Details

analyze65.0ms (1.7%)

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)

sample1.1s (29.2%)

Results

986.0ms	8256×	body	128	valid
7.0ms	68×	body	128	invalid

Compiler

Compiled 67 to 49 computations (26.9% saved)

simplify123.0ms (3.2%)

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

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series33.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
3.0ms	(*.f64 m (-.f64 1 m))

rewrite43.0ms (1.1%)

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:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify136.0ms (3.6%)

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	4962
1	502	4321
2	2059	4004
3	4566	3999
4	5030	3999

prune331.0ms (8.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	288	6	294
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	290	6	296

Error

0.0b

Counts

296 → 6

Alt Table

Status	Error	Program
	0.2b	(.f64 (fma.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v) -1) (-.f64 1 m))
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 3)) (+.f64 1 m)) v) 1) (-.f64 1 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))
	3.6b	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m))))

Compiler

Compiled 7297 to 4670 computations (36% saved)

localize10.0ms (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))
✓	0.3b	(*.f64 (/.f64 m v) m)
✓	8.9b	(/.f64 (pow.f64 m 3) v)

series53.0ms (1.4%)

Counts

4 → 72

Calls

4 calls:

17.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
13.0ms	(/.f64 (pow.f64 m 3) v)
12.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
11.0ms	(*.f64 (/.f64 m v) m)

rewrite48.0ms (1.3%)

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:

19.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
7.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
5.0ms	(/.f64 (pow.f64 m 3) v)
4.0ms	(*.f64 (/.f64 m v) m)

simplify139.0ms (3.7%)

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

prune388.0ms (10.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	254	2	256
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	257	5	262

Error

0.0b

Counts

262 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 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 (pow.f64 m 3) (/.f64 1 v)))
	0.2b	(.f64 (fma.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v) -1) (-.f64 1 m))
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))

Compiler

Compiled 8405 to 3721 computations (55.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 1) (/.f64 (pow.f64 m 3) v))
✓	0.0b	(-.f64 m (.f64 2 (.f64 m m)))
✓	0.0b	(/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)
	8.9b	(/.f64 (pow.f64 m 3) v)

series35.0ms (0.9%)

Counts

3 → 60

Calls

3 calls:

16.0ms	(/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)
16.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 1) (/.f64 (pow.f64 m 3) v))
2.0ms	(-.f64 m (.f64 2 (.f64 m m)))

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
17×	`associate-+l+_binary64`
15×	`prod-diff_binary64`

Counts

3 → 98

Calls

3 calls:

20.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 1) (/.f64 (pow.f64 m 3) v))
4.0ms	(-.f64 m (.f64 2 (.f64 m m)))
4.0ms	(/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Rules

841×	`distribute-rgt-in_binary64`
817×	`distribute-lft-in_binary64`
668×	`fma-def_binary64`
142×	`cancel-sign-sub-inv_binary64`
101×	`fma-neg_binary64`

Counts

158 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	3117
1	449	2877
2	1470	2531
3	5623	2531

prune257.0ms (6.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	247	5	252

Error

0.0b

Counts

252 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 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 (pow.f64 m 3) (/.f64 1 v)))
	0.2b	(.f64 (fma.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v) -1) (-.f64 1 m))
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))

Compiler

Compiled 7118 to 4243 computations (40.4% saved)

localize11.0ms (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) (/.f64 1 v)))
	0.0b	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
	0.3b	(*.f64 (/.f64 m v) m)
✓	9.0b	(*.f64 (pow.f64 m 3) (/.f64 1 v))

series31.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (.f64 (/.f64 m v) m) 1)) (.f64 (pow.f64 m 3) (/.f64 1 v)))
13.0ms	(*.f64 (pow.f64 m 3) (/.f64 1 v))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
25×	`add-exp-log_binary64`
21×	`add-cube-cbrt_binary64`
17×	`associate-+l+_binary64`

Counts

2 → 106

Calls

2 calls:

10.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (.f64 (/.f64 m v) m) 1)) (.f64 (pow.f64 m 3) (/.f64 1 v)))
7.0ms	(*.f64 (pow.f64 m 3) (/.f64 1 v))

simplify100.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary64`
337×	`associate-/l*_binary64`
285×	`cancel-sign-sub-inv_binary64`
283×	`associate-*l/_binary64`
167×	`associate-l_binary64`

Counts

154 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2814
1	444	2654
2	1842	2416
3	4550	2416
4	4983	2416

prune287.0ms (7.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	275	5	280

Error

0.0b

Counts

280 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 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 (pow.f64 m 3) (/.f64 1 v)))
	0.2b	(.f64 (fma.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v) -1) (-.f64 1 m))
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))

Compiler

Compiled 9255 to 4373 computations (52.7% saved)

regimes352.0ms (9.3%)

Accuracy

Total 0.1b remaining (85.5%)

Threshold costs 0.1b (85.5%)

Counts

132 → 1

Compiler

Compiled 7481 to 5115 computations (31.6% saved)

simplify3.0ms (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

end84.0ms (2.2%)

Compiler: Compiled 134 to 92 computations (31.3% saved)

Details

analyze65.0ms (1.7%)

sample1.1s (29.2%)

simplify123.0ms (3.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series33.0ms (0.9%)

rewrite43.0ms (1.1%)

simplify136.0ms (3.6%)

prune331.0ms (8.7%)

localize10.0ms (0.3%)

series53.0ms (1.4%)

rewrite48.0ms (1.3%)

simplify139.0ms (3.7%)

prune388.0ms (10.2%)

localize11.0ms (0.3%)

series35.0ms (0.9%)

rewrite34.0ms (0.9%)

simplify74.0ms (2%)

prune257.0ms (6.8%)

localize11.0ms (0.3%)

series31.0ms (0.8%)

rewrite28.0ms (0.7%)

simplify100.0ms (2.6%)

prune287.0ms (7.6%)

regimes352.0ms (9.3%)

simplify3.0ms (0.1%)

end84.0ms (2.2%)

Profiling