Details

sample94.0ms

Algorithm

intervals

Results

32.0ms	84×	body	2560	valid
23.0ms	90×	body	1280	valid
10.0ms	270×	body	80	nan
6.0ms	33×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	11×	body	80	valid

simplify3.3s

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	235	14
6	312	14
7	461	14
8	1202	14
done	5000	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)))

rewrite21.0ms

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)))
9.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 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)))

simplify2.1s

Counts

87 → 87

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	146	1376
1	351	1319
2	1072	1207
3	4260	1205
done	5000	1203

prune149.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

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

localize11.0ms

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:

8.0ms	(/ (- 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)))

series18.0ms

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)))

simplify1.8s

Counts

91 → 91

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	171	1732
1	406	1642
2	1136	1530
3	3929	1524
done	5000	1522

prune166.0ms

Filtered

70 candidates to 91 candidates (-30.0%)

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))))

rewrite21.0ms

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:

6.0ms	(* 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))))

simplify3.7s

Counts

77 → 77

Iterations

Useful iterations: 4 (386.0ms)

Iter	Nodes	Cost
0	56	904
1	119	895
2	305	739
3	573	595
4	874	568
5	1922	568
done	5000	568

prune134.0ms

Filtered

43 candidates to 77 candidates (-79.1%)

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

localize11.0ms

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

series31.0ms

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))
22.0ms	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

simplify2.1s

Counts

83 → 83

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	93	1656
1	204	1458
2	556	1257
3	2554	1257
done	5000	1257

prune116.0ms

Filtered

47 candidates to 83 candidates (-76.6%)

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

regimes241.0ms

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

sample2.8s

Algorithm

intervals

Results

1.1s	2993×	body	2560	valid
646.0ms	2457×	body	1280	valid
317.0ms	8034×	body	80	nan
254.0ms	1277×	body	640	valid
83.0ms	585×	body	320	valid
45.0ms	465×	body	160	valid
12.0ms	223×	body	80	valid

Details

sample94.0ms

simplify3.3s

prune3.0ms

localize8.0ms

rewrite21.0ms

series18.0ms

simplify2.1s

prune149.0ms

localize11.0ms

rewrite26.0ms

series18.0ms

simplify1.8s

prune166.0ms

localize15.0ms

rewrite21.0ms

series13.0ms

simplify3.7s

prune134.0ms

localize11.0ms

rewrite14.0ms

series31.0ms

simplify2.1s

prune116.0ms

regimes241.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling