Details

sample94.0ms

Algorithm

intervals

Results

32.0ms	84×	body	2560	valid
24.0ms	90×	body	1280	valid
11.0ms	270×	body	80	nan
7.0ms	33×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	11×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	14
1	19	14
2	41	14
3	81	14
4	150	14
5	236	14
6	349	14
7	980	14
8	3858	14
done	5001	14

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.7b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 5.0 (* v v)))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp`
4×	`associate-/r*` `difference-of-squares`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

3.0ms	(- 1.0 (* 5.0 (* v v)))
8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- 1.0 (* 5.0 (* v v)))
6.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
3.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.1s

Counts

87 → 87

Iterations

Useful iterations: 3 (386.0ms)

Iter	Nodes	Cost
0	146	1376
1	353	1329
2	1210	1209
3	4218	1205
done	5000	1205

prune152.0ms

Filtered

67 candidates to 87 candidates (-29.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.6b

Counts

88 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b	(* 5.0 (* v v))
0.7b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp` `difference-of-squares`
4×	`associate-/r*`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`asin-acos` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

9.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series19.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
3.0ms	(* 5.0 (* v v))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify999.0ms

Counts

91 → 91

Iterations

Useful iterations: done (995.0ms)

Iter	Nodes	Cost
0	171	1732
1	408	1652
2	1266	1532
3	3904	1524
done	5000	1522

prune165.0ms

Filtered

69 candidates to 91 candidates (-31.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	90	5	95

Merged error: 0.6b

Counts

95 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.6b	(acos (* (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`associate-r` `*-commutative` `unswap-sqr`
1×	`acos-asin`

Counts

4 → 65

Calls

4 calls:

7.0ms	(* 5.0 (* v v))
6.0ms	(* 5.0 (* v v))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series13.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 5.0 (* v v))
3.0ms	(* 5.0 (* v v))
3.0ms	(* 5.0 (* v v))
4.0ms	(acos (* (* (cbrt (- 1.0 (* 5.0 (* v v)))) (cbrt (- 1.0 (* 5.0 (* v v))))) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

simplify930.0ms

Counts

77 → 77

Iterations

Useful iterations: 4 (245.0ms)

Iter	Nodes	Cost
0	56	904
1	123	901
2	333	739
3	737	595
4	1146	568
5	2433	568
done	5000	568

prune141.0ms

Filtered

45 candidates to 77 candidates (-71.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Merged error: 0.6b

Counts

82 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3))
1.0b	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
4×	`add-log-exp`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `pow-pow` `pow1/3` `associate-r` `pow-exp` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
2.0ms	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3))
2.0ms	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

series30.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
3.0ms	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3))
20.0ms	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

simplify1.2s

Counts

83 → 83

Iterations

Useful iterations: 3 (244.0ms)

Iter	Nodes	Cost
0	93	1656
1	214	1528
2	615	1271
3	2550	1253
done	5000	1253

prune120.0ms

Filtered

49 candidates to 83 candidates (-69.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	82	6	88

Merged error: 0.6b

Counts

88 → 6

regimes231.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	14	33
done	14	33

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	2993×	body	2560	valid
670.0ms	2457×	body	1280	valid
332.0ms	8034×	body	80	nan
261.0ms	1277×	body	640	valid
85.0ms	585×	body	320	valid
52.0ms	465×	body	160	valid
12.0ms	223×	body	80	valid

Details

sample94.0ms

simplify1.9s

prune3.0ms

localize8.0ms

rewrite22.0ms

series18.0ms

simplify1.1s

prune152.0ms

localize14.0ms

rewrite26.0ms

series19.0ms

simplify999.0ms

prune165.0ms

localize15.0ms

rewrite22.0ms

series13.0ms

simplify930.0ms

prune141.0ms

localize14.0ms

rewrite14.0ms

series30.0ms

simplify1.2s

prune120.0ms

regimes231.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.9s

Profiling