Details

analyze102.0ms (2.5%)

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)

sample149.0ms (3.6%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
6.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify122.0ms (3%)

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
▶	0.1b	(.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)

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

series35.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite90.0ms (2.2%)

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:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
7.0ms	(-.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))

simplify140.0ms (3.4%)

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

prune255.0ms (6.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	290	4	294
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	292	4	296

Error

Counts

296 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 (-.f64 (/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m)))) v) 1) (-.f64 1 m))
▶	0.1b	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -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))
	26.1b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)

Compiler

Compiled 7201 to 4602 computations (36.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series38.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)
11.0ms	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 m))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 61

Calls

2 calls:

7.0ms	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 m))
0.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

simplify100.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

391×	`fma-neg_binary64`
371×	`distribute-rgt-in_binary64`
350×	`distribute-lft-in_binary64`
329×	`neg-mul-1_binary64`
319×	`fma-def_binary64`

Counts

109 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	2481
1	235	2251
2	825	2117
3	2623	1837
4	4254	1837
5	4882	1837

prune86.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	102	4	106

Error

Counts

106 → 4

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 (/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m)))) v) 1) (-.f64 1 m))
✓	0.1b	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -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))
	26.1b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)

Compiler

Compiled 2403 to 1340 computations (44.2% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 m m) (.f64 1 m))
✓	0.0b	(.f64 (-.f64 (/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m)))) v) 1) (-.f64 1 m))
✓	0.1b	(/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m)))) v)
✓	0.1b	(/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m))))

series125.0ms (3%)

Counts

4 → 72

Calls

4 calls:

63.0ms	(.f64 (-.f64 (/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m)))) v) 1) (-.f64 1 m))
55.0ms	(/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m)))) v)
4.0ms	(/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m))))
2.0ms	(+.f64 (.f64 m m) (.f64 1 m))

rewrite103.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

216×	`*-un-lft-identity_binary64`
187×	`times-frac_binary64`
124×	`add-sqr-sqrt_binary64`
98×	`add-cube-cbrt_binary64`
68×	`distribute-lft-out_binary64`

Counts

4 → 257

Calls

4 calls:

35.0ms	(.f64 (-.f64 (/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m)))) v) 1) (-.f64 1 m))
16.0ms	(/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m)))) v)
11.0ms	(/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (*.f64 1 m))))
3.0ms	(+.f64 (.f64 m m) (.f64 1 m))

simplify256.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

866×	`div-sub_binary64`
700×	`fma-neg_binary64`
233×	`distribute-rgt-in_binary64`
217×	`associate-l_binary64`
215×	`distribute-lft-in_binary64`

Counts

329 → 382

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	381	10685
1	905	10302
2	3394	9788
3	4366	9788
4	5739	9788

prune547.0ms (13.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	382	0	382
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	382	4	386

Error

Counts

386 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m)))) v) 1) (-.f64 1 m))
✓	0.1b	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -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))
	26.1b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)

Compiler

Compiled 15956 to 10625 computations (33.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) (-.f64 1 m))
✓	0.2b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
✓	0.3b	(fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1)
✓	0.3b	(/.f64 m (sqrt.f64 v))

series149.0ms (3.6%)

Counts

4 → 50

Calls

4 calls:

57.0ms	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) (-.f64 1 m))
40.0ms	(fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1)
26.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
25.0ms	(/.f64 m (sqrt.f64 v))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
56×	`add-cube-cbrt_binary64`
54×	`times-frac_binary64`
33×	`sqrt-prod_binary64`

Counts

4 → 167

Calls

4 calls:

6.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
6.0ms	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) (-.f64 1 m))
3.0ms	(/.f64 m (sqrt.f64 v))
0.0ms	(fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1)

simplify156.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

786×	`times-frac_binary64`
528×	`fma-def_binary64`
359×	`distribute-rgt-in_binary64`
331×	`distribute-lft-in_binary64`
302×	`fma-neg_binary64`

Counts

217 → 223

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	4642
1	440	4395
2	1475	3761
3	4284	3625
4	4952	3625
5	4925	3625

prune202.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	223	4	227

Error

Counts

227 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (/.f64 (+.f64 m (neg.f64 (pow.f64 m 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m)))) v) 1) (-.f64 1 m))
✓	0.1b	(*.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -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))
	26.1b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)

Compiler

Compiled 5617 to 2929 computations (47.9% saved)

regimes471.0ms (11.4%)

Accuracy

Total 0.1b remaining (76.5%)

Threshold costs 0.1b (76.5%)

Counts

160 → 1

Compiler

Compiled 10033 to 6992 computations (30.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
3×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	21	29
2	27	27
3	33	27
4	41	27
5	43	27
6	44	27
7	42	27

end1.0ms (0%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

sample917.0ms (22.2%)

Algorithm

1×

intervals

Results

388.0ms	8000×	body	128	valid
181.0ms	8056×	pre	128	true
3.0ms	56×	body	128	invalid

Compiler

Compiled 122 to 86 computations (29.5% saved)

Details

analyze102.0ms (2.5%)

sample149.0ms (3.6%)

simplify122.0ms (3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series35.0ms (0.9%)

rewrite90.0ms (2.2%)

simplify140.0ms (3.4%)

prune255.0ms (6.2%)

localize6.0ms (0.1%)

series38.0ms (0.9%)

rewrite13.0ms (0.3%)

simplify100.0ms (2.4%)

prune86.0ms (2.1%)

localize17.0ms (0.4%)

series125.0ms (3%)

rewrite103.0ms (2.5%)

simplify256.0ms (6.2%)

prune547.0ms (13.3%)

localize8.0ms (0.2%)

series149.0ms (3.6%)

rewrite27.0ms (0.7%)

simplify156.0ms (3.8%)

prune202.0ms (4.9%)

regimes471.0ms (11.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample917.0ms (22.2%)

Profiling