Details

Time bar (total: 13.7s)

sample53.0ms

Algorithm
intervals
Results
32.0ms631×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
01829
15327
217226
350926
4149726
5357326
done500026

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.3b
(* (* b b) (+ 3.0 a))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
18×prod-diff
15×pow1 add-exp-log
14×add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
9×associate-*r*
7×fma-def
6×unpow-prod-down pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
59.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
34.0ms
(* (* a a) (- 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
28.0ms
(* (* b b) (+ 3.0 a))

series308.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
55.0ms
(* (* a a) (- 1.0 a))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))

simplify1.2s

Counts
126 → 126
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02352118
16051768
220891545
done50021519

prune329.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* a a) (- 1.0 a))
0.2b
(/ (* (* b b) (+ (pow 3.0 3) (pow a 3))) (+ (* 3.0 3.0) (- (* a a) (* 3.0 a))))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
2.6b
(* (* b b) (+ (pow 3.0 3) (pow a 3)))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
26×add-sqr-sqrt
24×add-exp-log
23×add-cbrt-cube
22×add-cube-cbrt
18×prod-diff
15×pow1
14×associate-*r*
12×distribute-rgt-in distribute-lft-in
9×prod-exp cbrt-unprod
7×unpow-prod-down
6×associate-*r/ pow-prod-down
5×distribute-lft-out
4×expm1-log1p-u cube-prod log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow flip3-+ times-frac div-exp associate-/r* flip-+
2×sub-neg associate-*l* associate-/r/ *-commutative associate-/l/ unswap-sqr
1×pow-to-exp flip3-- pow-pow frac-2neg pow-exp clear-num sum-cubes flip-- div-inv associate-/l* distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 126
Calls
4 calls:
32.0ms
(* (* a a) (- 1.0 a))
64.0ms
(/ (* (* b b) (+ (pow 3.0 3) (pow a 3))) (+ (* 3.0 3.0) (- (* a a) (* 3.0 a))))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
79.0ms
(* (* b b) (+ (pow 3.0 3) (pow a 3)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* a a) (- 1.0 a))
146.0ms
(/ (* (* b b) (+ (pow 3.0 3) (pow a 3))) (+ (* 3.0 3.0) (- (* a a) (* 3.0 a))))
107.0ms
(pow (+ (* a a) (* b b)) 2.0)
92.0ms
(* (* b b) (+ (pow 3.0 3) (pow a 3)))

simplify1.5s

Counts
138 → 138
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02632633
17082172
228691834
done50011808

prune455.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma (* 2 a) a (* b b))
0.2b
(fma (* b b) (fma (* 2 a) a (* b b)) (pow a 4))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma (* 2 a) a (* b b))
0.0ms
(fma (* b b) (fma (* 2 a) a (* b b)) (pow a 4))

series97.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(fma (* 2 a) a (* b b))
59.0ms
(fma (* b b) (fma (* 2 a) a (* b b)) (pow a 4))

simplify1.6s

Counts
26 → 26
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
040395
175392
2186340
3652340
43424340
done5000340

prune78.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* a a) (- 1.0 a))
0.2b
(/ (* (* b b) (+ (pow 3.0 3) (pow a 3))) (+ (* 3.0 3.0) (- (* a a) (* 3.0 a))))
2.6b
(* (* b b) (+ (pow 3.0 3) (pow a 3)))
2.7b
(* (pow a 2) (pow b 2))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
36×*-un-lft-identity
35×add-exp-log
25×add-cbrt-cube
24×add-cube-cbrt
22×associate-*r*
18×unpow-prod-down prod-diff prod-exp unswap-sqr
14×pow1
12×distribute-rgt-in distribute-lft-in
10×associate-*l* cbrt-unprod unpow2 sqr-pow
7×pow-prod-down
6×pow-to-exp associate-*r/ pow-exp
5×distribute-lft-out
4×expm1-log1p-u cube-prod log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ times-frac div-exp associate-/r* *-commutative flip-+
2×sub-neg associate-/r/ associate-/l/
1×flip3-- frac-2neg clear-num sum-cubes flip-- div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 160
Calls
4 calls:
31.0ms
(* (* a a) (- 1.0 a))
62.0ms
(/ (* (* b b) (+ (pow 3.0 3) (pow a 3))) (+ (* 3.0 3.0) (- (* a a) (* 3.0 a))))
76.0ms
(* (* b b) (+ (pow 3.0 3) (pow a 3)))
16.0ms
(* (pow a 2) (pow b 2))

series319.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (* a a) (- 1.0 a))
142.0ms
(/ (* (* b b) (+ (pow 3.0 3) (pow a 3))) (+ (* 3.0 3.0) (- (* a a) (* 3.0 a))))
84.0ms
(* (* b b) (+ (pow 3.0 3) (pow a 3)))
37.0ms
(* (pow a 2) (pow b 2))

simplify1.4s

Counts
172 → 172
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02902958
17572433
231122000
done50001966

prune580.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02645
13545
done3545

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.0s20101×body80valid