Details

analyze349.0ms (13.4%)

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 (1.2%)

Algorithm

1×

intervals

Results

12.0ms	89×	body	1024	valid
4.0ms	47×	body	512	valid
2.0ms	92×	body	128	valid
1.0ms	21×	body	256	valid
1.0ms	7×	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

43.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	43.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.4b	(-.f64 (exp.f64 x) 1)

rewrite99.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

43.5b

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:

7.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 822 to 421 computations (48.8% saved)

series30.0ms (1.1%)

Error

0.2b

Counts

2 → 12

Calls

2 calls:

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

Compiler

Compiled 248 to 175 computations (29.4% saved)

simplify153.0ms (5.9%)

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

prune24.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	3	46

Error

Counts

46 → 3

Alt Table

Status	Error	Program
	43.2b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
▶	19.3b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
	43.5b	(/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)))

Compiler

Compiled 404 to 228 computations (43.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.3b	(*.f64 x 1/12)

rewrite37.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

7×	`add-log-exp_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
3×	`associate-l_binary64` `associate-r_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-+l+_binary64` `+-commutative_binary64`

Counts

2 → 31

Calls

2 calls:

11.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
4.0ms	(*.f64 x 1/12)

Compiler

Compiled 465 to 371 computations (20.2% saved)

series20.0ms (0.8%)

Error

Counts

2 → 12

Calls

2 calls:

11.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
5.0ms	(*.f64 x 1/12)

Compiler

Compiled 185 to 147 computations (20.5% saved)

simplify79.0ms (3%)

Algorithm

1×	egg-herbie

Rules

440×	`associate--r+_binary64`
388×	`cancel-sign-sub-inv_binary64`
330×	`associate--l+_binary64`
309×	`div-sub_binary64`
286×	`sub-neg_binary64`

Counts

43 → 22

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	486
1	154	459
2	478	453
3	1529	453
4	2121	453
5	4510	453
6	4921	453

prune16.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Error

Counts

25 → 3

Alt Table

Status	Error	Program
▶	43.2b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
✓	19.3b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
	43.5b	(/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)))

Compiler

Compiled 336 to 266 computations (20.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
5.4b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite51.0ms (2%)

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)

series23.0ms (0.9%)

Error

Counts

2 → 12

Calls

2 calls:

10.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
7.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 249 to 206 computations (17.3% saved)

simplify137.0ms (5.3%)

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

prune19.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	51	3	54

Error

Counts

54 → 3

Alt Table

Status	Error	Program
✓	43.2b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
✓	19.3b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
▶	43.5b	(/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)))

Compiler

Compiled 380 to 261 computations (31.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (exp.f64 x) 1) 3)
0.1b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
0.3b	(/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)))
5.4b	(-.f64 (exp.f64 x) 1)

rewrite146.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

103×	`add-sqr-sqrt_binary64`
100×	`cbrt-prod_binary64`
90×	`*-un-lft-identity_binary64`
69×	`times-frac_binary64`
51×	`add-cube-cbrt_binary64`

Counts

4 → 191

Calls

4 calls:

13.0ms	(/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)))
6.0ms	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
5.0ms	(pow.f64 (-.f64 (exp.f64 x) 1) 3)
5.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 2696 to 1697 computations (37.1% saved)

series50.0ms (1.9%)

Error

Counts

4 → 24

Calls

4 calls:

11.0ms	(pow.f64 (-.f64 (exp.f64 x) 1) 3)
10.0ms	(/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)))
9.0ms	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
8.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 603 to 441 computations (26.9% saved)

simplify159.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

606×	`associate-l_binary64`
362×	`associate-/l*_binary64`
287×	`associate-/r*_binary64`
281×	`distribute-rgt-in_binary64`
267×	`distribute-lft-in_binary64`

Counts

215 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	3953
1	343	3724
2	1128	3690
3	4208	3690
4	4944	3690

prune49.0ms (1.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	184	3	187

Error

Counts

187 → 3

Alt Table

Status	Error	Program
	43.2b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
	19.3b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
	43.5b	(/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)))

Compiler

Compiled 1205 to 713 computations (40.8% saved)

regimes182.0ms (7%)

Accuracy

Total 0.9b remaining (98.1%)

Threshold costs 0.9b (98.1%)

Compiler

Compiled 2532 to 1654 computations (34.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	16	21
2	16	21

end1.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

sample923.0ms (35.4%)

Algorithm

1×

intervals

Results

384.0ms	2710×	body	1024	valid
106.0ms	1327×	body	512	valid
78.0ms	3086×	body	128	valid
40.0ms	251×	body	2048	valid
31.0ms	626×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 54 to 40 computations (25.9% saved)

Details

analyze349.0ms (13.4%)

sample32.0ms (1.2%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite99.0ms (3.8%)

series30.0ms (1.1%)

simplify153.0ms (5.9%)

prune24.0ms (0.9%)

localize5.0ms (0.2%)

rewrite37.0ms (1.4%)

series20.0ms (0.8%)

simplify79.0ms (3%)

prune16.0ms (0.6%)

localize5.0ms (0.2%)

rewrite51.0ms (2%)

series23.0ms (0.9%)

simplify137.0ms (5.3%)

prune19.0ms (0.7%)

localize8.0ms (0.3%)

rewrite146.0ms (5.6%)

series50.0ms (1.9%)

simplify159.0ms (6.1%)

prune49.0ms (1.9%)

regimes182.0ms (7%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample923.0ms (35.4%)

Profiling