Details

analyze27.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

5.0ms	61×	body	512	valid
4.0ms	145×	body	128	valid
2.0ms	18×	body	1024	valid
2.0ms	32×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

16×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`
8×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	28	16
4	35	16
5	51	16
6	73	16
7	82	16
8	94	16
9	96	16
10	90	16
11	76	16

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 36 to 30 computations (16.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
1.8b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite234.0ms (7.6%)

Algorithm

1×	rewrite-expression-head

Error

13.1b

Rules

118×	`*-un-lft-identity_binary64`
95×	`add-sqr-sqrt_binary64`
90×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
30×	`distribute-lft-out--_binary64`

Counts

3 → 151

Calls

3 calls:

38.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 2350 to 1966 computations (16.3% saved)

series68.0ms (2.2%)

Error

0.7b

Counts

3 → 36

Calls

3 calls:

16.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
13.0ms	(/.f64 1 (+.f64 x 1))
11.0ms	(/.f64 1 (-.f64 x 1))

Compiler

Compiled 970 to 804 computations (17.1% saved)

simplify149.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

671×	`div-sub_binary64`
277×	`sub-neg_binary64`
231×	`associate-l_binary64`
227×	`associate-r_binary64`
188×	`distribute-rgt-in_binary64`

Counts

187 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2787
1	448	2685
2	1166	2676
3	3396	2660
4	4320	2660
5	5111	2660

prune67.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	160	3	163

Error

0.7b

Counts

163 → 3

Alt Table

Status	Error	Program
▶	29.5b	(-.f64 (.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 1 (-.f64 x 1)))
✓	14.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
	31.7b	(-.f64 (-.f64 (-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4))) (/.f64 2 (pow.f64 x 6))) (/.f64 2 (pow.f64 x 8)))

Compiler

Compiled 1307 to 1031 computations (21.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.7b	(/.f64 1 (+.f64 (*.f64 x x) -1))
7.1b	(-.f64 (.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 1 (-.f64 x 1)))
15.3b	(.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (-.f64 x 1))

rewrite231.0ms (7.6%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

88×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
68×	`times-frac_binary64`
49×	`add-cube-cbrt_binary64`
39×	`cancel-sign-sub-inv_binary64`

Counts

4 → 193

Calls

4 calls:

21.0ms	(-.f64 (.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 1 (-.f64 x 1)))
16.0ms	(.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (-.f64 x 1))
9.0ms	(/.f64 1 (+.f64 (*.f64 x x) -1))
6.0ms	(/.f64 1 (-.f64 x 1))

Compiler

Compiled 4673 to 3417 computations (26.9% saved)

series91.0ms (3%)

Error

0.7b

Counts

4 → 48

Calls

4 calls:

21.0ms	(-.f64 (.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 1 (-.f64 x 1)))
17.0ms	(/.f64 1 (+.f64 (*.f64 x x) -1))
13.0ms	(/.f64 1 (-.f64 x 1))
13.0ms	(.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (-.f64 x 1))

Compiler

Compiled 1532 to 1237 computations (19.3% saved)

simplify190.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

250×	`associate-/r/_binary64`
201×	`exp-prod_binary64`
198×	`associate--r+_binary64`
188×	`associate-/l/_binary64`
187×	`cancel-sign-sub-inv_binary64`

Counts

241 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	4056
1	647	3589
2	2234	3550
3	4555	3550
4	4982	3550
5	5006	3550

prune113.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	212	3	215

Error

0.7b

Counts

215 → 3

Alt Table

Status	Error	Program
▶	13.4b	(/.f64 (.f64 (+.f64 x -1) (-.f64 (+.f64 x -2) x)) (.f64 (+.f64 (*.f64 x x) -1) (+.f64 x -1)))
✓	14.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
	31.7b	(-.f64 (-.f64 (-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4))) (/.f64 2 (pow.f64 x 6))) (/.f64 2 (pow.f64 x 8)))

Compiler

Compiled 2570 to 1856 computations (27.8% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 x x) -1)
0.0b	(/.f64 (.f64 (+.f64 x -1) (-.f64 (+.f64 x -2) x)) (.f64 (+.f64 (*.f64 x x) -1) (+.f64 x -1)))
0.1b	(.f64 (+.f64 (.f64 x x) -1) (+.f64 x -1))
1.2b	(-.f64 (+.f64 x -2) x)

rewrite174.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
16×	`flip-+_binary64`
16×	`flip3-+_binary64`
14×	`*-un-lft-identity_binary64`

Counts

4 → 99

Calls

4 calls:

19.0ms	(/.f64 (.f64 (+.f64 x -1) (-.f64 (+.f64 x -2) x)) (.f64 (+.f64 (*.f64 x x) -1) (+.f64 x -1)))
10.0ms	(.f64 (+.f64 (.f64 x x) -1) (+.f64 x -1))
6.0ms	(-.f64 (+.f64 x -2) x)
4.0ms	(+.f64 (*.f64 x x) -1)

Compiler

Compiled 2968 to 1903 computations (35.9% saved)

series65.0ms (2.1%)

Error

0.7b

Counts

4 → 33

Calls

4 calls:

15.0ms	(/.f64 (.f64 (+.f64 x -1) (-.f64 (+.f64 x -2) x)) (.f64 (+.f64 (*.f64 x x) -1) (+.f64 x -1)))
12.0ms	(+.f64 (*.f64 x x) -1)
12.0ms	(.f64 (+.f64 (.f64 x x) -1) (+.f64 x -1))
5.0ms	(-.f64 (+.f64 x -2) x)

Compiler

Compiled 983 to 762 computations (22.5% saved)

simplify116.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

287×	`distribute-rgt-in_binary64`
273×	`distribute-lft-in_binary64`
219×	`times-frac_binary64`
215×	`associate-l_binary64`
196×	`div-sub_binary64`

Counts

132 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	2760
1	669	2345
2	2983	1834
3	4626	1834
4	4928	1834

prune88.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	95	5	100

Error

0.0b

Counts

100 → 5

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (*.f64 (/.f64 -2 (+.f64 1 x)) 1) (+.f64 x -1))
	6.0b	(/.f64 (+.f64 x -1) (.f64 (/.f64 (+.f64 (.f64 x x) -1) -2) (+.f64 x -1)))
	1.8b	(.f64 (.f64 (cbrt.f64 (/.f64 -2 (+.f64 (.f64 x x) -1))) (cbrt.f64 (/.f64 -2 (+.f64 (.f64 x x) -1)))) (cbrt.f64 (/.f64 -2 (+.f64 (*.f64 x x) -1))))
	0.7b	(/.f64 1 (/.f64 (+.f64 (*.f64 x x) -1) -2))
	11.3b	(cbrt.f64 (/.f64 -8 (pow.f64 (+.f64 (*.f64 x x) -1) 3)))

Compiler

Compiled 1776 to 1172 computations (34% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 -2 (+.f64 1 x))
0.1b	(/.f64 (*.f64 (/.f64 -2 (+.f64 1 x)) 1) (+.f64 x -1))

rewrite89.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`*-un-lft-identity_binary64`
18×	`add-exp-log_binary64`
17×	`times-frac_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

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

Compiler

Compiled 1103 to 922 computations (16.4% saved)

series45.0ms (1.5%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

16.0ms	(/.f64 (*.f64 (/.f64 -2 (+.f64 1 x)) 1) (+.f64 x -1))
14.0ms	(/.f64 -2 (+.f64 1 x))

Compiler

Compiled 722 to 618 computations (14.4% saved)

simplify102.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

477×	`cancel-sign-sub-inv_binary64`
315×	`div-sub_binary64`
226×	`times-frac_binary64`
222×	`sub-neg_binary64`
208×	`unsub-neg_binary64`

Counts

89 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1480
1	391	1261
2	1041	1255
3	2930	1255
4	4537	1255
5	4948	1255

prune63.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Error

0.0b

Counts

85 → 6

Alt Table

Status	Error	Program
	49.0b	(/.f64 (/.f64 (/.f64 -2 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1))) (sqrt.f64 (+.f64 x -1)))
	0.1b	(/.f64 (*.f64 (/.f64 -2 (+.f64 1 x)) 1) (+.f64 x -1))
	6.0b	(/.f64 (+.f64 x -1) (.f64 (/.f64 (+.f64 (.f64 x x) -1) -2) (+.f64 x -1)))
	1.8b	(.f64 (.f64 (cbrt.f64 (/.f64 -2 (+.f64 (.f64 x x) -1))) (cbrt.f64 (/.f64 -2 (+.f64 (.f64 x x) -1)))) (cbrt.f64 (/.f64 -2 (+.f64 (*.f64 x x) -1))))
	0.7b	(/.f64 1 (/.f64 (+.f64 (*.f64 x x) -1) -2))
	11.3b	(cbrt.f64 (/.f64 -8 (pow.f64 (+.f64 (*.f64 x x) -1) 3)))

Compiler

Compiled 997 to 774 computations (22.4% saved)

regimes384.0ms (12.6%)

Accuracy

Total 0.1b remaining (82.5%)

Threshold costs 0.1b (82.5%)

Compiler

Compiled 5960 to 4766 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	12	13

end1.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample692.0ms (22.6%)

Algorithm

1×

intervals

Results

157.0ms	1973×	body	512	valid
134.0ms	4652×	body	128	valid
53.0ms	952×	body	256	valid
47.0ms	423×	body	1024	valid

Compiler

Compiled 116 to 91 computations (21.6% saved)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	28	16
4	35	16
5	51	16
6	73	16
7	82	16
8	94	16
9	96	16
10	90	16
11	76	16

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	28	16
4	35	16
5	51	16
6	73	16
7	82	16
8	94	16
9	96	16
10	90	16
11	76	16

Details

analyze27.0ms (0.9%)

sample19.0ms (0.6%)

simplify12.0ms (0.4%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite234.0ms (7.6%)

series68.0ms (2.2%)

simplify149.0ms (4.9%)

prune67.0ms (2.2%)

localize9.0ms (0.3%)

rewrite231.0ms (7.6%)

series91.0ms (3%)

simplify190.0ms (6.2%)

prune113.0ms (3.7%)

localize13.0ms (0.4%)

rewrite174.0ms (5.7%)

series65.0ms (2.1%)

simplify116.0ms (3.8%)

prune88.0ms (2.9%)

localize6.0ms (0.2%)

rewrite89.0ms (2.9%)

series45.0ms (1.5%)

simplify102.0ms (3.3%)

prune63.0ms (2%)

regimes384.0ms (12.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample692.0ms (22.6%)

Profiling

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	28	16
4	35	16
5	51	16
6	73	16
7	82	16
8	94	16
9	96	16
10	90	16
11	76	16