Details

analyze2.7s (9.8%)

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)

sample109.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	185×	body	128	valid
14.0ms	30×	body	1024	valid
9.0ms	27×	body	512	valid
8.0ms	84×	body	128	invalid
4.0ms	10×	body	1024	invalid
4.0ms	12×	body	512	invalid
3.0ms	14×	body	256	valid
2.0ms	7×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify134.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (129.0ms)

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

40.4b

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))))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.3b	(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))))

rewrite372.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

40.4b

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-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
8×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
6×	`add-sqr-sqrt_binary64_1805`
5×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
4×	`add-log-exp_binary64_1822` `pow-prod-up_binary64_1853` `pow-sqr_binary64_1756`
3×	`sqrt-prod_binary64_1799`
2×	`pow-plus_binary64_1846`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `flip3-+_binary64_1786` `flip-+_binary64_1757` `rem-sqrt-square_binary64_1796` `pow2_binary64_1864` `swap-sqr_binary64_1750` `associate-l_binary64_1724` `associate-r_binary64_1723` `*-commutative_binary64_1714`

Counts

4 → 135

Calls

4 calls:

25.0ms	(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))

Compiler

Compiled 9145 to 2868 computations (68.6% saved)

series6.6s (23.9%)

Error

3.8b

Counts

4 → 68

Calls

4 calls:

5.7s	(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))))
559.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
38.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 16070 to 12073 computations (24.9% saved)

simplify136.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5766	14592

prune486.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	194	9	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	195	9	204

Error

3.8b

Counts

204 → 9

Compiler

Compiled 12138 to 4802 computations (60.4% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

3.8b

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-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732`
3×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `associate-l_binary64_1724`
2×	`sub-neg_binary64_1776` `associate-*r/_binary64_1725`
1×	`pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `add-log-exp_binary64_1822` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `flip3--_binary64_1787` `flip--_binary64_1758` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `*-commutative_binary64_1714`

Counts

1 → 30

Calls

1 calls:

7.0ms

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

Compiler

Compiled 338 to 113 computations (66.6% saved)

series95.0ms (0.3%)

Error

3.8b

Counts

1 → 15

Calls

1 calls:

87.0ms

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

Compiler

Compiled 219 to 198 computations (9.6% saved)

simplify48.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5690	386

prune36.0ms (0.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	43	11	54

Error

3.8b

Counts

54 → 11

Compiler

Compiled 760 to 338 computations (55.5% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 (-.f64 phi2 phi1) R)) (cbrt.f64 (*.f64 (-.f64 phi2 phi1) R)))
2.1b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
2.1b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
2.1b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

rewrite92.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

3.8b

Rules

20×	`associate-*l/_binary64_1726`
18×	`cbrt-div_binary64_1815`
11×	`pow1_binary64_1844`
10×	`add-sqr-sqrt_binary64_1805`
9×	`pow1/3_binary64_1865` `flip3--_binary64_1787` `flip--_binary64_1758`
8×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
7×	`cbrt-prod_binary64_1814`
6×	`add-exp-log_binary64_1821`
4×	`add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819` `frac-times_binary64_1793` `swap-sqr_binary64_1750` `associate-l_binary64_1724` `associate-r_binary64_1723`
2×	`pow-prod-down_binary64_1854` `pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `associate-*r/_binary64_1725`
1×	`pow2_binary64_1864` `pow-plus_binary64_1846` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`

Counts

4 → 72

Calls

4 calls:

8.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 phi2 phi1) R)) (cbrt.f64 (*.f64 (-.f64 phi2 phi1) R)))
5.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
5.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
5.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

Compiler

Compiled 2027 to 304 computations (85% saved)

series1.2s (4.3%)

Error

3.8b

Counts

4 → 63

Calls

4 calls:

287.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 phi2 phi1) R)) (cbrt.f64 (*.f64 (-.f64 phi2 phi1) R)))
282.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
266.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
261.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

Compiler

Compiled 5740 to 3878 computations (32.4% saved)

simplify52.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5384	2907

prune141.0ms (0.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	134	12	146

Error

3.8b

Counts

146 → 12

Compiler

Compiled 4058 to 1114 computations (72.5% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)
3.4b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.3b	(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))))

rewrite343.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

3.8b

Rules

128×	`associate-*l/_binary64_1726`
96×	`flip3--_binary64_1787` `flip--_binary64_1758`
66×	`sqrt-div_binary64_1800`
64×	`frac-times_binary64_1793` `frac-add_binary64_1791`
32×	`associate-*r/_binary64_1725`
9×	`add-sqr-sqrt_binary64_1805`
8×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`pow1_binary64_1844`
5×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
4×	`add-log-exp_binary64_1822`
3×	`sqrt-prod_binary64_1799` `unpow-prod-down_binary64_1862` `pow-unpow_binary64_1860` `cube-prod_binary64_1811`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `flip3-+_binary64_1786` `flip-+_binary64_1757` `rem-sqrt-square_binary64_1796` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `unpow3_binary64_1849` `cube-mult_binary64_1813` `rem-cube-cbrt_binary64_1806` `sqr-pow_binary64_1755`

Counts

4 → 116

Calls

4 calls:

22.0ms	(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))))
6.0ms	(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 (22.7%)

Error

3.8b

Counts

4 → 52

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))))
170.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)
41.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
37.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 14880 to 11279 computations (24.2% saved)

simplify129.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5820	13223

prune402.0ms (1.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	4	5	9
Picked	0	1	1
Done	0	2	2
Total	169	11	180

Error

3.8b

Counts

180 → 11

Compiler

Compiled 10883 to 4243 computations (61% saved)

regimes3.2s (11.6%)

Accuracy

Total 20.8b remaining (71.3%)

Threshold costs 0b (0%)

Compiler

Compiled 31328 to 21210 computations (32.3% saved)

bsearch8.0ms (0%)

Compiler: Compiled 29 to 19 computations (34.5% saved)

simplify50.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	129
1	65	129

Removed

((sort lambda1 lambda2))

Compiler

Compiled 504 to 270 computations (46.4% saved)

end0.0ms (0%)

sample4.9s (17.9%)

Algorithm

1×

intervals

Results

644.0ms	6034×	body	128	valid
397.0ms	811×	body	1024	valid
264.0ms	2437×	body	128	invalid
258.0ms	740×	body	512	valid
220.0ms	477×	body	1024	invalid
106.0ms	329×	body	512	invalid
103.0ms	410×	body	256	valid
38.0ms	173×	body	256	invalid
4.0ms	5×	body	2048	valid

Compiler

Compiled 3363 to 2272 computations (32.4% saved)

Details

analyze2.7s (9.8%)

sample109.0ms (0.4%)

simplify134.0ms (0.5%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite372.0ms (1.3%)

series6.6s (23.9%)

simplify136.0ms (0.5%)

prune486.0ms (1.8%)

localize4.0ms (0%)

rewrite28.0ms (0.1%)

series95.0ms (0.3%)

simplify48.0ms (0.2%)

prune36.0ms (0.1%)

localize10.0ms (0%)

rewrite92.0ms (0.3%)

series1.2s (4.3%)

simplify52.0ms (0.2%)

prune141.0ms (0.5%)

localize26.0ms (0.1%)

rewrite343.0ms (1.2%)

series6.3s (22.7%)

simplify129.0ms (0.5%)

prune402.0ms (1.5%)

regimes3.2s (11.6%)

bsearch8.0ms (0%)

simplify50.0ms (0.2%)

end0.0ms (0%)

sample4.9s (17.9%)

Profiling