Details

analyze371.0ms (15%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample32.0ms (1.3%)

Algorithm

1×

intervals

Results

13.0ms	87×	body	1024	valid
3.0ms	36×	body	512	valid
3.0ms	105×	body	128	valid
1.0ms	23×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64` `sub-neg_binary64` `+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	11	11
2	12	11
3	10	11

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

40.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	40.6b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.3b	(-.f64 (exp.f64 x) 1)

rewrite108.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

40.5b

Rules

35×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 822 to 421 computations (48.8% saved)

series32.0ms (1.3%)

Error

0.4b

Counts

2 → 12

Calls

2 calls:

10.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
8.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 248 to 175 computations (29.4% saved)

simplify157.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

459×	`div-sub_binary64`
349×	`associate-/l*_binary64`
317×	`associate-r_binary64`
262×	`unsub-neg_binary64` `associate-/l/_binary64`
195×	`*-commutative_binary64`

Counts

75 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1272
1	207	1207
2	549	1199
3	1388	1195
4	3540	1195
5	4897	1195
6	4997	1195
7	4991	1195
8	4892	1195

prune26.0ms (1.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	2	46

Error

Counts

46 → 2

Alt Table

Status	Error	Program
▶	22.4b	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
	40.1b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))

Compiler

Compiled 394 to 222 computations (43.7% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.1b	(*.f64 (pow.f64 x 3) 1/720)
0.3b	(*.f64 x 1/12)

rewrite106.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-sqr-sqrt_binary64`
18×	`add-log-exp_binary64`
15×	`associate-l_binary64`
11×	`add-exp-log_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 77

Calls

4 calls:

12.0ms	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
9.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
6.0ms	(*.f64 (pow.f64 x 3) 1/720)
4.0ms	(*.f64 x 1/12)

Compiler

Compiled 1587 to 1282 computations (19.2% saved)

series56.0ms (2.3%)

Error

Counts

4 → 27

Calls

4 calls:

17.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
13.0ms	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
10.0ms	(*.f64 (pow.f64 x 3) 1/720)
7.0ms	(*.f64 x 1/12)

Compiler

Compiled 621 to 503 computations (19% saved)

simplify89.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

569×	`distribute-rgt-in_binary64`
557×	`distribute-lft-in_binary64`
262×	`times-frac_binary64`
248×	`associate-+l+_binary64`
221×	`cancel-sign-sub-inv_binary64`

Counts

104 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1436
1	310	1391
2	1306	1370
3	4576	1346
4	5126	1346

prune45.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	2	68

Error

Counts

68 → 2

Alt Table

Status	Error	Program
✓	22.4b	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
▶	40.1b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))

Compiler

Compiled 996 to 802 computations (19.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
5.3b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite48.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

29×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
18×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
6×	`add-exp-log_binary64` `associate-/r*_binary64`

Counts

2 → 62

Calls

2 calls:

6.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
4.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 872 to 542 computations (37.8% saved)

series26.0ms (1.1%)

Error

Counts

2 → 12

Calls

2 calls:

10.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))
9.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))

Compiler

Compiled 249 to 206 computations (17.3% saved)

simplify143.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

515×	`unsub-neg_binary64`
441×	`times-frac_binary64`
360×	`div-sub_binary64`
314×	`cancel-sign-sub-inv_binary64`
251×	`associate-/l*_binary64`

Counts

74 → 51

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	93	1151
1	198	1072
2	429	1062
3	1288	1059
4	3400	1041
5	4904	1041
6	4996	1041
7	4866	1041

prune20.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	51	2	53

Error

Counts

53 → 2

Alt Table

Status	Error	Program
	22.4b	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
	40.1b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))

Compiler

Compiled 364 to 250 computations (31.3% saved)

regimes188.0ms (7.6%)

Accuracy

Total 1.0b remaining (98.8%)

Threshold costs 1.0b (98.8%)

Compiler

Compiled 2586 to 1708 computations (34% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64` `+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	20	27
2	20	27

end1.0ms (0%)

Compiler: Compiled 19 to 13 computations (31.6% saved)

sample977.0ms (39.7%)

Algorithm

1×

intervals

Results

391.0ms	2624×	body	1024	valid
116.0ms	1337×	body	512	valid
80.0ms	3085×	body	128	valid
44.0ms	266×	body	2048	valid
41.0ms	688×	body	256	valid
0.0ms	3×	body	2048	invalid

Compiler

Compiled 53 to 40 computations (24.5% saved)

Details

analyze371.0ms (15%)

sample32.0ms (1.3%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

rewrite108.0ms (4.4%)

series32.0ms (1.3%)

simplify157.0ms (6.4%)

prune26.0ms (1.1%)

localize11.0ms (0.4%)

rewrite106.0ms (4.3%)

series56.0ms (2.3%)

simplify89.0ms (3.6%)

prune45.0ms (1.8%)

localize5.0ms (0.2%)

rewrite48.0ms (1.9%)

series26.0ms (1.1%)

simplify143.0ms (5.8%)

prune20.0ms (0.8%)

regimes188.0ms (7.6%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample977.0ms (39.7%)

Profiling