Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample156.0ms

Algorithm

intervals

Results

43.0ms	95×	body	1280	valid
13.0ms	48×	body	640	valid
5.0ms	27×	body	320	valid
4.0ms	68×	body	80	valid
2.0ms	18×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 14.4b

Counts

2 → 1

localize27.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
14.3b	(cos (+ a b))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 67

Calls

3 calls:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
4.0ms	(cos (+ a b))

series43.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify58.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5018	783

prune115.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Merged error: 0.2b

Counts

77 → 9

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 99

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
10.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
53.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5901	1692

prune177.0ms

Filtered

90 candidates to 111 candidates (-23.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	99	12	111
Fresh	7	1	8
Picked	0	1	1
Done	0	0	0
Total	106	14	120

Merged error: 0.0b

Counts

120 → 14

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin b) r)
0.2b	(* (sin a) (sin b))
0.3b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin b) r)
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* (sin b) r)
11.0ms	(* (sin a) (sin b))
54.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify37.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4996	1008
1	4996	1008

prune136.0ms

Filtered

66 candidates to 87 candidates (-31.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	5	7	12
Picked	0	1	1
Done	1	0	1
Total	87	14	101

Merged error: 0b

Counts

101 → 14

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
0.2b	(* (sin b) (sin a))
0.2b	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
0.2b	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 99

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
4.0ms	(* (sin b) (sin a))
7.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
11.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
9.0ms	(* (sin b) (sin a))
45.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
54.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5575	1726

prune96.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	111	14	125

Merged error: 0b

Counts

125 → 14

regimes296.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	16
1	41	16

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	2841×	body	1280	valid
523.0ms	1863×	body	640	valid
152.0ms	778×	body	320	valid
140.0ms	2151×	body	80	valid
52.0ms	367×	body	160	valid

Details

analyze1.1s

sample156.0ms

simplify3.0ms

prune7.0ms

localize27.0ms

rewrite19.0ms

series43.0ms

simplify58.0ms

prune115.0ms

localize46.0ms

rewrite33.0ms

series108.0ms

simplify54.0ms

prune177.0ms

localize46.0ms

rewrite23.0ms

series89.0ms

simplify37.0ms

prune136.0ms

localize48.0ms

rewrite31.0ms

series125.0ms

simplify52.0ms

prune96.0ms

regimes296.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.5s

Profiling