Details

analyze64.0ms (1.6%)

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 24 to 17 computations (29.2% saved)

sample1.2s (31.2%)

Results

914.0ms	8256×	body	128	valid
6.0ms	59×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify118.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

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 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series24.0ms (0.6%)

Counts

3 → 56

Calls

3 calls:

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

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 102

Calls

3 calls:

8.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
5.0ms	(*.f64 m (-.f64 1 m))

simplify85.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
423×	`distribute-rgt-in_binary64`
385×	`distribute-lft-in_binary64`
346×	`associate-/l/_binary64`
288×	`fma-neg_binary64`

Counts

158 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	2119
1	364	1923
2	1597	1729
3	4495	1728
4	4950	1728

prune165.0ms (4.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	163	6	169
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	6	171

Error

0.0b

Counts

171 → 6

Alt Table

Status	Error	Program
	8.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	37.0b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	1.4b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
▶	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	12.7b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))

Compiler

Compiled 3407 to 1905 computations (44.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 m (*.f64 m m))
✓	0.1b	(/.f64 v (-.f64 m (*.f64 m m)))
✓	0.1b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
✓	0.2b	(/.f64 1 (/.f64 v (-.f64 m (*.f64 m m))))

series58.0ms (1.5%)

Counts

4 → 84

Calls

4 calls:

31.0ms	(/.f64 v (-.f64 m (*.f64 m m)))
13.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
11.0ms	(/.f64 1 (/.f64 v (-.f64 m (*.f64 m m))))
2.0ms	(-.f64 m (*.f64 m m))

rewrite51.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
127×	`add-sqr-sqrt_binary64`
107×	`*-un-lft-identity_binary64`
76×	`add-cube-cbrt_binary64`
27×	`difference-of-squares_binary64`

Counts

4 → 210

Calls

4 calls:

20.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
8.0ms	(/.f64 1 (/.f64 v (-.f64 m (*.f64 m m))))
3.0ms	(/.f64 v (-.f64 m (*.f64 m m)))
2.0ms	(-.f64 m (*.f64 m m))

simplify149.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

375×	`fma-neg_binary64`
361×	`fma-def_binary64`
342×	`distribute-rgt-in_binary64`
332×	`times-frac_binary64`
314×	`distribute-lft-in_binary64`

Counts

294 → 330

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	5283
1	491	4765
2	1492	4639
3	4301	4639
4	5170	4639

prune264.0ms (6.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	330	0	330
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	330	6	336

Error

0.0b

Counts

336 → 6

Alt Table

Status	Error	Program
	8.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	37.0b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	1.4b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
▶	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	12.7b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))

Compiler

Compiled 7408 to 3036 computations (59% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.2b	(/.f64 m (sqrt.f64 v))
✓	0.2b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
✓	0.4b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

series101.0ms (2.6%)

Counts

4 → 64

Calls

4 calls:

36.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
22.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
21.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
21.0ms	(/.f64 m (sqrt.f64 v))

rewrite60.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
113×	`*-un-lft-identity_binary64`
74×	`add-cube-cbrt_binary64`
66×	`sqrt-prod_binary64`

Counts

4 → 221

Calls

4 calls:

20.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
11.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
6.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
3.0ms	(/.f64 m (sqrt.f64 v))

simplify138.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

481×	`associate-/l/_binary64`
442×	`distribute-rgt-in_binary64`
429×	`distribute-lft-in_binary64`
194×	`fma-def_binary64`
178×	`associate-l_binary64`

Counts

285 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	5114
1	598	4634
2	1976	4496
3	4784	4496
4	4984	4496

prune228.0ms (5.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	292	6	298

Error

0.0b

Counts

298 → 6

Alt Table

Status	Error	Program
	8.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	37.0b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
▶	1.4b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
✓	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	12.7b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))

Compiler

Compiled 6872 to 3343 computations (51.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (.f64 (cbrt.f64 m) (cbrt.f64 m)))
✓	0.3b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.5b	(*.f64 (cbrt.f64 m) (cbrt.f64 m))
✓	0.6b	(cbrt.f64 m)

series184.0ms (4.7%)

Counts

4 → 72

Calls

4 calls:

100.0ms	(.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (.f64 (cbrt.f64 m) (cbrt.f64 m)))
35.0ms	(*.f64 (cbrt.f64 m) (cbrt.f64 m))
32.0ms	(cbrt.f64 m)
16.0ms	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 102

Calls

4 calls:

7.0ms	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
6.0ms	(*.f64 (cbrt.f64 m) (cbrt.f64 m))
5.0ms	(.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (.f64 (cbrt.f64 m) (cbrt.f64 m)))
1.0ms	(cbrt.f64 m)

simplify86.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-def_binary64`
731×	`unswap-sqr_binary64`
428×	`*-commutative_binary64`
304×	`fma-neg_binary64`
199×	`associate-l_binary64`

Counts

174 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2923
1	334	2349
2	1169	2180
3	2901	2152
4	5054	2152

prune104.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	210	6	216

Error

0.0b

Counts

216 → 6

Alt Table

Status	Error	Program
	8.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	37.0b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	1.4b	(.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (-.f64 m (.f64 m m)))) 1) m)
✓	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	12.7b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))

Compiler

Compiled 4599 to 2118 computations (53.9% saved)

regimes635.0ms (16.2%)

Accuracy

Total 0.1b remaining (80.3%)

Threshold costs 0.1b (80.3%)

Counts

209 → 1

Compiler

Compiled 12804 to 8149 computations (36.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	17	16
2	21	16
3	23	16
4	24	16
5	22	16

end90.0ms (2.3%)

Compiler: Compiled 150 to 99 computations (34% saved)

Details

analyze64.0ms (1.6%)

sample1.2s (31.2%)

simplify118.0ms (3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series24.0ms (0.6%)

rewrite25.0ms (0.6%)

simplify85.0ms (2.2%)

prune165.0ms (4.2%)

localize7.0ms (0.2%)

series58.0ms (1.5%)

rewrite51.0ms (1.3%)

simplify149.0ms (3.8%)

prune264.0ms (6.8%)

localize8.0ms (0.2%)

series101.0ms (2.6%)

rewrite60.0ms (1.5%)

simplify138.0ms (3.5%)

prune228.0ms (5.8%)

localize9.0ms (0.2%)

series184.0ms (4.7%)

rewrite23.0ms (0.6%)

simplify86.0ms (2.2%)

prune104.0ms (2.7%)

regimes635.0ms (16.2%)

simplify2.0ms (0.1%)

end90.0ms (2.3%)

Profiling