Details

analyze91.0ms (3.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample740.0ms (28.9%)

Results

711.0ms	8256×	body	128	valid
17.0ms	196×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess18.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

28×	`associate-l_binary64`
25×	`associate-r_binary64`
12×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	24	20
2	52	20
3	88	20
4	88	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

13×	`associate-l_binary64`
11×	`associate-r_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	14	10
2	29	10
3	46	10
4	47	10

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 (*.f64 x 3) y) y)
	8.4b	(.f64 x (.f64 3 (*.f64 y y)))

Compiler

Compiled 52 to 34 computations (34.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (*.f64 x 3) y) y)
✓	0.2b	(.f64 (.f64 x 3) y)

series15.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

2.0ms	(.f64 (.f64 x 3) y)	x	0
2.0ms	(.f64 (.f64 (*.f64 x 3) y) y)	x	0
2.0ms	(.f64 (.f64 (*.f64 x 3) y) y)	x	-inf
2.0ms	(.f64 (.f64 (*.f64 x 3) y) y)	x	inf
1.0ms	(.f64 (.f64 (*.f64 x 3) y) y)	y	-inf

rewrite37.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

608×	`log1p-expm1-u_binary64`
608×	`expm1-log1p-u_binary64`
377×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	142	17
2	1683	17

Stop Event

1×	node limit

Counts

2 → 36

simplify80.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

599×	`sqr-pow_binary64`
404×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
295×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	408
1	23	408
2	45	408
3	84	408
4	235	408
5	835	408
6	1081	408
7	1495	408
8	1595	408
9	1728	408
10	1897	408
11	2142	408
12	2455	408
13	2825	408
14	3284	408
15	3867	408
16	4575	408

Stop Event

1×	node limit

Counts

84 → 40

prune30.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	36	6	42

Error

0.0b

Counts

42 → 6

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 3 (*.f64 y x)) y)
✓	0.2b	(.f64 (.f64 (*.f64 x 3) y) y)
	0.3b	(.f64 3 (.f64 y (*.f64 y x)))
	8.4b	(.f64 x (.f64 3 (*.f64 y y)))
	30.9b	(cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 x (*.f64 3 y)) 3)))
	33.5b	(pow.f64 (.f64 (sqrt.f64 (.f64 x 3)) y) 2)

Compiler

Compiled 561 to 385 computations (31.4% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 3 (*.f64 y x)) y)
✓	0.3b	(.f64 3 (.f64 y x))

series16.0ms (0.6%)

Counts

2 → 24

Calls

12 calls:

3.0ms	(.f64 3 (.f64 y x))	x	inf
2.0ms	(.f64 (.f64 3 (*.f64 y x)) y)	x	0
2.0ms	(.f64 (.f64 3 (*.f64 y x)) y)	x	-inf
2.0ms	(.f64 (.f64 3 (*.f64 y x)) y)	x	inf
1.0ms	(.f64 (.f64 3 (*.f64 y x)) y)	y	inf

rewrite39.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

623×	`log1p-expm1-u_binary64`
623×	`expm1-log1p-u_binary64`
386×	`log-prod_binary64`
128×	`expm1-udef_binary64`
128×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	143	17
2	1718	17

Stop Event

1×	node limit

Counts

2 → 34

simplify76.0ms (3%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
402×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
256×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	240
1	17	240
2	37	240
3	82	240
4	216	240
5	710	240
6	966	240
7	1380	240
8	1480	240
9	1613	240
10	1782	240
11	2025	240
12	2338	240
13	2710	240
14	3169	240
15	3748	240
16	4458	240

Stop Event

1×	node limit

Counts

58 → 36

prune26.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	36	6	42

Error

0.0b

Counts

42 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 3 (*.f64 y x)) y)
✓	0.2b	(.f64 (.f64 (*.f64 x 3) y) y)
▶	0.3b	(.f64 3 (.f64 y (*.f64 y x)))
	8.4b	(.f64 x (.f64 3 (*.f64 y y)))
	0.9b	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y (*.f64 y x)))) 3)
	30.9b	(cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 x (*.f64 3 y)) 3)))

Compiler

Compiled 520 to 319 computations (38.7% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 y (.f64 y x))
✓	0.2b	(.f64 3 (.f64 y (*.f64 y x)))

series21.0ms (0.8%)

Counts

2 → 48

Calls

12 calls:

6.0ms	(.f64 3 (.f64 y (*.f64 y x)))	x	inf
2.0ms	(.f64 y (.f64 y x))	x	-inf
2.0ms	(.f64 3 (.f64 y (*.f64 y x)))	x	-inf
2.0ms	(.f64 3 (.f64 y (*.f64 y x)))	x	0
1.0ms	(.f64 y (.f64 y x))	x	inf

rewrite36.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`log1p-expm1-u_binary64`
610×	`expm1-log1p-u_binary64`
379×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	142	17
2	1687	17

Stop Event

1×	node limit

Counts

2 → 34

simplify84.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
402×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
256×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	408
1	17	408
2	37	408
3	82	408
4	216	408
5	710	408
6	966	408
7	1380	408
8	1480	408
9	1613	408
10	1782	408
11	2025	408
12	2338	408
13	2710	408
14	3169	408
15	3748	408
16	4458	408

Stop Event

1×	node limit

Counts

82 → 38

prune25.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	38	6	44

Error

0.0b

Counts

44 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 3 (*.f64 y x)) y)
✓	0.2b	(.f64 (.f64 (*.f64 x 3) y) y)
✓	0.3b	(.f64 3 (.f64 y (*.f64 y x)))
	8.4b	(.f64 x (.f64 3 (*.f64 y y)))
▶	0.9b	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y (*.f64 y x)))) 3)
	30.9b	(cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 x (*.f64 3 y)) 3)))

Compiler

Compiled 522 to 274 computations (47.5% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 y (.f64 y x))
	0.2b	(.f64 3 (.f64 y (*.f64 y x)))
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y (*.f64 y x)))) 3)
✓	22.1b	(cbrt.f64 (.f64 3 (.f64 y (*.f64 y x))))

series894.0ms (34.9%)

Counts

2 → 48

Calls

12 calls:

104.0ms	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y (*.f64 y x)))) 3)	x	-inf
95.0ms	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y (*.f64 y x)))) 3)	x	inf
89.0ms	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y (*.f64 y x)))) 3)	x	0
87.0ms	(cbrt.f64 (.f64 3 (.f64 y (*.f64 y x))))	x	0
85.0ms	(cbrt.f64 (.f64 3 (.f64 y (*.f64 y x))))	x	-inf

rewrite43.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

718×	`log1p-expm1-u_binary64`
718×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
90×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	183	22
2	2031	22

Stop Event

1×	node limit

Counts

2 → 67

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

357×	`associate-l_binary64`
302×	`associate-r_binary64`
281×	`fma-neg_binary64`
271×	`exp-sum_binary64`
245×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	1056
1	159	976
2	379	920
3	1001	600
4	3777	600

Stop Event

1×	node limit

Counts

115 → 83

prune79.0ms (3.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	120	7	127

Error

0.0b

Counts

127 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 3 (*.f64 y x)) y)
✓	0.2b	(.f64 (.f64 (*.f64 x 3) y) y)
✓	0.3b	(.f64 3 (.f64 y (*.f64 y x)))
	8.4b	(.f64 x (.f64 3 (*.f64 y y)))
	0.2b	(.f64 (.f64 y x) (*.f64 3 y))
✓	0.9b	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y (*.f64 y x)))) 3)
	30.9b	(cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 x (*.f64 3 y)) 3)))

Compiler

Compiled 1787 to 1043 computations (41.6% saved)

regimes57.0ms (2.2%)

Accuracy

Total 0.2b remaining (92.1%)

Threshold costs 0.2b (92.1%)

Counts

12 → 1

Compiler

Compiled 549 to 402 computations (26.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10

Stop Event

1×

saturated

end77.0ms (3%)

Stop Event

1×

fuel

Compiler

Compiled 89 to 62 computations (30.3% saved)

Details

analyze91.0ms (3.6%)

sample740.0ms (28.9%)

preprocess18.0ms (0.7%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series15.0ms (0.6%)

rewrite37.0ms (1.4%)

simplify80.0ms (3.1%)

prune30.0ms (1.2%)

localize4.0ms (0.2%)

series16.0ms (0.6%)

rewrite39.0ms (1.5%)

simplify76.0ms (3%)

prune26.0ms (1%)

localize4.0ms (0.2%)

series21.0ms (0.8%)

rewrite36.0ms (1.4%)

simplify84.0ms (3.3%)

prune25.0ms (1%)

localize7.0ms (0.3%)

series894.0ms (34.9%)

rewrite43.0ms (1.7%)

simplify48.0ms (1.9%)

prune79.0ms (3.1%)

regimes57.0ms (2.2%)

simplify2.0ms (0.1%)

end77.0ms (3%)

Profiling