Details

analyze2.1s (14.2%)

Algorithm

1×

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

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample76.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	210×	body	128	valid
8.0ms	17×	body	1024	valid
7.0ms	75×	body	128	invalid
6.0ms	17×	body	512	valid
4.0ms	13×	body	512	invalid
3.0ms	7×	body	1024	invalid
3.0ms	12×	body	256	valid
1.0ms	6×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify213.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune3.0ms (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

Error

36.1b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
33.4b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite77.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_1385`
102×	`flip3--_binary64_1446` `flip--_binary64_1417`
68×	`frac-times_binary64_1452`
66×	`sqrt-div_binary64_1459`
64×	`frac-add_binary64_1450`
44×	`pow1_binary64_1503`
34×	`associate-*r/_binary64_1384`
17×	`pow-prod-down_binary64_1513`
16×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
8×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
6×	`add-sqr-sqrt_binary64_1464`
5×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`pow-sqr_binary64_1415` `add-log-exp_binary64_1481` `pow-prod-up_binary64_1512`
3×	`sqrt-prod_binary64_1458`
2×	`pow-plus_binary64_1505`
1×	`pow2_binary64_1523` `sqrt-pow1_binary64_1460` `associate-r_binary64_1382` `rem-sqrt-square_binary64_1455` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

4 → 135

Calls

4 calls:

24.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series926.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

726.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
168.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify97.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5228	10334

prune300.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	141	6	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	6	148

Error

21.0b

Counts

148 → 6

Compiler

Compiled 8720 to 2900 computations (66.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
33.4b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite65.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`associate-*l/_binary64_1385`
97×	`flip3--_binary64_1446` `flip--_binary64_1417`
66×	`sqrt-div_binary64_1459`
64×	`frac-times_binary64_1452` `frac-add_binary64_1450`
32×	`associate-*r/_binary64_1384`
12×	`add-sqr-sqrt_binary64_1464`
9×	`*-un-lft-identity_binary64_1442`
7×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
6×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
5×	`associate-l_binary64_1383`
4×	`add-log-exp_binary64_1481`
3×	`associate-r_binary64_1382` `sqrt-prod_binary64_1458`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

4 → 115

Calls

4 calls:

22.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
8.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series847.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

726.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
89.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify120.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4981	9691
1	4981	9691

prune255.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	127	6	133

Error

21.0b

Counts

133 → 6

Compiler

Compiled 8163 to 2687 computations (67.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.5b	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
34.5b	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite110.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_1385`
192×	`flip3--_binary64_1446` `flip--_binary64_1417`
132×	`cbrt-div_binary64_1474`
128×	`frac-times_binary64_1452` `frac-add_binary64_1450`
64×	`associate-*r/_binary64_1384`
6×	`cbrt-prod_binary64_1473` `add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `pow1_binary64_1503`
2×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/3_binary64_1524`

Counts

4 → 168

Calls

4 calls:

23.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
20.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.0s (13.8%)

Counts

4 → 12

Calls

4 calls:

1.0s	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
1.0s	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify154.0ms (1%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4997	18474
1	4997	18474

prune705.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	179	7	186

Error

21.0b

Counts

186 → 7

Compiler

Compiled 19507 to 6629 computations (66% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.5b	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
36.4b	(pow.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))) 1/3)

rewrite89.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/_binary64_1385`
96×	`flip3--_binary64_1446` `flip--_binary64_1417`
66×	`cbrt-div_binary64_1474`
64×	`frac-times_binary64_1452` `frac-add_binary64_1450`
32×	`associate-*r/_binary64_1384`
7×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
5×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481`
3×	`cbrt-prod_binary64_1473` `pow-unpow_binary64_1519` `unpow-prod-down_binary64_1521`
1×	`pow-exp_binary64_1510` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/3_binary64_1524` `pow-to-exp_binary64_1511` `unpow1/3_binary64_1509` `pow-pow_binary64_1514`

Counts

4 → 109

Calls

4 calls:

23.0ms	(pow.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))) 1/3)
20.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.1s (14.3%)

Counts

4 → 12

Calls

4 calls:

1.1s	(pow.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))) 1/3)
1.0s	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5078	10269

prune404.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	122	6	128

Error

21.0b

Counts

128 → 6

Compiler

Compiled 11937 to 4331 computations (63.7% saved)

regimes770.0ms (5.2%)

Accuracy

Total 3.6b remaining (12.4%)

Threshold costs 0b (0%)

Compiler

Compiled 8048 to 5136 computations (36.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 32 to 21 computations (34.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	166
1	70	166

end0.0ms (0%)

sample3.1s (21.2%)

Algorithm

1×

intervals

Results

614.0ms	5983×	body	128	valid
399.0ms	838×	body	1024	valid
264.0ms	772×	body	512	valid
254.0ms	2388×	body	128	invalid
225.0ms	476×	body	1024	invalid
136.0ms	374×	body	512	invalid
95.0ms	405×	body	256	valid
45.0ms	208×	body	256	invalid
1.0ms	2×	body	2048	valid

Compiler

Compiled 955 to 595 computations (37.7% saved)

Details

analyze2.1s (14.2%)

sample76.0ms (0.5%)

simplify213.0ms (1.4%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite77.0ms (0.5%)

series926.0ms (6.3%)

simplify97.0ms (0.7%)

prune300.0ms (2%)

localize16.0ms (0.1%)

rewrite65.0ms (0.4%)

series847.0ms (5.7%)

simplify120.0ms (0.8%)

prune255.0ms (1.7%)

localize20.0ms (0.1%)

rewrite110.0ms (0.7%)

series2.0s (13.8%)

simplify154.0ms (1%)

prune705.0ms (4.8%)

localize22.0ms (0.2%)

rewrite89.0ms (0.6%)

series2.1s (14.3%)

simplify96.0ms (0.7%)

prune404.0ms (2.7%)

regimes770.0ms (5.2%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.1s (21.2%)

Profiling