Details

analyze2.2s (22.2%)

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)

sample95.0ms (1%)

Algorithm

1×

intervals

Results

19.0ms	189×	body	128	valid
16.0ms	33×	body	1024	valid
9.0ms	15×	body	256	valid
9.0ms	85×	body	128	invalid
8.0ms	17×	body	1024	invalid
6.0ms	19×	body	512	valid
3.0ms	9×	body	512	invalid
2.0ms	9×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify131.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune4.0ms (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

40.8b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize16.0ms (0.2%)

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))))
3.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.5b	(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 (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_1726`
102×	`flip3--_binary64_1787` `flip--_binary64_1758`
68×	`frac-times_binary64_1793`
66×	`sqrt-div_binary64_1800`
64×	`frac-add_binary64_1791`
44×	`pow1_binary64_1844`
34×	`associate-*r/_binary64_1725`
17×	`pow-prod-down_binary64_1854`
16×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
6×	`add-sqr-sqrt_binary64_1805`
5×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
4×	`pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `add-log-exp_binary64_1822`
3×	`sqrt-prod_binary64_1799`
2×	`pow-plus_binary64_1846`
1×	`swap-sqr_binary64_1750` `flip-+_binary64_1757` `pow1/2_binary64_1863` `associate-l_binary64_1724` `-commutative_binary64_1714` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `pow2_binary64_1864` `associate-r*_binary64_1723`

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))

series921.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

732.0ms	(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))))
156.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5228	10334

prune301.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Error

18.1b

Counts

148 → 8

Compiler

Compiled 8789 to 2950 computations (66.4% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_1805`
7×	`*-un-lft-identity_binary64_1783`
6×	`cancel-sign-sub-inv_binary64_1749`
5×	`add-cube-cbrt_binary64_1818` `associate-r_binary64_1723`
4×	`distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733`
3×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `pow1_binary64_1844`
2×	`associate-*r/_binary64_1725` `sub-neg_binary64_1776`
1×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `distribute-lft-out--_binary64_1735` `*-commutative_binary64_1714` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `flip--_binary64_1758` `add-log-exp_binary64_1822`

Counts

1 → 30

Calls

1 calls:

9.0ms

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

series33.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

32.0ms

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

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5688	314

prune42.0ms (0.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	23	10	33
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	24	17	41

Error

18.1b

Counts

41 → 17

Compiler

Compiled 683 to 347 computations (49.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (.f64 R phi2) (.f64 R (neg.f64 phi1)))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_1822`
1×	`add-cbrt-cube_binary64_1819` `unsub-neg_binary64_1777` `+-commutative_binary64_1713` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `distribute-rgt-neg-out_binary64_1743` `*-un-lft-identity_binary64_1783` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow1_binary64_1844`

Counts

1 → 13

Calls

1 calls:

4.0ms

(+.f64 (*.f64 R phi2) (*.f64 R (neg.f64 phi1)))

series32.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

32.0ms

(+.f64 (*.f64 R phi2) (*.f64 R (neg.f64 phi1)))

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5235	170

prune32.0ms (0.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	16	17	33

Error

18.1b

Counts

33 → 17

Compiler

Compiled 553 to 323 computations (41.6% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 phi2 phi1))
0.0b	(sqrt.f64 (-.f64 phi2 phi1))
0.2b	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
0.3b	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (-.f64 phi2 phi1)))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1805`
21×	`sqrt-prod_binary64_1799`
19×	`*-un-lft-identity_binary64_1783`
18×	`sqrt-div_binary64_1800`
16×	`associate-r_binary64_1723`
13×	`pow1_binary64_1844`
11×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818`
10×	`associate-*r/_binary64_1725`
9×	`flip3--_binary64_1787` `flip--_binary64_1758`
4×	`difference-of-squares_binary64_1752` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `distribute-lft-out--_binary64_1735` `associate-l_binary64_1724` `frac-times_binary64_1793` `pow-prod-down_binary64_1854` `add-log-exp_binary64_1822`
2×	`pow1/2_binary64_1863` `associate-l/_binary64_1726` `-commutative_binary64_1714` `sqrt-pow1_binary64_1801` `unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796`

Counts

4 → 91

Calls

4 calls:

13.0ms	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (-.f64 phi2 phi1)))
8.0ms	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
3.0ms	(sqrt.f64 (-.f64 phi2 phi1))
3.0ms	(sqrt.f64 (-.f64 phi2 phi1))

series168.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
35.0ms	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (-.f64 phi2 phi1)))
33.0ms	(sqrt.f64 (-.f64 phi2 phi1))
31.0ms	(sqrt.f64 (-.f64 phi2 phi1))

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5272	1453

prune74.0ms (0.8%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	4	11	15
Picked	1	0	1
Done	0	1	1
Total	98	22	120

Error

18.1b

Counts

120 → 22

Compiler

Compiled 1683 to 392 computations (76.7% saved)

regimes1.7s (17.3%)

Accuracy

Total 3.8b remaining (18.7%)

Threshold costs 0b (0%)

Compiler

Compiled 13133 to 8518 computations (35.1% saved)

bsearch4.0ms (0%)

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

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	92	178
1	92	178

Compiler

Compiled 464 to 232 computations (50% saved)

end0.0ms (0%)

sample3.6s (36.9%)

Algorithm

1×

intervals

Results

633.0ms	5995×	body	128	valid
406.0ms	839×	body	1024	valid
260.0ms	2384×	body	128	invalid
257.0ms	728×	body	512	valid
204.0ms	437×	body	1024	invalid
122.0ms	378×	body	512	invalid
103.0ms	435×	body	256	valid
38.0ms	175×	body	256	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 1437 to 912 computations (36.5% saved)

Details

analyze2.2s (22.2%)

sample95.0ms (1%)

simplify131.0ms (1.4%)

prune4.0ms (0%)

localize16.0ms (0.2%)

rewrite77.0ms (0.8%)

series921.0ms (9.5%)

simplify96.0ms (1%)

prune301.0ms (3.1%)

localize4.0ms (0%)

rewrite11.0ms (0.1%)

series33.0ms (0.3%)

simplify45.0ms (0.5%)

prune42.0ms (0.4%)

localize6.0ms (0.1%)

rewrite5.0ms (0%)

series32.0ms (0.3%)

simplify72.0ms (0.7%)

prune32.0ms (0.3%)

localize6.0ms (0.1%)

rewrite34.0ms (0.3%)

series168.0ms (1.7%)

simplify52.0ms (0.5%)

prune74.0ms (0.8%)

regimes1.7s (17.3%)

bsearch4.0ms (0%)

simplify24.0ms (0.2%)

end0.0ms (0%)

sample3.6s (36.9%)

Profiling