Details

analyze285.0ms (12.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample28.0ms (1.2%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify269.0ms (11.5%)

Algorithm

1×	egg-herbie

Rules

2074×	`distribute-lft-out--_binary64`
788×	`distribute-rgt-out--_binary64`
756×	`unsub-neg_binary64`
614×	`sub-neg_binary64`
581×	`distribute-rgt-out_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	31	20
4	45	20
5	60	20
6	96	20
7	213	20
8	364	20
9	486	20
10	1099	20
11	1877	20
12	1931	20
13	2167	20
14	2315	20
15	2313	20
16	2390	20
17	2649	20
18	3212	20
19	4204	20
20	4738	20
21	4780	20
22	4791	20
23	4788	20
24	4573	20
25	4366	20
26	4503	20
27	4563	20
28	4606	20
29	7544	20

prune1.0ms (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

0.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.2b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite133.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

66×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
43×	`add-sqr-sqrt_binary64`
31×	`sqrt-prod_binary64`
31×	`add-cube-cbrt_binary64`

Counts

4 → 117

Calls

4 calls:

18.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
18.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
5.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 2373 to 1498 computations (36.9% saved)

series44.0ms (1.9%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

11.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
6.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
6.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

Compiler

Compiled 721 to 592 computations (17.9% saved)

simplify168.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

440×	`distribute-rgt-neg-in_binary64`
355×	`distribute-lft-neg-in_binary64`
303×	`sub-neg_binary64`
296×	`cancel-sign-sub-inv_binary64`
285×	`associate-r_binary64`

Counts

141 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	3074
1	425	2865
2	1083	2831
3	3103	2701
4	4618	2701
5	4999	2701

prune43.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	2	78

Error

Counts

78 → 2

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (.f64 -2 (log.f64 (cbrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 x)))))
✓	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Status

Error

Program

▶

0.2b

(+.f64 (*.f64 -2 (log.f64 (cbrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 x)))))

✓

0.3b

(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 1174 to 779 computations (33.6% saved)

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 -2 (log.f64 (cbrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 x)))))
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)

rewrite116.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

46×	`*-un-lft-identity_binary64`
34×	`log-prod_binary64`
28×	`cbrt-prod_binary64`
26×	`times-frac_binary64`
26×	`add-sqr-sqrt_binary64`

Counts

4 → 81

Calls

4 calls:

47.0ms	(+.f64 (.f64 -2 (log.f64 (cbrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 x)))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 2384 to 1267 computations (46.9% saved)

series88.0ms (3.8%)

Error

Counts

4 → 15

Calls

4 calls:

39.0ms	(+.f64 (.f64 -2 (log.f64 (cbrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 x)))))
13.0ms	(cbrt.f64 x)
12.0ms	(cbrt.f64 x)
11.0ms	(cbrt.f64 x)

Compiler

Compiled 1314 to 1053 computations (19.9% saved)

simplify119.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

483×	`associate-l_binary64`
465×	`associate-r_binary64`
258×	`distribute-rgt-in_binary64`
241×	`times-frac_binary64`
216×	`log-prod_binary64`

Counts

96 → 72

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	2290
1	492	2011
2	1431	1906
3	4599	1806
4	4937	1806
5	4820	1806

prune49.0ms (2.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	72	2	74

Error

Counts

74 → 2

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 -2 (log.f64 (cbrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 x)))))
	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Status

Error

Program

0.2b

(+.f64 (*.f64 -2 (log.f64 (cbrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 x)))))

0.3b

(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 1745 to 1064 computations (39% saved)

regimes151.0ms (6.5%)

Accuracy

Total 0.2b remaining (99.1%)

Threshold costs 0.2b (99.1%)

Compiler

Compiled 2199 to 1585 computations (27.9% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	26	31
2	34	31
3	39	31
4	41	31
5	40	31

end1.0ms (0%)

Compiler: Compiled 20 to 13 computations (35% saved)

sample810.0ms (34.8%)

Algorithm

1×

intervals

Results

563.0ms	8000×	body	128	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 72 to 50 computations (30.6% saved)

Details

analyze285.0ms (12.2%)

sample28.0ms (1.2%)

simplify269.0ms (11.5%)

prune1.0ms (0.1%)

localize9.0ms (0.4%)

rewrite133.0ms (5.7%)

series44.0ms (1.9%)

simplify168.0ms (7.2%)

prune43.0ms (1.9%)

localize15.0ms (0.6%)

rewrite116.0ms (5%)

series88.0ms (3.8%)

simplify119.0ms (5.1%)

prune49.0ms (2.1%)

regimes151.0ms (6.5%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample810.0ms (34.8%)

Profiling