Details

analyze82.0ms (1.6%)

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
25%	37.5%	37.6%	6
31.2%	31.2%	37.6%	7
37.5%	18.7%	43.8%	8
39%	15.6%	45.4%	9
42.1%	9.4%	48.5%	10
42.9%	7.8%	49.3%	11
44.5%	4.7%	50.8%	12
44.9%	3.9%	51.2%	13
45.7%	2.3%	52%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample994.0ms (19.6%)

Results

893.0ms	8256×	body	128	valid
47.0ms	182×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

151×	`fma-def_binary64`
131×	`fma-neg_binary64`
45×	`cancel-sign-sub-inv_binary64`
38×	`sub-neg_binary64`
31×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 37 to 24 computations (35.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series18.0ms (0.3%)

Counts

2 → 15

Calls

2 calls:

9.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
8.0ms	(*.f64 y (sqrt.f64 x))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
13×	`associate-+l+_binary64`
13×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

2 → 58

Calls

2 calls:

6.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
3.0ms	(*.f64 y (sqrt.f64 x))

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

433×	`fma-neg_binary64`
391×	`times-frac_binary64`
347×	`fma-def_binary64`
321×	`associate-l_binary64`
256×	`distribute-rgt-in_binary64`

Counts

73 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	672
1	214	646
2	643	637
3	2361	637
4	4129	637
5	4926	637

prune84.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Error

0.0b

Counts

85 → 8

Alt Table

Status	Error	Program
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
	33.6b	(+.f64 (-.f64 1 x) (.f64 (sqrt.f64 (.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 y (sqrt.f64 x)))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) (cbrt.f64 (.f64 y (sqrt.f64 x)))) (cbrt.f64 (*.f64 y (sqrt.f64 x)))))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
▶	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (cbrt.f64 (sqrt.f64 x))))
	34.8b	(+.f64 (-.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (sqrt.f64 x))))

Compiler

Compiled 1519 to 694 computations (54.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
✓	0.1b	(sqrt.f64 (sqrt.f64 x))
✓	0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

series252.0ms (5%)

Counts

4 → 55

Calls

4 calls:

217.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
19.0ms	(sqrt.f64 (sqrt.f64 x))
8.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
7.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
31×	`sqrt-prod_binary64`
24×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

4 → 109

Calls

4 calls:

10.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
7.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
6.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
1.0ms	(sqrt.f64 (sqrt.f64 x))

simplify111.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

500×	`times-frac_binary64`
485×	`fma-neg_binary64`
437×	`fma-def_binary64`
287×	`distribute-rgt-in_binary64`
268×	`distribute-lft-in_binary64`

Counts

164 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1445
1	297	1396
2	938	1387
3	2579	1387
4	4265	1387
5	5337	1387

prune193.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	167	9	176

Error

Counts

176 → 9

Alt Table

Status	Error	Program
	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) (cbrt.f64 (.f64 y (sqrt.f64 x)))) (cbrt.f64 (*.f64 y (sqrt.f64 x)))))
	21.9b	(/.f64 (-.f64 (.f64 (-.f64 1 x) (-.f64 1 x)) (.f64 y (*.f64 y x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
▶	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
✓	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (cbrt.f64 (sqrt.f64 x))))
	34.8b	(+.f64 (-.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (sqrt.f64 x))))

Compiler

Compiled 3392 to 1250 computations (63.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 x))
✓	0.3b	(*.f64 y (fabs.f64 (cbrt.f64 x)))
✓	0.3b	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
✓	0.6b	(cbrt.f64 x)

series1.1s (22.1%)

Counts

4 → 72

Calls

4 calls:

844.0ms	(cbrt.f64 x)
233.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
35.0ms	(sqrt.f64 (cbrt.f64 x))
11.0ms	(*.f64 y (fabs.f64 (cbrt.f64 x)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
16×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 91

Calls

4 calls:

11.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
4.0ms	(*.f64 y (fabs.f64 (cbrt.f64 x)))
1.0ms	(sqrt.f64 (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify129.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

455×	`associate-/l/_binary64`
436×	`*-commutative_binary64`
344×	`associate-+l+_binary64`
278×	`associate-+r+_binary64`
259×	`sqr-pow_binary64`

Counts

163 → 146

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	1880
1	234	1544
2	663	1451
3	874	1281
4	1503	1275
5	3321	1275
6	4980	1275
7	4745	1275

prune215.0ms (4.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	164	9	173

Error

Counts

173 → 9

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) (cbrt.f64 (.f64 y (sqrt.f64 x)))) (cbrt.f64 (*.f64 y (sqrt.f64 x)))))
	21.9b	(/.f64 (-.f64 (.f64 (-.f64 1 x) (-.f64 1 x)) (.f64 y (*.f64 y x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
✓	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (cbrt.f64 (sqrt.f64 x))))
	34.8b	(+.f64 (-.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (sqrt.f64 x))))

Compiler

Compiled 3185 to 1310 computations (58.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 x)))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x)))))
✓	2.2b	(cbrt.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))))

series953.0ms (18.8%)

Counts

4 → 72

Calls

4 calls:

396.0ms	(.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x)))))
331.0ms	(cbrt.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))))
205.0ms	(.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x)))))
21.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 x)))

rewrite67.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`pow1_binary64`
20×	`add-exp-log_binary64`
17×	`associate-r_binary64`
16×	`pow1/3_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

4 → 108

Calls

4 calls:

46.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 x)))
6.0ms	(.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x)))))
6.0ms	(.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x)))))
3.0ms	(cbrt.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))))

simplify144.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
603×	`unswap-sqr_binary64`
395×	`associate-+l+_binary64`
344×	`*-commutative_binary64`
291×	`associate-+r+_binary64`

Counts

180 → 147

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2400
1	240	2089
2	850	1950
3	1381	1877
4	2922	1759
5	4020	1759
6	4530	1759
7	4933	1759

prune202.0ms (4%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	181	9	190

Error

Counts

190 → 9

Alt Table

Status	Error	Program
✓	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) (cbrt.f64 (.f64 y (sqrt.f64 x)))) (cbrt.f64 (*.f64 y (sqrt.f64 x)))))
	21.9b	(/.f64 (-.f64 (.f64 (-.f64 1 x) (-.f64 1 x)) (.f64 y (*.f64 y x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
✓	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
	0.5b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (cbrt.f64 (sqrt.f64 x))))
	34.8b	(+.f64 (-.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (sqrt.f64 x))))

Compiler

Compiled 5726 to 1388 computations (75.8% saved)

regimes208.0ms (4.1%)

Accuracy

Total 0.1b remaining (86.4%)

Threshold costs 0.1b (86.4%)

Counts

67 → 1

Compiler

Compiled 3725 to 2335 computations (37.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	15	10
3	17	10
4	18	10
5	17	10

end107.0ms (2.1%)

Compiler: Compiled 184 to 104 computations (43.5% saved)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Details

analyze82.0ms (1.6%)

sample994.0ms (19.6%)

simplify16.0ms (0.3%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

series18.0ms (0.3%)

rewrite19.0ms (0.4%)

simplify71.0ms (1.4%)

prune84.0ms (1.7%)

localize9.0ms (0.2%)

series252.0ms (5%)

rewrite30.0ms (0.6%)

simplify111.0ms (2.2%)

prune193.0ms (3.8%)

localize8.0ms (0.2%)

series1.1s (22.1%)

rewrite21.0ms (0.4%)

simplify129.0ms (2.5%)

prune215.0ms (4.2%)

localize13.0ms (0.2%)

series953.0ms (18.8%)

rewrite67.0ms (1.3%)

simplify144.0ms (2.8%)

prune202.0ms (4%)

regimes208.0ms (4.1%)

simplify2.0ms (0%)

end107.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10