Details

analyze519.0ms (17.1%)

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
40.6%	56.9%	2.5%	9
46%	49.5%	4.4%	10
50.3%	44.9%	4.8%	11
60.3%	30.5%	9.2%	12
62.9%	25.7%	11.4%	13
65.2%	23.2%	11.7%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.1s (37.2%)

Results

958.0ms	8256×	body	128	valid
121.0ms	1017×	body	128	invalid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify19.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
608×	`associate-/l*_binary64`
410×	`fma-neg_binary64`
310×	`div-sub_binary64`
285×	`associate-/r/_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	17
2	55	15
3	142	15
4	341	14
5	759	11
6	2089	11

Stop Event

1×	node limit

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(fma.f64 (/.f64 4 y) (-.f64 x z) 2)
▶	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

Compiler

Compiled 78 to 57 computations (26.9% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
✓	0.0b	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)

series29.0ms (1%)

Counts

2 → 72

Calls

2 calls:

15.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
14.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)

rewrite56.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

261×	`expm1-udef_binary64`
261×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
142×	`log1p-expm1-u_binary64`
142×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	296	31
2	4207	31

Stop Event

1×	node limit

Counts

2 → 75

Calls

2 calls:

55.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
55.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

559×	`times-frac_binary64`
532×	`associate-/r*_binary64`
474×	`fma-neg_binary64`
470×	`associate-/l*_binary64`
203×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	824
1	91	824
2	172	711
3	305	706
4	599	706
5	1497	706

Stop Event

1×	node limit

Counts

147 → 97

prune68.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	2	99

Error

Counts

99 → 2

Alt Table

Status	Error	Program
	24.3b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1) 3))
▶	0.0b	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 2) (.f64 4 (/.f64 z y)))

Compiler

Compiled 1777 to 1245 computations (29.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 2) (.f64 4 (/.f64 z y)))
✓	0.0b	(*.f64 4 (/.f64 x y))
✓	0.0b	(*.f64 4 (/.f64 z y))

series29.0ms (1%)

Counts

3 → 27

Calls

3 calls:

16.0ms	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 2) (.f64 4 (/.f64 z y)))
7.0ms	(*.f64 4 (/.f64 z y))
6.0ms	(*.f64 4 (/.f64 x y))

rewrite58.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
241×	`fma-neg_binary64`
139×	`add-sqr-sqrt_binary64`
135×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	280	31
2	3964	31

Stop Event

1×	node limit

Counts

3 → 99

Calls

3 calls:

56.0ms	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 2) (.f64 4 (/.f64 z y)))
56.0ms	(*.f64 4 (/.f64 x y))
56.0ms	(*.f64 4 (/.f64 z y))

simplify59.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-neg_binary64`
499×	`fma-def_binary64`
301×	`cancel-sign-sub-inv_binary64`
119×	`distribute-rgt-in_binary64`
86×	`div-sub_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	292
1	45	292
2	90	290
3	155	254
4	281	254
5	473	254
6	786	254
7	1199	254
8	1772	254
9	2700	254
10	3288	254
11	3334	254
12	3348	254
13	3353	254
14	3357	254

Stop Event

1×

saturated

Counts

126 → 112

prune70.0ms (2.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	112	2	114

Error

Counts

114 → 2

Alt Table

Status	Error	Program
▶	24.3b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1) 3))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 2) (.f64 4 (/.f64 z y)))

Compiler

Compiled 2115 to 1324 computations (37.4% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1)
✓	0.0b	(/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)
✓	0.2b	(pow.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1) 3)
✓	22.9b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1) 3))

series82.0ms (2.7%)

Counts

4 → 144

Calls

4 calls:

37.0ms	(pow.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1) 3)
17.0ms	(cbrt.f64 (pow.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1) 3))
16.0ms	(+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1)
11.0ms	(/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)

rewrite110.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`prod-diff_binary64`
289×	`egg-rr`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`
145×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	327	59
2	4043	59

Stop Event

1×	node limit

Counts

4 → 289

Calls

4 calls:

102.0ms	(+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1)
102.0ms	(/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)
101.0ms	(pow.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1) 3)
101.0ms	(cbrt.f64 (pow.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1) 3))

simplify68.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

555×	`fma-def_binary64`
457×	`times-frac_binary64`
339×	`associate-/l*_binary64`
329×	`cancel-sign-sub-inv_binary64`
250×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	3475
1	479	3453
2	1704	3060

Stop Event

1×	node limit

Counts

433 → 317

prune324.0ms (10.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	317	0	317
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	317	2	319

Error

Counts

319 → 2

Alt Table

Status	Error	Program
✓	24.3b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (fma.f64 y 1/4 x) z) y)) 1) 3))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 2) (.f64 4 (/.f64 z y)))

Compiler

Compiled 12459 to 7032 computations (43.6% saved)

regimes292.0ms (9.7%)

Accuracy

Total 0.0b remaining (84%)

Threshold costs 0.0b (84%)

Counts

61 → 1

Compiler

Compiled 4008 to 3142 computations (21.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	14	17

Stop Event

1×

saturated

end50.0ms (1.7%)

Compiler: Compiled 64 to 48 computations (25% saved)

Details

analyze519.0ms (17.1%)

sample1.1s (37.2%)

simplify19.0ms (0.6%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series29.0ms (1%)

rewrite56.0ms (1.9%)

simplify36.0ms (1.2%)

prune68.0ms (2.2%)

localize7.0ms (0.2%)

series29.0ms (1%)

rewrite58.0ms (1.9%)

simplify59.0ms (1.9%)

prune70.0ms (2.3%)

localize11.0ms (0.4%)

series82.0ms (2.7%)

rewrite110.0ms (3.6%)

simplify68.0ms (2.2%)

prune324.0ms (10.7%)

regimes292.0ms (9.7%)

simplify3.0ms (0.1%)

end50.0ms (1.7%)

Profiling