Details

analyze3.4s (12.3%)

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)

sample158.0ms (0.6%)

Algorithm

1×

intervals

Results

27.0ms	193×	body	128	valid
20.0ms	19×	body	1024	invalid
20.0ms	28×	body	1024	valid
13.0ms	98×	body	128	invalid
11.0ms	21×	body	512	valid
5.0ms	12×	body	512	invalid
4.0ms	14×	body	256	valid
3.0ms	9×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify145.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (140.0ms)

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

39.5b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
3.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.8b	(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))))

rewrite429.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

39.5b

Rules

130×	`associate-*l/_binary64_3431`
97×	`flip3--_binary64_3492` `flip--_binary64_3463`
66×	`sqrt-div_binary64_3505`
64×	`frac-times_binary64_3498` `frac-add_binary64_3496`
32×	`associate-*r/_binary64_3430`
12×	`add-sqr-sqrt_binary64_3510`
9×	`*-un-lft-identity_binary64_3488`
7×	`pow1_binary64_3549` `add-cube-cbrt_binary64_3523`
6×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
5×	`associate-l_binary64_3429`
4×	`add-log-exp_binary64_3527`
3×	`sqrt-prod_binary64_3504` `associate-r_binary64_3428`
1×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `flip3-+_binary64_3491` `flip-+_binary64_3462` `rem-sqrt-square_binary64_3501` `pow-prod-down_binary64_3559` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `unswap-sqr_binary64_3456` `difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440` `*-commutative_binary64_3419`

Counts

4 → 115

Calls

4 calls:

39.0ms	(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))))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
9.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
8.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

Compiler

Compiled 8305 to 2543 computations (69.4% saved)

series9.4s (34%)

Error

3.7b

Counts

4 → 64

Calls

4 calls:

8.7s	(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))))
348.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
60.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
48.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 16211 to 12024 computations (25.8% saved)

simplify181.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5660	13481

prune559.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	168	11	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	169	11	180

Error

3.7b

Counts

180 → 11

Compiler

Compiled 11672 to 4579 computations (60.8% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

3.6b

Rules

9×	`add-sqr-sqrt_binary64_3510`
7×	`*-un-lft-identity_binary64_3488`
6×	`cancel-sign-sub-inv_binary64_3454`
5×	`add-cube-cbrt_binary64_3523` `associate-r_binary64_3428`
4×	`distribute-rgt-in_binary64_3438` `distribute-lft-in_binary64_3437`
3×	`pow1_binary64_3549` `add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `associate-l_binary64_3429`
2×	`sub-neg_binary64_3481` `associate-*r/_binary64_3430`
1×	`pow-prod-down_binary64_3559` `prod-exp_binary64_3537` `add-log-exp_binary64_3527` `cbrt-unprod_binary64_3521` `unswap-sqr_binary64_3456` `flip3--_binary64_3492` `flip--_binary64_3463` `difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440` `*-commutative_binary64_3419`

Counts

1 → 30

Calls

1 calls:

8.0ms

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

Compiler

Compiled 338 to 113 computations (66.6% saved)

series120.0ms (0.4%)

Error

3.7b

Counts

1 → 15

Calls

1 calls:

113.0ms

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

Compiler

Compiled 219 to 198 computations (9.6% saved)

simplify55.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5690	386

prune64.0ms (0.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	41	15	56

Error

3.6b

Counts

56 → 15

Compiler

Compiled 915 to 457 computations (50.1% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite143.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.6b

Rules

43×	`cbrt-prod_binary64_3519`
37×	`add-sqr-sqrt_binary64_3510`
35×	`*-un-lft-identity_binary64_3488`
18×	`cbrt-div_binary64_3520`
15×	`add-cube-cbrt_binary64_3523`
11×	`pow1_binary64_3549`
10×	`swap-sqr_binary64_3455`
9×	`pow1/3_binary64_3570` `flip3--_binary64_3492` `flip--_binary64_3463` `distribute-lft-out--_binary64_3440`
8×	`associate-l_binary64_3429` `associate-r_binary64_3428`
7×	`difference-of-squares_binary64_3457`
6×	`add-exp-log_binary64_3526`
4×	`add-log-exp_binary64_3527` `add-cbrt-cube_binary64_3524` `frac-times_binary64_3498` `unswap-sqr_binary64_3456`
2×	`pow-prod-down_binary64_3559` `pow-prod-up_binary64_3558` `pow-sqr_binary64_3461` `associate-l/_binary64_3431` `associate-r/_binary64_3430`
1×	`pow2_binary64_3569` `pow-plus_binary64_3551` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `*-commutative_binary64_3419`

Counts

4 → 101

Calls

4 calls:

25.0ms	(*.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)

series430.0ms (1.6%)

Error

3.6b

Counts

4 → 33

Calls

4 calls:

141.0ms	(*.f64 (cbrt.f64 (-.f64 phi2 phi1)) (cbrt.f64 (-.f64 phi2 phi1)))
91.0ms	(cbrt.f64 (-.f64 phi2 phi1))
89.0ms	(cbrt.f64 (-.f64 phi2 phi1))
81.0ms	(cbrt.f64 (-.f64 phi2 phi1))

Compiler

Compiled 2097 to 1580 computations (24.7% saved)

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4908	1755
1	4908	1755

prune161.0ms (0.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	135	14	149

Error

3.6b

Counts

149 → 14

Compiler

Compiled 3270 to 1043 computations (68.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 phi2 phi1)) 2))
0.6b	(pow.f64 (cbrt.f64 (-.f64 phi2 phi1)) 2)
0.6b	(cbrt.f64 (cbrt.f64 (-.f64 phi2 phi1)))
0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 phi2 phi1))) 4)

rewrite188.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

3.6b

Rules

49×	`cbrt-prod_binary64_3519`
27×	`unpow-prod-down_binary64_3567`
24×	`add-sqr-sqrt_binary64_3510` `*-un-lft-identity_binary64_3488`
16×	`add-cube-cbrt_binary64_3523`
6×	`pow-unpow_binary64_3565` `pow1_binary64_3549` `add-exp-log_binary64_3526`
4×	`difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440` `pow1/3_binary64_3570` `pow-pow_binary64_3560` `add-log-exp_binary64_3527` `add-cbrt-cube_binary64_3524` `cbrt-div_binary64_3520`
3×	`sqr-pow_binary64_3460`
2×	`pow-to-exp_binary64_3557` `pow-exp_binary64_3556` `unpow2_binary64_3553`
1×	`flip3--_binary64_3492` `flip--_binary64_3463`

Counts

4 → 89

Calls

4 calls:

11.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 phi2 phi1)) 2))
9.0ms	(pow.f64 (cbrt.f64 (-.f64 phi2 phi1)) 2)
6.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 phi2 phi1))) 4)
4.0ms	(cbrt.f64 (cbrt.f64 (-.f64 phi2 phi1)))

Compiler

Compiled 2629 to 1068 computations (59.4% saved)

series612.0ms (2.2%)

Error

3.6b

Counts

4 → 33

Calls

4 calls:

229.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 phi2 phi1))) 4)
144.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 phi2 phi1)) 2))
129.0ms	(pow.f64 (cbrt.f64 (-.f64 phi2 phi1)) 2)
70.0ms	(cbrt.f64 (cbrt.f64 (-.f64 phi2 phi1)))

Compiler

Compiled 2723 to 2107 computations (22.6% saved)

simplify136.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4889	1766
1	4889	1766

prune173.0ms (0.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	122	14	136

Error

3.6b

Counts

136 → 14

Compiler

Compiled 3226 to 1337 computations (58.6% saved)

regimes4.1s (14.7%)

Accuracy

Total 15.4b remaining (79.2%)

Threshold costs 0b (0%)

Compiler

Compiled 36336 to 24326 computations (33.1% saved)

bsearch9.0ms (0%)

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

simplify65.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	174
1	81	174

Remove

(sort lambda1 lambda2)

Compiler

Compiled 684 to 336 computations (50.9% saved)

end0.0ms (0%)

sample7.0s (25.2%)

Algorithm

1×

intervals

Results

766.0ms	6046×	body	128	valid
452.0ms	764×	body	1024	valid
314.0ms	769×	body	512	valid
310.0ms	2393×	body	128	invalid
257.0ms	441×	body	1024	invalid
151.0ms	363×	body	512	invalid
114.0ms	418×	body	256	valid
51.0ms	199×	body	256	invalid
3.0ms	3×	body	2048	valid

Compiler

Compiled 3944 to 2629 computations (33.3% saved)

Details

analyze3.4s (12.3%)

sample158.0ms (0.6%)

simplify145.0ms (0.5%)

prune4.0ms (0%)

localize42.0ms (0.1%)

rewrite429.0ms (1.5%)

series9.4s (34%)

simplify181.0ms (0.7%)

prune559.0ms (2%)

localize4.0ms (0%)

rewrite30.0ms (0.1%)

series120.0ms (0.4%)

simplify55.0ms (0.2%)

prune64.0ms (0.2%)

localize7.0ms (0%)

rewrite143.0ms (0.5%)

series430.0ms (1.6%)

simplify92.0ms (0.3%)

prune161.0ms (0.6%)

localize16.0ms (0.1%)

rewrite188.0ms (0.7%)

series612.0ms (2.2%)

simplify136.0ms (0.5%)

prune173.0ms (0.6%)

regimes4.1s (14.7%)

bsearch9.0ms (0%)

simplify65.0ms (0.2%)

end0.0ms (0%)

sample7.0s (25.2%)

Profiling