Details

analyze57.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.2s (24.7%)

Results

952.0ms	8256×	body	128	valid
15.0ms	106×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify33.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
309×	`fma-def_binary64`
228×	`cancel-sign-sub-inv_binary64`
83×	`associate-/l*_binary64`
72×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
▶	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
✓	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.7b	(/.f64 1 (*.f64 x 9))

series57.0ms (1.2%)

Counts

4 → 38

Calls

4 calls:

25.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
22.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
8.0ms	(*.f64 3 (sqrt.f64 x))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite41.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`*-un-lft-identity_binary64`
80×	`add-sqr-sqrt_binary64`
70×	`prod-diff_binary64`
50×	`add-cube-cbrt_binary64`
42×	`times-frac_binary64`

Counts

4 → 190

Calls

4 calls:

17.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
3.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
3.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify157.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
276×	`fma-neg_binary64`
266×	`exp-prod_binary64`
243×	`cancel-sign-sub-inv_binary64`
236×	`distribute-rgt-in_binary64`

Counts

228 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	5841
1	609	3520
2	1862	2992
3	4354	2992
4	4859	2992
5	4769	2992

prune298.0ms (6.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	227	9	236
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	228	10	238

Error

0.0b

Counts

238 → 10

Alt Table

Status	Error	Program
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x))))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.5b	(-.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 1/9 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1 (*.f64 3 (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 1 (/.f64 (.f64 3 (sqrt.f64 x)) y)))
	0.3b	(-.f64 1 (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (*.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))))
	0.4b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))

Compiler

Compiled 6978 to 5053 computations (27.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series25.0ms (0.5%)

Counts

2 → 26

Calls

2 calls:

23.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
1.0ms	(/.f64 (/.f64 1 x) 9)

rewrite94.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

458×	`times-frac_binary64`
423×	`add-sqr-sqrt_binary64`
330×	`*-un-lft-identity_binary64`
261×	`add-cube-cbrt_binary64`
213×	`prod-diff_binary64`

Counts

2 → 370

Calls

2 calls:

29.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
4.0ms	(/.f64 (/.f64 1 x) 9)

simplify282.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-neg_binary64`
780×	`times-frac_binary64`
216×	`associate-*r/_binary64`
196×	`associate-*l/_binary64`
179×	`*-commutative_binary64`

Counts

396 → 542

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	378	14432
1	976	9574
2	2673	8625
3	4403	8501
4	4877	8501

prune1.1s (22.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	594	4	598
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	597	11	608

Error

Counts

608 → 11

Alt Table

Status	Error	Program
	0.6b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 (neg.f64 (/.f64 1/9 (cbrt.f64 x))) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (.f64 y (/.f64 1 (.f64 3 (sqrt.f64 x)))))
	0.3b	(-.f64 1 (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
	0.6b	(-.f64 (-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) 3) (/.f64 (cbrt.f64 (/.f64 1 x)) 3))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x))))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
	0.3b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 (sqrt.f64 x)) (.f64 9 (sqrt.f64 x)))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 1 (/.f64 (.f64 3 (sqrt.f64 x)) y)))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (*.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))))
	0.4b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))

Compiler

Compiled 24122 to 17979 computations (25.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series37.0ms (0.8%)

Counts

2 → 12

Calls

2 calls:

23.0ms	(.f64 y (/.f64 1 (.f64 3 (sqrt.f64 x))))
14.0ms	(/.f64 1 (*.f64 3 (sqrt.f64 x)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`div-exp_binary64`

Counts

2 → 64

Calls

2 calls:

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

simplify125.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
467×	`sqr-pow_binary64`
460×	`fabs-mul_binary64`
445×	`associate-/r/_binary64`
368×	`fma-neg_binary64`

Counts

76 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	808
1	166	693
2	484	692
3	1662	692
4	2027	692
5	2266	692
6	2704	692
7	3328	692
8	3893	692
9	4678	692
10	4935	692

prune295.0ms (6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	219	9	228

Error

Counts

228 → 9

Alt Table

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

Compiler

Compiled 5147 to 3862 computations (25% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series37.0ms (0.7%)

Counts

3 → 12

Calls

3 calls:

23.0ms	(.f64 (.f64 1/3 y) (/.f64 1 (sqrt.f64 x)))
12.0ms	(/.f64 1 (sqrt.f64 x))
1.0ms	(*.f64 1/3 y)

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 116

Calls

3 calls:

8.0ms	(.f64 (.f64 1/3 y) (/.f64 1 (sqrt.f64 x)))
3.0ms	(/.f64 1 (sqrt.f64 x))
2.0ms	(*.f64 1/3 y)

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Rules

658×	`associate-/l*_binary64`
568×	`times-frac_binary64`
506×	`fma-def_binary64`
412×	`associate-*l/_binary64`
394×	`fma-neg_binary64`

Counts

128 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1351
1	211	1215
2	584	1214
3	1125	1171
4	2957	1171
5	3135	1171
6	3647	1171
7	5138	1171

prune307.0ms (6.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	246	9	255

Error

Counts

255 → 9

Alt Table

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

Compiler

Compiled 5727 to 4225 computations (26.2% saved)

regimes417.0ms (8.5%)

Accuracy

Total 0.2b remaining (93%)

Threshold costs 0.2b (93%)

Counts

142 → 1

Compiler

Compiled 8033 to 6511 computations (18.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	19	21
2	30	21
3	42	21
4	50	21
5	54	21
6	55	21
7	53	21

end142.0ms (2.9%)

Compiler: Compiled 213 to 168 computations (21.1% saved)

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

Details

analyze57.0ms (1.2%)

sample1.2s (24.7%)

simplify33.0ms (0.7%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series57.0ms (1.2%)

rewrite41.0ms (0.8%)

simplify157.0ms (3.2%)

prune298.0ms (6.1%)

localize8.0ms (0.2%)

series25.0ms (0.5%)

rewrite94.0ms (1.9%)

simplify282.0ms (5.8%)

prune1.1s (22.7%)

localize9.0ms (0.2%)

series37.0ms (0.8%)

rewrite13.0ms (0.3%)

simplify125.0ms (2.6%)

prune295.0ms (6%)

localize9.0ms (0.2%)

series37.0ms (0.7%)

rewrite19.0ms (0.4%)

simplify97.0ms (2%)

prune307.0ms (6.3%)

regimes417.0ms (8.5%)

simplify3.0ms (0.1%)

end142.0ms (2.9%)

Profiling

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16