Details

analyze1.9s (35.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
28.1%	68.6%	3.3%	10
29.6%	65.5%	4.9%	11
32%	61.7%	6.3%	12
35.5%	56.9%	7.6%	13
48%	38.7%	13.4%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample65.0ms (1.2%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
6.0ms	65×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify113.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1400×	`fma-neg_binary64`
654×	`fma-def_binary64`
233×	`sub-neg_binary64`
210×	`unsub-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	32	14
2	94	13
3	263	13
4	655	13
5	1556	13
6	1691	13
7	1500	13
8	1500	13
9	2739	13
10	2707	13
11	2707	13
12	2632	13

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 92 to 53 computations (42.4% saved)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`flip3-+_binary64`
6×	`add-exp-log_binary64`
6×	`distribute-rgt-in_binary64`

Counts

1 → 49

Calls

1 calls:

37.0ms

(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

series72.0ms (1.4%)

Counts

1 → 48

Calls

1 calls:

72.0ms

(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

simplify103.0ms (2%)

Algorithm

1×	egg-herbie

Rules

768×	`distribute-rgt-in_binary64`
730×	`distribute-lft-in_binary64`
404×	`fma-def_binary64`
148×	`cancel-sign-sub-inv_binary64`
102×	`fma-neg_binary64`

Counts

97 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1647
1	289	1424
2	1132	1312
3	5313	1312

prune54.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	173	3	176

Error

0.0b

Counts

176 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
▶	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
	1.5b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

Compiler

Compiled 1499 to 350 computations (76.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 d3))
✓	0.0b	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))

rewrite71.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-log-exp_binary64`
23×	`add-cube-cbrt_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
11×	`flip3--_binary64`

Counts

3 → 150

Calls

3 calls:

21.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
21.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))
20.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))

series132.0ms (2.5%)

Counts

3 → 132

Calls

3 calls:

57.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
48.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
26.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

simplify156.0ms (3%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-neg_binary64`
561×	`cancel-sign-sub-inv_binary64`
523×	`times-frac_binary64`
198×	`div-sub_binary64`
185×	`fma-def_binary64`

Counts

282 → 488

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	4261
1	571	3654
2	2314	3458
3	4296	3409
4	4973	3409

prune129.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	487	1	488
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	487	4	491

Error

Counts

491 → 4

Alt Table

Status	Error	Program
	18.6b	(fma.f64 d1 (-.f64 d2 d3) (neg.f64 (*.f64 d1 d1)))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
▶	1.5b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

Compiler

Compiled 6017 to 1059 computations (82.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
	0.6b	(cbrt.f64 d1)
	0.6b	(cbrt.f64 d1)
✓	0.6b	(cbrt.f64 d1)

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`pow1/3_binary64`
14×	`add-cube-cbrt_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
6×	`log1p-expm1-u_binary64`

Counts

2 → 72

Calls

2 calls:

13.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
11.0ms	(cbrt.f64 d1)

series442.0ms (8.4%)

Counts

2 → 24

Calls

2 calls:

221.0ms	(cbrt.f64 d1)
221.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))

simplify105.0ms (2%)

Algorithm

1×	egg-herbie

Rules

928×	`fma-def_binary64`
860×	`log-prod_binary64`
504×	`exp-prod_binary64`
299×	`*-commutative_binary64`
263×	`associate-l_binary64`

Counts

96 → 155

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	57	550
1	102	494
2	246	462
3	874	455
4	1999	401
5	4161	401
6	4605	393
7	4907	393

prune44.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	350	4	354

Error

Counts

354 → 4

Alt Table

Status	Error	Program
▶	18.6b	(fma.f64 d1 (-.f64 d2 d3) (neg.f64 (*.f64 d1 d1)))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	1.5b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

Compiler

Compiled 2632 to 598 computations (77.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 d1 (-.f64 d2 d3) (neg.f64 (*.f64 d1 d1)))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`fma-udef_binary64`
5×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

1 → 34

Calls

1 calls:

10.0ms

(fma.f64 d1 (-.f64 d2 d3) (neg.f64 (*.f64 d1 d1)))

series31.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

31.0ms

(fma.f64 d1 (-.f64 d2 d3) (neg.f64 (*.f64 d1 d1)))

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-neg_binary64`
408×	`neg-mul-1_binary64`
266×	`associate-l_binary64`
253×	`distribute-lft-neg-out_binary64`
214×	`distribute-rgt-neg-out_binary64`

Counts

70 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	968
1	138	813
2	437	677
3	1738	677
4	4359	677
5	5102	677

prune21.0ms (0.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	121	4	125

Error

Counts

125 → 4

Alt Table

Status	Error	Program
✓	18.6b	(fma.f64 d1 (-.f64 d2 d3) (neg.f64 (*.f64 d1 d1)))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	1.5b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

Compiler

Compiled 845 to 188 computations (77.8% saved)

regimes302.0ms (5.7%)

Accuracy

Total 0.0b remaining (60.9%)

Threshold costs 0.0b (60.9%)

Compiler

Compiled 4038 to 2554 computations (36.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	14
2	22	14
3	26	14
4	28	14
5	28	14

end67.0ms (1.3%)

Compiler: Compiled 42 to 24 computations (42.9% saved)

sample1.3s (24.1%)

Algorithm

1×

intervals

Results

413.0ms	8000×	body	128	valid
136.0ms	2389×	body	128	invalid

Compiler

Compiled 103 to 62 computations (39.8% saved)

Details

analyze1.9s (35.5%)

sample65.0ms (1.2%)

simplify113.0ms (2.1%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite42.0ms (0.8%)

series72.0ms (1.4%)

simplify103.0ms (2%)

prune54.0ms (1%)

localize9.0ms (0.2%)

rewrite71.0ms (1.3%)

series132.0ms (2.5%)

simplify156.0ms (3%)

prune129.0ms (2.5%)

localize10.0ms (0.2%)

rewrite27.0ms (0.5%)

series442.0ms (8.4%)

simplify105.0ms (2%)

prune44.0ms (0.8%)

localize6.0ms (0.1%)

rewrite12.0ms (0.2%)

series31.0ms (0.6%)

simplify87.0ms (1.6%)

prune21.0ms (0.4%)

regimes302.0ms (5.7%)

simplify3.0ms (0.1%)

end67.0ms (1.3%)

sample1.3s (24.1%)

Profiling