Details

analyze68.0ms (1.8%)

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)

sample1.1s (28.3%)

Results

927.0ms	8256×	body	128	valid
29.0ms	231×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify179.0ms (4.7%)

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

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
▶	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize9.0ms (0.2%)

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))

series41.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

25.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
9.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite31.0ms (0.8%)

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

simplify73.0ms (1.9%)

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

prune209.0ms (5.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	10	171
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	10	173

Error

0.0b

Counts

173 → 10

Alt Table

Status	Error	Program
	12.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1)) (-.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))
	0.5b	(+.f64 (.f64 3 (.f64 (sqrt.f64 x) y)) (*.f64 (sqrt.f64 x) (fma.f64 (/.f64 1/9 x) 3 -3)))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))))
▶	0.3b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	28.3b	(/.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (.f64 (+.f64 y (/.f64 1 (.f64 x 9))) (+.f64 y (/.f64 1 (.f64 x 9)))) (.f64 1 1))) (+.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	44.2b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x))) (.f64 (.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))))
	0.5b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (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))

Compiler

Compiled 4433 to 3348 computations (24.5% saved)

localize8.0ms (0.2%)

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 (1.2%)

Counts

2 → 24

Calls

2 calls:

27.0ms	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
18.0ms	(.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))

rewrite45.0ms (1.2%)

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:

13.0ms	(.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
13.0ms	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

simplify155.0ms (4%)

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

prune251.0ms (6.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	248	3	251
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	253	8	261

Error

0.0b

Counts

261 → 8

Alt Table

Status	Error	Program
	0.9b	(.f64 3 (.f64 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (+.f64 (-.f64 (/.f64 1/9 x) 1) y) (sqrt.f64 (cbrt.f64 x)))))
▶	0.4b	(+.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x))) (.f64 (sqrt.f64 x) -3))
✓	0.3b	(.f64 3 (.f64 (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))
	33.3b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 (/.f64 1/9 x) y) -3)) 3))
	0.5b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (.f64 (.f64 3 (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))

Compiler

Compiled 6796 to 5163 computations (24% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 y (/.f64 1/3 x))
✓	0.3b	(*.f64 (sqrt.f64 x) -3)
✓	0.3b	(*.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x)))
✓	0.4b	(/.f64 1/3 x)

series31.0ms (0.8%)

Counts

4 → 36

Calls

4 calls:

17.0ms	(*.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x)))
7.0ms	(*.f64 (sqrt.f64 x) -3)
6.0ms	(fma.f64 3 y (/.f64 1/3 x))
2.0ms	(/.f64 1/3 x)

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64`
10×	`add-cbrt-cube_binary64`

Counts

4 → 89

Calls

4 calls:

3.0ms	(*.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x)))
3.0ms	(*.f64 (sqrt.f64 x) -3)
2.0ms	(/.f64 1/3 x)
0.0ms	(fma.f64 3 y (/.f64 1/3 x))

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

819×	`distribute-rgt-in_binary64`
815×	`distribute-lft-in_binary64`
358×	`associate-/l/_binary64`
323×	`fma-def_binary64`
297×	`associate-l_binary64`

Counts

125 → 102

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	132	1448
1	227	1367
2	612	1367
3	1531	1367
4	4896	1367
5	4933	1367

prune93.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	102	8	110

Error

0.0b

Counts

110 → 8

Alt Table

Status	Error	Program
	0.9b	(.f64 3 (.f64 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (+.f64 (-.f64 (/.f64 1/9 x) 1) y) (sqrt.f64 (cbrt.f64 x)))))
✓	0.4b	(+.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x))) (.f64 (sqrt.f64 x) -3))
▶	0.5b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x)))) (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x))))) (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x))))) (.f64 (sqrt.f64 x) -3))
✓	0.3b	(.f64 3 (.f64 (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))
	33.3b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 (/.f64 1/9 x) y) -3)) 3))
	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))

Compiler

Compiled 2283 to 1422 computations (37.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.3b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (sqrt.f64 x)))
	0.3b	(/.f64 1 (*.f64 x 9))
✓	0.4b	(*.f64 (cbrt.f64 3) (sqrt.f64 x))

series55.0ms (1.4%)

Counts

3 → 12

Calls

3 calls:

34.0ms

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

12.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (sqrt.f64 x)))

9.0ms

(*.f64 (cbrt.f64 3) (sqrt.f64 x))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
35×	`add-exp-log_binary64`
35×	`pow1_binary64`
30×	`prod-diff_binary64`

Counts

3 → 130

Calls

3 calls:

18.0ms

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

8.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (sqrt.f64 x)))

4.0ms

(*.f64 (cbrt.f64 3) (sqrt.f64 x))

simplify104.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

594×	`distribute-rgt-in_binary64`
545×	`distribute-lft-in_binary64`
420×	`fma-neg_binary64`
418×	`times-frac_binary64`
328×	`associate-l_binary64`

Counts

142 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	3099
1	364	2232
2	1396	2208
3	4954	2208
4	5273	2208

prune199.0ms (5.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	193	9	202

Error

Counts

202 → 9

Alt Table

Status	Error	Program
	0.9b	(.f64 3 (.f64 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (+.f64 (-.f64 (/.f64 1/9 x) 1) y) (sqrt.f64 (cbrt.f64 x)))))
✓	0.4b	(+.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x))) (.f64 (sqrt.f64 x) -3))
	0.7b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 (.f64 (cbrt.f64 3) (sqrt.f64 x))) (sqrt.f64 (.f64 (cbrt.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))
✓	0.5b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x)))) (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x))))) (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y (/.f64 1/3 x))))) (.f64 (sqrt.f64 x) -3))
✓	0.3b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	33.3b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 (/.f64 1/9 x) y) -3)) 3))
	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))

Compiler

Compiled 6013 to 4871 computations (19% saved)

regimes847.0ms (22.1%)

Accuracy

Total 0.4b remaining (89.3%)

Threshold costs 0.4b (89.3%)

Counts

201 → 1

Compiler

Compiled 13092 to 10310 computations (21.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	22	21
2	23	21
3	21	21

end147.0ms (3.8%)

Compiler: Compiled 239 to 183 computations (23.4% saved)

Details

analyze68.0ms (1.8%)

sample1.1s (28.3%)

simplify179.0ms (4.7%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series41.0ms (1.1%)

rewrite31.0ms (0.8%)

simplify73.0ms (1.9%)

prune209.0ms (5.4%)

localize8.0ms (0.2%)

series45.0ms (1.2%)

rewrite45.0ms (1.2%)

simplify155.0ms (4%)

prune251.0ms (6.5%)

localize8.0ms (0.2%)

series31.0ms (0.8%)

rewrite12.0ms (0.3%)

simplify80.0ms (2.1%)

prune93.0ms (2.4%)

localize13.0ms (0.3%)

series55.0ms (1.4%)

rewrite42.0ms (1.1%)

simplify104.0ms (2.7%)

prune199.0ms (5.2%)

regimes847.0ms (22.1%)

simplify2.0ms (0.1%)

end147.0ms (3.8%)

Profiling