Calls

38 calls. Slowest were:

299.0ms
(* (+ (* a a) (- (* b b) (* a b))) (+ (* a a) (- (* b b) (* a b))))
185.0ms
(+ (* (* a (+ (pow a 3) (pow b 3))) (+ (* a a) (- (* b b) (* a b)))) (* (+ (* a a) (- (* b b) (* a b))) (* b (+ (pow a 3) (pow b 3)))))
182.0ms
(* (- a b) (+ (* a a) (- (* b b) (* a b))))

prune560.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 3 expressions with local error:

0.5b
(* (+ (pow a 3) (pow b 3)) (+ (pow a 3) (pow b 3)))
0.4b
(* (fma (- b a) b (* a a)) (fma (- b a) b (* a a)))
0.3b
(/ (* (+ (pow a 3) (pow b 3)) (+ (pow a 3) (pow b 3))) (* (fma (- b a) b (* a a)) (fma (- b a) b (* a a))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Counts
3 → 91
Calls

3 calls. Slowest were:

13.0ms
(/ (* (+ (pow a 3) (pow b 3)) (+ (pow a 3) (pow b 3))) (* (fma (- b a) b (* a a)) (fma (- b a) b (* a a))))
12.0ms
(* (+ (pow a 3) (pow b 3)) (+ (pow a 3) (pow b 3)))
4.0ms
(* (fma (- b a) b (* a a)) (fma (- b a) b (* a a)))

series142.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

54.0ms
(* (fma (- b a) b (* a a)) (fma (- b a) b (* a a)))
46.0ms
(/ (* (+ (pow a 3) (pow b 3)) (+ (pow a 3) (pow b 3))) (* (fma (- b a) b (* a a)) (fma (- b a) b (* a a))))
43.0ms
(* (+ (pow a 3) (pow b 3)) (+ (pow a 3) (pow b 3)))

simplify11.6s

Counts
70 → 100
Calls

70 calls. Slowest were:

775.0ms
(* (+ (pow a 3) (pow b 3)) (+ (pow (pow a 3) 3) (pow (pow b 3) 3)))
673.0ms
(* (+ (pow (pow a 3) 3) (pow (pow b 3) 3)) (+ (pow (pow a 3) 3) (pow (pow b 3) 3)))
662.0ms
(* (+ (pow (pow a 3) 3) (pow (pow b 3) 3)) (+ (pow (pow a 3) 3) (pow (pow b 3) 3)))

prune955.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample671.0ms

Algorithm
intervals