Details

analyze2.1s (11.6%)

Algorithm

1×

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)

sample218.0ms (1.2%)

Algorithm

1×

intervals

Results

159.0ms	154×	body	1024	valid
30.0ms	48×	body	512	valid
7.0ms	39×	body	128	valid
6.0ms	15×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify315.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	5170	26

prune9.0ms (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

4.6b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite98.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`associate-l_binary64`
26×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
21×	`sqrt-prod_binary64`
14×	`unpow-prod-down_binary64`
11×	`add-exp-log_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
8×	`distribute-lft-out_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `prod-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 103

Calls

4 calls:

35.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
19.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
16.0ms	(pow.f64 (sin.f64 kx) 2)
6.0ms	(pow.f64 (sin.f64 ky) 2)

series615.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

372.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
187.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
28.0ms	(pow.f64 (sin.f64 ky) 2)
27.0ms	(pow.f64 (sin.f64 kx) 2)

simplify100.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5006	2288

prune331.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	11	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	11	116

Error

2.8b

Counts

116 → 11

Compiler

Compiled 2978 to 1674 computations (43.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite96.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
49×	`add-sqr-sqrt_binary64`
41×	`sqrt-prod_binary64`
40×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`
19×	`unpow-prod-down_binary64`
16×	`distribute-lft-out_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`associate-/r*_binary64` `pow1_binary64`
6×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `unpow2_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

42.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
23.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series828.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

360.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
292.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
160.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
16.0ms	(pow.f64 (sin.f64 ky) 2)

simplify119.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4967	3544
1	4967	3544

prune299.0ms (1.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	145	12	157

Error

2.8b

Counts

157 → 12

Compiler

Compiled 3834 to 2088 computations (45.5% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
0.5b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite211.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`sqrt-prod_binary64`
65×	`add-sqr-sqrt_binary64`
52×	`sqrt-div_binary64`
51×	`*-un-lft-identity_binary64`
34×	`sqrt-pow1_binary64`
31×	`pow1_binary64`
26×	`associate-r_binary64`
21×	`add-cube-cbrt_binary64`
19×	`swap-sqr_binary64`
18×	`pow1/2_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `flip-+_binary64`
12×	`unpow-prod-down_binary64`
11×	`unswap-sqr_binary64`
10×	`rem-sqrt-square_binary64`
9×	`pow-prod-up_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
6×	`pow-prod-down_binary64`
5×	`cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `times-frac_binary64` `sqr-abs_binary64` `associate-*l/_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `div-inv_binary64` `pow2_binary64`

Counts

4 → 165

Calls

4 calls:

62.0ms	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
56.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
21.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
17.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series695.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

294.0ms	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
177.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
134.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
89.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify183.0ms (1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4957	4153
1	4957	4153

prune411.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	178	11	189

Error

2.8b

Counts

189 → 11

Compiler

Compiled 5584 to 3357 computations (39.9% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 ky))
0.6b	(cbrt.f64 (sin.f64 ky))
0.6b	(cbrt.f64 (sin.f64 ky))
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
5×	`pow1_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`
2×	`distribute-lft-out_binary64` `unpow-prod-down_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 50

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
1.0ms	(cbrt.f64 (sin.f64 ky))
1.0ms	(cbrt.f64 (sin.f64 ky))
1.0ms	(cbrt.f64 (sin.f64 ky))

series507.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
135.0ms	(cbrt.f64 (sin.f64 ky))
127.0ms	(cbrt.f64 (sin.f64 ky))
94.0ms	(cbrt.f64 (sin.f64 ky))

simplify124.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4881	783
1	4881	783

prune109.0ms (0.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	60	13	73

Error

2.8b

Counts

73 → 13

Compiler

Compiled 1960 to 888 computations (54.7% saved)

regimes1.5s (8.2%)

Accuracy

Total 0.4b remaining (15.2%)

Threshold costs 0.4b (15.2%)

Compiler

Compiled 12223 to 9651 computations (21% saved)

bsearch5.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	84
1	63	84

end0.0ms (0%)

sample9.1s (50.3%)

Algorithm

1×

intervals

Results

4.9s	4622×	body	1024	valid
1.0s	1459×	body	512	valid
267.0ms	1406×	body	128	valid
206.0ms	498×	body	256	valid
31.0ms	15×	body	2048	valid

Compiler

Compiled 1394 to 1095 computations (21.4% saved)

Details

analyze2.1s (11.6%)

sample218.0ms (1.2%)

simplify315.0ms (1.7%)

prune9.0ms (0%)

localize28.0ms (0.2%)

rewrite98.0ms (0.5%)

series615.0ms (3.4%)

simplify100.0ms (0.6%)

prune331.0ms (1.8%)

localize13.0ms (0.1%)

rewrite96.0ms (0.5%)

series828.0ms (4.6%)

simplify119.0ms (0.7%)

prune299.0ms (1.7%)

localize33.0ms (0.2%)

rewrite211.0ms (1.2%)

series695.0ms (3.8%)

simplify183.0ms (1%)

prune411.0ms (2.3%)

localize37.0ms (0.2%)

rewrite21.0ms (0.1%)

series507.0ms (2.8%)

simplify124.0ms (0.7%)

prune109.0ms (0.6%)

regimes1.5s (8.2%)

bsearch5.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample9.1s (50.3%)

Profiling