Details

analyze2.8s (4.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5562	539
0	5	5
1	5	5

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

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample98.0ms (0.2%)

Algorithm

1×

intervals

Results

20.0ms	191×	body	128	valid
13.0ms	27×	body	1024	valid
7.0ms	20×	body	512	valid
7.0ms	65×	body	128	invalid
5.0ms	11×	body	1024	invalid
4.0ms	18×	body	256	valid
4.0ms	11×	body	512	invalid
1.0ms	4×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify139.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune5.0ms (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

38.2b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize15.0ms (0%)

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))))
2.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.4b	(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))))

rewrite407.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

38.2b

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-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
6×	`add-sqr-sqrt_binary64_1464`
5×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481` `pow-prod-up_binary64_1512` `pow-sqr_binary64_1415`
3×	`sqrt-prod_binary64_1458`
2×	`pow-plus_binary64_1505`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455` `pow2_binary64_1523` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `associate-r_binary64_1382` `*-commutative_binary64_1373`

Counts

4 → 135

Calls

4 calls:

19.0ms	(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))))
13.0ms	(.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))

Compiler

Compiled 9145 to 2868 computations (68.6% saved)

series6.8s (11.4%)

Error

2.3b

Counts

4 → 70

Calls

4 calls:

5.8s	(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))))
569.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
53.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
50.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 16503 to 12387 computations (24.9% saved)

simplify148.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5715	14563

prune538.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	195	10	205
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	196	10	206

Error

2.3b

Counts

206 → 10

Compiler

Compiled 12211 to 4851 computations (60.3% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 R (-.f64 phi2 phi1))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

2.3b

Rules

9×	`add-sqr-sqrt_binary64_1464`
7×	`*-un-lft-identity_binary64_1442`
6×	`cancel-sign-sub-inv_binary64_1408`
5×	`add-cube-cbrt_binary64_1477` `associate-r_binary64_1382`
4×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`
3×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `associate-l_binary64_1383`
2×	`sub-neg_binary64_1435` `associate-*r/_binary64_1384`
1×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `add-log-exp_binary64_1481` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `flip3--_binary64_1446` `flip--_binary64_1417` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `*-commutative_binary64_1373`

Counts

1 → 30

Calls

1 calls:

7.0ms

(*.f64 R (-.f64 phi2 phi1))

Compiler

Compiled 338 to 113 computations (66.6% saved)

series99.0ms (0.2%)

Error

2.3b

Counts

1 → 15

Calls

1 calls:

91.0ms

(*.f64 R (-.f64 phi2 phi1))

Compiler

Compiled 219 to 198 computations (9.6% saved)

simplify48.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5690	386

prune40.0ms (0.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	45	10	55

Error

2.3b

Counts

55 → 10

Compiler

Compiled 726 to 324 computations (55.4% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
2.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.5b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
35.4b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite339.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

2.3b

Rules

128×	`associate-*l/_binary64_1385`
96×	`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`
8×	`add-sqr-sqrt_binary64_1464`
7×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`pow1_binary64_1503`
4×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `log-pow_binary64_1531`
3×	`sqrt-prod_binary64_1458` `exp-prod_binary64_1494` `log-prod_binary64_1528`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455` `rem-log-exp_binary64_1483`

Counts

4 → 108

Calls

4 calls:

21.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 8251 to 2688 computations (67.4% saved)

series29.5s (50%)

Error

2.3b

Counts

4 → 48

Calls

4 calls:

28.8s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
183.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
53.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
41.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 30331 to 23728 computations (21.8% saved)

simplify157.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5867	15206

prune493.0ms (0.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	156	10	166

Error

2.3b

Counts

166 → 10

Compiler

Compiled 12229 to 5169 computations (57.7% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)
2.5b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
2.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.4b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite368.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

2.3b

Rules

128×	`associate-*l/_binary64_1385`
96×	`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`
9×	`add-sqr-sqrt_binary64_1464`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`pow1_binary64_1503`
5×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
4×	`add-log-exp_binary64_1481`
3×	`sqrt-prod_binary64_1458` `unpow-prod-down_binary64_1521` `pow-unpow_binary64_1519` `cube-prod_binary64_1470`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `unpow3_binary64_1508` `cube-mult_binary64_1472` `rem-cube-cbrt_binary64_1465` `sqr-pow_binary64_1414`

Counts

4 → 116

Calls

4 calls:

21.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)

Compiler

Compiled 8726 to 2982 computations (65.8% saved)

series6.3s (10.6%)

Error

2.3b

Counts

4 → 54

Calls

4 calls:

5.8s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
167.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)
59.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
57.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 15319 to 11602 computations (24.3% saved)

simplify139.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5760	13194

prune453.0ms (0.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	3	4	7
Picked	0	1	1
Done	0	2	2
Total	170	10	180

Error

2.3b

Counts

180 → 10

Compiler

Compiled 10975 to 4299 computations (60.8% saved)

regimes3.7s (6.3%)

Accuracy

Total 16.6b remaining (80.5%)

Threshold costs 0b (0%)

Compiler

Compiled 33828 to 23015 computations (32% saved)

bsearch6.0ms (0%)

Compiler: Compiled 3 to 6 computations (-100% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	131	248
1	131	248

Compiler

Compiled 644 to 332 computations (48.4% saved)

end0.0ms (0%)

sample6.3s (10.7%)

Algorithm

1×

intervals

Results

636.0ms	6074×	body	128	valid
395.0ms	777×	body	1024	valid
252.0ms	734×	body	512	valid
238.0ms	2325×	body	128	invalid
219.0ms	454×	body	1024	invalid
126.0ms	375×	body	512	invalid
109.0ms	408×	body	256	valid
39.0ms	177×	body	256	invalid
5.0ms	7×	body	2048	valid

Compiler

Compiled 3684 to 2498 computations (32.2% saved)

Details

analyze2.8s (4.8%)

sample98.0ms (0.2%)

simplify139.0ms (0.2%)

prune5.0ms (0%)

localize15.0ms (0%)

rewrite407.0ms (0.7%)

series6.8s (11.4%)

simplify148.0ms (0.3%)

prune538.0ms (0.9%)

localize4.0ms (0%)

rewrite29.0ms (0%)

series99.0ms (0.2%)

simplify48.0ms (0.1%)

prune40.0ms (0.1%)

localize26.0ms (0%)

rewrite339.0ms (0.6%)

series29.5s (50%)

simplify157.0ms (0.3%)

prune493.0ms (0.8%)

localize26.0ms (0%)

rewrite368.0ms (0.6%)

series6.3s (10.6%)

simplify139.0ms (0.2%)

prune453.0ms (0.8%)

regimes3.7s (6.3%)

bsearch6.0ms (0%)

simplify62.0ms (0.1%)

end0.0ms (0%)

sample6.3s (10.7%)

Profiling