Details

analyze175.0ms (6.3%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample20.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify167.0ms (6%)

Algorithm

1×	egg-herbie

Rules

974×	`associate--r-_binary64`
537×	`associate--r+_binary64`
526×	`associate--l+_binary64`
473×	`associate--l-_binary64`
342×	`associate-+r-_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	7	10
2	12	10
3	18	10
4	24	10
5	39	10
6	62	10
7	79	10
8	120	10
9	223	10
10	401	10
11	942	10
12	1300	10
13	1198	10
14	1317	10
15	1365	10
16	1375	10
17	1375	10
18	1401	10
19	1409	10
20	1413	10
21	4014	10
22	4211	10
23	4719	10
24	4911	10

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

0.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))

Compiler

Compiled 14 to 8 computations (42.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(log.f64 (log.f64 x))
0.3b	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))

rewrite21.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`log-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`pow1_binary64`
8×	`log-pow_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

5.0ms	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
1.0ms	(log.f64 (log.f64 x))

Compiler

Compiled 402 to 108 computations (73.1% saved)

series41.0ms (1.5%)

Error

0.3b

Counts

2 → 6

Calls

2 calls:

22.0ms	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
17.0ms	(log.f64 (log.f64 x))

Compiler

Compiled 190 to 149 computations (21.6% saved)

simplify96.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

800×	`div-sub_binary64`
446×	`unsub-neg_binary64`
289×	`distribute-rgt-neg-out_binary64`
284×	`cancel-sign-sub-inv_binary64`
269×	`exp-sum_binary64`

Counts

46 → 21

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	71	521
1	146	492
2	300	492
3	1086	490
4	2186	486
5	4178	480
6	4317	480
7	5192	480

prune16.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	17	4	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	5	22

Error

0.1b

Counts

22 → 5

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
	0.5b	(/.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))
	0.6b	(cbrt.f64 (pow.f64 (-.f64 (log.f64 x) (log.f64 (log.f64 x))) 3))
	0.5b	(/.f64 (-.f64 (pow.f64 (log.f64 x) 3) (pow.f64 (log.f64 (log.f64 x)) 3)) (+.f64 (pow.f64 (log.f64 x) 2) (*.f64 (log.f64 (log.f64 x)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))))
▶	0.3b	(-.f64 (-.f64 (log.f64 x) (*.f64 (log.f64 (cbrt.f64 (log.f64 x))) 2)) (log.f64 (cbrt.f64 (log.f64 x))))

Compiler

Compiled 280 to 135 computations (51.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (-.f64 (log.f64 x) (*.f64 (log.f64 (cbrt.f64 (log.f64 x))) 2)) (log.f64 (cbrt.f64 (log.f64 x))))
0.3b	(-.f64 (log.f64 x) (*.f64 (log.f64 (cbrt.f64 (log.f64 x))) 2))
0.4b	(cbrt.f64 (log.f64 x))
0.4b	(cbrt.f64 (log.f64 x))

rewrite64.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`*-un-lft-identity_binary64`
13×	`log-prod_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
11×	`associate--l+_binary64`

Counts

4 → 72

Calls

4 calls:

8.0ms	(-.f64 (-.f64 (log.f64 x) (*.f64 (log.f64 (cbrt.f64 (log.f64 x))) 2)) (log.f64 (cbrt.f64 (log.f64 x))))
3.0ms	(-.f64 (log.f64 x) (*.f64 (log.f64 (cbrt.f64 (log.f64 x))) 2))
1.0ms	(cbrt.f64 (log.f64 x))
1.0ms	(cbrt.f64 (log.f64 x))

Compiler

Compiled 1448 to 503 computations (65.3% saved)

series124.0ms (4.4%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

36.0ms	(-.f64 (-.f64 (log.f64 x) (*.f64 (log.f64 (cbrt.f64 (log.f64 x))) 2)) (log.f64 (cbrt.f64 (log.f64 x))))
33.0ms	(-.f64 (log.f64 x) (*.f64 (log.f64 (cbrt.f64 (log.f64 x))) 2))
22.0ms	(cbrt.f64 (log.f64 x))
21.0ms	(cbrt.f64 (log.f64 x))

Compiler

Compiled 676 to 519 computations (23.2% saved)

simplify90.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

669×	`associate-l_binary64`
554×	`associate-r_binary64`
252×	`distribute-rgt-in_binary64`
249×	`cancel-sign-sub-inv_binary64`
222×	`distribute-lft-in_binary64`

Counts

84 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	1525
1	322	1182
2	851	1083
3	4183	1081
4	4908	1081

prune111.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	64	7	71

Error

0.0b

Counts

71 → 7

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log.f64 x) (log.f64 (log.f64 x)))
	0.5b	(/.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (sqrt.f64 (log.f64 (log.f64 x))) 4)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))
	0.3b	(+.f64 (log.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (-.f64 (log.f64 (cbrt.f64 x)) (log.f64 (log.f64 x))))
	0.8b	(/.f64 (-.f64 (pow.f64 (-.f64 (log.f64 x) (.f64 (log.f64 (log.f64 x)) 2/3)) 3) (pow.f64 (log.f64 (cbrt.f64 (log.f64 x))) 3)) (+.f64 (.f64 (log.f64 (log.f64 x)) (.f64 (log.f64 (log.f64 x)) 1/9)) (.f64 (-.f64 (log.f64 x) (*.f64 (log.f64 (log.f64 x)) 2/3)) (-.f64 (log.f64 x) (log.f64 (cbrt.f64 (log.f64 x)))))))
	0.6b	(-.f64 (/.f64 (-.f64 (pow.f64 (log.f64 x) 3) (.f64 (pow.f64 (log.f64 (log.f64 x)) 3) 8/27)) (+.f64 (.f64 (log.f64 x) (log.f64 x)) (.f64 (.f64 (log.f64 (log.f64 x)) 2/3) (+.f64 (log.f64 x) (*.f64 (log.f64 (log.f64 x)) 2/3))))) (log.f64 (cbrt.f64 (log.f64 x))))
	0.5b	(/.f64 (-.f64 (pow.f64 (log.f64 x) 3) (pow.f64 (log.f64 (log.f64 x)) 3)) (+.f64 (pow.f64 (log.f64 x) 2) (*.f64 (log.f64 (log.f64 x)) (+.f64 (log.f64 x) (log.f64 (log.f64 x))))))
▶	0.3b	(-.f64 (log.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))) (log.f64 (cbrt.f64 (log.f64 x))))

Compiler

Compiled 1009 to 437 computations (56.7% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (pow.f64 (log.f64 x) 2/3))
0.3b	(-.f64 (log.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))) (log.f64 (cbrt.f64 (log.f64 x))))
0.4b	(cbrt.f64 (log.f64 x))
1.2b	(pow.f64 (log.f64 x) 2/3)

rewrite118.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

48×	`times-frac_binary64`
46×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
42×	`add-cube-cbrt_binary64`
35×	`log-prod_binary64`

Counts

4 → 136

Calls

4 calls:

8.0ms	(-.f64 (log.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))) (log.f64 (cbrt.f64 (log.f64 x))))
5.0ms	(/.f64 x (pow.f64 (log.f64 x) 2/3))
2.0ms	(pow.f64 (log.f64 x) 2/3)
1.0ms	(cbrt.f64 (log.f64 x))

Compiler

Compiled 2490 to 1197 computations (51.9% saved)

series152.0ms (5.5%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

68.0ms	(-.f64 (log.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))) (log.f64 (cbrt.f64 (log.f64 x))))
35.0ms	(/.f64 x (pow.f64 (log.f64 x) 2/3))
19.0ms	(pow.f64 (log.f64 x) 2/3)
19.0ms	(cbrt.f64 (log.f64 x))

Compiler

Compiled 706 to 564 computations (20.1% saved)

simplify120.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

370×	`associate-l_binary64`
329×	`associate-r_binary64`
296×	`log-prod_binary64`
274×	`cancel-sign-sub-inv_binary64`
228×	`associate-/r*_binary64`

Counts

148 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	2689
1	468	2410
2	1161	1960
3	3980	1922
4	4902	1922

prune77.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	4	1	5
Picked	0	1	1
Done	1	0	1
Total	123	5	128

Error

Counts

128 → 5

Alt Table

Status	Error	Program
	0.3b	(-.f64 (-.f64 (log.f64 x) (.f64 2/3 (.f64 4/3 (log.f64 (log.f64 x))))) (log.f64 (cbrt.f64 (cbrt.f64 (log.f64 x)))))
▶	0.3b	(+.f64 (log.f64 (.f64 (cbrt.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))) (cbrt.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))))) (-.f64 (log.f64 (cbrt.f64 (.f64 x (pow.f64 (log.f64 x) -2/3)))) (log.f64 (cbrt.f64 (log.f64 x)))))
	0.3b	(+.f64 (log.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (-.f64 (log.f64 (cbrt.f64 x)) (log.f64 (log.f64 x))))
	0.3b	(+.f64 (log.f64 (/.f64 1 (pow.f64 (.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 (log.f64 x))) 2/3))) (-.f64 (log.f64 x) (.f64 (log.f64 (cbrt.f64 (log.f64 x))) 5/3)))
✓	0.3b	(-.f64 (log.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))) (log.f64 (cbrt.f64 (log.f64 x))))

Compiler

Compiled 1485 to 712 computations (52.1% saved)

localize25.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3)))
1.2b	(pow.f64 (log.f64 x) 2/3)
1.2b	(pow.f64 (log.f64 x) 2/3)
1.2b	(pow.f64 (log.f64 x) -2/3)

rewrite129.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

28×	`cbrt-prod_binary64`
25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`

Counts

4 → 91

Calls

4 calls:

4.0ms	(pow.f64 (log.f64 x) 2/3)
3.0ms	(cbrt.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3)))
2.0ms	(pow.f64 (log.f64 x) -2/3)
2.0ms	(pow.f64 (log.f64 x) 2/3)

Compiler

Compiled 3083 to 1802 computations (41.6% saved)

series119.0ms (4.3%)

Error

Counts

4 → 12

Calls

4 calls:

41.0ms	(cbrt.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3)))
22.0ms	(pow.f64 (log.f64 x) 2/3)
22.0ms	(pow.f64 (log.f64 x) 2/3)
21.0ms	(pow.f64 (log.f64 x) -2/3)

Compiler

Compiled 1321 to 952 computations (27.9% saved)

simplify90.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-/r*_binary64`
571×	`associate-/l*_binary64`
502×	`associate-/l/_binary64`
276×	`unswap-sqr_binary64`
224×	`associate-/r/_binary64`

Counts

103 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	1489
1	293	1422
2	589	1363
3	1651	1340
4	4854	1340
5	4897	1340

prune49.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	67	5	72

Error

Counts

72 → 5

Alt Table

Status	Error	Program
	0.3b	(-.f64 (-.f64 (log.f64 x) (.f64 2/3 (.f64 4/3 (log.f64 (log.f64 x))))) (log.f64 (cbrt.f64 (cbrt.f64 (log.f64 x)))))
	0.3b	(+.f64 (log.f64 (.f64 (cbrt.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))) (cbrt.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))))) (-.f64 (log.f64 (cbrt.f64 (.f64 x (pow.f64 (log.f64 x) -2/3)))) (log.f64 (cbrt.f64 (log.f64 x)))))
	0.3b	(+.f64 (log.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (-.f64 (log.f64 (cbrt.f64 x)) (log.f64 (log.f64 x))))
	0.3b	(+.f64 (log.f64 (/.f64 1 (pow.f64 (.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 (log.f64 x))) 2/3))) (-.f64 (log.f64 x) (.f64 (log.f64 (cbrt.f64 (log.f64 x))) 5/3)))
	0.3b	(-.f64 (log.f64 (/.f64 x (pow.f64 (log.f64 x) 2/3))) (log.f64 (cbrt.f64 (log.f64 x))))

Compiler

Compiled 1330 to 776 computations (41.7% saved)

regimes283.0ms (10.1%)

Accuracy

Total -0.0b remaining (-160%)

Threshold costs -0.0b (-160%)

Compiler

Compiled 5008 to 2924 computations (41.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

sample669.0ms (24%)

Algorithm

1×

intervals

Results

387.0ms	8000×	body	128	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 114 to 75 computations (34.2% saved)

Details

analyze175.0ms (6.3%)

sample20.0ms (0.7%)

simplify167.0ms (6%)

prune1.0ms (0%)

localize5.0ms (0.2%)

rewrite21.0ms (0.7%)

series41.0ms (1.5%)

simplify96.0ms (3.4%)

prune16.0ms (0.6%)

localize12.0ms (0.4%)

rewrite64.0ms (2.3%)

series124.0ms (4.4%)

simplify90.0ms (3.2%)

prune111.0ms (4%)

localize14.0ms (0.5%)

rewrite118.0ms (4.2%)

series152.0ms (5.5%)

simplify120.0ms (4.3%)

prune77.0ms (2.7%)

localize25.0ms (0.9%)

rewrite129.0ms (4.6%)

series119.0ms (4.3%)

simplify90.0ms (3.2%)

prune49.0ms (1.7%)

regimes283.0ms (10.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample669.0ms (24%)

Profiling