Details

analyze2.2s (1.4%)

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)

sample82.0ms (0.1%)

Algorithm

1×

intervals

Results

25.0ms	190×	body	128	valid
13.0ms	28×	body	1024	valid
9.0ms	26×	body	512	valid
6.0ms	58×	body	128	invalid
5.0ms	11×	body	1024	invalid
3.0ms	11×	body	256	valid
2.0ms	7×	body	512	invalid
1.0ms	1×	body	2048	valid
1.0ms	3×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify215.0ms (0.1%)

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

38.7b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.3b	(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))))

rewrite65.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`associate-*l/_binary64_1044`
97×	`flip--_binary64_1076` `flip3--_binary64_1105`
66×	`sqrt-div_binary64_1118`
64×	`frac-times_binary64_1111` `frac-add_binary64_1109`
32×	`associate-*r/_binary64_1043`
12×	`add-sqr-sqrt_binary64_1123`
9×	`*-un-lft-identity_binary64_1101`
7×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140`
3×	`sqrt-prod_binary64_1117` `associate-r_binary64_1041`
1×	`*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `sqrt-pow1_binary64_1119` `distribute-lft-out--_binary64_1053` `flip3-+_binary64_1104` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `unswap-sqr_binary64_1069` `pow1/2_binary64_1181`

Counts

4 → 115

Calls

4 calls:

21.0ms	(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))))
7.0ms	(*.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))

series2.9s (1.9%)

Counts

4 → 76

Calls

4 calls:

2.4s	(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))))
354.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
54.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
51.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 8334 to 6386 computations (23.4% saved)

simplify123.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	6166	13542

prune452.0ms (0.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	181	10	191
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	10	192

Error

4.6b

Counts

192 → 10

Compiler

Compiled 11542 to 4509 computations (60.9% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 lambda1 lambda2))
2.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.3b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cbrt.f64 (-.f64 lambda1 lambda2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite472.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

1408×	`frac-times_binary64_1111`
1345×	`flip--_binary64_1076` `flip3--_binary64_1105`
1298×	`cbrt-div_binary64_1133`
992×	`associate-*r/_binary64_1043`
944×	`associate-*l/_binary64_1044`
642×	`sqrt-div_binary64_1118`
640×	`frac-add_binary64_1109`
9×	`add-sqr-sqrt_binary64_1123`
8×	`*-un-lft-identity_binary64_1101`
6×	`add-cube-cbrt_binary64_1136`
5×	`pow1_binary64_1162` `cbrt-prod_binary64_1132`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`sqrt-prod_binary64_1117`
1×	`rem-sqrt-square_binary64_1114` `pow1/3_binary64_1183` `difference-of-squares_binary64_1070` `sqrt-pow1_binary64_1119` `distribute-lft-out--_binary64_1053` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

4 → 684

Calls

4 calls:

91.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cbrt.f64 (-.f64 lambda1 lambda2))))) (.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))
3.0ms	(cbrt.f64 (-.f64 lambda1 lambda2))

series2.9s (1.9%)

Counts

4 → 64

Calls

4 calls:

2.7s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cbrt.f64 (-.f64 lambda1 lambda2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
85.0ms	(cbrt.f64 (-.f64 lambda1 lambda2))
57.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
55.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 8577 to 6461 computations (24.7% saved)

simplify834.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

748 → 748

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5133	122562

prune3.5s (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	745	3	748
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	747	11	758

Error

4.6b

Counts

758 → 11

Compiler

Compiled 84429 to 22076 computations (73.9% saved)

localize29.0ms (0%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (cbrt.f64 (-.f64 lambda1 lambda2))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
2.5b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.6b	(+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (cbrt.f64 (-.f64 lambda1 lambda2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))
26.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (cbrt.f64 (-.f64 lambda1 lambda2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite5.0s (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

16536×	`frac-times_binary64_1111`
14076×	`flip--_binary64_1076` `flip3--_binary64_1105`
11664×	`cbrt-div_binary64_1133`
8556×	`associate-*l/_binary64_1044`
8478×	`associate-*r/_binary64_1043`
5808×	`frac-add_binary64_1109`
3876×	`sqrt-div_binary64_1118`
15×	`add-sqr-sqrt_binary64_1123`
10×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
8×	`associate-+r+_binary64_1033`
7×	`pow1_binary64_1162` `sqrt-prod_binary64_1117`
6×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-r_binary64_1041` `cancel-sign-sub-inv_binary64_1067`
4×	`distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-l_binary64_1042`
2×	`sub-neg_binary64_1094` `unswap-sqr_binary64_1069`
1×	`*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `pow1/2_binary64_1181`

Counts

4 → 5873

Calls

4 calls:

366.0ms	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (cbrt.f64 (-.f64 lambda1 lambda2))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
217.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (cbrt.f64 (-.f64 lambda1 lambda2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
120.0ms	(+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (cbrt.f64 (-.f64 lambda1 lambda2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series28.1s (18.7%)

Counts

4 → 113

Calls

4 calls:

15.1s	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (cbrt.f64 (-.f64 lambda1 lambda2))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
8.1s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (cbrt.f64 (-.f64 lambda1 lambda2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
4.8s	(+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (cbrt.f64 (-.f64 lambda1 lambda2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))
58.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 39433 to 29788 computations (24.5% saved)

simplify10.0s (6.7%)

Algorithm

1×	egg-herbie

Counts

5986 → 5986

Iterations

Useful iterations: 0 (249.0ms)

Iter	Nodes	Cost
0	13714	1478145

Details

analyze2.2s (1.4%)

sample82.0ms (0.1%)

simplify215.0ms (0.1%)

prune4.0ms (0%)

localize19.0ms (0%)

rewrite65.0ms (0%)

series2.9s (1.9%)

simplify123.0ms (0.1%)

prune452.0ms (0.3%)

localize22.0ms (0%)

rewrite472.0ms (0.3%)

series2.9s (1.9%)

simplify834.0ms (0.6%)

prune3.5s (2.3%)

localize29.0ms (0%)

rewrite5.0s (3.3%)

series28.1s (18.7%)

simplify10.0s (6.7%)

prune1.6min (62.1%)

Profiling