Details

analyze466.0ms (9.9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
23.4%	71%	5.6%	9
35.1%	56.2%	8.7%	10
41%	49.9%	9.1%	11
45.1%	41.2%	13.7%	12
52.6%	31.2%	16.2%	13
56.3%	27.3%	16.4%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample890.0ms (18.9%)

Results

775.0ms	8256×	body	128	valid
89.0ms	978×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`
1×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	12	8
3	14	8
4	15	8
5	15	8

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
▶	0.1b	(fma.f64 y (/.f64 y z) x)
	8.1b	(+.f64 x (/.f64 (*.f64 y y) z))

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (/.f64 y z) x)

series13.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(fma.f64 y (/.f64 y z) x)

rewrite39.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

612×	`log1p-expm1-u_binary64`
612×	`expm1-log1p-u_binary64`
323×	`log-prod_binary64`
119×	`expm1-udef_binary64`
119×	`log1p-udef_binary64`

Counts

1 → 29

Calls

1 calls:

39.0ms

(fma.f64 y (/.f64 y z) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	8
2	1577	8
3	5040	8
0	0	0
1	0	0

simplify131.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

610×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
428×	`*-commutative_binary64`
423×	`associate-*r/_binary64`
405×	`associate-/r/_binary64`

Counts

65 → 34

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	303
1	14	303
2	22	303
3	39	249
4	84	249
5	216	249
6	722	249
7	2100	249
8	2712	249
9	2884	249
10	3043	249
11	3141	249
12	3306	249
13	3580	249
14	4056	249
15	4615	249
16	4916	249
17	4774	249

prune16.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	30	6	36

Error

0.0b

Counts

36 → 6

Alt Table

Status	Error	Program
	26.8b	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 y z) x)))
	8.1b	(+.f64 x (/.f64 (*.f64 y y) z))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)
▶	1.3b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))

Compiler

Compiled 516 to 184 computations (64.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (/.f64 y z) x)
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))
✓	0.6b	(cbrt.f64 (fma.f64 y (/.f64 y z) x))
✓	0.6b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2)

series159.0ms (3.4%)

Counts

3 → 108

Calls

3 calls:

89.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2)
59.0ms	(cbrt.f64 (fma.f64 y (/.f64 y z) x))
12.0ms	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))

rewrite51.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

802×	`log1p-expm1-u_binary64`
802×	`expm1-log1p-u_binary64`
91×	`add-sqr-sqrt_binary64`
87×	`prod-diff_binary64`
85×	`add-cube-cbrt_binary64`

Counts

3 → 60

Calls

3 calls:

50.0ms	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))
50.0ms	(cbrt.f64 (fma.f64 y (/.f64 y z) x))
50.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	187	29
2	2088	29
3	5031	29
0	0	0
1	0	0

simplify131.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

751×	`fma-def_binary64`
311×	`unswap-sqr_binary64`
291×	`cancel-sign-sub-inv_binary64`
269×	`associate-r_binary64`
202×	`neg-mul-1_binary64`

Counts

168 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	254	4465
1	840	4245
2	2752	3870
3	4654	3422
4	4944	3422

prune162.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	285	1	286
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	285	7	292

Error

0.0b

Counts

292 → 7

Alt Table

Status	Error	Program
	26.8b	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 y z) x)))
	8.1b	(+.f64 x (/.f64 (*.f64 y y) z))
	1.7b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))) 3) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)) 2)
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)
✓	1.3b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))

Compiler

Compiled 9457 to 4664 computations (50.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (/.f64 y z) x)
	0.6b	(cbrt.f64 (fma.f64 y (/.f64 y z) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)

series1.7s (35.2%)

Counts

1 → 36

Calls

1 calls:

1.7s	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)

rewrite44.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

780×	`log1p-expm1-u_binary64`
780×	`expm1-log1p-u_binary64`
149×	`log1p-udef_binary64`
87×	`prod-diff_binary64`
84×	`add-sqr-sqrt_binary64`

Counts

1 → 27

Calls

1 calls:

43.0ms

(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	8
1	172	8
2	2023	8
3	5115	8
0	0	0
1	0	0

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

805×	`associate-/r*_binary64`
479×	`associate-/l/_binary64`
453×	`associate-/r/_binary64`
332×	`fma-def_binary64`
181×	`associate-/l*_binary64`

Counts

63 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	950
1	142	884
2	412	764
3	1747	405
4	5373	405

prune76.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	143	8	151

Error

0.0b

Counts

151 → 8

Alt Table

Status	Error	Program
	26.8b	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 y z) x)))
	8.1b	(+.f64 x (/.f64 (*.f64 y y) z))
▶	1.7b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))) 3) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))
	45.9b	(/.f64 (pow.f64 (/.f64 -1 y) -2) z)
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)) 2)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)
✓	1.3b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))

Compiler

Compiled 3334 to 1897 computations (43.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
	0.6b	(cbrt.f64 (fma.f64 y (/.f64 y z) x))
	0.6b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2)
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))) 3)

series171.0ms (3.6%)

Counts

2 → 72

Calls

2 calls:

120.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))) 3)
51.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

rewrite48.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

835×	`log1p-expm1-u_binary64`
835×	`expm1-log1p-u_binary64`
91×	`add-sqr-sqrt_binary64`
87×	`prod-diff_binary64`
86×	`add-cbrt-cube_binary64`

Counts

2 → 47

Calls

2 calls:

47.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
47.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	188	21
2	2179	21
3	5213	21
0	0	0
1	0	0

simplify115.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-def_binary64`
315×	`unswap-sqr_binary64`
295×	`cancel-sign-sub-inv_binary64`
287×	`associate-r_binary64`
177×	`times-frac_binary64`

Counts

119 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	254	4198
1	854	3976
2	3003	3756
3	4871	3636
4	4905	3636

prune259.0ms (5.5%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	328	0	328
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	328	8	336

Error

0.0b

Counts

336 → 8

Alt Table

Status	Error	Program
	26.8b	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 y z) x)))
	8.1b	(+.f64 x (/.f64 (*.f64 y y) z))
✓	1.7b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))) 3) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))
	45.9b	(/.f64 (pow.f64 (/.f64 -1 y) -2) z)
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)) 2)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)
✓	1.3b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 2))

Compiler

Compiled 13984 to 7870 computations (43.7% saved)

regimes118.0ms (2.5%)

Accuracy

Total 0.1b remaining (71.7%)

Threshold costs 0.1b (71.7%)

Counts

19 → 1

Compiler

Compiled 1680 to 1064 computations (36.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end84.0ms (1.8%)

Compiler: Compiled 125 to 73 computations (41.6% saved)

Details

analyze466.0ms (9.9%)

sample890.0ms (18.9%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series13.0ms (0.3%)

rewrite39.0ms (0.8%)

simplify131.0ms (2.8%)

prune16.0ms (0.3%)

localize7.0ms (0.2%)

series159.0ms (3.4%)

rewrite51.0ms (1.1%)

simplify131.0ms (2.8%)

prune162.0ms (3.4%)

localize6.0ms (0.1%)

series1.7s (35.2%)

rewrite44.0ms (0.9%)

simplify43.0ms (0.9%)

prune76.0ms (1.6%)

localize12.0ms (0.3%)

series171.0ms (3.6%)

rewrite48.0ms (1%)

simplify115.0ms (2.4%)

prune259.0ms (5.5%)

regimes118.0ms (2.5%)

simplify2.0ms (0%)

end84.0ms (1.8%)

Profiling