Details

analyze4.0ms (0.2%)

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)

sample733.0ms (45.5%)

Results

706.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify8.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 x (log.f64 x))

Compiler

Compiled 15 to 9 computations (40% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (log.f64 x))

series32.0ms (2%)

Counts

1 → 12

Calls

1 calls:

32.0ms

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

rewrite29.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

319×	`log1p-expm1-u_binary64`
319×	`expm1-log1p-u_binary64`
286×	`add-log-exp_binary64`
285×	`add-exp-log_binary64`
266×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	76	6
2	895	6

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

29.0ms

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

simplify41.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1161×	`fma-neg_binary64`
786×	`fma-def_binary64`
322×	`unsub-neg_binary64`
233×	`distribute-rgt-in_binary64`
168×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	72
1	30	72
2	57	72
3	131	72
4	357	72
5	1022	72
6	2544	72
7	3677	72
8	4075	72
9	4166	72
10	4176	72
11	4339	72

Stop Event

1×	node limit

Counts

33 → 25

prune13.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Error

0.1b

Counts

26 → 4

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 x (log.f64 x))
	40.4b	(cbrt.f64 (pow.f64 (*.f64 x (log.f64 x)) 3))
	31.6b	(pow.f64 (sqrt.f64 (*.f64 x (log.f64 x))) 2)
▶	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)

Compiler

Compiled 254 to 125 computations (50.8% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(*.f64 x (log.f64 x))
✓	0.7b	(cbrt.f64 (*.f64 x (log.f64 x)))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)

series40.0ms (2.5%)

Counts

2 → 0

Calls

2 calls:

25.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
14.0ms	(cbrt.f64 (*.f64 x (log.f64 x)))

rewrite41.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

493×	`log1p-expm1-u_binary64`
493×	`expm1-log1p-u_binary64`
485×	`unpow-prod-down_binary64`
269×	`log-prod_binary64`
140×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	138	14
2	1413	14

Stop Event

1×	node limit

Counts

2 → 110

Calls

2 calls:

39.0ms	(cbrt.f64 (*.f64 x (log.f64 x)))
38.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)

simplify9.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

110 → 110

prune59.0ms (3.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	128	7	135
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	129	10	139

Error

0.0b

Counts

139 → 10

Alt Table

Status	Error	Program
	3.6b	(pow.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 x))))) 2) 3) (cbrt.f64 (cbrt.f64 (*.f64 x (log.f64 x))))) 3)
▶	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
✓	0.2b	(*.f64 x (log.f64 x))
	40.4b	(cbrt.f64 (pow.f64 (*.f64 x (log.f64 x)) 3))
	1.3b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
✓	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
	31.5b	(.f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) x))
	1.3b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 x)))
	1.3b	(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (log.f64 x)) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2)))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2) (.f64 (cbrt.f64 (log.f64 x)) x))

Compiler

Compiled 1989 to 889 computations (55.3% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
✓	0.4b	(*.f64 (sqrt.f64 x) (log.f64 x))

series30.0ms (1.8%)

Counts

2 → 8

Calls

2 calls:

20.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
10.0ms	(*.f64 (sqrt.f64 x) (log.f64 x))

rewrite32.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

485×	`log1p-expm1-u_binary64`
485×	`expm1-log1p-u_binary64`
457×	`unpow-prod-down_binary64`
305×	`log-prod_binary64`
143×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	117	14
2	1389	14

Stop Event

1×	node limit

Counts

2 → 34

Calls

2 calls:

32.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
31.0ms	(*.f64 (sqrt.f64 x) (log.f64 x))

simplify50.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1640×	`fma-neg_binary64`
564×	`fma-def_binary64`
213×	`distribute-rgt-in_binary64`
196×	`unsub-neg_binary64`
175×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	21	48
2	36	48
3	75	48
4	140	48
5	199	48
6	224	48
7	290	48
8	676	48
9	1176	48
10	2498	48
11	3219	48
12	3492	48
13	3558	48
14	3580	48
15	3585	48

Stop Event

1×	node limit

Counts

42 → 37

prune22.0ms (1.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	36	11	47

Error

0.0b

Counts

47 → 11

Alt Table

Status	Error	Program
	3.6b	(pow.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (.f64 x (log.f64 x))))) 2) 3) (cbrt.f64 (cbrt.f64 (*.f64 x (log.f64 x))))) 3)
✓	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	22.4b	(.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (log.f64 x)) 3)))
✓	0.2b	(*.f64 x (log.f64 x))
	40.4b	(cbrt.f64 (pow.f64 (*.f64 x (log.f64 x)) 3))
	1.3b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
✓	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
	31.5b	(.f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) x))
▶	1.3b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 x)))
	1.3b	(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (log.f64 x)) (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 2)))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2) (.f64 (cbrt.f64 (log.f64 x)) x))

Compiler

Compiled 571 to 275 computations (51.8% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 x)))
✓	0.3b	(*.f64 (cbrt.f64 x) (log.f64 x))
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
✓	0.6b	(cbrt.f64 x)

series122.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 x)))
22.0ms	(*.f64 (cbrt.f64 x) (log.f64 x))
22.0ms	(pow.f64 (cbrt.f64 x) 2)
9.0ms	(cbrt.f64 x)

rewrite47.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

605×	`log1p-expm1-u_binary64`
605×	`expm1-log1p-u_binary64`
355×	`log-prod_binary64`
125×	`expm1-udef_binary64`
125×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	158	23
2	1777	23

Stop Event

1×	node limit

Counts

4 → 84

Calls

4 calls:

46.0ms	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 x)))
46.0ms	(*.f64 (cbrt.f64 x) (log.f64 x))
46.0ms	(pow.f64 (cbrt.f64 x) 2)
46.0ms	(cbrt.f64 x)

simplify46.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1161×	`fma-neg_binary64`
786×	`fma-def_binary64`
322×	`unsub-neg_binary64`
233×	`distribute-rgt-in_binary64`
168×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	72
1	30	72
2	57	72
3	131	72
4	357	72
5	1022	72
6	2544	72
7	3677	72
8	4075	72
9	4166	72
10	4176	72
11	4339	72

Stop Event

1×	node limit

Counts

96 → 88

prune48.0ms (3%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	4	7
Picked	0	1	1
Done	0	3	3
Total	114	11	125

Error

0.0b

Counts

125 → 11

Alt Table

Status	Error	Program
	22.4b	(.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (log.f64 x)) 3)))
✓	0.2b	(*.f64 x (log.f64 x))
	40.4b	(cbrt.f64 (pow.f64 (*.f64 x (log.f64 x)) 3))
	1.3b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
✓	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
✓	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	31.5b	(.f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) x))
✓	1.3b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 x)))
	2.1b	(.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (.f64 x (pow.f64 (log.f64 x) 3))))
	15.5b	(.f64 (sqrt.f64 (.f64 x (cbrt.f64 x))) (*.f64 (cbrt.f64 x) (log.f64 x)))
	1.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 x))) (.f64 (cbrt.f64 x) (log.f64 x)))

Compiler

Compiled 1598 to 703 computations (56% saved)

regimes67.0ms (4.2%)

Accuracy

Total 0.2b remaining (79.7%)

Threshold costs 0.2b (79.7%)

Counts

33 → 1

Compiler

Compiled 868 to 556 computations (35.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6

Stop Event

1×

saturated

end114.0ms (7.1%)

Compiler: Compiled 129 to 80 computations (38% saved)

Details

analyze4.0ms (0.2%)

sample733.0ms (45.5%)

simplify8.0ms (0.5%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series32.0ms (2%)

rewrite29.0ms (1.8%)

simplify41.0ms (2.5%)

prune13.0ms (0.8%)

localize6.0ms (0.3%)

series40.0ms (2.5%)

rewrite41.0ms (2.5%)

simplify9.0ms (0.6%)

prune59.0ms (3.7%)

localize5.0ms (0.3%)

series30.0ms (1.8%)

rewrite32.0ms (2%)

simplify50.0ms (3.1%)

prune22.0ms (1.4%)

localize7.0ms (0.4%)

series122.0ms (7.6%)

rewrite47.0ms (2.9%)

simplify46.0ms (2.9%)

prune48.0ms (3%)

regimes67.0ms (4.2%)

simplify2.0ms (0.1%)

end114.0ms (7.1%)

Profiling