Details

analyze2.8s (11.4%)

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)

sample124.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	179×	body	128	valid
14.0ms	20×	body	1024	invalid
13.0ms	28×	body	1024	valid
11.0ms	106×	body	128	invalid
11.0ms	31×	body	512	valid
6.0ms	17×	body	512	invalid
4.0ms	18×	body	256	valid
2.0ms	9×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify130.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune8.0ms (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

39.6b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize16.0ms (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))))
4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.1b	(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))))

rewrite376.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

39.5b

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:

20.0ms	(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)

series8.6s (35.4%)

Error

5.9b

Counts

4 → 79

Calls

4 calls:

7.5s	(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))))
651.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
64.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
63.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 19034 to 14176 computations (25.5% saved)

simplify151.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	6201	15893

prune538.0ms (2.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	201	13	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	202	13	215

Error

5.9b

Counts

215 → 13

Compiler

Compiled 13633 to 5641 computations (58.6% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

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)

series96.0ms (0.4%)

Error

5.9b

Counts

1 → 15

Calls

1 calls:

89.0ms

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

Compiler

Compiled 219 to 198 computations (9.6% saved)

simplify47.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5690	386

prune58.0ms (0.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	43	15	58

Error

5.9b

Counts

58 → 15

Compiler

Compiled 1120 to 578 computations (48.4% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

Rules

5×	`add-log-exp_binary64_1822`
2×	`sum-log_binary64_1874`
1×	`neg-log_binary64_1876` `pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805` `flip3-+_binary64_1786` `*-un-lft-identity_binary64_1783` `unsub-neg_binary64_1777` `flip-+_binary64_1757` `distribute-lft-neg-in_binary64_1740` `distribute-rgt-out_binary64_1736` `neg-sub0_binary64_1778` `associate-+r-_binary64_1717` `+-commutative_binary64_1713`

Counts

1 → 15

Calls

1 calls:

5.0ms

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

Compiler

Compiled 233 to 56 computations (76% saved)

series116.0ms (0.5%)

Error

5.9b

Counts

1 → 15

Calls

1 calls:

109.0ms

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

Compiler

Compiled 225 to 206 computations (8.4% saved)

simplify61.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5032	255

prune46.0ms (0.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	30	15	45

Error

5.9b

Counts

45 → 15

Compiler

Compiled 985 to 546 computations (44.6% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (-.f64 phi2 phi1)) (cbrt.f64 (-.f64 phi2 phi1)))
0.6b	(cbrt.f64 (-.f64 phi2 phi1))
0.6b	(cbrt.f64 (-.f64 phi2 phi1))
0.6b	(cbrt.f64 (-.f64 phi2 phi1))

rewrite115.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

Rules

43×	`cbrt-prod_binary64_1814`
37×	`add-sqr-sqrt_binary64_1805`
35×	`*-un-lft-identity_binary64_1783`
18×	`cbrt-div_binary64_1815`
15×	`add-cube-cbrt_binary64_1818`
11×	`pow1_binary64_1844`
10×	`swap-sqr_binary64_1750`
9×	`pow1/3_binary64_1865` `flip3--_binary64_1787` `flip--_binary64_1758` `distribute-lft-out--_binary64_1735`
8×	`associate-l_binary64_1724` `associate-r_binary64_1723`
7×	`difference-of-squares_binary64_1752`
6×	`add-exp-log_binary64_1821`
4×	`add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819` `frac-times_binary64_1793` `unswap-sqr_binary64_1751`
2×	`pow-prod-down_binary64_1854` `pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `associate-l/_binary64_1726` `associate-r/_binary64_1725`
1×	`pow2_binary64_1864` `pow-plus_binary64_1846` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `*-commutative_binary64_1714`

Counts

4 → 101

Calls

4 calls:

14.0ms	(*.f64 (cbrt.f64 (-.f64 phi2 phi1)) (cbrt.f64 (-.f64 phi2 phi1)))
3.0ms	(cbrt.f64 (-.f64 phi2 phi1))
3.0ms	(cbrt.f64 (-.f64 phi2 phi1))
3.0ms	(cbrt.f64 (-.f64 phi2 phi1))

Compiler

Compiled 2422 to 491 computations (79.7% saved)

series341.0ms (1.4%)

Error

5.9b

Counts

4 → 33

Calls

4 calls:

97.0ms	(*.f64 (cbrt.f64 (-.f64 phi2 phi1)) (cbrt.f64 (-.f64 phi2 phi1)))
73.0ms	(cbrt.f64 (-.f64 phi2 phi1))
73.0ms	(cbrt.f64 (-.f64 phi2 phi1))
70.0ms	(cbrt.f64 (-.f64 phi2 phi1))

Compiler

Compiled 2097 to 1580 computations (24.7% saved)

simplify99.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4910	1755
1	4910	1755

prune106.0ms (0.4%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	133	16	149

Error

5.9b

Counts

149 → 16

Compiler

Compiled 2715 to 651 computations (76% saved)

regimes4.2s (17.3%)

Accuracy

Total 15.8b remaining (80.6%)

Threshold costs 0b (0%)

Compiler

Compiled 43056 to 30036 computations (30.2% saved)

bsearch8.0ms (0%)

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

simplify46.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	105
1	61	105

Remove

(sort lambda1 lambda2)

Compiler

Compiled 414 to 216 computations (47.8% saved)

end0.0ms (0%)

sample6.1s (25.4%)

Algorithm

1×

intervals

Results

636.0ms	6009×	body	128	valid
367.0ms	814×	body	1024	valid
267.0ms	2518×	body	128	invalid
255.0ms	766×	body	512	valid
211.0ms	458×	body	1024	invalid
114.0ms	365×	body	512	invalid
95.0ms	406×	body	256	valid
33.0ms	153×	body	256	invalid
3.0ms	5×	body	2048	valid

Compiler

Compiled 4603 to 3220 computations (30% saved)

Details

analyze2.8s (11.4%)

sample124.0ms (0.5%)

simplify130.0ms (0.5%)

prune8.0ms (0%)

localize16.0ms (0.1%)

rewrite376.0ms (1.6%)

series8.6s (35.4%)

simplify151.0ms (0.6%)

prune538.0ms (2.2%)

localize4.0ms (0%)

rewrite29.0ms (0.1%)

series96.0ms (0.4%)

simplify47.0ms (0.2%)

prune58.0ms (0.2%)

localize6.0ms (0%)

rewrite16.0ms (0.1%)

series116.0ms (0.5%)

simplify61.0ms (0.3%)

prune46.0ms (0.2%)

localize8.0ms (0%)

rewrite115.0ms (0.5%)

series341.0ms (1.4%)

simplify99.0ms (0.4%)

prune106.0ms (0.4%)

regimes4.2s (17.3%)

bsearch8.0ms (0%)

simplify46.0ms (0.2%)

end0.0ms (0%)

sample6.1s (25.4%)

Profiling