Details

analyze2.3s (3.7%)

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)

sample85.0ms (0.1%)

Algorithm

1×

intervals

Results

26.0ms	197×	body	128	valid
11.0ms	23×	body	1024	valid
7.0ms	73×	body	128	invalid
7.0ms	16×	body	1024	invalid
6.0ms	19×	body	512	valid
5.0ms	14×	body	512	invalid
4.0ms	17×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify219.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (124.0ms)

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

41.0b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize17.0ms (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))))
2.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.1b	(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))))

rewrite77.0ms (0.1%)

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:

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))

series12.5s (20.1%)

Counts

4 → 84

Calls

4 calls:

11.7s	(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))))
733.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
52.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
49.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 17679 to 13866 computations (21.6% saved)

simplify161.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5285	17883

prune669.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	206	13	219
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	207	13	220

Error

3.8b

Counts

220 → 13

Compiler

Compiled 14698 to 6224 computations (57.7% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2))
0.4b	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)
2.6b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
38.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite41.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1805`
19×	`unpow-prod-down_binary64_1862`
17×	`add-exp-log_binary64_1821`
16×	`unswap-sqr_binary64_1751`
13×	`*-un-lft-identity_binary64_1783`
11×	`sqr-pow_binary64_1755` `add-cube-cbrt_binary64_1818` `unpow2_binary64_1848`
10×	`associate-l_binary64_1724`
9×	`prod-exp_binary64_1832`
8×	`associate-r_binary64_1723`
7×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
6×	`add-cbrt-cube_binary64_1819` `pow1_binary64_1844`
4×	`add-log-exp_binary64_1822`
3×	`pow-unpow_binary64_1860` `sqrt-prod_binary64_1799`
2×	`sqrt-div_binary64_1800`
1×	`difference-of-squares_binary64_1752` `cbrt-unprod_binary64_1816` `flip-+_binary64_1757` `pow1/2_binary64_1863` `distribute-lft-out--_binary64_1735` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `pow-pow_binary64_1855` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796`

Counts

4 → 93

Calls

4 calls:

16.0ms	(.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2))
10.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
3.0ms	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)
2.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series12.4s (20%)

Counts

4 → 84

Calls

4 calls:

11.6s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
683.0ms	(.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2))
102.0ms	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)
52.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

Compiler

Compiled 17594 to 13900 computations (21% saved)

simplify129.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5829	10274

prune449.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	178	12	190

Error

3.8b

Counts

190 → 12

Compiler

Compiled 9442 to 4924 computations (47.9% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
2.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.1b	(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 phi1 phi2) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite62.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

23.0ms	(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 phi1 phi2) 2)) 3)))) (.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))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)

series11.8s (18.9%)

Counts

4 → 66

Calls

4 calls:

11.5s	(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 phi1 phi2) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
169.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
55.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
53.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 16326 to 12826 computations (21.4% saved)

simplify151.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5179	15982

prune505.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	182	12	194

Error

3.8b

Counts

194 → 12

Compiler

Compiled 13376 to 5675 computations (57.6% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

2.6b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
2.6b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
38.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
38.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_1805`
6×	`add-cube-cbrt_binary64_1818` `sqrt-prod_binary64_1799` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `sqrt-div_binary64_1800` `add-log-exp_binary64_1822`
2×	`flip-+_binary64_1757` `pow1/2_binary64_1863` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`

Counts

4 → 44

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
11.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
3.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
3.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series12.0s (19.4%)

Counts

4 → 98

Calls

4 calls:

6.0s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.9s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
58.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
56.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

Compiler

Compiled 23950 to 18432 computations (23% saved)

simplify113.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5177	11400

prune621.0ms (1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	142	12	154

Error

3.8b

Counts

154 → 12

Compiler

Compiled 12228 to 6348 computations (48.1% saved)

regimes2.6s (4.2%)

Accuracy

Total 28.3b remaining (87.6%)

Threshold costs 0b (0%)

Compiler

Compiled 27368 to 18179 computations (33.6% saved)

bsearch627.0ms (1%)

Steps

Iters	Range		Point
10	1.1569613031117088e+55	6.44471226568136e+64	2.553943994428835e+59
6	4.264105002834433e-22	1.735319939653826e-21	9.269945814378616e-22
10	7.059847739651766e-107	5.052140652234905e-88	4.962564261877504e-88
6	5.3236936499144107e-250	3.4385825239769795e-249	5.38115258344735e-250
10	3.765442572561619e-297	9.392056497535112e-287	9.303407807589607e-287
7	-1.1764515258037537e-237	-2.005506759109202e-239	-1.1623653209688043e-237
10	-1.6014761761670567e-211	-1.7827968156930586e-225	-1.3217438363980596e-213
4	-1.9807340572064363e-182	-1.1447653956167122e-182	-1.4628256157457647e-182
8	-1.6829780562314203e-156	-3.43709299734827e-159	-7.263758197549583e-158
8	-2.730961321106729e-67	-8.630650363512903e-71	-1.1432798135583093e-70
10	-633803985042621.9	-3443.2902253181373	-623511300567565.1

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	332	485
1	332	485

end0.0ms (0%)

sample4.5s (7.3%)

Algorithm

1×

intervals

Results

650.0ms	6017×	body	128	valid
372.0ms	775×	body	1024	valid
267.0ms	766×	body	512	valid
263.0ms	2455×	body	128	invalid
215.0ms	448×	body	1024	invalid
119.0ms	364×	body	512	invalid
105.0ms	437×	body	256	valid
38.0ms	169×	body	256	invalid
4.0ms	5×	body	2048	valid

Compiler

Compiled 3266 to 2121 computations (35.1% saved)

Details

analyze2.3s (3.7%)

sample85.0ms (0.1%)

simplify219.0ms (0.4%)

prune4.0ms (0%)

localize17.0ms (0%)

rewrite77.0ms (0.1%)

series12.5s (20.1%)

simplify161.0ms (0.3%)

prune669.0ms (1.1%)

localize19.0ms (0%)

rewrite41.0ms (0.1%)

series12.4s (20%)

simplify129.0ms (0.2%)

prune449.0ms (0.7%)

localize23.0ms (0%)

rewrite62.0ms (0.1%)

series11.8s (18.9%)

simplify151.0ms (0.2%)

prune505.0ms (0.8%)

localize22.0ms (0%)

rewrite33.0ms (0.1%)

series12.0s (19.4%)

simplify113.0ms (0.2%)

prune621.0ms (1%)

regimes2.6s (4.2%)

bsearch627.0ms (1%)

simplify10.0ms (0%)

end0.0ms (0%)

sample4.5s (7.3%)

Profiling