Details

analyze80.0ms (2.7%)

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)

sample846.0ms (28.6%)

Results

779.0ms	8254×	body	128	valid
20.0ms	218×	body	128	invalid
1.0ms	2×	body	1024	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify14.0ms (0.5%)

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

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 35 to 22 computations (37.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series17.0ms (0.6%)

Counts

2 → 28

Calls

2 calls:

10.0ms	(fma.f64 y (sqrt.f64 x) 1)
7.0ms	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)

rewrite61.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

690×	`log1p-expm1-u_binary64`
690×	`expm1-log1p-u_binary64`
373×	`prod-diff_binary64`
94×	`egg-rr`
71×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	144	17
2	1819	17

Stop Event

1×	node limit

Counts

2 → 94

Calls

2 calls:

58.0ms	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
58.0ms	(fma.f64 y (sqrt.f64 x) 1)

simplify35.0ms (1.2%)

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	190
1	25	190
2	36	190
3	56	190
4	92	190
5	151	190
6	287	190
7	441	190
8	612	190
9	750	190
10	842	190
11	848	190

Stop Event

1×

saturated

Counts

122 → 103

prune87.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	6	104

Error

0.1b

Counts

104 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	25.9b	(.f64 (-.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 2) (.f64 x x)) (/.f64 1 (+.f64 x (fma.f64 y (sqrt.f64 x) 1))))
	22.1b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3)) x)
	15.9b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) x)
	0.6b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	22.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 x)) 3) 1) (+.f64 (.f64 (.f64 y (sqrt.f64 x)) (.f64 y (sqrt.f64 x))) (-.f64 1 (.f64 (.f64 y (sqrt.f64 x)) 1)))) x)

Compiler

Compiled 2213 to 1092 computations (50.7% 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))

series8.0ms (0.3%)

Counts

1 → 15

Calls

1 calls:

8.0ms

(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

rewrite36.0ms (1.2%)

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

Calls

1 calls:

35.0ms

(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

simplify22.0ms (0.7%)

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

prune27.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	33	6	39

Error

0.1b

Counts

39 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	25.9b	(.f64 (-.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 2) (.f64 x x)) (/.f64 1 (+.f64 x (fma.f64 y (sqrt.f64 x) 1))))
	22.1b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3)) x)
	15.9b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) x)
▶	0.6b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	22.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 x)) 3) 1) (+.f64 (.f64 (.f64 y (sqrt.f64 x)) (.f64 y (sqrt.f64 x))) (-.f64 1 (.f64 (.f64 y (sqrt.f64 x)) 1)))) x)

Compiler

Compiled 530 to 303 computations (42.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	0.2b	(fma.f64 y (sqrt.f64 x) 1)
✓	0.3b	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))
✓	0.4b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3)

series85.0ms (2.9%)

Counts

3 → 25

Calls

3 calls:

53.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3)
23.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))
9.0ms	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)

rewrite97.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

847×	`log1p-expm1-u_binary64`
847×	`expm1-log1p-u_binary64`
568×	`prod-diff_binary64`
179×	`egg-rr`
89×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	205	26
2	2320	26

Stop Event

1×	node limit

Counts

3 → 179

Calls

3 calls:

92.0ms	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
92.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))
92.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3)

simplify41.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

580×	`fma-neg_binary64`
476×	`cancel-sign-sub-inv_binary64`
324×	`*-commutative_binary64`
246×	`sub-neg_binary64`
186×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	256
1	132	250
2	379	240
3	1429	240
4	2718	238
5	4589	238

Stop Event

1×	node limit

Counts

204 → 197

prune277.0ms (9.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	221	8	229

Error

0.1b

Counts

229 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	1.0b	(-.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 3) 3) x)
▶	0.6b	(-.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) x)
	25.9b	(.f64 (-.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 2) (.f64 x x)) (/.f64 1 (+.f64 x (fma.f64 y (sqrt.f64 x) 1))))
	22.1b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3)) x)
	15.9b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) x)
✓	0.6b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	22.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 x)) 3) 1) (+.f64 (.f64 (.f64 y (sqrt.f64 x)) (.f64 y (sqrt.f64 x))) (-.f64 1 (.f64 (.f64 y (sqrt.f64 x)) 1)))) x)

Compiler

Compiled 5811 to 3079 computations (47% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))
✓	0.3b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)
✓	0.3b	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))
✓	0.3b	(cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))

series158.0ms (5.3%)

Counts

3 → 31

Calls

3 calls:

86.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))
37.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)
34.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))

rewrite54.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

716×	`log1p-expm1-u_binary64`
716×	`expm1-log1p-u_binary64`
149×	`expm1-udef_binary64`
149×	`log1p-udef_binary64`
90×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	207	37
2	2120	37

Stop Event

1×	node limit

Counts

3 → 70

Calls

3 calls:

52.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)
52.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))
52.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))

simplify91.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

524×	`fma-def_binary64`
514×	`fma-neg_binary64`
236×	`associate-r_binary64`
216×	`times-frac_binary64`
201×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	1331
1	392	1275
2	1226	1199
3	4556	1199

Stop Event

1×	node limit

Counts

101 → 121

prune473.0ms (16%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	225	6	231
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	225	14	239

Error

0.0b

Counts

239 → 14

Alt Table

Status	Error	Program
	0.9b	(-.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 3) 2))) x)
	1.0b	(-.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 3) 3) x)
	0.7b	(-.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))) 3) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) x)
	25.9b	(.f64 (-.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 2) (.f64 x x)) (/.f64 1 (+.f64 x (fma.f64 y (sqrt.f64 x) 1))))
	15.7b	(-.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (.f64 (*.f64 (sqrt.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 4)))) (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 2)))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) x)
	22.1b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) 1) 3)) x)
	0.7b	(-.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 3) 2)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) x)
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	0.7b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 2) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) x)
	1.5b	(-.f64 (.f64 (cbrt.f64 (exp.f64 (log.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) x)
✓	0.6b	(-.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) x)
	15.9b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) x)
✓	0.6b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	22.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 x)) 3) 1) (+.f64 (.f64 (.f64 y (sqrt.f64 x)) (.f64 y (sqrt.f64 x))) (-.f64 1 (.f64 (.f64 y (sqrt.f64 x)) 1)))) x)

Compiler

Compiled 9129 to 6066 computations (33.6% saved)

regimes143.0ms (4.8%)

Accuracy

Total 0.1b remaining (61.8%)

Threshold costs 0.1b (61.8%)

Counts

34 → 1

Compiler

Compiled 2180 to 1537 computations (29.5% 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

end278.0ms (9.4%)

Compiler: Compiled 369 to 259 computations (29.8% saved)

Iter	Nodes	Cost
0	13	190
1	25	190
2	36	190
3	56	190
4	92	190
5	151	190
6	287	190
7	441	190
8	612	190
9	750	190
10	842	190
11	848	190

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	190
1	25	190
2	36	190
3	56	190
4	92	190
5	151	190
6	287	190
7	441	190
8	612	190
9	750	190
10	842	190
11	848	190

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

analyze80.0ms (2.7%)

sample846.0ms (28.6%)

simplify14.0ms (0.5%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series17.0ms (0.6%)

rewrite61.0ms (2%)

simplify35.0ms (1.2%)

prune87.0ms (2.9%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite36.0ms (1.2%)

simplify22.0ms (0.7%)

prune27.0ms (0.9%)

localize7.0ms (0.2%)

series85.0ms (2.9%)

rewrite97.0ms (3.3%)

simplify41.0ms (1.4%)

prune277.0ms (9.3%)

localize14.0ms (0.5%)

series158.0ms (5.3%)

rewrite54.0ms (1.8%)

simplify91.0ms (3.1%)

prune473.0ms (16%)

regimes143.0ms (4.8%)

simplify2.0ms (0.1%)

end278.0ms (9.4%)

Profiling

Iter	Nodes	Cost
0	13	190
1	25	190
2	36	190
3	56	190
4	92	190
5	151	190
6	287	190
7	441	190
8	612	190
9	750	190
10	842	190
11	848	190

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