Details

analyze9.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample93.0ms (3.1%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 56 to 37 computations (33.9% saved)

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
463×	`fma-neg_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	185	17
3	915	13
4	2340	13
5	4455	13
6	4958	13
7	5077	13

prune5.0ms (0.2%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	46.4b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
▶	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
✓	0.2b	(/.f64 1 (*.f64 i i))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
2.0ms	(/.f64 1 (*.f64 i i))
2.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
49×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

3 → 134

Calls

3 calls:

7.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
6.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
3.0ms	(/.f64 1 (*.f64 i i))

simplify138.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-neg_binary64`
446×	`unswap-sqr_binary64`
409×	`associate-l_binary64`
361×	`fma-def_binary64`
294×	`associate-r_binary64`

Counts

170 → 196

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	203	2573
1	382	2324
2	977	2089
3	3418	2089
4	4641	2081
5	4949	2081
6	4780	2081

prune182.0ms (6.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	195	3	198

Error

Counts

198 → 3

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	0.3b	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i)))))
	33.0b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 3734 to 2772 computations (25.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 2 (/.f64 1 i))
✓	0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
✓	0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

series14.0ms (0.5%)

Counts

4 → 39

Calls

4 calls:

7.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
3.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
2.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
1.0ms	(-.f64 2 (/.f64 1 i))

rewrite98.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`add-sqr-sqrt_binary64`
143×	`*-un-lft-identity_binary64`
134×	`times-frac_binary64`
90×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

4 → 240

Calls

4 calls:

59.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
8.0ms	(-.f64 2 (/.f64 1 i))
7.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
6.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

simplify197.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
446×	`fma-neg_binary64`
279×	`times-frac_binary64`
230×	`cancel-sign-sub-inv_binary64`
190×	`distribute-rgt-in_binary64`

Counts

279 → 349

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	322	5864
1	811	4962
2	2486	4702
3	4394	4700
4	4948	4700
5	4844	4700

prune327.0ms (11.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	349	3	352

Error

Counts

352 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	0.3b	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i)))))
	33.0b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 9347 to 7905 computations (15.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4 (/.f64 -1 (*.f64 i i)))
✓	0.2b	(/.f64 -1 (*.f64 i i))
✓	0.2b	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i)))))
✓	0.2b	(/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i))))

series19.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

8.0ms	(/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i))))
6.0ms	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i)))))
3.0ms	(+.f64 4 (/.f64 -1 (*.f64 i i)))
2.0ms	(/.f64 -1 (*.f64 i i))

rewrite36.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
53×	`times-frac_binary64`
44×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`

Counts

4 → 145

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i)))))
6.0ms	(/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i))))
4.0ms	(+.f64 4 (/.f64 -1 (*.f64 i i)))
3.0ms	(/.f64 -1 (*.f64 i i))

simplify117.0ms (4%)

Algorithm

1×	egg-herbie

Rules

603×	`associate-/l*_binary64`
473×	`fma-def_binary64`
354×	`associate-*l/_binary64`
289×	`times-frac_binary64`
275×	`associate-/l/_binary64`

Counts

193 → 210

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	3734
1	580	3450
2	1782	3422
3	4854	3422
4	4945	3422

prune215.0ms (7.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	210	3	213

Error

Counts

213 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.3b	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i)))))
▶	33.0b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 5182 to 4186 computations (19.2% saved)

localize15.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
✓	0.0b	(*.f64 16 (pow.f64 i 8))
✓	0.0b	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))

series13.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
4.0ms	(fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
3.0ms	(*.f64 16 (pow.f64 i 8))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

6.0ms	(*.f64 16 (pow.f64 i 8))
0.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
0.0ms	(fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))

simplify47.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

969×	`distribute-rgt-in_binary64`
967×	`distribute-lft-in_binary64`
601×	`fma-def_binary64`
249×	`associate-l_binary64`
218×	`associate-r_binary64`

Counts

71 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1165
1	162	1063
2	365	1039
3	1330	1039
4	5671	1039

prune66.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.3b	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (+.f64 4 (/.f64 -1 (*.f64 i i)))))
✓	33.0b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 1868 to 1290 computations (30.9% saved)

regimes287.0ms (9.7%)

Accuracy

Total 0.1b remaining (92.2%)

Threshold costs 0.1b (92.2%)

Counts

151 → 1

Compiler

Compiled 4232 to 3535 computations (16.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	17	22
2	23	22
3	25	22
4	26	22
5	24	22

end1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

sample958.0ms (32.4%)

Algorithm

1×

intervals

Results

547.0ms	8000×	body	128	valid
94.0ms	8000×	pre	128	true

Compiler

Compiled 99 to 77 computations (22.2% saved)

Details

analyze9.0ms (0.3%)

sample93.0ms (3.1%)

simplify57.0ms (1.9%)

prune5.0ms (0.2%)

localize7.0ms (0.2%)

series8.0ms (0.3%)

rewrite23.0ms (0.8%)

simplify138.0ms (4.7%)

prune182.0ms (6.2%)

localize7.0ms (0.2%)

series14.0ms (0.5%)

rewrite98.0ms (3.3%)

simplify197.0ms (6.6%)

prune327.0ms (11.1%)

localize8.0ms (0.3%)

series19.0ms (0.7%)

rewrite36.0ms (1.2%)

simplify117.0ms (4%)

prune215.0ms (7.3%)

localize15.0ms (0.5%)

series13.0ms (0.4%)

rewrite8.0ms (0.3%)

simplify47.0ms (1.6%)

prune66.0ms (2.2%)

regimes287.0ms (9.7%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample958.0ms (32.4%)

Profiling