Details

analyze509.0ms (10.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample140.0ms (2.9%)

Algorithm

1×

intervals

Results

102.0ms	95×	body	1024	valid
15.0ms	40×	body	2048	valid
8.0ms	33×	body	512	valid
4.0ms	67×	body	128	valid
3.0ms	21×	body	256	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	12	14
2	11	14

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

53.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	53.2b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))

Compiler

Compiled 20 to 14 computations (30% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.6b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.9b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
13.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite57.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

52.9b

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
5×	`pow1_binary64`

Counts

3 → 42

Calls

3 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
4.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 704 to 424 computations (39.8% saved)

series60.0ms (1.2%)

Error

0.0b

Counts

3 → 25

Calls

3 calls:

14.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
12.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))

Compiler

Compiled 709 to 576 computations (18.8% saved)

simplify117.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

485×	`unswap-sqr_binary64`
436×	`times-frac_binary64`
364×	`sub-neg_binary64`
319×	`cancel-sign-sub-inv_binary64`
264×	`*-commutative_binary64`

Counts

67 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1047
1	284	971
2	610	941
3	1613	935
4	3591	935
5	4994	935

prune31.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Error

0.0b

Counts

51 → 3

Alt Table

Status	Error	Program
	48.3b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
	47.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
▶	30.3b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))

Compiler

Compiled 718 to 471 computations (34.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
0.1b	(*.f64 3/40 (pow.f64 x 5))
0.3b	(*.f64 (pow.f64 x 3) 1/6)
18.9b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))

rewrite76.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

23×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(*.f64 3/40 (pow.f64 x 5))
5.0ms	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))
4.0ms	(*.f64 (pow.f64 x 3) 1/6)
2.0ms	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))

Compiler

Compiled 1554 to 1223 computations (21.3% saved)

series42.0ms (0.9%)

Error

0.0b

Counts

4 → 17

Calls

4 calls:

14.0ms	(-.f64 x (*.f64 (pow.f64 x 3) 1/6))
9.0ms	(*.f64 (pow.f64 x 3) 1/6)
8.0ms	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))
7.0ms	(*.f64 3/40 (pow.f64 x 5))

Compiler

Compiled 429 to 337 computations (21.4% saved)

simplify104.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

466×	`cancel-sign-sub-inv_binary64`
392×	`exp-prod_binary64`
369×	`*-commutative_binary64`
351×	`log-prod_binary64`
315×	`unswap-sqr_binary64`

Counts

100 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	147	1317
1	323	1278
2	1061	1263
3	2693	1239
4	4581	1210
5	4920	1210

prune31.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Error

0.0b

Counts

69 → 3

Alt Table

Status	Error	Program
	48.3b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
▶	47.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	30.3b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))

Compiler

Compiled 906 to 710 computations (21.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
0.5b	(/.f64 1/8 (pow.f64 x 3))
11.2b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

rewrite104.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

41×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
12×	`associate-/r*_binary64`

Counts

3 → 96

Calls

3 calls:

27.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
21.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
8.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 1484 to 1199 computations (19.2% saved)

series26.0ms (0.5%)

Error

0.0b

Counts

3 → 13

Calls

3 calls:

10.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
7.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 338 to 288 computations (14.8% saved)

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Rules

671×	`associate-l_binary64`
378×	`associate-/l*_binary64`
330×	`associate-*l/_binary64`
301×	`log-prod_binary64`
298×	`associate-*r/_binary64`

Counts

109 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	1708
1	297	1616
2	993	1558
3	4581	1557
4	4947	1557

prune30.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	77	4	81

Error

Counts

81 → 4

Alt Table

Status	Error	Program
	48.3b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
▶	47.8b	(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))))) (log.f64 (cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))))
✓	47.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
✓	30.3b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))

Compiler

Compiled 891 to 694 computations (22.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1/8 (pow.f64 x 3))
0.5b	(/.f64 1/8 (pow.f64 x 3))
21.3b	(cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
21.3b	(cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))

rewrite194.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

118×	`add-sqr-sqrt_binary64`
102×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
56×	`add-cube-cbrt_binary64`
30×	`cbrt-prod_binary64`

Counts

4 → 182

Calls

4 calls:

25.0ms	(cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
23.0ms	(cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
4.0ms	(/.f64 1/8 (pow.f64 x 3))
4.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 5139 to 4272 computations (16.9% saved)

series56.0ms (1.2%)

Error

Counts

4 → 14

Calls

4 calls:

19.0ms	(cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
13.0ms	(cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
8.0ms	(/.f64 1/8 (pow.f64 x 3))
8.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 1106 to 961 computations (13.1% saved)

simplify152.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

746×	`associate-l_binary64`
394×	`associate-/l*_binary64`
325×	`associate-*l/_binary64`
304×	`associate-/l/_binary64`
285×	`associate-*r/_binary64`

Counts

196 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	3554
1	337	3460
2	1053	3304
3	4644	3304
4	5028	3304

prune78.0ms (1.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	154	4	158

Error

Counts

158 → 4

Alt Table

Status	Error	Program
	48.3b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
	47.8b	(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))))) (log.f64 (cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))))
	47.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	30.3b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))

Compiler

Compiled 3010 to 2433 computations (19.2% saved)

regimes245.0ms (5.1%)

Accuracy

Total 0.0b remaining (0.2%)

Threshold costs 0.0b (0.2%)

Compiler

Compiled 2820 to 2049 computations (27.3% saved)

bsearch41.0ms (0.8%)

Steps

Iters	Range		Point
10	0.0006063109915053789	3111334.702144331	1.0257505134280076
9	-9668.862751551294	-0.0007700972522206666	-1.1570741760631404

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	58
1	41	58
2	52	58
3	56	58
4	58	58
5	57	58

end1.0ms (0%)

Compiler: Compiled 40 to 30 computations (25% saved)

sample2.6s (53.3%)

Algorithm

1×

intervals

Results

1.2s	2587×	body	1024	valid
479.0ms	1225×	body	2048	valid
335.0ms	1248×	body	512	valid
137.0ms	2275×	body	128	valid
94.0ms	627×	body	256	valid
22.0ms	38×	body	4096	valid

Compiler

Compiled 112 to 87 computations (22.3% saved)

Details

analyze509.0ms (10.6%)

sample140.0ms (2.9%)

simplify10.0ms (0.2%)

prune1.0ms (0%)

localize6.0ms (0.1%)

rewrite57.0ms (1.2%)

series60.0ms (1.2%)

simplify117.0ms (2.4%)

prune31.0ms (0.6%)

localize8.0ms (0.2%)

rewrite76.0ms (1.6%)

series42.0ms (0.9%)

simplify104.0ms (2.2%)

prune31.0ms (0.6%)

localize9.0ms (0.2%)

rewrite104.0ms (2.2%)

series26.0ms (0.5%)

simplify98.0ms (2%)

prune30.0ms (0.6%)

localize11.0ms (0.2%)

rewrite194.0ms (4%)

series56.0ms (1.2%)

simplify152.0ms (3.2%)

prune78.0ms (1.6%)

regimes245.0ms (5.1%)

bsearch41.0ms (0.8%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample2.6s (53.3%)

Profiling