Details

Time bar (total: 7.8s)

sample12.0ms

Algorithm
intervals
Results
5.0ms342×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
1117
2167
3207
4217
done217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x x) 3.0)
0.1b
(/ (- (* x x) 3.0) 6.0)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×times-frac
11×add-cube-cbrt *-un-lft-identity
5×difference-of-squares
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 47
Calls
2 calls:
3.0ms
(- (* x x) 3.0)
9.0ms
(/ (- (* x x) 3.0) 6.0)

series106.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(- (* x x) 3.0)
64.0ms
(/ (- (* x x) 3.0) 6.0)

simplify1.1s

Counts
53 → 53
Iterations

Useful iterations: done (1.1s)

IterNodesCost
089587
1204571
2548519
32251519
done5000518

prune96.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x x) 3.0)
0.2b
(* (- (* x x) 3.0) (/ 1 6.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×associate-*r*
11×add-exp-log *-un-lft-identity times-frac
10×add-cube-cbrt
7×add-cbrt-cube
4×pow1 associate-*l* prod-exp add-log-exp
3×flip3-- flip-- unswap-sqr
2×frac-times div-exp associate-*l/ cbrt-unprod difference-of-squares
1×cbrt-undiv sub-neg rec-exp diff-log 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
2 → 54
Calls
2 calls:
3.0ms
(- (* x x) 3.0)
17.0ms
(* (- (* x x) 3.0) (/ 1 6.0))

series110.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(- (* x x) 3.0)
68.0ms
(* (- (* x x) 3.0) (/ 1 6.0))

simplify2.3s

Counts
60 → 60
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
0109708
1262608
2826508
34274508
done5000508

prune97.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (- (* x x) 3.0))
0.2b
(cbrt (- (* x x) 3.0))
0.2b
(* (* (* (cbrt (- (* x x) 3.0)) (cbrt (- (* x x) 3.0))) (cbrt (- (* x x) 3.0))) (/ 1 6.0))
0.2b
(* (cbrt (- (* x x) 3.0)) (cbrt (- (* x x) 3.0)))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
124×cbrt-div
86×frac-times
62×flip3-- flip--
56×associate-*l/
45×add-exp-log
35×add-sqr-sqrt
28×cbrt-prod
25×prod-exp
21×add-cube-cbrt *-un-lft-identity
20×pow1 associate-*r*
19×associate-*r/
17×add-cbrt-cube
13×cbrt-unprod
9×times-frac
8×pow1/3 associate-*l* pow-prod-down
7×swap-sqr
6×div-exp difference-of-squares
4×add-log-exp unswap-sqr
3×cbrt-undiv rec-exp 1-exp
2×pow-sqr *-commutative pow-prod-up
1×pow2 pow-plus un-div-inv div-inv
Counts
4 → 176
Calls
4 calls:
3.0ms
(cbrt (- (* x x) 3.0))
3.0ms
(cbrt (- (* x x) 3.0))
151.0ms
(* (* (* (cbrt (- (* x x) 3.0)) (cbrt (- (* x x) 3.0))) (cbrt (- (* x x) 3.0))) (/ 1 6.0))
24.0ms
(* (cbrt (- (* x x) 3.0)) (cbrt (- (* x x) 3.0)))

series701.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(cbrt (- (* x x) 3.0))
188.0ms
(cbrt (- (* x x) 3.0))
69.0ms
(* (* (* (cbrt (- (* x x) 3.0)) (cbrt (- (* x x) 3.0))) (cbrt (- (* x x) 3.0))) (/ 1 6.0))
222.0ms
(* (cbrt (- (* x x) 3.0)) (cbrt (- (* x x) 3.0)))

simplify1.1s

Counts
188 → 188
Iterations

Useful iterations: 2 (331.0ms)

IterNodesCost
03365422
18264584
225923941
done50013941

prune428.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (sqrt 3.0))
0.0b
(- x (sqrt 3.0))
0.0b
(/ (- x (sqrt 3.0)) 6.0)
0.7b
(* (+ x (sqrt 3.0)) (/ (- x (sqrt 3.0)) 6.0))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
46×*-un-lft-identity
37×times-frac
26×add-cube-cbrt
22×associate-*r*
16×difference-of-squares
11×add-exp-log add-cbrt-cube
8×sqrt-prod distribute-lft-out-- add-log-exp
6×pow1 associate-/l*
4×associate-*l*
3×flip3-+ associate-/r* flip-+
2×cbrt-undiv frac-times flip3-- div-exp associate-*l/ prod-exp flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out unswap-sqr
1×+-commutative sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 115
Calls
4 calls:
3.0ms
(+ x (sqrt 3.0))
3.0ms
(- x (sqrt 3.0))
10.0ms
(/ (- x (sqrt 3.0)) 6.0)
34.0ms
(* (+ x (sqrt 3.0)) (/ (- x (sqrt 3.0)) 6.0))

series311.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ x (sqrt 3.0))
39.0ms
(- x (sqrt 3.0))
69.0ms
(/ (- x (sqrt 3.0)) 6.0)
164.0ms
(* (+ x (sqrt 3.0)) (/ (- x (sqrt 3.0)) 6.0))

simplify623.0ms

Counts
127 → 127
Iterations

Useful iterations: 2 (143.0ms)

IterNodesCost
01421516
13491349
213081239
done50001239

prune197.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
done67

end0.0ms

sample280.0ms

Algorithm
intervals
Results
173.0ms10709×body80valid