Details

analyze2.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

sample96.0ms

Algorithm

intervals

Results

18.0ms	188×	body	80	valid
17.0ms	26×	body	640	valid
11.0ms	16×	body	1280	valid
8.0ms	78×	body	80	invalid
7.0ms	10×	body	1280	invalid
7.0ms	20×	body	320	valid
5.0ms	12×	body	640	invalid
2.0ms	6×	body	320	invalid
1.0ms	6×	body	160	valid
1.0ms	4×	body	160	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	32
1	37	32

prune15.0ms

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: 39.3b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.8b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
98×	`associate-r/` `associate-l/`
73×	`cos-mult`
12×	`pow1` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
1×	`pow2` `sqr-cos-a` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

4.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series157.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify114.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5516	11780

prune487.0ms

Filtered

138 candidates to 204 candidates (-47.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	196	8	204
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	196	10	206

Merged error: 22.9b

Counts

206 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

6.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series173.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
143.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5053	6382

prune251.0ms

Filtered

76 candidates to 127 candidates (-67.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	8	8
Picked	0	1	1
Done	1	0	1
Total	127	10	137

Merged error: 22.9b

Counts

137 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.8b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--` `flip--`
80×	`associate-*l/`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
138.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify83.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4963	5807
1	4963	5807

prune271.0ms

Filtered

67 candidates to 112 candidates (-67.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	112	10	122

Merged error: 22.9b

Counts

122 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

2240×	`associate-*l/`
1408×	`frac-times`
1344×	`flip3--` `flip--`
1296×	`cbrt-div`
642×	`sqrt-div`
640×	`frac-add`
560×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 676

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
65.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series156.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
142.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify356.0ms

Algorithm

egg-herbie

Counts

688 → 688

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5622	87706

prune6.3s

Filtered

681 candidates to 688 candidates (-1.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	687	1	688
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	687	11	698

Merged error: 22.9b

Counts

698 → 11

regimes1.2s

Accuracy

57.3% (6.9b remaining)

Error of 29.8b against oracle of 22.9b and baseline of 39.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	108
1	33	108

end0.0ms

analyze2.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

sample2.8s

Algorithm

intervals

Results

601.0ms	5858×	body	80	valid
424.0ms	882×	body	640	valid
359.0ms	508×	body	1280	valid
236.0ms	2295×	body	80	invalid
211.0ms	319×	body	1280	invalid
191.0ms	426×	body	640	invalid
170.0ms	520×	body	320	valid
71.0ms	221×	body	320	invalid
54.0ms	232×	body	160	valid
27.0ms	106×	body	160	invalid

Details

analyze2.1s

sample96.0ms

simplify3.0ms

prune15.0ms

localize17.0ms

rewrite60.0ms

series157.0ms

simplify114.0ms

prune487.0ms

localize17.0ms

rewrite43.0ms

series173.0ms

simplify46.0ms

prune251.0ms

localize22.0ms

rewrite52.0ms

series152.0ms

simplify83.0ms

prune271.0ms

localize21.0ms

rewrite252.0ms

series156.0ms

simplify356.0ms

prune6.3s

regimes1.2s

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze2.1s

sample2.8s

Profiling