Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	91×	body	80	nan

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
done	8	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 45

Calls

2 calls:

47.0ms	(+ 1.0 (sqrt (+ x 1.0)))
68.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series270.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(+ 1.0 (sqrt (+ x 1.0)))
213.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.1s

Counts

51 → 51

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	117	739
1	277	693
2	831	636
3	3565	630
done	5000	628

prune186.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

15.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.3s

Counts

4 → 12

Calls

4 calls:

329.0ms	(* (cbrt x) (cbrt x))
305.0ms	(cbrt x)
319.0ms	(cbrt x)
350.0ms	(cbrt x)

simplify4.3s

Counts

85 → 85

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	61	524
1	115	417
2	319	397
3	1092	379
4	4427	374
done	5001	364

prune205.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
0.2b	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
8.3b	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

70×	`cbrt-prod` `*-un-lft-identity`
51×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `flip-+`
3×	`pow-unpow` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 149

Calls

4 calls:

18.0ms	(+ 1.0 (sqrt (+ x 1.0)))
30.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
78.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
34.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series488.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ 1.0 (sqrt (+ x 1.0)))
169.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
189.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
56.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify1.0s

Counts

161 → 161

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	228	3012
1	482	2359
2	1608	2124
done	5002	2116

prune323.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) 1.0)
0.2b	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
30×	`associate-r`
28×	`times-frac`
20×	`sqrt-prod`
19×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-l` `unswap-sqr`
4×	`pow1` `add-log-exp`
2×	`flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `div-inv`

Counts

2 → 68

Calls

2 calls:

31.0ms	(+ (sqrt (+ x 1.0)) 1.0)
102.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

series285.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(+ (sqrt (+ x 1.0)) 1.0)
228.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

simplify1.3s

Counts

74 → 74

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	150	1194
1	390	1012
2	1329	887
done	5000	877

prune153.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes42.0ms

Accuracy

98.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.4b

bsearch23.0ms

Steps

Iters	Range		Point
3	2.5852715992345188e-23	3.219064609783079e-23	2.653971370452548e-23

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	27
1	18	27
done	18	27

end0.0ms

sample810.0ms

Algorithm

intervals

Results

381.0ms	7994×	body	80	valid
158.0ms	2707×	body	80	nan
1.0ms	6×	body	1280	valid