Details

analyze1.5s (9.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4881	464
1	4881	464
0	6	6
1	6	6

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	74.8%	25.2%	10
0%	74.8%	25.2%	11
0%	74.8%	25.2%	12
24.9%	49.9%	25.2%	13
24.9%	37.4%	37.7%	14

Symmetry

(sort z t)

Compiler

Compiled 20 to 20 computations (0% saved)

sample93.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	60×	body	1024	valid
11.0ms	140×	body	128	valid
10.0ms	22×	body	2048	valid
6.0ms	79×	body	128	nan
5.0ms	23×	body	512	valid
4.0ms	51×	body	128	invalid
2.0ms	11×	body	256	valid

Compiler

Compiled 39 to 45 computations (-15.4% saved)

simplify49.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	757	29
1	757	29

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

22.0b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 z t) 3)
0.2b	(/.f64 a (*.f64 b 3))
0.3b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
26.2b	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

rewrite174.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

20.2b

Rules

19×	`add-exp-log_binary64_16143` `add-cbrt-cube_binary64_16141`
11×	`add-cube-cbrt_binary64_16140` `add-sqr-sqrt_binary64_16127` `*-un-lft-identity_binary64_16105`
9×	`times-frac_binary64_16111` `pow1_binary64_16166`
8×	`cos-sum_binary64_16239`
7×	`cancel-sign-sub-inv_binary64_16071`
5×	`prod-exp_binary64_16154` `cbrt-unprod_binary64_16138`
4×	`add-log-exp_binary64_16144` `div-exp_binary64_16156` `cbrt-undiv_binary64_16139` `associate-/l_binary64_16050` `associate-/r_binary64_16049`
3×	`cos-diff_binary64_16242` `div-inv_binary64_16102` `pow-prod-down_binary64_16176` `associate-r_binary64_16045`
2×	`frac-2neg_binary64_16116` `clear-num_binary64_16104`
1×	`sub-neg_binary64_16098` `distribute-rgt-in_binary64_16055` `distribute-lft-in_binary64_16054` `associate-l_binary64_16046` `*-commutative_binary64_16036`

Counts

4 → 78

Calls

4 calls:

8.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
7.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
4.0ms	(/.f64 (*.f64 z t) 3)
4.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 2173 to 1334 computations (38.6% saved)

series558.0ms (3.4%)

Error

16.9b

Counts

4 → 45

Calls

4 calls:

278.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
108.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
63.0ms	(/.f64 a (*.f64 b 3))
57.0ms	(/.f64 (*.f64 z t) 3)

Compiler

Compiled 2890 to 2315 computations (19.9% saved)

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4932	1991
1	4932	1991

prune208.0ms (1.3%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	96	27	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	27	124

Error

16.2b

Counts

124 → 27

Compiler

Compiled 3548 to 2321 computations (34.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(/.f64 a (*.f64 b 3))

rewrite97.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

16.1b

Rules

13×	`add-exp-log_binary64_16143` `add-cbrt-cube_binary64_16141`
8×	`pow1_binary64_16166` `add-cube-cbrt_binary64_16140` `add-sqr-sqrt_binary64_16127` `*-un-lft-identity_binary64_16105`
7×	`cancel-sign-sub-inv_binary64_16071`
6×	`times-frac_binary64_16111`
5×	`add-log-exp_binary64_16144`
4×	`prod-exp_binary64_16154` `cbrt-unprod_binary64_16138`
3×	`associate-/l_binary64_16050` `pow-prod-down_binary64_16176` `associate-r*_binary64_16045`
2×	`div-exp_binary64_16156` `cbrt-undiv_binary64_16139` `div-inv_binary64_16102`
1×	`frac-2neg_binary64_16116` `clear-num_binary64_16104` `associate-/r_binary64_16049` `associate-l_binary64_16046` `-commutative_binary64_16036` `diff-log_binary64_16197` `flip3--_binary64_16109` `sub-neg_binary64_16098` `flip--_binary64_16080`

Counts

3 → 57

Calls

3 calls:

8.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
6.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
4.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 1174 to 678 computations (42.2% saved)

series453.0ms (2.8%)

Error

15.8b

Counts

3 → 32

Calls

3 calls:

293.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
76.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
61.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 1123 to 1034 computations (7.9% saved)

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4915	1209
1	4915	1209

prune136.0ms (0.8%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	6	20	26
Picked	1	0	1
Done	0	0	0
Total	85	31	116

Error

15.8b

Counts

116 → 31

Compiler

Compiled 2100 to 1372 computations (34.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 1 (/.f64 b (/.f64 a 3))))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(/.f64 b (/.f64 a 3))
0.6b	(/.f64 1 (/.f64 b (/.f64 a 3)))

rewrite1.0s (6.3%)

Algorithm

1×	rewrite-expression-head

Error

15.8b

Rules

801×	`times-frac_binary64_16111`
382×	`add-cube-cbrt_binary64_16140` `add-sqr-sqrt_binary64_16127` `*-un-lft-identity_binary64_16105`
137×	`cancel-sign-sub-inv_binary64_16071`
57×	`associate-/r*_binary64_16049`
35×	`add-exp-log_binary64_16143` `div-inv_binary64_16102`
23×	`add-cbrt-cube_binary64_16141`
18×	`div-exp_binary64_16156`
10×	`pow1_binary64_16166` `associate-/r/_binary64_16051`
9×	`cbrt-undiv_binary64_16139`
6×	`add-log-exp_binary64_16144` `associate-/l*_binary64_16050`
3×	`1-exp_binary64_16149` `rec-exp_binary64_16155` `pow-prod-down_binary64_16176` `prod-exp_binary64_16154` `cbrt-unprod_binary64_16138` `associate-r_binary64_16045`
2×	`frac-2neg_binary64_16116` `clear-num_binary64_16104`
1×	`inv-pow_binary64_16190` `pow-flip_binary64_16179` `associate-l_binary64_16046` `*-commutative_binary64_16036` `diff-log_binary64_16197` `flip3--_binary64_16109` `sub-neg_binary64_16098` `flip--_binary64_16080`

Counts

4 → 440

Calls

4 calls:

43.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 1 (/.f64 b (/.f64 a 3))))
13.0ms	(/.f64 1 (/.f64 b (/.f64 a 3)))
6.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
6.0ms	(/.f64 b (/.f64 a 3))

Compiler

Compiled 12475 to 7918 computations (36.5% saved)

series533.0ms (3.3%)

Error

15.8b

Counts

4 → 38

Calls

4 calls:

313.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 1 (/.f64 b (/.f64 a 3))))
71.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
62.0ms	(/.f64 b (/.f64 a 3))
62.0ms	(/.f64 1 (/.f64 b (/.f64 a 3)))

Compiler

Compiled 1433 to 1327 computations (7.4% saved)

simplify128.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

478 → 478

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5509	10650

prune746.0ms (4.6%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	477	1	478
Fresh	1	29	30
Picked	0	1	1
Done	0	0	0
Total	478	31	509

Error

15.8b

Counts

509 → 31

Compiler

Compiled 11944 to 6991 computations (41.5% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (*.f64 (/.f64 1 b) (/.f64 a 3)))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.3b	(*.f64 (/.f64 1 b) (/.f64 a 3))

rewrite133.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

15.8b

Rules

35×	`add-sqr-sqrt_binary64_16127`
30×	`add-exp-log_binary64_16143`
25×	`times-frac_binary64_16111`
20×	`add-cbrt-cube_binary64_16141` `*-un-lft-identity_binary64_16105`
18×	`add-cube-cbrt_binary64_16140`
16×	`associate-r_binary64_16045`
14×	`associate-l_binary64_16046`
11×	`prod-exp_binary64_16154`
10×	`pow1_binary64_16166`
8×	`div-exp_binary64_16156`
7×	`cbrt-unprod_binary64_16138`
6×	`unswap-sqr_binary64_16073`
5×	`add-log-exp_binary64_16144`
4×	`pow-prod-down_binary64_16176` `cbrt-undiv_binary64_16139`
2×	`1-exp_binary64_16149` `rec-exp_binary64_16155` `div-inv_binary64_16102` `*-commutative_binary64_16036`
1×	`frac-times_binary64_16115` `associate-l/_binary64_16048` `associate-r/_binary64_16047` `diff-log_binary64_16197` `flip3--_binary64_16109` `sub-neg_binary64_16098` `flip--_binary64_16080` `cancel-sign-sub-inv_binary64_16071`

Counts

3 → 86

Calls

3 calls:

11.0ms	(*.f64 (/.f64 1 b) (/.f64 a 3))
10.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (*.f64 (/.f64 1 b) (/.f64 a 3)))
6.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

Compiler

Compiled 2020 to 1285 computations (36.4% saved)

series463.0ms (2.8%)

Error

15.8b

Counts

3 → 32

Calls

3 calls:

301.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (*.f64 (/.f64 1 b) (/.f64 a 3)))
74.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
65.0ms	(*.f64 (/.f64 1 b) (/.f64 a 3))

Compiler

Compiled 1163 to 1074 computations (7.7% saved)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4966	1607
1	4966	1607

prune108.0ms (0.7%)

Pruning

31 alts after pruning (29 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	29	29
Picked	0	1	1
Done	0	1	1
Total	118	31	149

Error

15.8b

Counts

149 → 31

Compiler

Compiled 2055 to 1130 computations (45% saved)

regimes4.4s (27.2%)

Accuracy

Total 2.3b remaining (13.8%)

Threshold costs 0b (0%)

Compiler

Compiled 51767 to 47765 computations (7.7% saved)

bsearch2.0ms (0%)

Steps

Iters	Range		Point
0	0.9999999999973972	0.9999999999999699	0.9999999999986835

Compiler

Compiled 8 to 11 computations (-37.5% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	61
1	105	61

Remove

(sort z t)

Compiler

Compiled 80 to 64 computations (20% saved)

end0.0ms (0%)

sample5.2s (31.8%)

Algorithm

1×

intervals

Results

518.0ms	1591×	body	1024	valid
363.0ms	4582×	body	128	valid
343.0ms	744×	body	2048	valid
187.0ms	750×	body	512	valid
175.0ms	2252×	body	128	nan
94.0ms	1197×	body	128	invalid
61.0ms	332×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 3218 to 2952 computations (8.3% saved)

Details

analyze1.5s (9.1%)

sample93.0ms (0.6%)

simplify49.0ms (0.3%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite174.0ms (1.1%)

series558.0ms (3.4%)

simplify79.0ms (0.5%)

prune208.0ms (1.3%)

localize11.0ms (0.1%)

rewrite97.0ms (0.6%)

series453.0ms (2.8%)

simplify89.0ms (0.5%)

prune136.0ms (0.8%)

localize12.0ms (0.1%)

rewrite1.0s (6.3%)

series533.0ms (3.3%)

simplify128.0ms (0.8%)

prune746.0ms (4.6%)

localize12.0ms (0.1%)

rewrite133.0ms (0.8%)

series463.0ms (2.8%)

simplify76.0ms (0.5%)

prune108.0ms (0.7%)

regimes4.4s (27.2%)

bsearch2.0ms (0%)

simplify13.0ms (0.1%)

end0.0ms (0%)

sample5.2s (31.8%)

Profiling