Details

analyze1.2s

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

sample95.0ms

Algorithm

intervals

Results

62.0ms	121×	body	1280	valid
12.0ms	42×	body	640	valid
5.0ms	23×	body	320	valid
4.0ms	56×	body	80	valid
2.0ms	14×	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

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 15.8b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ b a))))
0.2b	(/ (sin b) (cos (+ b a)))
2.0b	(cos (+ b a))

rewrite16.0ms

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:

7.0ms	(* r (/ (sin b) (cos (+ b a))))
4.0ms	(/ (sin b) (cos (+ b a)))
4.0ms	(cos (+ b a))

series44.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* r (/ (sin b) (cos (+ b a))))
12.0ms	(/ (sin b) (cos (+ b a)))
6.0ms	(cos (+ b a))

simplify57.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4966	783
1	4966	783

prune100.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	71	7	78

Merged error: 0.2b

Counts

78 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
0.1b	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
0.2b	(* (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 b) (cos a)) (* (sin b) (sin a)))
11.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
5.0ms	(* (sin b) (sin a))

series102.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
50.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
27.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
9.0ms	(* (sin b) (sin a))

simplify67.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4927	1675
1	4927	1675

prune162.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0b

Counts

118 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

6.0ms	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
7.0ms	(* (cos b) (/ (cos a) (sin b)))
8.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))
4.0ms	(/ (cos a) (sin b))

series87.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
14.0ms	(* (cos b) (/ (cos a) (sin b)))
45.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))
10.0ms	(/ (cos a) (sin b))

simplify59.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5144	1445

prune145.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	111	11	122

Merged error: 0b

Counts

122 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin b) r)
0.2b	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
0.2b	(* (sin b) (sin a))
0.3b	(* (* (sin b) r) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

4.0ms	(* (sin b) r)
7.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
4.0ms	(* (sin b) (sin a))
12.0ms	(* (* (sin b) r) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sin b) r)
22.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
9.0ms	(* (sin b) (sin a))
54.0ms	(* (* (sin b) r) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5211	1572

prune92.0ms

Filtered

76 candidates to 126 candidates (-65.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	126	11	137

Merged error: 0b

Counts

137 → 11

regimes244.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	16
1	41	16

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	3035×	body	1280	valid
524.0ms	1813×	body	640	valid
146.0ms	732×	body	320	valid
142.0ms	2069×	body	80	valid
52.0ms	351×	body	160	valid

Details

analyze1.2s

sample95.0ms

simplify3.0ms

prune10.0ms

localize10.0ms

rewrite16.0ms

series44.0ms

simplify57.0ms

prune100.0ms

localize16.0ms

rewrite31.0ms

series102.0ms

simplify67.0ms

prune162.0ms

localize16.0ms

rewrite27.0ms

series87.0ms

simplify59.0ms

prune145.0ms

localize18.0ms

rewrite31.0ms

series92.0ms

simplify51.0ms

prune92.0ms

regimes244.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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