Details

analyze74.0ms (2.3%)

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
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample137.0ms (4.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	4×	body	128	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify180.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1205×	`fma-neg_binary64`
900×	`fma-def_binary64`
326×	`associate-/l*_binary64`
318×	`cancel-sign-sub-inv_binary64`
290×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	28	18
2	68	18
3	145	16
4	257	16
5	411	16
6	861	16
7	1371	16
8	2386	16
9	2493	16
10	2675	16
11	2607	16
12	2581	16
13	2581	16
14	3531	16
15	3364	16
16	3364	16
17	3364	16
18	3364	16
19	3171	16

prune4.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.3b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(*.f64 3 (sqrt.f64 x))

series42.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

27.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
9.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
30×	`prod-diff_binary64`
29×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 140

Calls

4 calls:

11.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
7.0ms	(/.f64 1 (*.f64 x 9))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
3.0ms	(*.f64 3 (sqrt.f64 x))

simplify75.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

625×	`times-frac_binary64`
456×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
305×	`fma-def_binary64`
289×	`associate-/l*_binary64`

Counts

188 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2841
1	412	2251
2	1241	2225
3	5098	2225

prune181.0ms (5.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	164	7	171
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	165	8	173

Error

0.0b

Counts

173 → 8

Alt Table

Status	Error	Program
	18.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (*.f64 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)) (sqrt.f64 (+.f64 (/.f64 1/9 x) y))) 1))
	0.8b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	18.2b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1))
▶	0.3b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

Compiler

Compiled 4171 to 3145 computations (24.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 y -3)
✓	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.2b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
✓	0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series41.0ms (1.3%)

Counts

4 → 24

Calls

4 calls:

26.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
7.0ms	(sqrt.f64 (/.f64 1 x))
7.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
1.0ms	(fma.f64 3 y -3)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
29×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`

Counts

4 → 87

Calls

4 calls:

6.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
2.0ms	(sqrt.f64 (/.f64 1 x))
0.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
0.0ms	(fma.f64 3 y -3)

simplify71.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

853×	`associate-+l+_binary64`
393×	`distribute-lft-in_binary64`
393×	`distribute-rgt-in_binary64`
288×	`associate-l_binary64`
263×	`distribute-rgt-out_binary64`

Counts

111 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1378
1	155	1248
2	265	1247
3	574	1247
4	2181	1247
5	5373	1247

prune126.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	115	9	124

Error

0.0b

Counts

124 → 9

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (sqrt.f64 x) (-.f64 (.f64 3 y) 3) (.f64 1/3 (sqrt.f64 (/.f64 1 x))))
✓	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.8b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
▶	0.3b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (pow.f64 x -1/2)))
	18.2b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1))
	20.3b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

Compiler

Compiled 2484 to 1813 computations (27% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 3 y -3)
✓	0.2b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (pow.f64 x -1/2)))
✓	0.4b	(*.f64 1/3 (pow.f64 x -1/2))

series36.0ms (1.2%)

Counts

2 → 12

Calls

2 calls:

26.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (pow.f64 x -1/2)))
10.0ms	(*.f64 1/3 (pow.f64 x -1/2))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 1/3 (pow.f64 x -1/2))
0.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (pow.f64 x -1/2)))

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-def_binary64`
415×	`*-commutative_binary64`
378×	`associate-+l+_binary64`
286×	`unswap-sqr_binary64`
201×	`associate-l_binary64`

Counts

49 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	800
1	148	688
2	304	675
3	884	655
4	1985	655
5	4977	655
6	4974	655

prune79.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	74	8	82

Error

0.0b

Counts

82 → 8

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (sqrt.f64 x) (-.f64 (.f64 3 y) 3) (.f64 1/3 (sqrt.f64 (/.f64 1 x))))
✓	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.8b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.7b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (.f64 (.f64 1/3 (*.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (pow.f64 x -1/2)))) (cbrt.f64 (pow.f64 x -1/2))))
	18.2b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	20.3b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (*.f64 1/3 (pow.f64 x -1/2)))
▶	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

Compiler

Compiled 1547 to 1131 computations (26.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.2b	(.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.3b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

series45.0ms (1.4%)

Counts

2 → 24

Calls

2 calls:

27.0ms	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
19.0ms	(.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))

rewrite44.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`*-un-lft-identity_binary64`
100×	`distribute-lft-in_binary64`
100×	`distribute-rgt-in_binary64`
90×	`prod-diff_binary64`
68×	`add-sqr-sqrt_binary64`

Counts

2 → 174

Calls

2 calls:

12.0ms	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
12.0ms	(.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))

simplify156.0ms (5%)

Algorithm

1×	egg-herbie

Rules

593×	`distribute-rgt-in_binary64`
565×	`distribute-lft-in_binary64`
312×	`fma-neg_binary64`
302×	`times-frac_binary64`
271×	`*-commutative_binary64`

Counts

198 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	4787
1	319	3611
2	906	3392
3	3318	3385
4	4791	3385
5	5002	3385

prune260.0ms (8.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	251	8	259

Error

0.0b

Counts

259 → 8

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (sqrt.f64 x) (-.f64 (.f64 3 y) 3) (.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1)))
✓	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.8b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	18.2b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	20.3b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (*.f64 1/3 (pow.f64 x -1/2)))
✓	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

Compiler

Compiled 6588 to 5009 computations (24% saved)

regimes626.0ms (19.8%)

Accuracy

Total 0.3b remaining (88.9%)

Threshold costs 0.3b (88.9%)

Counts

184 → 1

Compiler

Compiled 10847 to 8632 computations (20.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	18	23
2	18	23

end1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

sample812.0ms (25.7%)

Algorithm

1×

intervals

Results

477.0ms	8000×	body	128	valid
7.0ms	134×	body	128	nan
3.0ms	63×	body	128	invalid

Compiler

Compiled 184 to 147 computations (20.1% saved)

Details

analyze74.0ms (2.3%)

sample137.0ms (4.3%)

simplify180.0ms (5.7%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

series42.0ms (1.3%)

rewrite37.0ms (1.2%)

simplify75.0ms (2.4%)

prune181.0ms (5.7%)

localize10.0ms (0.3%)

series41.0ms (1.3%)

rewrite12.0ms (0.4%)

simplify71.0ms (2.3%)

prune126.0ms (4%)

localize13.0ms (0.4%)

series36.0ms (1.2%)

rewrite5.0ms (0.2%)

simplify68.0ms (2.1%)

prune79.0ms (2.5%)

localize10.0ms (0.3%)

series45.0ms (1.4%)

rewrite44.0ms (1.4%)

simplify156.0ms (5%)

prune260.0ms (8.2%)

regimes626.0ms (19.8%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample812.0ms (25.7%)

Profiling