Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample117.0ms (2.7%)

Algorithm

1×

intervals

Results

9.0ms	62×	body	1024	valid
5.0ms	141×	body	128	valid
3.0ms	26×	body	512	valid
2.0ms	23×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify90.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

prune2.0ms (0%)

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

29.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	4.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite214.0ms (5%)

Algorithm

1×	rewrite-expression-head

Rules

1322×	`*-un-lft-identity_binary64`
1012×	`times-frac_binary64`
869×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
533×	`add-cube-cbrt_binary64`

Counts

3 → 783

Calls

3 calls:

38.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
11.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0ms	(/.f64 x (+.f64 x 1))

simplify930.0ms (21.6%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
367×	`unsub-neg_binary64`
299×	`fma-udef_binary64`
213×	`sub-neg_binary64`
202×	`associate-+r-_binary64`

Counts

819 → 619

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	545	54602
1	1290	31108
2	3043	22839
3	4323	22837
4	4983	22837
5	4991	22837
6	4742	22837

prune921.0ms (21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	615	4	619
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	616	4	620

Error

0.0b

Counts

620 → 4

Alt Table

Status	Error	Program
	31.8b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	32.0b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
▶	29.4b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
	29.8b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

Compiler

Compiled 30394 to 22393 computations (26.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (-.f64 -1 x) (+.f64 x -1))
✓	4.0b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 (-.f64 -1 x) (+.f64 x -1))
3.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
53×	`times-frac_binary64`
40×	`add-sqr-sqrt_binary64`
26×	`distribute-lft-out_binary64`
22×	`add-cube-cbrt_binary64`

Counts

2 → 96

Calls

2 calls:

28.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
7.0ms	(/.f64 (-.f64 -1 x) (+.f64 x -1))

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Rules

613×	`div-sub_binary64`
552×	`fma-neg_binary64`
440×	`fma-def_binary64`
261×	`distribute-rgt-in_binary64`
193×	`distribute-lft-in_binary64`

Counts

120 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	1942
1	462	1850
2	1215	1844
3	3853	1844
4	5590	1844

prune130.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	198	4	202

Error

0.0b

Counts

202 → 4

Alt Table

Status	Error	Program
	31.8b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	32.0b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
✓	29.4b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
▶	29.8b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

Compiler

Compiled 4146 to 2935 computations (29.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
	0.0b	(/.f64 (-.f64 -1 x) (+.f64 x -1))
✓	29.8b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
6×	`add-exp-log_binary64`

Counts

2 → 49

Calls

2 calls:

4.0ms	(/.f64 1 (+.f64 x 1))
0.0ms	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

simplify90.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-def_binary64`
718×	`fma-neg_binary64`
304×	`associate-l_binary64`
236×	`distribute-rgt-in_binary64`
232×	`associate-r_binary64`

Counts

73 → 96

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	1050
1	217	929
2	512	925
3	1371	923
4	4408	915
5	4998	915
6	4939	915

prune188.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	168	4	172

Error

0.0b

Counts

172 → 4

Alt Table

Status	Error	Program
✓	29.4b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
	31.8b	(fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x))
▶	30.7b	(exp.f64 (log.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))))
	32.0b	(fma.f64 3 (pow.f64 x 3) (fma.f64 x (+.f64 3 x) 1))

Compiler

Compiled 3540 to 2622 computations (25.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 -1 x) (+.f64 x -1))
✓	0.2b	(exp.f64 (log.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))))
✓	2.9b	(log.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1))))
	29.8b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(log.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1))))
3.0ms	(exp.f64 (log.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(exp.f64 (log.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))))
1.0ms	(log.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1))))

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

989×	`fma-neg_binary64`
382×	`associate-l_binary64`
284×	`cancel-sign-sub-inv_binary64`
264×	`fma-def_binary64`
239×	`associate-+l+_binary64`

Counts

55 → 87

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	1358
1	262	1186
2	695	1145
3	1971	1131
4	4510	1122
5	5136	1122

prune130.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	191	4	195

Error

Counts

195 → 4

Alt Table

Status	Error	Program
✓	29.4b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
	31.8b	(fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x))
	30.7b	(pow.f64 (E.f64) (log.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))))
	32.0b	(fma.f64 3 (pow.f64 x 3) (fma.f64 x (+.f64 3 x) 1))

Compiler

Compiled 4266 to 3253 computations (23.7% saved)

regimes133.0ms (3.1%)

Accuracy

Total 0.1b remaining (76.1%)

Threshold costs 0.1b (76.1%)

Counts

48 → 2

Compiler

Compiled 1834 to 1410 computations (23.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
6×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	72
1	43	72
2	58	72
3	74	72
4	83	72
5	86	72
6	83	72

end1.0ms (0%)

Compiler: Compiled 49 to 37 computations (24.5% saved)

sample1.1s (24.6%)

Algorithm

1×

intervals

Results

327.0ms	2042×	body	1024	valid
228.0ms	4235×	body	128	valid
166.0ms	1018×	body	512	valid
44.0ms	212×	body	2048	valid
40.0ms	493×	body	256	valid

Compiler

Compiled 124 to 93 computations (25% saved)

Details

analyze5.0ms (0.1%)

sample117.0ms (2.7%)

simplify90.0ms (2.1%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series8.0ms (0.2%)

rewrite214.0ms (5%)

simplify930.0ms (21.6%)

prune921.0ms (21.4%)

localize7.0ms (0.2%)

series7.0ms (0.2%)

rewrite44.0ms (1%)

simplify87.0ms (2%)

prune130.0ms (3%)

localize9.0ms (0.2%)

series6.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify90.0ms (2.1%)

prune188.0ms (4.4%)

localize11.0ms (0.3%)

series7.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify78.0ms (1.8%)

prune130.0ms (3%)

regimes133.0ms (3.1%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (24.6%)

Profiling