Details

analyze782.0ms (4.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	49.9%	50.1%	5
0%	43.7%	56.3%	6
0%	34.3%	65.7%	7
3.1%	31.2%	65.7%	8
3.5%	27.7%	68.8%	9
5.3%	24.4%	70.4%	10
7.5%	19.8%	72.7%	11
11.1%	16.2%	72.7%	12
11.3%	15.3%	73.5%	13
13.2%	13%	73.9%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample56.0ms (0.3%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
2.0ms	19×	body	128	nan

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify262.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

2537×	`fma-neg_binary64`
490×	`associate--r-_binary64`
460×	`associate--l-_binary64`
401×	`distribute-rgt-in_binary64`
373×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	22	17
2	59	17
3	145	15
4	313	15
5	593	15
6	714	15
7	958	15
8	1168	15
9	1549	15
10	2712	15
11	2613	15
12	2654	15
13	2663	15
14	2669	15
15	2671	15
16	2759	15
17	2777	15
18	2785	15
19	2807	15
20	2793	15
21	2793	15
22	5107	15

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) (log.f64 t))

Compiler

Compiled 55 to 33 computations (40% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x (log.f64 y)) y)
✓	0.0b	(+.f64 (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) (log.f64 t))
✓	0.0b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)
✓	0.3b	(*.f64 x (log.f64 y))

series1.2s (6.7%)

Counts

4 → 132

Calls

4 calls:

642.0ms	(+.f64 (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) (log.f64 t))
357.0ms	(*.f64 x (log.f64 y))
155.0ms	(-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)
92.0ms	(-.f64 (*.f64 x (log.f64 y)) y)

rewrite82.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
44×	`associate--l+_binary64`
43×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
27×	`prod-diff_binary64`

Counts

4 → 152

Calls

4 calls:

23.0ms	(+.f64 (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) (log.f64 t))
17.0ms	(-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)
8.0ms	(-.f64 (*.f64 x (log.f64 y)) y)
6.0ms	(*.f64 x (log.f64 y))

simplify241.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1023×	`fma-neg_binary64`
638×	`distribute-rgt-in_binary64`
579×	`distribute-lft-in_binary64`
226×	`sub-neg_binary64`
131×	`fma-def_binary64`

Counts

284 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3308
1	531	3200
2	1822	3122
3	4702	3122
4	4967	3122

prune398.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	245	7	252
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	245	8	253

Error

0.0b

Counts

253 → 8

Alt Table

Status	Error	Program
	55.7b	(log.f64 (*.f64 t (/.f64 (pow.f64 y x) (exp.f64 (+.f64 y z)))))
	0.4b	(+.f64 (-.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (log.f64 y))) (cbrt.f64 (.f64 x (log.f64 y)))) (cbrt.f64 (*.f64 x (log.f64 y)))) y) z) (log.f64 t))
	34.2b	(+.f64 (-.f64 (-.f64 (.f64 (.f64 x (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y))) y) z) (log.f64 t))
	0.4b	(+.f64 (-.f64 (-.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y))) y) z) (log.f64 t))
	32.7b	(+.f64 (-.f64 (-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y))) y) z) (log.f64 t))
✓	0.1b	(+.f64 (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) (log.f64 t))
▶	0.1b	(+.f64 (-.f64 (-.f64 (+.f64 (.f64 x (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 x (log.f64 (cbrt.f64 y)))) y) z) (log.f64 t))
	24.9b	(+.f64 (-.f64 (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 (log.f64 y) (log.f64 y)) (log.f64 y)))) y) z) (log.f64 t))

Compiler

Compiled 5136 to 1251 computations (75.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (log.f64 (cbrt.f64 y)))
✓	0.2b	(.f64 x (.f64 2 (log.f64 (cbrt.f64 y))))
✓	0.3b	(+.f64 (.f64 x (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 x (log.f64 (cbrt.f64 y))))
✓	0.6b	(cbrt.f64 y)

series5.3s (28.8%)

Counts

4 → 84

Calls

4 calls:

1.8s	(+.f64 (.f64 x (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 x (log.f64 (cbrt.f64 y))))
1.8s	(*.f64 x (log.f64 (cbrt.f64 y)))
1.7s	(.f64 x (.f64 2 (log.f64 (cbrt.f64 y))))
53.0ms	(cbrt.f64 y)

rewrite54.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`log-prod_binary64`
60×	`distribute-lft-in_binary64`
60×	`distribute-rgt-in_binary64`
39×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`

Counts

4 → 142

Calls

4 calls:

15.0ms	(+.f64 (.f64 x (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 x (log.f64 (cbrt.f64 y))))
12.0ms	(.f64 x (.f64 2 (log.f64 (cbrt.f64 y))))
8.0ms	(*.f64 x (log.f64 (cbrt.f64 y)))
2.0ms	(cbrt.f64 y)

simplify120.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
475×	`fma-neg_binary64`
441×	`*-commutative_binary64`
440×	`cancel-sign-sub-inv_binary64`
306×	`distribute-rgt-in_binary64`

Counts

226 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3066
1	407	2725
2	1353	2500
3	3821	2492
4	4971	2492

prune482.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	245	3	248
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	248	8	256

Error

Counts

256 → 8

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (-.f64 (fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (cbrt.f64 y)))) y) z) (log.f64 t))
	0.4b	(+.f64 (-.f64 (-.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y))) y) z) (log.f64 t))
	55.7b	(log.f64 (*.f64 t (/.f64 (pow.f64 y x) (exp.f64 (+.f64 y z)))))
	0.1b	(+.f64 (-.f64 (-.f64 (+.f64 (.f64 x (fma.f64 2/3 (log.f64 y) (log.f64 (cbrt.f64 (pow.f64 y 2/3))))) (.f64 (log.f64 (cbrt.f64 (cbrt.f64 y))) x)) y) z) (log.f64 t))
	34.2b	(+.f64 (-.f64 (-.f64 (.f64 (.f64 x (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y))) y) z) (log.f64 t))
✓	0.1b	(+.f64 (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) (log.f64 t))
	0.1b	(+.f64 (-.f64 (-.f64 (+.f64 (.f64 x (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 x (log.f64 (pow.f64 y 1/3)))) y) z) (log.f64 t))
	24.9b	(+.f64 (-.f64 (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 (log.f64 y) (log.f64 y)) (log.f64 y)))) y) z) (log.f64 t))

Compiler

Compiled 6788 to 2780 computations (59% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (cbrt.f64 y))
	0.2b	(*.f64 x (log.f64 (cbrt.f64 y)))
✓	0.2b	(fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (cbrt.f64 y))))
	0.6b	(cbrt.f64 y)

series3.5s (19%)

Counts

2 → 36

Calls

2 calls:

2.5s	(fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (cbrt.f64 y))))
998.0ms	(log.f64 (cbrt.f64 y))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`cbrt-prod_binary64`

Counts

2 → 28

Calls

2 calls:

2.0ms	(log.f64 (cbrt.f64 y))
1.0ms	(fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (cbrt.f64 y))))

simplify113.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

468×	`distribute-rgt-in_binary64`
453×	`distribute-lft-in_binary64`
242×	`*-commutative_binary64`
218×	`fma-neg_binary64`
204×	`unsub-neg_binary64`

Counts

64 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	811
1	104	661
2	233	519
3	700	507
4	2681	507
5	4750	507
6	4888	507

prune293.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	164	7	171

Error

Counts

171 → 7

Alt Table

Status	Error	Program
	55.7b	(log.f64 (*.f64 t (/.f64 (pow.f64 y x) (exp.f64 (+.f64 y z)))))
	0.1b	(+.f64 (-.f64 (-.f64 (+.f64 (.f64 x (fma.f64 2/3 (log.f64 y) (log.f64 (cbrt.f64 (pow.f64 y 2/3))))) (.f64 (log.f64 (cbrt.f64 (cbrt.f64 y))) x)) y) z) (log.f64 t))
	34.2b	(+.f64 (-.f64 (-.f64 (.f64 (.f64 x (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y))) y) z) (log.f64 t))
	0.4b	(+.f64 (-.f64 (-.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y))) y) z) (log.f64 t))
✓	0.1b	(+.f64 (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) (log.f64 t))
	24.9b	(+.f64 (-.f64 (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 (log.f64 y) (log.f64 y)) (log.f64 y)))) y) z) (log.f64 t))
▶	0.1b	(+.f64 (-.f64 (-.f64 (fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (pow.f64 y 1/3)))) y) z) (log.f64 t))

Compiler

Compiled 4106 to 1648 computations (59.9% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (log.f64 (pow.f64 y 1/3)))
✓	0.2b	(fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (pow.f64 y 1/3))))
	0.6b	(cbrt.f64 y)
✓	5.0b	(pow.f64 y 1/3)

series3.5s (18.6%)

Counts

3 → 52

Calls

3 calls:

2.5s	(fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (pow.f64 y 1/3))))
910.0ms	(*.f64 x (log.f64 (pow.f64 y 1/3)))
47.0ms	(pow.f64 y 1/3)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`log-prod_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`

Counts

3 → 65

Calls

3 calls:

6.0ms	(*.f64 x (log.f64 (pow.f64 y 1/3)))
1.0ms	(pow.f64 y 1/3)
0.0ms	(fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (pow.f64 y 1/3))))

simplify98.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary64`
379×	`fma-neg_binary64`
346×	`*-commutative_binary64`
317×	`log-prod_binary64`
239×	`exp-prod_binary64`

Counts

117 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	1400
1	254	1141
2	751	1011
3	1660	966
4	3824	966
5	4853	966
6	4820	966

prune142.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	125	6	131

Error

Counts

131 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) (log.f64 t))
	0.1b	(+.f64 (-.f64 (-.f64 (fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (pow.f64 (pow.f64 y (sqrt.f64 1/3)) (sqrt.f64 1/3))))) y) z) (log.f64 t))
	34.2b	(+.f64 (-.f64 (-.f64 (.f64 (.f64 x (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y))) y) z) (log.f64 t))
	0.4b	(+.f64 (-.f64 (-.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y))) y) z) (log.f64 t))
	55.7b	(log.f64 (*.f64 t (/.f64 (pow.f64 y x) (exp.f64 (+.f64 y z)))))
✓	0.1b	(+.f64 (-.f64 (-.f64 (fma.f64 x (.f64 2 (log.f64 (cbrt.f64 y))) (.f64 x (log.f64 (pow.f64 y 1/3)))) y) z) (log.f64 t))

Compiler

Compiled 3174 to 1673 computations (47.3% saved)

regimes572.0ms (3.1%)

Accuracy

Total 0.1b remaining (76.9%)

Threshold costs 0.1b (76.9%)

Counts

57 → 1

Compiler

Compiled 8876 to 5875 computations (33.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	25	31
2	33	31
3	37	31
4	39	31
5	39	31

end1.0ms (0%)

Compiler: Compiled 24 to 17 computations (29.2% saved)

sample1.1s (6.1%)

Algorithm

1×

intervals

Results

663.0ms	8000×	body	128	valid
23.0ms	382×	body	128	nan
2.0ms	27×	body	128	invalid

Compiler

Compiled 170 to 115 computations (32.4% saved)

Details

analyze782.0ms (4.2%)

sample56.0ms (0.3%)

simplify262.0ms (1.4%)

prune6.0ms (0%)

localize23.0ms (0.1%)

series1.2s (6.7%)

rewrite82.0ms (0.4%)

simplify241.0ms (1.3%)

prune398.0ms (2.1%)

localize15.0ms (0.1%)

series5.3s (28.8%)

rewrite54.0ms (0.3%)

simplify120.0ms (0.6%)

prune482.0ms (2.6%)

localize29.0ms (0.2%)

series3.5s (19%)

rewrite5.0ms (0%)

simplify113.0ms (0.6%)

prune293.0ms (1.6%)

localize39.0ms (0.2%)

series3.5s (18.6%)

rewrite10.0ms (0.1%)

simplify98.0ms (0.5%)

prune142.0ms (0.8%)

regimes572.0ms (3.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.1s (6.1%)

Profiling