Details

analyze1.4s (12.1%)

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)

sample60.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	202×	body	128	valid
7.0ms	22×	body	1024	valid
5.0ms	23×	body	512	valid
5.0ms	64×	body	128	invalid
2.0ms	7×	body	1024	invalid
2.0ms	7×	body	512	invalid
1.0ms	9×	body	256	valid
1.0ms	4×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify177.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (171.0ms)

Iter	Nodes	Cost
0	7278	24

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

30.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
3.5b	(.f64 (.f64 x (pow.f64 s 2)) x)
8.8b	(*.f64 x (pow.f64 s 2))
20.6b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite217.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

16.3b

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)

series663.0ms (5.6%)

Error

29.8b

Counts

4 → 31

Calls

4 calls:

329.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
182.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
72.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
51.0ms	(*.f64 x (pow.f64 s 2))

Compiler

Compiled 1507 to 1303 computations (13.5% saved)

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4991	2501
1	4991	2501

prune154.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	141	9	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	9	151

Error

1.7b

Counts

151 → 9

Compiler

Compiled 2992 to 1428 computations (52.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (*.f64 x c))))
0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (.f64 x c)))))
5.1b	(.f64 s (.f64 x c))
5.1b	(.f64 s (.f64 x c))

rewrite122.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

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` `times-frac_binary64_425` `associate-/l_binary64_364` `swap-sqr_binary64_386`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`frac-2neg_binary64_430` `cos-2_binary64_561` `div-sub_binary64_424` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/r*_binary64_363` `pow2_binary64_500` `pow-prod-up_binary64_489` `pow-plus_binary64_482` `sqr-abs_binary64_434` `pow-sqr_binary64_392` `unswap-sqr_binary64_387`

Counts

4 → 84

Calls

4 calls:

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

series637.0ms (5.4%)

Error

1.7b

Counts

4 → 38

Calls

4 calls:

337.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (.f64 x c)))))
93.0ms	(.f64 s (.f64 x c))
92.0ms	(.f64 s (.f64 x c))
85.0ms	(.f64 (fabs.f64 (.f64 s (.f64 x c))) (fabs.f64 (.f64 s (*.f64 x c))))

Compiler

Compiled 1840 to 1109 computations (39.7% saved)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5017	1675

prune137.0ms (1.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	112	10	122
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	116	15	131

Error

1.5b

Counts

131 → 15

Compiler

Compiled 2639 to 1098 computations (58.4% saved)

localize12.0ms (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))))
0.5b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 x c))))
5.1b	(.f64 s (.f64 x c))
5.1b	(.f64 s (.f64 x c))

rewrite199.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

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:

6.0ms	(/.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)

series777.0ms (6.6%)

Error

1.5b

Counts

4 → 40

Calls

4 calls:

339.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 x c)))) (fabs.f64 (.f64 s (*.f64 x c))))
210.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 x c))))
101.0ms	(.f64 s (.f64 x c))
99.0ms	(.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

prune206.0ms (1.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	166	7	173
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	172	16	188

Error

1.5b

Counts

188 → 16

Compiler

Compiled 4692 to 1832 computations (61% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.f64 s (.f64 x c))
5.1b	(.f64 s (.f64 x c))
10.4b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 x c))))
10.4b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 x c))))

rewrite91.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

16×	`pow1_binary64_480`
14×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
10×	`add-sqr-sqrt_binary64_441`
8×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
6×	`sqrt-prod_binary64_435` `pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-r_binary64_359` `*-commutative_binary64_350`

Counts

4 → 62

Calls

4 calls:

5.0ms	(.f64 s (.f64 x c))
5.0ms	(.f64 s (.f64 x c))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 x c))))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 x c))))

Compiler

Compiled 2166 to 652 computations (69.9% saved)

series350.0ms (3%)

Error

1.5b

Counts

4 → 36

Calls

4 calls:

89.0ms	(.f64 s (.f64 x c))
88.0ms	(.f64 s (.f64 x c))
74.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 x c))))
68.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 x c))))

Compiler

Compiled 3132 to 1375 computations (56.1% saved)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4985	980
1	4985	980

prune103.0ms (0.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	99	15	114

Error

1.5b

Counts

114 → 15

Compiler

Compiled 3094 to 928 computations (70% saved)

regimes1.7s (14%)

Accuracy

Total 1.6b remaining (60.1%)

Threshold costs 0b (0%)

Compiler

Compiled 23234 to 15909 computations (31.5% saved)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	28
1	15	28

Remove

(sort c s)

Compiler

Compiled 36 to 22 computations (38.9% saved)

end0.0ms (0%)

sample4.4s (37.7%)

Algorithm

1×

intervals

Results

479.0ms	6148×	body	128	valid
303.0ms	912×	body	1024	valid
159.0ms	1968×	body	128	invalid
151.0ms	626×	body	512	valid
76.0ms	226×	body	1024	invalid
56.0ms	236×	body	512	invalid
53.0ms	310×	body	256	valid
25.0ms	164×	body	256	invalid
2.0ms	4×	body	2048	valid

Compiler

Compiled 3573 to 2402 computations (32.8% saved)

Details

analyze1.4s (12.1%)

sample60.0ms (0.5%)

simplify177.0ms (1.5%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite217.0ms (1.8%)

series663.0ms (5.6%)

simplify78.0ms (0.7%)

prune154.0ms (1.3%)

localize10.0ms (0.1%)

rewrite122.0ms (1%)

series637.0ms (5.4%)

simplify53.0ms (0.5%)

prune137.0ms (1.2%)

localize12.0ms (0.1%)

rewrite199.0ms (1.7%)

series777.0ms (6.6%)

simplify81.0ms (0.7%)

prune206.0ms (1.8%)

localize14.0ms (0.1%)

rewrite91.0ms (0.8%)

series350.0ms (3%)

simplify79.0ms (0.7%)

prune103.0ms (0.9%)

regimes1.7s (14%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample4.4s (37.7%)

Profiling