Details

analyze426.0ms (13.9%)

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 (1%)

Algorithm

1×

intervals

Results

13.0ms	84×	body	1024	valid
3.0ms	35×	body	512	valid
3.0ms	100×	body	128	valid
2.0ms	28×	body	256	valid
2.0ms	9×	body	2048	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify10.0ms (0.3%)

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

41.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	41.6b	(/.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))
4.4b	(-.f64 (exp.f64 x) 1)

rewrite78.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

41.6b

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)

series21.0ms (0.7%)

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)

simplify88.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

547×	`div-sub_binary64`
382×	`associate-/l*_binary64`
309×	`unsub-neg_binary64`
279×	`associate-/l/_binary64`
224×	`*-commutative_binary64`

Counts

75 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1302
1	209	1237
2	570	1229
3	1440	1228
4	3587	1228
5	5006	1228

prune18.0ms (0.6%)

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
	41.1b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
	41.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1)) 3))
▶	20.7b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))

Compiler

Compiled 413 to 239 computations (42.1% saved)

localize9.0ms (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)

rewrite75.0ms (2.4%)

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)

series37.0ms (1.2%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

12.0ms	(+.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)

simplify129.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

105 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	149	1632
1	314	1575
2	1233	1560
3	3767	1536
4	4816	1527
5	4986	1527
6	4840	1527

prune22.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	63	3	66

Error

0.0b

Counts

66 → 3

Alt Table

Status	Error	Program
▶	41.1b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
	41.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1)) 3))
✓	20.7b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))

Compiler

Compiled 638 to 505 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))))
4.2b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite42.0ms (1.4%)

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:

11.0ms	(/.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 (0.6%)

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)

simplify110.0ms (3.6%)

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 → 51

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	1169
1	202	1090
2	436	1080
3	1294	1077
4	3579	1059
5	4958	1059
6	4882	1059

prune16.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	51	3	54

Error

0.0b

Counts

54 → 3

Alt Table

Status	Error	Program
✓	41.1b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
✓	20.7b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
▶	61.2b	(/.f64 1 (/.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2)) (+.f64 1 (exp.f64 (neg.f64 x)))))

Compiler

Compiled 394 to 276 computations (29.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2)) (+.f64 1 (exp.f64 (neg.f64 x))))
0.0b	(/.f64 1 (/.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2)) (+.f64 1 (exp.f64 (neg.f64 x)))))
0.0b	(pow.f64 (exp.f64 x) -2)
4.3b	(-.f64 1 (pow.f64 (exp.f64 x) -2))

rewrite237.0ms (7.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

344×	`*-un-lft-identity_binary64`
338×	`times-frac_binary64`
286×	`add-sqr-sqrt_binary64`
132×	`difference-of-squares_binary64`
132×	`add-cube-cbrt_binary64`

Counts

4 → 324

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2)) (+.f64 1 (exp.f64 (neg.f64 x)))))
9.0ms	(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2)) (+.f64 1 (exp.f64 (neg.f64 x))))
4.0ms	(-.f64 1 (pow.f64 (exp.f64 x) -2))
2.0ms	(pow.f64 (exp.f64 x) -2)

Compiler

Compiled 7612 to 5268 computations (30.8% saved)

series61.0ms (2%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2)) (+.f64 1 (exp.f64 (neg.f64 x)))))
13.0ms	(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2)) (+.f64 1 (exp.f64 (neg.f64 x))))
11.0ms	(pow.f64 (exp.f64 x) -2)
10.0ms	(-.f64 1 (pow.f64 (exp.f64 x) -2))

Compiler

Compiled 812 to 670 computations (17.5% saved)

simplify363.0ms (11.9%)

Algorithm

1×	egg-herbie

Rules

588×	`times-frac_binary64`
321×	`distribute-rgt-in_binary64`
294×	`cancel-sign-sub-inv_binary64`
279×	`distribute-lft-in_binary64`
236×	`div-sub_binary64`

Counts

348 → 298

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	11334
1	653	10244
2	1937	9794
3	4095	9794
4	4910	9794
5	4971	9794

prune65.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	298	3	301

Error

0.0b

Counts

301 → 3

Alt Table

Status	Error	Program
✓	41.1b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
	61.2b	(.f64 (.f64 (cbrt.f64 (+.f64 1 (exp.f64 (neg.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 (neg.f64 x))))) (/.f64 (cbrt.f64 (+.f64 1 (exp.f64 (neg.f64 x)))) (-.f64 1 (pow.f64 (exp.f64 x) -2))))
✓	20.7b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))

Compiler

Compiled 2614 to 1662 computations (36.4% saved)

regimes149.0ms (4.9%)

Accuracy

Total 0.9b remaining (99.1%)

Threshold costs 0.9b (99.1%)

Compiler

Compiled 3047 to 2170 computations (28.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	19	21
2	18	21

end1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample1.0s (33.7%)

Algorithm

1×

intervals

Results

426.0ms	2657×	body	1024	valid
150.0ms	1345×	body	512	valid
95.0ms	3089×	body	128	valid
51.0ms	286×	body	2048	valid
38.0ms	623×	body	256	valid

Compiler

Compiled 77 to 58 computations (24.7% saved)

Details

analyze426.0ms (13.9%)

sample30.0ms (1%)

simplify10.0ms (0.3%)

prune1.0ms (0%)

localize4.0ms (0.1%)

rewrite78.0ms (2.6%)

series21.0ms (0.7%)

simplify88.0ms (2.9%)

prune18.0ms (0.6%)

localize9.0ms (0.3%)

rewrite75.0ms (2.4%)

series37.0ms (1.2%)

simplify129.0ms (4.2%)

prune22.0ms (0.7%)

localize5.0ms (0.2%)

rewrite42.0ms (1.4%)

series18.0ms (0.6%)

simplify110.0ms (3.6%)

prune16.0ms (0.5%)

localize9.0ms (0.3%)

rewrite237.0ms (7.7%)

series61.0ms (2%)

simplify363.0ms (11.9%)

prune65.0ms (2.1%)

regimes149.0ms (4.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.0s (33.7%)

Profiling