Details

analyze229.0ms (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify105.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-neg_binary64`
504×	`div-sub_binary64`
481×	`fma-def_binary64`
326×	`times-frac_binary64`
174×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	21	10
3	37	10
4	64	10
5	113	10
6	216	10
7	415	10
8	754	10
9	1183	10
10	1537	10
11	1612	10
12	1657	10
13	1684	10
14	1694	10
15	1702	10
16	1702	10
17	1600	10

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

62.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	62.0b	(/.f64 (-.f64 x lo) (-.f64 hi lo))

Compiler

Compiled 30 to 18 computations (40% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	62.0b	(/.f64 (-.f64 x lo) (-.f64 hi lo))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

1 → 54

Calls

1 calls:

14.0ms

(/.f64 (-.f64 x lo) (-.f64 hi lo))

series48.0ms (1%)

Counts

1 → 36

Calls

1 calls:

48.0ms

(/.f64 (-.f64 x lo) (-.f64 hi lo))

simplify150.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-neg_binary64`
418×	`fma-def_binary64`
402×	`associate--l+_binary64`
279×	`cancel-sign-sub-inv_binary64`
264×	`times-frac_binary64`

Counts

90 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	2093
1	436	2033
2	1358	1879
3	4643	1879
4	5346	1879

prune83.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Error

51.3b

Counts

139 → 4

Alt Table

Status	Error	Program
	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	57.4b	(-.f64 (+.f64 1 (+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
▶	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))

Compiler

Compiled 1901 to 683 computations (64.1% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo))
✓	0.4b	(*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))
	1.5b	(+.f64 1 (/.f64 hi lo))
✓	1.5b	(+.f64 1 (/.f64 hi lo))

rewrite55.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
26×	`associate-r_binary64`
26×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`

Counts

3 → 95

Calls

3 calls:

18.0ms	(*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))
18.0ms	(*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo))
9.0ms	(+.f64 1 (/.f64 hi lo))

series180.0ms (3.7%)

Counts

3 → 66

Calls

3 calls:

103.0ms	(*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo))
56.0ms	(*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))
20.0ms	(+.f64 1 (/.f64 hi lo))

simplify226.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-*r/_binary64`
511×	`associate-*l/_binary64`
415×	`distribute-rgt-in_binary64`
394×	`distribute-lft-in_binary64`
387×	`associate-/l*_binary64`

Counts

161 → 276

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	155	2542
1	384	2296
2	1338	2015
3	4458	2013
4	4805	1995
5	4985	1995
6	4975	1995

prune262.0ms (5.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	295	9	304
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	297	11	308

Error

51.3b

Counts

308 → 11

Alt Table

Status	Error	Program
	51.9b	(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (/.f64 x lo))
	51.9b	(-.f64 (+.f64 1 (.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)) (.f64 (cbrt.f64 lo) (cbrt.f64 lo)))) (/.f64 (cbrt.f64 hi) (cbrt.f64 lo)))) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	57.4b	(-.f64 (+.f64 1 (+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.9b	(-.f64 (+.f64 1 (log.f64 (exp.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	51.9b	(-.f64 (+.f64 1 (.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (.f64 (cbrt.f64 hi) (cbrt.f64 hi))) (/.f64 (cbrt.f64 hi) lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	51.9b	(-.f64 (+.f64 1 (.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 1 (.f64 (cbrt.f64 lo) (cbrt.f64 lo)))) (/.f64 hi (cbrt.f64 lo)))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
▶	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.9b	(-.f64 (+.f64 1 (/.f64 (-.f64 (/.f64 hi lo) (pow.f64 (/.f64 hi lo) 3)) (-.f64 1 (/.f64 hi lo)))) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
	51.9b	(-.f64 (+.f64 1 (.f64 (log.f64 (exp.f64 (+.f64 1 (/.f64 hi lo)))) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	51.9b	(-.f64 (+.f64 1 (.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 (sqrt.f64 hi) (.f64 (cbrt.f64 lo) (cbrt.f64 lo)))) (/.f64 (sqrt.f64 hi) (cbrt.f64 lo)))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))

Compiler

Compiled 5294 to 2432 computations (54.1% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))
✓	0.2b	(*.f64 (/.f64 hi lo) (/.f64 x lo))
	0.4b	(*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))
	1.5b	(+.f64 1 (/.f64 hi lo))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

2 → 68

Calls

2 calls:

16.0ms	(*.f64 (/.f64 hi lo) (/.f64 x lo))
5.0ms	(+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))

series163.0ms (3.4%)

Counts

2 → 60

Calls

2 calls:

132.0ms	(*.f64 (/.f64 hi lo) (/.f64 x lo))
31.0ms	(+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))

simplify155.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-def_binary64`
591×	`associate-*l/_binary64`
540×	`associate-*r/_binary64`
524×	`associate-/l*_binary64`
367×	`times-frac_binary64`

Counts

128 → 231

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	1836
1	394	1602
2	1175	1584
3	4530	1570
4	5290	1570

prune157.0ms (3.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	397	2	399
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	406	4	410

Error

50.7b

Counts

410 → 4

Alt Table

Status	Error	Program
▶	51.5b	(-.f64 (.f64 (/.f64 hi lo) (/.f64 hi lo)) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	57.4b	(-.f64 (+.f64 1 (+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	57.7b	(-.f64 (/.f64 (fma.f64 hi (/.f64 hi lo) hi) lo) (*.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))

Compiler

Compiled 5269 to 1888 computations (64.2% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (/.f64 hi lo) (/.f64 hi lo)) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	0.2b	(*.f64 (/.f64 hi lo) (/.f64 x lo))
✓	0.5b	(*.f64 (/.f64 hi lo) (/.f64 hi lo))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

2 → 100

Calls

2 calls:

16.0ms	(*.f64 (/.f64 hi lo) (/.f64 hi lo))
13.0ms	(-.f64 (.f64 (/.f64 hi lo) (/.f64 hi lo)) (.f64 (/.f64 hi lo) (/.f64 x lo)))

series247.0ms (5.1%)

Counts

2 → 60

Calls

2 calls:

170.0ms	(-.f64 (.f64 (/.f64 hi lo) (/.f64 hi lo)) (.f64 (/.f64 hi lo) (/.f64 x lo)))
77.0ms	(*.f64 (/.f64 hi lo) (/.f64 hi lo))

simplify183.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

629×	`fma-neg_binary64`
565×	`times-frac_binary64`
360×	`associate-/l/_binary64`
359×	`fma-def_binary64`
189×	`associate-l_binary64`

Counts

160 → 308

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2488
1	516	2195
2	1727	2023
3	4411	2023
4	5016	2023

prune171.0ms (3.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	457	14	471
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	458	17	475

Error

50.7b

Counts

475 → 17

Alt Table

Status	Error	Program
	57.7b	(-.f64 (/.f64 (fma.f64 hi (/.f64 hi lo) hi) lo) (*.f64 (/.f64 hi lo) (/.f64 x lo)))
	54.6b	(-.f64 (.f64 (/.f64 1 lo) (.f64 hi (/.f64 hi lo))) (*.f64 (/.f64 hi lo) (/.f64 x lo)))
	57.4b	(-.f64 (+.f64 1 (+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.5b	(-.f64 (.f64 (.f64 (/.f64 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)) (.f64 (cbrt.f64 lo) (cbrt.f64 lo))) (/.f64 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)) (.f64 (cbrt.f64 lo) (cbrt.f64 lo)))) (.f64 (/.f64 (cbrt.f64 hi) (cbrt.f64 lo)) (/.f64 (cbrt.f64 hi) (cbrt.f64 lo)))) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(-.f64 (.f64 (/.f64 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)) 1) (.f64 (/.f64 (cbrt.f64 hi) lo) (/.f64 hi lo))) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(-.f64 (log.f64 (exp.f64 (.f64 (/.f64 hi lo) (/.f64 hi lo)))) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(-.f64 (.f64 (/.f64 hi lo) (/.f64 hi lo)) (.f64 hi (/.f64 x (*.f64 lo lo))))
	51.5b	(-.f64 (.f64 hi (.f64 (/.f64 1 lo) (/.f64 hi lo))) (*.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(-.f64 (.f64 (.f64 hi (/.f64 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)) lo)) (/.f64 (cbrt.f64 hi) lo)) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(-.f64 (.f64 (.f64 (/.f64 (cbrt.f64 hi) (cbrt.f64 lo)) (pow.f64 (/.f64 (cbrt.f64 hi) (cbrt.f64 lo)) 3)) (/.f64 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)) (.f64 (cbrt.f64 lo) (cbrt.f64 lo)))) (*.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 hi lo)) (pow.f64 (cbrt.f64 (/.f64 hi lo)) 4)) (cbrt.f64 (/.f64 hi lo))) (*.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(-.f64 (.f64 (.f64 (/.f64 (sqrt.f64 hi) 1) (/.f64 (sqrt.f64 hi) 1)) (.f64 (/.f64 (sqrt.f64 hi) lo) (/.f64 (sqrt.f64 hi) lo))) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(-.f64 (.f64 (.f64 (/.f64 (sqrt.f64 hi) (.f64 (cbrt.f64 lo) (cbrt.f64 lo))) (/.f64 (sqrt.f64 hi) (.f64 (cbrt.f64 lo) (cbrt.f64 lo)))) (.f64 (/.f64 (sqrt.f64 hi) (cbrt.f64 lo)) (/.f64 (sqrt.f64 hi) (cbrt.f64 lo)))) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(-.f64 (.f64 (.f64 (.f64 (cbrt.f64 (/.f64 hi lo)) (cbrt.f64 (/.f64 hi lo))) (.f64 (cbrt.f64 (/.f64 hi lo)) (cbrt.f64 (/.f64 hi lo)))) (.f64 (cbrt.f64 (/.f64 hi lo)) (cbrt.f64 (/.f64 hi lo)))) (.f64 (/.f64 hi lo) (/.f64 x lo)))
	51.5b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (/.f64 hi lo) (/.f64 hi lo)) (.f64 (/.f64 hi lo) (/.f64 x lo)))) (cbrt.f64 (-.f64 (.f64 (/.f64 hi lo) (/.f64 hi lo)) (.f64 (/.f64 hi lo) (/.f64 x lo))))) (cbrt.f64 (-.f64 (.f64 (/.f64 hi lo) (/.f64 hi lo)) (.f64 (/.f64 hi lo) (/.f64 x lo)))))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
	51.5b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 hi lo) 6)) (*.f64 (/.f64 hi lo) (/.f64 x lo)))

Compiler

Compiled 5665 to 1163 computations (79.5% saved)

regimes607.0ms (12.5%)

Accuracy

Total 0.9b remaining (1.7%)

Threshold costs 0.9b (1.7%)

Compiler

Compiled 8266 to 4256 computations (48.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	16	22
2	26	22
3	34	22
4	40	22
5	43	22
6	44	22
7	44	22

end1.0ms (0%)

Compiler: Compiled 18 to 9 computations (50% saved)

sample1.6s (33.8%)

Algorithm

1×

intervals

Results

430.0ms	8000×	body	128	valid
280.0ms	8000×	pre	128	true

Compiler

Compiled 549 to 243 computations (55.7% saved)

Details

analyze229.0ms (4.7%)

sample41.0ms (0.8%)

simplify105.0ms (2.2%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite19.0ms (0.4%)

series48.0ms (1%)

simplify150.0ms (3.1%)

prune83.0ms (1.7%)

localize17.0ms (0.4%)

rewrite55.0ms (1.1%)

series180.0ms (3.7%)

simplify226.0ms (4.7%)

prune262.0ms (5.4%)

localize19.0ms (0.4%)

rewrite28.0ms (0.6%)

series163.0ms (3.4%)

simplify155.0ms (3.2%)

prune157.0ms (3.2%)

localize14.0ms (0.3%)

rewrite40.0ms (0.8%)

series247.0ms (5.1%)

simplify183.0ms (3.8%)

prune171.0ms (3.5%)

regimes607.0ms (12.5%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.6s (33.8%)

Profiling