Details

analyze407.0ms (11.6%)

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)

sample30.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms	83×	body	1024	valid
4.0ms	49×	body	512	valid
3.0ms	97×	body	128	valid
1.0ms	20×	body	256	valid
1.0ms	7×	body	2048	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

prune1.0ms (0%)

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

42.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	42.3b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.3b	(-.f64 (exp.f64 x) 1)

rewrite66.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

42.3b

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:

5.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 822 to 421 computations (48.8% saved)

series22.0ms (0.6%)

Error

0.4b

Counts

2 → 12

Calls

2 calls:

7.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 248 to 175 computations (29.4% saved)

simplify154.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

75 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	1272
1	205	1207
2	542	1199
3	1375	1198
4	3524	1198
5	4891	1198
6	4994	1198
7	4987	1198
8	4887	1198

prune29.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	3	45

Error

0.0b

Counts

45 → 3

Alt Table

Status	Error	Program
	41.8b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
	42.3b	(/.f64 (exp.f64 x) (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
▶	21.1b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))

Compiler

Compiled 431 to 247 computations (42.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite78.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 78

Calls

4 calls:

10.0ms	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
6.0ms	(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
4.0ms	(*.f64 (pow.f64 x 3) 1/720)
3.0ms	(*.f64 x 1/12)

Compiler

Compiled 1587 to 1282 computations (19.2% saved)

series38.0ms (1.1%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

11.0ms	(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
9.0ms	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
6.0ms	(*.f64 (pow.f64 x 3) 1/720)
5.0ms	(*.f64 x 1/12)

Compiler

Compiled 606 to 491 computations (19% saved)

simplify126.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

384×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
356×	`distribute-lft-in_binary64`
294×	`exp-prod_binary64`
293×	`times-frac_binary64`

Counts

105 → 78

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	143	1452
1	310	1395
2	1222	1380
3	3766	1356
4	4807	1347
5	4977	1347
6	4835	1347

prune36.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	78	3	81

Error

0.0b

Counts

81 → 3

Alt Table

Status	Error	Program
▶	41.8b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
	42.3b	(/.f64 (exp.f64 x) (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
✓	21.1b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))

Compiler

Compiled 1111 to 888 computations (20.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
4.0b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite63.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

2 → 62

Calls

2 calls:

5.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
3.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 872 to 542 computations (37.8% saved)

series18.0ms (0.5%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

7.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
5.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 249 to 206 computations (17.3% saved)

simplify115.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

74 → 50

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	94	1151
1	199	1072
2	433	1062
3	1291	1059
4	3574	1041
5	4953	1041
6	4877	1041

prune20.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	50	3	53

Error

0.0b

Counts

53 → 3

Alt Table

Status	Error	Program
	41.8b	(cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 (exp.f64 (neg.f64 x))) 3)))
▶	41.8b	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -1/2))) (-.f64 1 (sqrt.f64 (exp.f64 (neg.f64 x)))))
✓	21.1b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))

Compiler

Compiled 405 to 287 computations (29.1% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -1/2)))
0.0b	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -1/2))) (-.f64 1 (sqrt.f64 (exp.f64 (neg.f64 x)))))
4.0b	(-.f64 1 (sqrt.f64 (exp.f64 (neg.f64 x))))

rewrite277.0ms (7.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

294×	`times-frac_binary64`
281×	`*-un-lft-identity_binary64`
253×	`add-sqr-sqrt_binary64`
113×	`add-cube-cbrt_binary64`
80×	`difference-of-squares_binary64`

Counts

3 → 268

Calls

3 calls:

15.0ms	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -1/2))) (-.f64 1 (sqrt.f64 (exp.f64 (neg.f64 x)))))
5.0ms	(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -1/2)))
4.0ms	(-.f64 1 (sqrt.f64 (exp.f64 (neg.f64 x))))

Compiler

Compiled 5396 to 3571 computations (33.8% saved)

series110.0ms (3.1%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

24.0ms	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -1/2))) (-.f64 1 (sqrt.f64 (exp.f64 (neg.f64 x)))))
14.0ms	(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -1/2)))
8.0ms	(-.f64 1 (sqrt.f64 (exp.f64 (neg.f64 x))))

Compiler

Compiled 627 to 511 computations (18.5% saved)

simplify512.0ms (14.5%)

Algorithm

1×	egg-herbie

Rules

678×	`div-sub_binary64`
368×	`associate-r_binary64`
363×	`associate-l_binary64`
210×	`associate-/r*_binary64`
209×	`unswap-sqr_binary64`

Counts

286 → 264

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	213	10421
1	529	10126
2	1285	10117
3	3713	9749
4	4246	9435
5	4970	9435
6	4999	9435
7	4894	9435

prune73.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	263	4	267

Error

0.0b

Counts

267 → 4

Alt Table

Status	Error	Program
	41.8b	(cbrt.f64 (/.f64 1 (pow.f64 (-.f64 1 (exp.f64 (neg.f64 x))) 3)))
	62.5b	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -1/2))) (exp.f64 (log.f64 (-.f64 1 (pow.f64 (exp.f64 x) -1/2)))))
	41.8b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -1/2)))) (*.f64 (-.f64 1 (pow.f64 (exp.f64 x) -1/2)) (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -1/2)))))
	21.1b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))

Compiler

Compiled 2429 to 1780 computations (26.7% saved)

regimes327.0ms (9.3%)

Accuracy

Total 0.8b remaining (98.9%)

Threshold costs 0.8b (98.9%)

Compiler

Compiled 5901 to 4399 computations (25.5% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	50
1	27	50
2	31	50
3	33	50
4	34	50
5	33	50

end1.0ms (0%)

Compiler: Compiled 33 to 23 computations (30.3% saved)

sample971.0ms (27.6%)

Algorithm

1×

intervals

Results

404.0ms	2568×	body	1024	valid
107.0ms	1262×	body	512	valid
91.0ms	3213×	body	128	valid
46.0ms	272×	body	2048	valid
39.0ms	685×	body	256	valid
0.0ms	2×	body	2048	invalid

Compiler

Compiled 113 to 88 computations (22.1% saved)

Details

analyze407.0ms (11.6%)

sample30.0ms (0.9%)

simplify9.0ms (0.2%)

prune1.0ms (0%)

localize4.0ms (0.1%)

rewrite66.0ms (1.9%)

series22.0ms (0.6%)

simplify154.0ms (4.4%)

prune29.0ms (0.8%)

localize10.0ms (0.3%)

rewrite78.0ms (2.2%)

series38.0ms (1.1%)

simplify126.0ms (3.6%)

prune36.0ms (1%)

localize5.0ms (0.1%)

rewrite63.0ms (1.8%)

series18.0ms (0.5%)

simplify115.0ms (3.3%)

prune20.0ms (0.6%)

localize10.0ms (0.3%)

rewrite277.0ms (7.9%)

series110.0ms (3.1%)

simplify512.0ms (14.5%)

prune73.0ms (2.1%)

regimes327.0ms (9.3%)

bsearch3.0ms (0.1%)

simplify7.0ms (0.2%)

end1.0ms (0%)

sample971.0ms (27.6%)

Profiling