Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	0%	50%	2

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.3s (12.7%)

Results

833.0ms

8256×

body

128

valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify75.0ms (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

prune6.0ms (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
	0.2b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize16.0ms (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))
✓	0.5b	(/.f64 1 (*.f64 x 9))

series124.0ms (1.2%)

Counts

4 → 38

Calls

4 calls:

51.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
51.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
19.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

rewrite66.0ms (0.6%)

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))))
15.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(/.f64 1 (*.f64 x 9))
5.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))

simplify298.0ms (2.9%)

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

prune692.0ms (6.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	227	9	236
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	229	9	238

Error

0.0b

Counts

238 → 9

Alt Table

Status	Error	Program
	27.4b	(/.f64 (fma.f64 (+.f64 1 (/.f64 -1/9 x)) (+.f64 1 (/.f64 -1/9 x)) (.f64 (/.f64 (.f64 y y) x) -1/9)) (fma.f64 1/3 (/.f64 y (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))))
	0.3b	(+.f64 (fma.f64 (+.f64 1 (sqrt.f64 (/.f64 1/9 x))) (-.f64 1 (sqrt.f64 (/.f64 1/9 x))) (*.f64 -1/3 (/.f64 y (sqrt.f64 x)))) 0)
	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))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (*.f64 3 (sqrt.f64 x)) (cbrt.f64 y))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	19.1b	(-.f64 (-.f64 1 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (.f64 x 9) (.f64 x 9)) (.f64 x 9))))) (/.f64 y (.f64 3 (sqrt.f64 x))))

Compiler

Compiled 6998 to 5065 computations (27.6% saved)

localize19.0ms (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))

series50.0ms (0.5%)

Counts

2 → 26

Calls

2 calls:

47.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
3.0ms	(/.f64 (/.f64 1 x) 9)

rewrite231.0ms (2.2%)

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:

81.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
12.0ms	(/.f64 (/.f64 1 x) 9)

simplify600.0ms (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

prune2.2s (21.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	594	4	598
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	598	9	607

Error

Counts

607 → 9

Alt Table

Status	Error	Program
	27.4b	(/.f64 (fma.f64 (+.f64 1 (/.f64 -1/9 x)) (+.f64 1 (/.f64 -1/9 x)) (.f64 (/.f64 (.f64 y y) x) -1/9)) (fma.f64 1/3 (/.f64 y (sqrt.f64 x)) (+.f64 1 (/.f64 -1/9 x))))
	0.6b	(-.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 9 (cbrt.f64 (/.f64 1 x))))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.6b	(-.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 (cbrt.f64 (/.f64 1 x)) 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (*.f64 3 (sqrt.f64 x)) (cbrt.f64 y))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1/3 x) (sqrt.f64 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y)))
	0.3b	(+.f64 (fma.f64 (+.f64 1 (sqrt.f64 (/.f64 1/9 x))) (-.f64 1 (sqrt.f64 (/.f64 1/9 x))) (*.f64 -1/3 (/.f64 y (sqrt.f64 x)))) 0)

Compiler

Compiled 24086 to 17955 computations (25.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series75.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

48.0ms	(/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y))
27.0ms	(/.f64 (*.f64 3 (sqrt.f64 x)) y)

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
28×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 81

Calls

2 calls:

11.0ms	(/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y))
7.0ms	(/.f64 (*.f64 3 (sqrt.f64 x)) y)

simplify221.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

744×	`div-sub_binary64`
432×	`*-commutative_binary64`
368×	`associate-/l*_binary64`
281×	`sub-neg_binary64`
275×	`associate-/r*_binary64`

Counts

105 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1477
1	198	1284
2	622	1265
3	2287	1265
4	2702	1265
5	3041	1265
6	3954	1265
7	4231	1265
8	4936	1265
9	4833	1265

prune706.0ms (6.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	244	2	246
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	246	9	255

Error

Counts

255 → 9

Alt Table

Status	Error	Program
	27.4b	(/.f64 (fma.f64 (+.f64 1 (/.f64 -1/9 x)) (+.f64 1 (/.f64 -1/9 x)) (.f64 (/.f64 (.f64 y y) x) -1/9)) (fma.f64 1/3 (/.f64 y (sqrt.f64 x)) (+.f64 1 (/.f64 -1/9 x))))
	0.6b	(-.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 9 (cbrt.f64 (/.f64 1 x))))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(+.f64 (fma.f64 (+.f64 1 (sqrt.f64 (/.f64 1/9 x))) (-.f64 1 (sqrt.f64 (/.f64 1/9 x))) (*.f64 -1/3 (/.f64 y (sqrt.f64 x)))) 0)
▶	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (*.f64 (/.f64 1/3 (sqrt.f64 x)) y))
	0.6b	(-.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 (cbrt.f64 (/.f64 1 x)) 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 1 (*.f64 3 (/.f64 (sqrt.f64 x) y))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1/3 x) (sqrt.f64 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y)))

Compiler

Compiled 5903 to 4348 computations (26.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (*.f64 (/.f64 1/3 (sqrt.f64 x)) y))
✓	0.2b	(*.f64 (/.f64 1/3 (sqrt.f64 x)) y)
	0.3b	(/.f64 (/.f64 1 x) 9)
✓	0.4b	(/.f64 1/3 (sqrt.f64 x))

series110.0ms (1.1%)

Counts

3 → 26

Calls

3 calls:

44.0ms	(*.f64 (/.f64 1/3 (sqrt.f64 x)) y)
40.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (*.f64 (/.f64 1/3 (sqrt.f64 x)) y))
25.0ms	(/.f64 1/3 (sqrt.f64 x))

rewrite152.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

322×	`times-frac_binary64`
265×	`add-sqr-sqrt_binary64`
233×	`*-un-lft-identity_binary64`
217×	`add-cube-cbrt_binary64`
173×	`associate--l+_binary64`

Counts

3 → 300

Calls

3 calls:

52.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (*.f64 (/.f64 1/3 (sqrt.f64 x)) y))
15.0ms	(*.f64 (/.f64 1/3 (sqrt.f64 x)) y)
5.0ms	(/.f64 1/3 (sqrt.f64 x))

simplify398.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

622×	`times-frac_binary64`
563×	`fma-neg_binary64`
248×	`exp-prod_binary64`
244×	`cancel-sign-sub-inv_binary64`
229×	`distribute-neg-frac_binary64`

Counts

326 → 474

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	351	9249
1	925	6548
2	2451	6091
3	4454	6027
4	4837	6027

prune1.9s (17.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	574	1	575
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	575	9	584

Error

Counts

584 → 9

Alt Table

Status	Error	Program
	0.3b	(+.f64 (fma.f64 (+.f64 1 (sqrt.f64 (/.f64 1/9 x))) (-.f64 1 (sqrt.f64 (/.f64 1/9 x))) (*.f64 -1/3 (/.f64 y (sqrt.f64 x)))) 0)
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (*.f64 (/.f64 1/3 (sqrt.f64 x)) y))
	0.6b	(-.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 (cbrt.f64 (/.f64 1 x)) 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 1 (*.f64 3 (/.f64 (sqrt.f64 x) y))))
	0.6b	(-.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 9 (cbrt.f64 (/.f64 1 x))))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1/3 x) (sqrt.f64 9))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y)))
	0.3b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (.f64 (.f64 (sqrt.f64 1/3) (/.f64 (sqrt.f64 1/3) (sqrt.f64 x))) y))

Compiler

Compiled 20465 to 15555 computations (24% saved)

regimes892.0ms (8.6%)

Accuracy

Total 0.2b remaining (89.6%)

Threshold costs 0.2b (89.6%)

Counts

166 → 1

Compiler

Compiled 10136 to 8041 computations (20.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`distribute-neg-frac_binary64`
3×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	22	24
2	32	24
3	40	24
4	44	24
5	45	24
6	42	24

end212.0ms (2%)

Compiler: Compiled 220 to 182 computations (17.3% 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

analyze1.0ms (0%)

sample1.3s (12.7%)

simplify75.0ms (0.7%)

prune6.0ms (0.1%)

localize16.0ms (0.2%)

series124.0ms (1.2%)

rewrite66.0ms (0.6%)

simplify298.0ms (2.9%)

prune692.0ms (6.7%)

localize19.0ms (0.2%)

series50.0ms (0.5%)

rewrite231.0ms (2.2%)

simplify600.0ms (5.8%)

prune2.2s (21.3%)

localize15.0ms (0.1%)

series75.0ms (0.7%)

rewrite24.0ms (0.2%)

simplify221.0ms (2.1%)

prune706.0ms (6.8%)

localize9.0ms (0.1%)

series110.0ms (1.1%)

rewrite152.0ms (1.5%)

simplify398.0ms (3.8%)

prune1.9s (17.8%)

regimes892.0ms (8.6%)

simplify8.0ms (0.1%)

end212.0ms (2%)

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