Details

analyze1.4s (9.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5547	104
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample149.0ms (1%)

Algorithm

1×

intervals

Results

99.0ms	144×	body	1024	valid
21.0ms	49×	body	512	valid
10.0ms	19×	body	256	valid
5.0ms	44×	body	128	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5170	26

prune3.0ms (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

5.1b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
4.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite209.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.0b

Rules

46×	`*-un-lft-identity_binary64_78`
27×	`add-sqr-sqrt_binary64_100`
26×	`add-cube-cbrt_binary64_113`
25×	`sqrt-prod_binary64_94`
24×	`times-frac_binary64_84`
16×	`unpow-prod-down_binary64_157`
10×	`distribute-lft-out_binary64_29`
8×	`add-exp-log_binary64_116` `associate-/r*_binary64_22`
7×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-/l*_binary64_23`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75`

Counts

4 → 102

Calls

4 calls:

17.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2664 to 1486 computations (44.2% saved)

series549.0ms (3.8%)

Error

2.7b

Counts

4 → 29

Calls

4 calls:

282.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
175.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
32.0ms	(pow.f64 (sin.f64 ky) 2)
27.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1536 to 1143 computations (25.6% saved)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5003	2594

prune194.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	12	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Error

2.6b

Counts

132 → 12

Compiler

Compiled 3215 to 1807 computations (43.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 kx))
0.6b	(cbrt.f64 (sin.f64 kx))
0.7b	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
4.7b	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

rewrite107.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

11×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`cbrt-prod_binary64_109`
6×	`pow1_binary64_139` `unpow-prod-down_binary64_157`
5×	`add-exp-log_binary64_116`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114`
3×	`sqrt-prod_binary64_94` `pow-unpow_binary64_155` `pow1/3_binary64_160`
2×	`sqrt-div_binary64_95` `pow-pow_binary64_150`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `sqr-pow_binary64_50`

Counts

4 → 58

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
2.0ms	(cbrt.f64 (sin.f64 kx))
2.0ms	(cbrt.f64 (sin.f64 kx))

Compiler

Compiled 1827 to 913 computations (50% saved)

series528.0ms (3.7%)

Error

2.6b

Counts

4 → 25

Calls

4 calls:

193.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
131.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
87.0ms	(cbrt.f64 (sin.f64 kx))
86.0ms	(cbrt.f64 (sin.f64 kx))

Compiler

Compiled 1707 to 1275 computations (25.3% saved)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5043	1057

prune122.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	83	12	95

Error

2.6b

Counts

95 → 12

Compiler

Compiled 2421 to 1346 computations (44.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.8b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite216.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

54×	`*-un-lft-identity_binary64_78`
45×	`sqrt-prod_binary64_94`
41×	`add-sqr-sqrt_binary64_100`
34×	`times-frac_binary64_84`
28×	`add-cube-cbrt_binary64_113`
24×	`associate-r_binary64_18`
18×	`unpow-prod-down_binary64_157`
12×	`distribute-lft-out_binary64_29`
10×	`pow1_binary64_139`
8×	`add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114` `pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24` `unswap-sqr_binary64_46`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `associate-l_binary64_19`
2×	`sqrt-div_binary64_95` `div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50`
1×	`pow1/2_binary64_158` `inv-pow_binary64_163` `pow-flip_binary64_152` `pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `associate-r/_binary64_20` `-commutative_binary64_9`

Counts

4 → 115

Calls

4 calls:

19.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3246 to 2028 computations (37.5% saved)

series601.0ms (4.2%)

Error

2.6b

Counts

4 → 27

Calls

4 calls:

291.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
223.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
31.0ms	(pow.f64 (sin.f64 ky) 2)
29.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1440 to 1114 computations (22.6% saved)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4958	2611
1	4958	2611

prune197.0ms (1.4%)

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

2.6b

Counts

154 → 12

Compiler

Compiled 3663 to 2220 computations (39.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 (sin.f64 kx)))
0.6b	(cbrt.f64 (cbrt.f64 (sin.f64 kx)))
0.7b	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
4.7b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 kx))) 2) (cbrt.f64 (cbrt.f64 (sin.f64 kx)))) 2)) (pow.f64 (sin.f64 ky) 2)))

rewrite139.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

21×	`cbrt-prod_binary64_109`
13×	`add-sqr-sqrt_binary64_100`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`pow1_binary64_139` `unpow-prod-down_binary64_157`
5×	`add-exp-log_binary64_116`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114`
3×	`sqrt-prod_binary64_94` `pow-unpow_binary64_155` `pow1/3_binary64_160`
2×	`sqrt-div_binary64_95` `pow-pow_binary64_150`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `sqr-pow_binary64_50`

Counts

4 → 64

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 kx))) 2) (cbrt.f64 (cbrt.f64 (sin.f64 kx)))) 2)) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
2.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 kx)))
2.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 kx)))

Compiler

Compiled 2641 to 1228 computations (53.5% saved)

series542.0ms (3.7%)

Error

2.6b

Counts

4 → 25

Calls

4 calls:

187.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 kx))) 2) (cbrt.f64 (cbrt.f64 (sin.f64 kx)))) 2)) (pow.f64 (sin.f64 ky) 2)))
136.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
92.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 kx)))
91.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 kx)))

Compiler

Compiled 1993 to 1417 computations (28.9% saved)

simplify102.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4912	1275
1	4912	1275

prune137.0ms (0.9%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	89	12	101

Error

2.6b

Counts

101 → 12

Compiler

Compiled 2874 to 1424 computations (50.5% saved)

regimes1.7s (11.7%)

Accuracy

Total 1.7b remaining (48.4%)

Threshold costs 0b (0%)

Compiler

Compiled 19326 to 15109 computations (21.8% saved)

bsearch5.0ms (0%)

Compiler: Compiled 13 to 12 computations (7.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	55
1	24	55

end0.0ms (0%)

sample7.2s (50%)

Algorithm

1×

intervals

Results

3.4s	4645×	body	1024	valid
625.0ms	1391×	body	512	valid
196.0ms	1419×	body	128	valid
157.0ms	525×	body	256	valid
26.0ms	20×	body	2048	valid

Compiler

Compiled 2189 to 1709 computations (21.9% saved)

Details

analyze1.4s (9.5%)

sample149.0ms (1%)

simplify84.0ms (0.6%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite209.0ms (1.4%)

series549.0ms (3.8%)

simplify70.0ms (0.5%)

prune194.0ms (1.3%)

localize17.0ms (0.1%)

rewrite107.0ms (0.7%)

series528.0ms (3.7%)

simplify68.0ms (0.5%)

prune122.0ms (0.8%)

localize14.0ms (0.1%)

rewrite216.0ms (1.5%)

series601.0ms (4.2%)

simplify76.0ms (0.5%)

prune197.0ms (1.4%)

localize21.0ms (0.1%)

rewrite139.0ms (1%)

series542.0ms (3.7%)

simplify102.0ms (0.7%)

prune137.0ms (0.9%)

regimes1.7s (11.7%)

bsearch5.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.2s (50%)

Profiling