Details

analyze73.0ms (2.2%)

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)

sample1.0s (30.9%)

Results

880.0ms	8256×	body	128	valid
24.0ms	204×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify181.0ms (5.4%)

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
	0.7b	(*.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)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.5b	(/.f64 1 (*.f64 x 9))

series41.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

27.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
7.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite32.0ms (1%)

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))
6.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify75.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

625×	`times-frac_binary64`
456×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
305×	`fma-def_binary64`
290×	`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

prune196.0ms (5.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	159	12	171
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	160	13	173

Error

0.0b

Counts

173 → 13

Alt Table

Status	Error	Program
	13.6b	(.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))
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.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))
▶	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1/9 x)) 1))
	33.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (cbrt.f64 (.f64 (.f64 (+.f64 y (/.f64 1 (.f64 x 9))) (+.f64 y (/.f64 1 (.f64 x 9)))) (+.f64 y (/.f64 1 (*.f64 x 9))))) 1))
	0.7b	(.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))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (/.f64 1 (.f64 x 9))) 1))
	0.4b	(+.f64 (.f64 y (.f64 3 (sqrt.f64 x))) (.f64 (-.f64 (/.f64 1 (.f64 x 9)) 1) (*.f64 3 (sqrt.f64 x))))
	0.7b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.7b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	35.9b	(/.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 -1 (pow.f64 (+.f64 (/.f64 1/9 x) y) 3))) (+.f64 (.f64 (+.f64 y (/.f64 1 (.f64 x 9))) (+.f64 y (/.f64 1 (.f64 x 9)))) (+.f64 (.f64 1 1) (.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))))

Compiler

Compiled 4465 to 3370 computations (24.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series29.0ms (0.8%)

Counts

3 → 0

Calls

3 calls:

12.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
10.0ms	(*.f64 y (sqrt.f64 x))
7.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
23×	`associate-r_binary64`
20×	`sqrt-prod_binary64`
17×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 81

Calls

3 calls:

6.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
4.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
3.0ms	(*.f64 y (sqrt.f64 x))

simplify112.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

923×	`fma-def_binary64`
458×	`unswap-sqr_binary64`
457×	`associate-l_binary64`
344×	`*-commutative_binary64`
324×	`associate-/r*_binary64`

Counts

81 → 114

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	112	894
1	200	843
2	485	842
3	1076	842
4	1485	842
5	2218	801
6	2929	801
7	3312	801
8	4823	801
9	4913	801

prune167.0ms (5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	142	10	152

Error

0.0b

Counts

152 → 10

Alt Table

Status	Error	Program
	13.6b	(.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))
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 (.f64 1/3 (sqrt.f64 (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))))) (*.f64 3 (sqrt.f64 x)))
▶	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.8b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.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 1/9 x)) 1))
	0.7b	(.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 (.f64 3 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (/.f64 1 (.f64 x 9))) 1))
	0.6b	(-.f64 (+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))

Compiler

Compiled 3693 to 2365 computations (36% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series16.0ms (0.5%)

Counts

1 → 0

Calls

1 calls:

16.0ms

(/.f64 1/3 (sqrt.f64 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`

Counts

1 → 41

Calls

1 calls:

3.0ms

(/.f64 1/3 (sqrt.f64 x))

simplify96.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1051×	`fma-neg_binary64`
416×	`unswap-sqr_binary64`
375×	`associate-/l/_binary64`
356×	`times-frac_binary64`
325×	`associate-/l*_binary64`

Counts

41 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	540
1	101	514
2	165	514
3	221	514
4	353	514
5	469	514
6	645	514
7	1189	514
8	2252	514
9	2826	514
10	3214	514
11	4235	514
12	4855	514

prune144.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Error

0.0b

Counts

141 → 9

Alt Table

Status	Error	Program
	13.6b	(.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))
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 (.f64 1/3 (sqrt.f64 (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))))) (*.f64 3 (sqrt.f64 x)))
▶	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1/9 x)) 1))
	0.7b	(.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 (.f64 3 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
	0.5b	(-.f64 (+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (/.f64 1 (.f64 x 9))) 1))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (sqrt.f64 3))))

Compiler

Compiled 3224 to 1797 computations (44.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1/9 x))
✓	0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1/9 x)) 1))
	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.4b	(/.f64 1/9 x)

series37.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

31.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1/9 x)) 1))
5.0ms	(+.f64 y (/.f64 1/9 x))
1.0ms	(/.f64 1/9 x)

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
24×	`prod-diff_binary64`
17×	`distribute-lft-in_binary64`

Counts

3 → 107

Calls

3 calls:

13.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1/9 x)) 1))
4.0ms	(+.f64 y (/.f64 1/9 x))
2.0ms	(/.f64 1/9 x)

simplify108.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

468×	`distribute-rgt-in_binary64`
415×	`distribute-lft-in_binary64`
361×	`associate-/l/_binary64`
321×	`fma-neg_binary64`
318×	`fma-def_binary64`

Counts

143 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	2203
1	379	1954
2	1114	1925
3	3525	1843
4	4951	1843
5	4998	1843

prune165.0ms (4.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	165	9	174

Error

0.0b

Counts

174 → 9

Alt Table

Status	Error	Program
	13.6b	(.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))
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.4b	(+.f64 (.f64 3 (.f64 (sqrt.f64 x) y)) (*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) -3)))
✓	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1/9 x)) 1))
	0.7b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1/9 x)) 1))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
	0.5b	(-.f64 (+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (/.f64 1 (.f64 x 9))) 1))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (sqrt.f64 3))))

Compiler

Compiled 3643 to 2618 computations (28.1% saved)

regimes626.0ms (18.6%)

Accuracy

Total 0.3b remaining (87.3%)

Threshold costs 0.3b (87.3%)

Counts

189 → 1

Compiler

Compiled 12736 to 9736 computations (23.6% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	27	25
2	34	25
3	38	25
4	41	25
5	42	25
6	40	25

end133.0ms (4%)

Compiler: Compiled 224 to 162 computations (27.7% saved)

Details

analyze73.0ms (2.2%)

sample1.0s (30.9%)

simplify181.0ms (5.4%)

prune4.0ms (0.1%)

localize8.0ms (0.3%)

series41.0ms (1.2%)

rewrite32.0ms (1%)

simplify75.0ms (2.2%)

prune196.0ms (5.8%)

localize12.0ms (0.4%)

series29.0ms (0.8%)

rewrite18.0ms (0.5%)

simplify112.0ms (3.3%)

prune167.0ms (5%)

localize8.0ms (0.2%)

series16.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify96.0ms (2.8%)

prune144.0ms (4.3%)

localize7.0ms (0.2%)

series37.0ms (1.1%)

rewrite25.0ms (0.7%)

simplify108.0ms (3.2%)

prune165.0ms (4.9%)

regimes626.0ms (18.6%)

simplify7.0ms (0.2%)

end133.0ms (4%)

Profiling