Details

analyze24.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	50%	25%	3
37.5%	25%	37.5%	4
43.7%	12.5%	43.8%	5
46.9%	6.2%	46.9%	6
48.4%	3.1%	48.5%	7
49.2%	1.6%	49.2%	8
49.6%	0.8%	49.6%	9
49.6%	0.4%	50%	10
49.7%	0.2%	50.1%	11
49.7%	0.1%	50.2%	12
49.7%	0%	50.2%	13
49.7%	0%	50.2%	14

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample15.0ms (0.2%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6
2	5	6

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.3b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 15 to 9 computations (40% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x (log.f64 x))

series29.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

29.0ms

(*.f64 x (log.f64 x))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
4×	`associate-r_binary64`

Counts

1 → 27

Calls

1 calls:

3.0ms

(*.f64 x (log.f64 x))

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1025×	`fma-def_binary64`
501×	`sub-neg_binary64`
395×	`div-sub_binary64`
347×	`fma-neg_binary64`
343×	`distribute-rgt-neg-out_binary64`

Counts

39 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	359
1	96	325
2	258	325
3	452	325
4	1256	325
5	2761	325
6	4564	325
7	5019	325

prune22.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	28	5	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	6	34

Error

0.0b

Counts

34 → 6

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
▶	0.4b	(+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (*.f64 x (log.f64 (cbrt.f64 x))))
	32.8b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (log.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (log.f64 x))))
	41.2b	(cbrt.f64 (.f64 (.f64 (.f64 x (log.f64 x)) (.f64 x (log.f64 x))) (*.f64 x (log.f64 x))))
✓	0.3b	(*.f64 x (log.f64 x))
	32.7b	(.f64 (.f64 x (sqrt.f64 (log.f64 x))) (sqrt.f64 (log.f64 x)))

Compiler

Compiled 435 to 164 computations (62.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.0s (25.9%)

Counts

4 → 48

Calls

4 calls:

686.0ms	(+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (*.f64 x (log.f64 (cbrt.f64 x))))
676.0ms	(*.f64 x (log.f64 (cbrt.f64 x)))
643.0ms	(.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2))
30.0ms	(cbrt.f64 x)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`log-prod_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
15×	`cbrt-prod_binary64`

Counts

4 → 94

Calls

4 calls:

10.0ms	(+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (*.f64 x (log.f64 (cbrt.f64 x))))
4.0ms	(.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2))
4.0ms	(*.f64 x (log.f64 (cbrt.f64 x)))
1.0ms	(cbrt.f64 x)

simplify109.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-def_binary64`
553×	`fma-neg_binary64`
539×	`*-commutative_binary64`
343×	`distribute-rgt-in_binary64`
313×	`distribute-lft-in_binary64`

Counts

142 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1944
1	331	1653
2	1351	1504
3	4065	1496
4	4920	1496
5	4931	1496

prune117.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	166	6	172

Error

Counts

172 → 6

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 x (log.f64 x))
	0.4b	(+.f64 (.f64 x (fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x))))) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
▶	0.3b	(+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (+.f64 (.f64 x (.f64 2 (log.f64 (cbrt.f64 (cbrt.f64 x))))) (*.f64 x (log.f64 (cbrt.f64 (cbrt.f64 x))))))
	0.4b	(+.f64 (+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x)) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
	0.4b	(+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 (cbrt.f64 x)))))
	41.2b	(cbrt.f64 (.f64 (.f64 (.f64 x (log.f64 x)) (.f64 x (log.f64 x))) (*.f64 x (log.f64 x))))

Compiler

Compiled 3169 to 1260 computations (60.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series2.9s (36.9%)

Counts

3 → 36

Calls

3 calls:

1.6s

(+.f64 (*.f64 x (*.f64 (log.f64 (cbrt.f64 x)) 2)) (+.f64 (*.f64 x (*.f64 2 (log.f64 (cbrt.f64 (cbrt.f64 x))))) (*.f64 x (log.f64 (cbrt.f64 (cbrt.f64 x))))))

1.0s

(+.f64 (*.f64 x (*.f64 2 (log.f64 (cbrt.f64 (cbrt.f64 x))))) (*.f64 x (log.f64 (cbrt.f64 (cbrt.f64 x)))))

280.0ms

(cbrt.f64 (cbrt.f64 x))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
54×	`log-prod_binary64`
45×	`distribute-lft-in_binary64`
45×	`distribute-rgt-in_binary64`
36×	`associate-+l+_binary64`

Counts

3 → 102

Calls

3 calls:

10.0ms

(+.f64 (*.f64 x (*.f64 (log.f64 (cbrt.f64 x)) 2)) (+.f64 (*.f64 x (*.f64 2 (log.f64 (cbrt.f64 (cbrt.f64 x))))) (*.f64 x (log.f64 (cbrt.f64 (cbrt.f64 x))))))

9.0ms

(+.f64 (*.f64 x (*.f64 2 (log.f64 (cbrt.f64 (cbrt.f64 x))))) (*.f64 x (log.f64 (cbrt.f64 (cbrt.f64 x)))))

1.0ms

(cbrt.f64 (cbrt.f64 x))

simplify125.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

482×	`distribute-rgt-in_binary64`
435×	`distribute-lft-in_binary64`
284×	`cancel-sign-sub-inv_binary64`
228×	`fma-def_binary64`
198×	`fma-neg_binary64`

Counts

138 → 187

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	205	2837
1	470	2457
2	1583	2040
3	4363	1952
4	4822	1940
5	4929	1940

prune221.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	263	6	269

Error

Counts

269 → 6

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 x (log.f64 x))
▶	0.4b	(+.f64 (.f64 x (fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x))))) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
✓	0.3b	(+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (+.f64 (.f64 x (.f64 2 (log.f64 (cbrt.f64 (cbrt.f64 x))))) (*.f64 x (log.f64 (cbrt.f64 (cbrt.f64 x))))))
	0.4b	(+.f64 (+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x)) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
	0.4b	(+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 (cbrt.f64 x)))))
	41.2b	(cbrt.f64 (.f64 (.f64 (.f64 x (log.f64 x)) (.f64 x (log.f64 x))) (*.f64 x (log.f64 x))))

Compiler

Compiled 7757 to 3136 computations (59.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (.f64 x (fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x))))) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
✓	0.3b	(*.f64 x (fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x)))))
✓	0.3b	(fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x))))
✓	0.6b	(cbrt.f64 (sqrt.f64 x))

series1.0s (13.2%)

Counts

4 → 32

Calls

4 calls:

512.0ms	(+.f64 (.f64 x (fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x))))) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
271.0ms	(*.f64 x (fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x)))))
235.0ms	(fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x))))
19.0ms	(cbrt.f64 (sqrt.f64 x))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cbrt-prod_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 64

Calls

4 calls:

3.0ms	(+.f64 (.f64 x (fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x))))) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
3.0ms	(*.f64 x (fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x)))))
1.0ms	(cbrt.f64 (sqrt.f64 x))
0.0ms	(fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x))))

simplify118.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

446×	`associate-+l+_binary64`
407×	`associate-l_binary64`
343×	`fma-def_binary64`
316×	`associate-r_binary64`
316×	`distribute-rgt-out_binary64`

Counts

96 → 90

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	1704
1	250	1486
2	760	1352
3	2280	1312
4	4599	1300
5	4985	1300
6	4891	1300

prune82.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	110	5	115

Error

Counts

115 → 5

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 x (.f64 (log.f64 x) 5/6)) (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
✓	0.3b	(+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (+.f64 (.f64 x (.f64 2 (log.f64 (cbrt.f64 (cbrt.f64 x))))) (*.f64 x (log.f64 (cbrt.f64 (cbrt.f64 x))))))
	0.4b	(+.f64 (+.f64 (.f64 x (.f64 (log.f64 (cbrt.f64 x)) 2)) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x)) (.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
	0.3b	(fma.f64 x (fma.f64 2/3 (log.f64 x) (log.f64 (cbrt.f64 (sqrt.f64 x)))) (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) x))
✓	0.3b	(*.f64 x (log.f64 x))

Compiler

Compiled 2603 to 911 computations (65% saved)

regimes284.0ms (3.6%)

Accuracy

Total 0.2b remaining (91.2%)

Threshold costs 0.2b (91.2%)

Counts

116 → 1

Compiler

Compiled 4192 to 2617 computations (37.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	18	36
2	18	36

end1.0ms (0%)

Compiler: Compiled 23 to 13 computations (43.5% saved)

sample563.0ms (7.2%)

Algorithm

1×

intervals

Results

306.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 112 to 66 computations (41.1% saved)

Details

analyze24.0ms (0.3%)

sample15.0ms (0.2%)

simplify8.0ms (0.1%)

prune1.0ms (0%)

localize3.0ms (0%)

series29.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify67.0ms (0.9%)

prune22.0ms (0.3%)

localize8.0ms (0.1%)

series2.0s (25.9%)

rewrite24.0ms (0.3%)

simplify109.0ms (1.4%)

prune117.0ms (1.5%)

localize13.0ms (0.2%)

series2.9s (36.9%)

rewrite31.0ms (0.4%)

simplify125.0ms (1.6%)

prune221.0ms (2.8%)

localize13.0ms (0.2%)

series1.0s (13.2%)

rewrite10.0ms (0.1%)

simplify118.0ms (1.5%)

prune82.0ms (1%)

regimes284.0ms (3.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample563.0ms (7.2%)

Profiling