Details

analyze841.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

sample94.0ms

Algorithm

intervals

Results

37.0ms	94×	body	2560	valid
20.0ms	75×	body	1280	valid
9.0ms	48×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	15×	body	160	valid
1.0ms	10×	body	80	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5797	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

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.7b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

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

series12.0ms

Counts

3 → 9

Calls

3 calls:

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)))

simplify77.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4960	1050
1	4960	1050

prune119.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.7b

Counts

73 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.8b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite24.0ms

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 → 78

Calls

4 calls:

7.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(* 5.0 (* v v))
2.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5203	1507

prune153.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 0.7b

Counts

94 → 4

localize10.0ms

Local error

Found 1 expressions with local error:

0.7b	(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `acos-asin` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

1 → 8

Calls

1 calls:

1.0ms

(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

11 → 11

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4961	157
1	4961	157

prune36.0ms

Filtered

8 candidates to 11 candidates (-37.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	10	1	11
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	10	5	15

Merged error: 0.7b

Counts

15 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite11.0ms

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:

1.0ms	(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms	(* (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series175.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
41.0ms	(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
39.0ms	(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
54.0ms	(* (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5496	1672

prune219.0ms

Filtered

57 candidates to 85 candidates (-49.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	84	6	90

Merged error: 0.7b

Counts

90 → 6

regimes209.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	12
1	23	12

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2990×	body	2560	valid
668.0ms	2472×	body	1280	valid
252.0ms	1284×	body	640	valid
88.0ms	616×	body	320	valid
41.0ms	423×	body	160	valid
12.0ms	215×	body	80	valid

Details

analyze841.0ms

sample94.0ms

simplify98.0ms

prune3.0ms

localize9.0ms

rewrite16.0ms

series12.0ms

simplify77.0ms

prune119.0ms

localize12.0ms

rewrite24.0ms

series17.0ms

simplify61.0ms

prune153.0ms

localize10.0ms

rewrite1.0ms

series4.0ms

simplify66.0ms

prune36.0ms

localize18.0ms

rewrite11.0ms

series175.0ms

simplify71.0ms

prune219.0ms

regimes209.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling