Details

analyze118.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample218.0ms (2.7%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
10.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify201.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1247×	`unsub-neg_binary64`
616×	`neg-sub0_binary64`
571×	`neg-mul-1_binary64`
560×	`fma-neg_binary64`
452×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	46	17
3	116	17
4	358	17
5	1331	17
6	3463	17
7	3625	17
8	4293	17
9	4678	17
10	4650	17
11	4895	17
12	4905	17

prune7.0ms (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
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
✓	0.0b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
✓	0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)

series74.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

26.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
22.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
20.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
5.0ms	(*.f64 m (-.f64 1 m))

rewrite104.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
57×	`prod-diff_binary64`
54×	`add-cube-cbrt_binary64`
26×	`distribute-lft-in_binary64`

Counts

4 → 188

Calls

4 calls:

30.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
17.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
14.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
13.0ms	(*.f64 m (-.f64 1 m))

simplify261.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

359×	`associate-/l/_binary64`
345×	`associate-/r*_binary64`
257×	`associate-/r/_binary64`
250×	`associate-l_binary64`
225×	`exp-prod_binary64`

Counts

268 → 294

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4650
1	502	4087
2	2059	4004
3	4566	3999
4	5030	3999

prune643.0ms (8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	290	4	294
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	291	5	296

Error

Counts

296 → 5

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (cbrt.f64 (.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1)))) (cbrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.1b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
▶	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 7283 to 4652 computations (36.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
✓	0.0b	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
✓	0.2b	(*.f64 (/.f64 m v) m)
✓	7.8b	(/.f64 (pow.f64 m 3) v)

series116.0ms (1.5%)

Counts

4 → 72

Calls

4 calls:

36.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
28.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
28.0ms	(/.f64 (pow.f64 m 3) v)
24.0ms	(*.f64 (/.f64 m v) m)

rewrite120.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`*-un-lft-identity_binary64`
64×	`add-sqr-sqrt_binary64`
55×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
24×	`prod-diff_binary64`

Counts

4 → 183

Calls

4 calls:

52.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
17.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
11.0ms	(/.f64 (pow.f64 m 3) v)
10.0ms	(*.f64 (/.f64 m v) m)

simplify256.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
301×	`cancel-sign-sub-inv_binary64`
264×	`unswap-sqr_binary64`
188×	`log-prod_binary64`
174×	`associate-r_binary64`

Counts

255 → 256

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	270	4662
1	552	4309
2	2340	3942
3	4392	3846
4	5016	3846

prune736.0ms (9.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	256	5	261

Error

Counts

261 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (/.f64 (pow.f64 m 3) (sqrt.f64 v)) (sqrt.f64 v)))
▶	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
	0.1b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 8389 to 3706 computations (55.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 m (pow.f64 m 2))
✓	0.0b	(-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1)
✓	0.0b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
✓	0.1b	(/.f64 (-.f64 m (pow.f64 m 2)) v)

series75.0ms (0.9%)

Counts

4 → 67

Calls

4 calls:

25.0ms	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
25.0ms	(/.f64 (-.f64 m (pow.f64 m 2)) v)
20.0ms	(-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1)
5.0ms	(-.f64 m (pow.f64 m 2))

rewrite180.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

264×	`add-sqr-sqrt_binary64`
197×	`*-un-lft-identity_binary64`
141×	`times-frac_binary64`
135×	`prod-diff_binary64`
135×	`add-cube-cbrt_binary64`

Counts

4 → 324

Calls

4 calls:

41.0ms	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
36.0ms	(-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1)
16.0ms	(/.f64 (-.f64 m (pow.f64 m 2)) v)
11.0ms	(-.f64 m (pow.f64 m 2))

simplify467.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

455×	`exp-prod_binary64`
271×	`times-frac_binary64`
248×	`fma-neg_binary64`
222×	`log-prod_binary64`
205×	`div-sub_binary64`

Counts

391 → 455

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	354	7238
1	652	6569
2	2281	6334
3	3874	6316
4	4576	6310
5	4822	6310

prune954.0ms (11.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	455	0	455
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	455	5	460

Error

Counts

460 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (/.f64 (pow.f64 m 3) (sqrt.f64 v)) (sqrt.f64 v)))
✓	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
▶	0.1b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 12671 to 8295 computations (34.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (sqrt.f64 m))
✓	0.1b	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)
✓	0.1b	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m)))
✓	0.1b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

series186.0ms (2.3%)

Counts

4 → 52

Calls

4 calls:

116.0ms	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
42.0ms	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m)))
14.0ms	(-.f64 1 (sqrt.f64 m))
13.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

rewrite76.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
54×	`prod-diff_binary64`
50×	`add-cube-cbrt_binary64`
43×	`sqrt-prod_binary64`

Counts

4 → 166

Calls

4 calls:

24.0ms	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
13.0ms	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m)))
8.0ms	(-.f64 1 (sqrt.f64 m))
1.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

simplify294.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-neg_binary64`
395×	`associate-+l+_binary64`
315×	`associate-l_binary64`
254×	`associate-r_binary64`
174×	`distribute-rgt-in_binary64`

Counts

218 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	6494
1	529	5783
2	2209	5392
3	4457	5392
4	4962	5392

prune513.0ms (6.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	219	5	224

Error

Counts

224 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (/.f64 (pow.f64 m 3) (sqrt.f64 v)) (sqrt.f64 v)))
✓	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
✓	0.1b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 7146 to 3759 computations (47.4% saved)

regimes687.0ms (8.6%)

Accuracy

Total 0.1b remaining (86.9%)

Threshold costs 0.1b (86.9%)

Counts

120 → 1

Compiler

Compiled 6358 to 4393 computations (30.9% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	26	26
2	32	26
3	36	26
4	39	26
5	40	26
6	38	26

end1.0ms (0%)

Compiler: Compiled 20 to 14 computations (30% saved)

sample1.6s (20.6%)

Algorithm

1×

intervals

Results

699.0ms	8000×	body	128	valid
315.0ms	8059×	pre	128	true
5.0ms	59×	body	128	invalid

Compiler

Compiled 145 to 98 computations (32.4% saved)

Details

analyze118.0ms (1.5%)

sample218.0ms (2.7%)

simplify201.0ms (2.5%)

prune7.0ms (0.1%)

localize13.0ms (0.2%)

series74.0ms (0.9%)

rewrite104.0ms (1.3%)

simplify261.0ms (3.3%)

prune643.0ms (8%)

localize23.0ms (0.3%)

series116.0ms (1.5%)

rewrite120.0ms (1.5%)

simplify256.0ms (3.2%)

prune736.0ms (9.2%)

localize15.0ms (0.2%)

series75.0ms (0.9%)

rewrite180.0ms (2.2%)

simplify467.0ms (5.8%)

prune954.0ms (11.9%)

localize20.0ms (0.2%)

series186.0ms (2.3%)

rewrite76.0ms (0.9%)

simplify294.0ms (3.7%)

prune513.0ms (6.4%)

regimes687.0ms (8.6%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.6s (20.6%)

Profiling