Details

analyze4.4s (9.5%)

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

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample187.0ms (0.4%)

Algorithm

1×

intervals

Results

39.0ms	195×	body	128	valid
27.0ms	29×	body	1024	valid
18.0ms	16×	body	256	valid
14.0ms	15×	body	1024	invalid
11.0ms	16×	body	512	valid
11.0ms	55×	body	128	invalid
6.0ms	10×	body	512	invalid
3.0ms	7×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify248.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (237.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune7.0ms (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

39.4b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize32.0ms (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))))
4.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
36.1b	(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))))

rewrite154.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_2408`
102×	`flip--_binary64_2440` `flip3--_binary64_2469`
68×	`frac-times_binary64_2475`
66×	`sqrt-div_binary64_2482`
64×	`frac-add_binary64_2473`
44×	`pow1_binary64_2526`
34×	`associate-*r/_binary64_2407`
17×	`pow-prod-down_binary64_2536`
16×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
6×	`add-sqr-sqrt_binary64_2487`
5×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
4×	`add-log-exp_binary64_2504` `pow-sqr_binary64_2438` `pow-prod-up_binary64_2535`
3×	`sqrt-prod_binary64_2481`
2×	`pow-plus_binary64_2528`
1×	`flip3-+_binary64_2468` `-commutative_binary64_2396` `pow1/2_binary64_2545` `swap-sqr_binary64_2432` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478` `pow2_binary64_2546` `associate-r_binary64_2405` `sqrt-pow1_binary64_2483` `associate-l*_binary64_2406`

Counts

4 → 135

Calls

4 calls:

36.0ms	(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))))
30.0ms	(.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))
9.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series22.5s (48.6%)

Counts

4 → 79

Calls

4 calls:

21.0s	(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))))
1.3s	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
95.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
91.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 17456 to 13701 computations (21.5% saved)

simplify328.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5214	17821

prune1.2s (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	204	10	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	10	215

Error

3.7b

Counts

215 → 10

Compiler

Compiled 14681 to 6260 computations (57.4% saved)

localize8.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_2487`
7×	`*-un-lft-identity_binary64_2465`
6×	`cancel-sign-sub-inv_binary64_2431`
5×	`add-cube-cbrt_binary64_2500` `associate-r_binary64_2405`
4×	`distribute-lft-in_binary64_2414` `distribute-rgt-in_binary64_2415`
3×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `associate-l_binary64_2406`
2×	`associate-*r/_binary64_2407` `sub-neg_binary64_2458`
1×	`difference-of-squares_binary64_2434` `add-log-exp_binary64_2504` `*-commutative_binary64_2396` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417` `unswap-sqr_binary64_2433` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `flip3--_binary64_2469` `cbrt-unprod_binary64_2498`

Counts

1 → 30

Calls

1 calls:

13.0ms

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

series191.0ms (0.4%)

Counts

1 → 15

Calls

1 calls:

191.0ms

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

Compiler

Compiled 138 to 180 computations (-30.4% saved)

simplify91.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5690	386

prune105.0ms (0.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	41	14	55

Error

3.7b

Counts

55 → 14

Compiler

Compiled 1071 to 560 computations (47.7% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 R) (cbrt.f64 R))
0.6b	(cbrt.f64 R)
0.6b	(cbrt.f64 R)
0.6b	(cbrt.f64 R)

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_2496`
23×	`add-sqr-sqrt_binary64_2487`
15×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
11×	`pow1_binary64_2526`
9×	`pow1/3_binary64_2547`
6×	`swap-sqr_binary64_2432` `add-exp-log_binary64_2503` `associate-r_binary64_2405` `associate-l_binary64_2406`
4×	`add-log-exp_binary64_2504` `unswap-sqr_binary64_2433` `add-cbrt-cube_binary64_2501`
2×	`pow-prod-down_binary64_2536` `pow-sqr_binary64_2438` `pow-prod-up_binary64_2535`
1×	`*-commutative_binary64_2396` `pow-plus_binary64_2528` `pow2_binary64_2546` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`

Counts

4 → 73

Calls

4 calls:

11.0ms	(*.f64 (cbrt.f64 R) (cbrt.f64 R))
2.0ms	(cbrt.f64 R)
2.0ms	(cbrt.f64 R)
2.0ms	(cbrt.f64 R)

series570.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(*.f64 (cbrt.f64 R) (cbrt.f64 R))
140.0ms	(cbrt.f64 R)
135.0ms	(cbrt.f64 R)
130.0ms	(cbrt.f64 R)

Compiler

Compiled 346 to 334 computations (3.5% saved)

simplify137.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune155.0ms (0.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	84	15	99

Error

3.7b

Counts

99 → 15

Compiler

Compiled 1952 to 793 computations (59.4% saved)

localize20.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda2 lambda1))
0.2b	(.f64 R (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda2 lambda1)))
4.4b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

rewrite54.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`distribute-lft-in_binary64_2414` `distribute-rgt-in_binary64_2415`
18×	`cancel-sign-sub-inv_binary64_2431`
16×	`add-sqr-sqrt_binary64_2487`
14×	`*-un-lft-identity_binary64_2465`
12×	`add-cube-cbrt_binary64_2500`
10×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
6×	`associate-r/_binary64_2407` `sub-neg_binary64_2458` `associate-r_binary64_2405` `associate-l*_binary64_2406`
4×	`prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
3×	`add-log-exp_binary64_2504`
2×	`*-commutative_binary64_2396` `flip--_binary64_2440` `flip3--_binary64_2469`
1×	`difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417` `unswap-sqr_binary64_2433`

Counts

3 → 73

Calls

3 calls:

18.0ms	(.f64 R (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda2 lambda1)))
15.0ms	(.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda2 lambda1))
4.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series1.6s (3.4%)

Counts

3 → 63

Calls

3 calls:

839.0ms	(.f64 R (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda2 lambda1)))
617.0ms	(.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda2 lambda1))
98.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

Compiler

Compiled 2042 to 1771 computations (13.3% saved)

simplify130.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5305	3415

prune283.0ms (0.6%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	3	9	12
Picked	1	0	1
Done	0	2	2
Total	133	18	151

Error

3.7b

Counts

151 → 18

Compiler

Compiled 2699 to 1424 computations (47.2% saved)

regimes4.2s (9%)

Accuracy

Total 15.8b remaining (79.9%)

Threshold costs 0b (0%)

Compiler

Compiled 20762 to 15219 computations (26.7% saved)

bsearch10.0ms (0%)

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

simplify78.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	61	166
1	61	166

Compiler

Compiled 432 to 216 computations (50% saved)

end0.0ms (0%)

sample9.6s (20.7%)

Algorithm

1×

intervals

Results

1.2s	6052×	body	128	valid
758.0ms	800×	body	1024	valid
486.0ms	2398×	body	128	invalid
480.0ms	722×	body	512	valid
399.0ms	440×	body	1024	invalid
222.0ms	351×	body	512	invalid
201.0ms	422×	body	256	valid
77.0ms	182×	body	256	invalid
6.0ms	4×	body	2048	valid

Compiler

Compiled 2354 to 1696 computations (28% saved)

Details

analyze4.4s (9.5%)

sample187.0ms (0.4%)

simplify248.0ms (0.5%)

prune7.0ms (0%)

localize32.0ms (0.1%)

rewrite154.0ms (0.3%)

series22.5s (48.6%)

simplify328.0ms (0.7%)

prune1.2s (2.6%)

localize8.0ms (0%)

rewrite17.0ms (0%)

series191.0ms (0.4%)

simplify91.0ms (0.2%)

prune105.0ms (0.2%)

localize17.0ms (0%)

rewrite30.0ms (0.1%)

series570.0ms (1.2%)

simplify137.0ms (0.3%)

prune155.0ms (0.3%)

localize20.0ms (0%)

rewrite54.0ms (0.1%)

series1.6s (3.4%)

simplify130.0ms (0.3%)

prune283.0ms (0.6%)

regimes4.2s (9%)

bsearch10.0ms (0%)

simplify78.0ms (0.2%)

end0.0ms (0%)

sample9.6s (20.7%)

Profiling