Details

analyze1.5s (12%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5083	96
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
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

Symmetry

(sort c s)

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample62.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	201×	body	128	valid
12.0ms	39×	body	1024	valid
4.0ms	58×	body	128	invalid
3.0ms	14×	body	512	valid
2.0ms	9×	body	512	invalid
2.0ms	6×	body	1024	invalid
1.0ms	5×	body	256	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify174.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (168.0ms)

Iter	Nodes	Cost
0	7278	24

prune8.0ms (0.1%)

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

27.4b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
3.2b	(.f64 (.f64 x (pow.f64 s 2)) x)
8.9b	(*.f64 x (pow.f64 s 2))
19.6b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite218.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

13.6b

Rules

122×	`add-exp-log_binary64_457`
82×	`prod-exp_binary64_468`
34×	`add-cbrt-cube_binary64_455`
18×	`pow-to-exp_binary64_488` `pow-exp_binary64_487` `add-sqr-sqrt_binary64_441`
16×	`cbrt-unprod_binary64_452` `div-exp_binary64_470`
12×	`add-cube-cbrt_binary64_454` `-un-lft-identity_binary64_419` `associate-l_binary64_360` `associate-r*_binary64_359`
7×	`unpow-prod-down_binary64_498`
6×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `cbrt-undiv_binary64_453`
3×	`unpow2_binary64_484` `sqr-pow_binary64_391` `-commutative_binary64_350` `times-frac_binary64_425` `associate-/l_binary64_364`
1×	`pow-prod-down_binary64_490` `frac-2neg_binary64_430` `cos-2_binary64_561` `div-sub_binary64_424` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/r*_binary64_363`

Counts

4 → 119

Calls

4 calls:

11.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
10.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
6.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
6.0ms	(*.f64 x (pow.f64 s 2))

Compiler

Compiled 2836 to 1920 computations (32.3% saved)

series664.0ms (5.5%)

Error

26.0b

Counts

4 → 31

Calls

4 calls:

337.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
168.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
76.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
54.0ms	(*.f64 x (pow.f64 s 2))

Compiler

Compiled 1507 to 1303 computations (13.5% saved)

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4991	2501
1	4991	2501

prune163.0ms (1.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	139	11	150
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	139	12	151

Error

0.8b

Counts

151 → 12

Compiler

Compiled 3013 to 1459 computations (51.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (.f64 x c)))))
0.3b	(.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (*.f64 x c))))
4.7b	(.f64 s (.f64 x c))
4.7b	(.f64 s (.f64 x c))

rewrite129.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

21×	`pow1_binary64_480` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
14×	`add-sqr-sqrt_binary64_441`
12×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
9×	`associate-l_binary64_360`
8×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
7×	`pow-prod-down_binary64_490`
5×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458`
3×	`-commutative_binary64_350` `swap-sqr_binary64_386` `times-frac_binary64_425` `associate-/l_binary64_364`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow2_binary64_500` `pow-prod-up_binary64_489` `pow-plus_binary64_482` `sqr-abs_binary64_434` `pow-sqr_binary64_392` `unswap-sqr_binary64_387` `frac-2neg_binary64_430` `cos-2_binary64_561` `div-sub_binary64_424` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/r*_binary64_363`

Counts

4 → 84

Calls

4 calls:

5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (.f64 x c)))))
5.0ms	(.f64 s (.f64 x c))
5.0ms	(.f64 s (.f64 x c))
4.0ms	(.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (*.f64 x c))))

Compiler

Compiled 2197 to 640 computations (70.9% saved)

series651.0ms (5.4%)

Error

0.8b

Counts

4 → 38

Calls

4 calls:

334.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (.f64 x c)))))
99.0ms	(.f64 s (.f64 x c))
99.0ms	(.f64 s (.f64 x c))
90.0ms	(.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (*.f64 x c))))

Compiler

Compiled 1840 to 1109 computations (39.7% saved)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5017	1675

prune144.0ms (1.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	111	11	122
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	117	17	134

Error

0.6b

Counts

134 → 17

Compiler

Compiled 2645 to 1103 computations (58.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 x c)))) (fabs.f64 (.f64 s (*.f64 x c))))
0.6b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 x c))))
4.7b	(.f64 s (.f64 x c))
4.7b	(.f64 s (.f64 x c))

rewrite203.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

84×	`times-frac_binary64_425`
56×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
21×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
16×	`associate-/l*_binary64_364`
14×	`pow1_binary64_480`
6×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360` `div-inv_binary64_416` `associate-/r*_binary64_363`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`associate-r_binary64_359` `*-commutative_binary64_350` `frac-2neg_binary64_430` `clear-num_binary64_418`
1×	`associate-/l/_binary64_366`

Counts

4 → 133

Calls

4 calls:

7.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 x c)))) (fabs.f64 (.f64 s (*.f64 x c))))
5.0ms	(.f64 s (.f64 x c))
5.0ms	(.f64 s (.f64 x c))
4.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 x c))))

Compiler

Compiled 4262 to 1412 computations (66.9% saved)

series751.0ms (6.2%)

Error

0.6b

Counts

4 → 40

Calls

4 calls:

338.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 x c)))) (fabs.f64 (.f64 s (*.f64 x c))))
200.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 x c))))
93.0ms	(.f64 s (.f64 x c))
92.0ms	(.f64 s (.f64 x c))

Compiler

Compiled 2143 to 1171 computations (45.4% saved)

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5046	4502

prune210.0ms (1.7%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	165	8	173
Fresh	5	10	15
Picked	1	0	1
Done	0	1	1
Total	171	19	190

Error

0.5b

Counts

190 → 19

Compiler

Compiled 4759 to 1867 computations (60.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 x c))) 3/2))
4.7b	(.f64 s (.f64 x c))
4.7b	(.f64 s (.f64 x c))
13.5b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 x c))))

rewrite145.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

24×	`add-sqr-sqrt_binary64_441`
23×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
21×	`times-frac_binary64_425`
19×	`add-exp-log_binary64_457`
16×	`add-cbrt-cube_binary64_455`
15×	`pow1_binary64_480`
12×	`unpow-prod-down_binary64_498`
7×	`associate-/r*_binary64_363`
6×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sqr-pow_binary64_391`
3×	`sqrt-prod_binary64_435` `div-exp_binary64_470` `associate-/l*_binary64_364`
2×	`associate-r_binary64_359` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `pow-to-exp_binary64_488` `pow-exp_binary64_487` `cbrt-undiv_binary64_453` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416`

Counts

4 → 94

Calls

4 calls:

5.0ms	(.f64 s (.f64 x c))
5.0ms	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 x c))) 3/2))
5.0ms	(.f64 s (.f64 x c))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 x c))))

Compiler

Compiled 2880 to 1163 computations (59.6% saved)

series858.0ms (7.1%)

Error

0.5b

Counts

4 → 38

Calls

4 calls:

535.0ms	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 x c))) 3/2))
106.0ms	(.f64 s (.f64 x c))
104.0ms	(.f64 s (.f64 x c))
78.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 x c))))

Compiler

Compiled 2572 to 1473 computations (42.7% saved)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4966	2513
1	4966	2513

prune153.0ms (1.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	3	14	17
Picked	1	0	1
Done	0	1	1
Total	135	16	151

Error

0.5b

Counts

151 → 16

Compiler

Compiled 3534 to 1391 computations (60.6% saved)

regimes1.5s (12.6%)

Accuracy

Total 1.5b remaining (60.4%)

Threshold costs 0b (0%)

Compiler

Compiled 20883 to 14445 computations (30.8% saved)

bsearch0.0ms (0%)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	31
1	20	31

Remove

(sort c s)

Compiler

Compiled 40 to 26 computations (35% saved)

end0.0ms (0%)

sample4.3s (35.3%)

Algorithm

1×

intervals

Results

474.0ms	6111×	body	128	valid
328.0ms	984×	body	1024	valid
161.0ms	1906×	body	128	invalid
147.0ms	603×	body	512	valid
61.0ms	195×	body	1024	invalid
54.0ms	238×	body	512	invalid
52.0ms	298×	body	256	valid
24.0ms	158×	body	256	invalid
2.0ms	4×	body	2048	valid

Compiler

Compiled 3242 to 2205 computations (32% saved)

Details

analyze1.5s (12%)

sample62.0ms (0.5%)

simplify174.0ms (1.4%)

prune8.0ms (0.1%)

localize12.0ms (0.1%)

rewrite218.0ms (1.8%)

series664.0ms (5.5%)

simplify79.0ms (0.6%)

prune163.0ms (1.3%)

localize10.0ms (0.1%)

rewrite129.0ms (1.1%)

series651.0ms (5.4%)

simplify54.0ms (0.4%)

prune144.0ms (1.2%)

localize10.0ms (0.1%)

rewrite203.0ms (1.7%)

series751.0ms (6.2%)

simplify81.0ms (0.7%)

prune210.0ms (1.7%)

localize15.0ms (0.1%)

rewrite145.0ms (1.2%)

series858.0ms (7.1%)

simplify75.0ms (0.6%)

prune153.0ms (1.3%)

regimes1.5s (12.6%)

bsearch0.0ms (0%)

simplify12.0ms (0.1%)

end0.0ms (0%)

sample4.3s (35.3%)

Profiling