Details

analyze76.0ms (3.1%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
25%	37.5%	37.6%	6
31.2%	31.2%	37.6%	7
37.5%	18.7%	43.8%	8
39%	15.6%	45.4%	9
42.1%	9.4%	48.5%	10
42.9%	7.8%	49.3%	11
44.5%	4.7%	50.8%	12
44.9%	3.9%	51.2%	13
45.7%	2.3%	52%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample835.0ms (34.1%)

Results

805.0ms	8256×	body	128	valid
17.0ms	191×	body	128	invalid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess30.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

262×	`fma-neg_binary64`
254×	`fma-def_binary64`
74×	`cancel-sign-sub-inv_binary64`
60×	`sub-neg_binary64`
40×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	26	20
2	65	20
3	130	20
4	285	20
5	593	20
6	977	20
7	1145	20
8	1205	20
9	1217	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 7 computations (30% saved)

simplify14.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

151×	`fma-def_binary64`
131×	`fma-neg_binary64`
46×	`cancel-sign-sub-inv_binary64`
36×	`sub-neg_binary64`
30×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	72	10
4	150	10
5	312	10
6	502	10
7	626	10
8	708	10
9	722	10

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 37 to 24 computations (35.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	0.2b	(*.f64 y (sqrt.f64 x))

series21.0ms (0.8%)

Counts

2 → 15

Calls

12 calls:

7.0ms	(*.f64 y (sqrt.f64 x))	y	-inf
2.0ms	(*.f64 y (sqrt.f64 x))	x	0
2.0ms	(*.f64 y (sqrt.f64 x))	x	-inf
2.0ms	(*.f64 y (sqrt.f64 x))	x	inf
1.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))	x	-inf

rewrite47.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

903×	`log1p-expm1-u_binary64`
903×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`
80×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	175	16
2	2387	16

Stop Event

1×	node limit

Counts

2 → 54

simplify20.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

189×	`fma-def_binary64`
157×	`fma-neg_binary64`
55×	`cancel-sign-sub-inv_binary64`
34×	`associate--r+_binary64`
34×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	113
1	25	113
2	36	113
3	56	113
4	92	113
5	152	113
6	288	113
7	441	113
8	619	113
9	757	113
10	849	113
11	855	113

Stop Event

1×

saturated

Counts

69 → 60

prune53.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	5	61

Error

0.0b

Counts

61 → 5

Alt Table

Status	Error	Program
	16.1b	(fma.f64 (cbrt.f64 (.f64 x (.f64 y y))) (cbrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))
	15.6b	(+.f64 (-.f64 1 x) (cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3)))
	0.5b	(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
	26.8b	(-.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))) (/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))))
▶	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

Compiler

Compiled 996 to 530 computations (46.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

series7.0ms (0.3%)

Counts

1 → 15

Calls

6 calls:

1.0ms	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))	x	0
1.0ms	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))	x	-inf
1.0ms	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))	x	inf
1.0ms	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))	y	-inf
1.0ms	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))	y	inf

rewrite38.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

649×	`log1p-expm1-u_binary64`
649×	`expm1-log1p-u_binary64`
230×	`prod-diff_binary64`
123×	`expm1-udef_binary64`
122×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	144	10
2	1721	10

Stop Event

1×	node limit

Counts

1 → 25

simplify20.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

189×	`fma-def_binary64`
157×	`fma-neg_binary64`
55×	`cancel-sign-sub-inv_binary64`
34×	`associate--r+_binary64`
34×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	113
1	25	113
2	36	113
3	56	113
4	92	113
5	151	113
6	287	113
7	441	113
8	608	113
9	746	113
10	838	113
11	844	113

Stop Event

1×

saturated

Counts

40 → 33

prune32.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	33	5	38

Error

0.0b

Counts

38 → 5

Alt Table

Status	Error	Program
	16.1b	(fma.f64 (cbrt.f64 (.f64 x (.f64 y y))) (cbrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))
	15.6b	(+.f64 (-.f64 1 x) (cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3)))
▶	0.5b	(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
	26.8b	(-.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))) (/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

Compiler

Compiled 498 to 287 computations (42.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
	0.2b	(*.f64 y (sqrt.f64 x))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
✓	3.8b	(cbrt.f64 (*.f64 y (sqrt.f64 x)))

series206.0ms (8.4%)

Counts

3 → 31

Calls

18 calls:

27.0ms	(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))	y	-inf
26.0ms	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)	x	inf
26.0ms	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)	y	-inf
25.0ms	(cbrt.f64 (*.f64 y (sqrt.f64 x)))	x	0
24.0ms	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)	x	0

rewrite59.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`fma-def_binary64`
479×	`log-prod_binary64`
207×	`fma-neg_binary64`
182×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	237	24
2	2904	24

Stop Event

1×	node limit

Counts

3 → 133

simplify79.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

727×	`associate-l_binary64`
498×	`associate-r_binary64`
457×	`*-commutative_binary64`
396×	`sqr-pow_binary64`
252×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	233
1	40	233
2	71	233
3	154	233
4	522	233
5	2516	233
6	2703	233
7	2986	233
8	3344	233
9	3665	233
10	4018	233
11	4601	233
12	4995	233

Stop Event

1×	node limit

Counts

164 → 141

prune122.0ms (5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	153	6	159

Error

0.0b

Counts

159 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (cbrt.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 x)) y) (-.f64 1 x))
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (sqrt.f64 x)) (-.f64 1 x))
✓	0.5b	(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
	26.8b	(-.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))) (/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
▶	0.2b	(fma.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y) (-.f64 1 x))

Compiler

Compiled 2455 to 1183 computations (51.8% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y) (-.f64 1 x))
✓	0.3b	(*.f64 (pow.f64 x 1/4) y)

series262.0ms (10.7%)

Counts

2 → 48

Calls

12 calls:

60.0ms	(*.f64 (pow.f64 x 1/4) y)	y	0
46.0ms	(*.f64 (pow.f64 x 1/4) y)	y	inf
45.0ms	(*.f64 (pow.f64 x 1/4) y)	y	-inf
23.0ms	(fma.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y) (-.f64 1 x))	y	-inf
22.0ms	(fma.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y) (-.f64 1 x))	y	0

rewrite42.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`log1p-expm1-u_binary64`
835×	`expm1-log1p-u_binary64`
223×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
88×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	192	19
2	2263	19

Stop Event

1×	node limit

Counts

2 → 40

simplify36.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-l_binary64`
442×	`associate-r_binary64`
375×	`fma-neg_binary64`
198×	`times-frac_binary64`
184×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	377
1	62	377
2	119	377
3	324	377
4	993	377
5	3936	377

Stop Event

1×	node limit

Counts

88 → 52

prune65.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	51	7	58

Error

0.0b

Counts

58 → 7

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (sqrt.f64 x)) (-.f64 1 x))
	22.5b	(.f64 (cbrt.f64 (+.f64 (-.f64 1 x) (.f64 (sqrt.f64 x) y))) (cbrt.f64 (pow.f64 (+.f64 (-.f64 1 x) (*.f64 (sqrt.f64 x) y)) 2)))
	0.3b	(fma.f64 (cbrt.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 x)) y) (-.f64 1 x))
✓	0.5b	(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
	26.8b	(-.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))) (/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
✓	0.2b	(fma.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y) (-.f64 1 x))

Compiler

Compiled 769 to 467 computations (39.3% saved)

regimes253.0ms (10.3%)

Accuracy

Total 0.1b remaining (77.3%)

Threshold costs 0.1b (77.3%)

Counts

82 → 1

Compiler

Compiled 3413 to 2419 computations (29.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	15	10
3	17	10
4	18	10

Stop Event

1×

saturated

end99.0ms (4.1%)

Stop Event

1×

fuel

Compiler

Compiled 136 to 91 computations (33.1% saved)

Iter	Nodes	Cost
0	13	113
1	25	113
2	36	113
3	56	113
4	92	113
5	152	113
6	288	113
7	441	113
8	619	113
9	757	113
10	849	113
11	855	113

Iter	Nodes	Cost
0	13	113
1	25	113
2	36	113
3	56	113
4	92	113
5	151	113
6	287	113
7	441	113
8	608	113
9	746	113
10	838	113
11	844	113

Iter	Nodes	Cost
0	13	113
1	25	113
2	36	113
3	56	113
4	92	113
5	152	113
6	288	113
7	441	113
8	619	113
9	757	113
10	849	113
11	855	113

Iter	Nodes	Cost
0	13	113
1	25	113
2	36	113
3	56	113
4	92	113
5	151	113
6	287	113
7	441	113
8	608	113
9	746	113
10	838	113
11	844	113

Details

analyze76.0ms (3.1%)

sample835.0ms (34.1%)

preprocess30.0ms (1.2%)

simplify14.0ms (0.6%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series21.0ms (0.8%)

rewrite47.0ms (1.9%)

simplify20.0ms (0.8%)

prune53.0ms (2.2%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite38.0ms (1.5%)

simplify20.0ms (0.8%)

prune32.0ms (1.3%)

localize8.0ms (0.3%)

series206.0ms (8.4%)

rewrite59.0ms (2.4%)

simplify79.0ms (3.2%)

prune122.0ms (5%)

localize8.0ms (0.3%)

series262.0ms (10.7%)

rewrite42.0ms (1.7%)

simplify36.0ms (1.5%)

prune65.0ms (2.7%)

regimes253.0ms (10.3%)

simplify2.0ms (0.1%)

end99.0ms (4.1%)

Profiling

Iter	Nodes	Cost
0	13	113
1	25	113
2	36	113
3	56	113
4	92	113
5	152	113
6	288	113
7	441	113
8	619	113
9	757	113
10	849	113
11	855	113

Iter	Nodes	Cost
0	13	113
1	25	113
2	36	113
3	56	113
4	92	113
5	151	113
6	287	113
7	441	113
8	608	113
9	746	113
10	838	113
11	844	113