Details

analyze774.0ms (12.4%)

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
1.6%	98.2%	0.2%	8
19.1%	80.7%	0.2%	9
22%	77.8%	0.2%	10
34.5%	65.3%	0.2%	11
44.2%	55.7%	0.2%	12
53.3%	45.5%	1.2%	13
55.8%	42.7%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (17.9%)

Results

959.0ms	8256×	body	128	valid
62.0ms	580×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify115.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-neg_binary64`
909×	`div-sub_binary64`
615×	`times-frac_binary64`
547×	`fma-def_binary64`
362×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	29	13
3	67	13
4	136	13
5	250	13
6	551	13
7	1395	13
8	2791	13
9	2886	13
10	3210	13
11	3295	13
12	3304	13
13	3354	13
14	4929	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

1.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	1.1b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series51.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
20.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

9.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
6.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify134.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
905×	`times-frac_binary64`
465×	`fma-neg_binary64`
154×	`associate-/l*_binary64`
144×	`+-commutative_binary64`

Counts

190 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4749
1	800	4617
2	2672	4102
3	4971	4102
4	5241	4102

prune145.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	186	7	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	7	194

Error

Counts

194 → 7

Alt Table

Status	Error	Program
	36.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
▶	1.2b	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
	1.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 z y))) t))
	17.7b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	1.2b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	10.8b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	12.1b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 4667 to 1339 computations (71.3% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 z y))
✓	0.0b	(-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y)))
✓	0.0b	(/.f64 y (-.f64 z y))
✓	1.1b	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)

series91.0ms (1.4%)

Counts

4 → 111

Calls

4 calls:

43.0ms	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
21.0ms	(-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y)))
17.0ms	(/.f64 x (-.f64 z y))
10.0ms	(/.f64 y (-.f64 z y))

rewrite180.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

758×	`*-un-lft-identity_binary64`
740×	`add-sqr-sqrt_binary64`
726×	`times-frac_binary64`
441×	`prod-diff_binary64`
426×	`add-cube-cbrt_binary64`

Counts

4 → 630

Calls

4 calls:

29.0ms	(-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y)))
23.0ms	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
4.0ms	(/.f64 x (-.f64 z y))
3.0ms	(/.f64 y (-.f64 z y))

simplify593.0ms (9.5%)

Algorithm

1×	egg-herbie

Rules

306×	`fma-udef_binary64`
281×	`fma-neg_binary64`
262×	`unsub-neg_binary64`
259×	`associate-+r-_binary64`
206×	`associate-/l*_binary64`

Counts

741 → 715

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	726	45215
1	1746	27881
2	4397	27065
3	5070	27065

prune492.0ms (7.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	715	0	715
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	715	7	722

Error

Counts

722 → 7

Alt Table

Status	Error	Program
	36.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
✓	1.2b	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
▶	1.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 z y))) t))
	17.7b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	1.2b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	10.8b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	12.1b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 32649 to 6103 computations (81.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
✓	0.5b	(cbrt.f64 (-.f64 x y))
✓	0.5b	(cbrt.f64 (-.f64 z y))

series138.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

37.0ms	(*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))
36.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
34.0ms	(cbrt.f64 (-.f64 x y))
31.0ms	(cbrt.f64 (-.f64 z y))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`cbrt-prod_binary64`
58×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
28×	`cbrt-div_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 150

Calls

4 calls:

10.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
8.0ms	(*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))
2.0ms	(cbrt.f64 (-.f64 z y))
2.0ms	(cbrt.f64 (-.f64 x y))

simplify145.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

420×	`associate-r_binary64`
395×	`times-frac_binary64`
371×	`fma-neg_binary64`
315×	`associate-l_binary64`
230×	`fma-def_binary64`

Counts

246 → 289

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	425	6024
1	1123	5824
2	3769	5644
3	4975	5644

prune351.0ms (5.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	491	0	491
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	491	7	498

Error

Counts

498 → 7

Alt Table

Status	Error	Program
	36.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
✓	1.2b	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
✓	1.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 z y))) t))
	17.7b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
▶	1.2b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	10.8b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	12.1b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 22725 to 6935 computations (69.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z y) (-.f64 x y))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
✓	1.1b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)

series81.0ms (1.3%)

Counts

3 → 120

Calls

3 calls:

33.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
29.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
20.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

rewrite79.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

392×	`times-frac_binary64`
335×	`add-sqr-sqrt_binary64`
323×	`*-un-lft-identity_binary64`
157×	`add-cube-cbrt_binary64`
98×	`associate-l_binary64`

Counts

3 → 332

Calls

3 calls:

19.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
9.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
8.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

simplify210.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

543×	`sub-neg_binary64`
246×	`associate-/l*_binary64`
241×	`fma-neg_binary64`
211×	`+-commutative_binary64`
210×	`associate--l+_binary64`

Counts

452 → 498

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	10707
1	1107	10159
2	4250	9700
3	5224	9700

prune322.0ms (5.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	498	0	498
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	498	7	505

Error

Counts

505 → 7

Alt Table

Status	Error	Program
	36.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
✓	1.2b	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
✓	1.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 z y))) t))
	17.7b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	1.2b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	10.8b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	12.1b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 12465 to 3977 computations (68.1% saved)

regimes1.0s (16.7%)

Accuracy

Total 2.2b remaining (99.3%)

Threshold costs 0b (0%)

Counts

150 → 1

Compiler

Compiled 18705 to 10545 computations (43.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	18	13
3	20	13
4	21	13
5	21	13

end92.0ms (1.5%)

Compiler: Compiled 169 to 89 computations (47.3% saved)

Details

analyze774.0ms (12.4%)

sample1.1s (17.9%)

simplify115.0ms (1.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series51.0ms (0.8%)

rewrite23.0ms (0.4%)

simplify134.0ms (2.1%)

prune145.0ms (2.3%)

localize7.0ms (0.1%)

series91.0ms (1.4%)

rewrite180.0ms (2.9%)

simplify593.0ms (9.5%)

prune492.0ms (7.9%)

localize13.0ms (0.2%)

series138.0ms (2.2%)

rewrite34.0ms (0.5%)

simplify145.0ms (2.3%)

prune351.0ms (5.6%)

localize7.0ms (0.1%)

series81.0ms (1.3%)

rewrite79.0ms (1.3%)

simplify210.0ms (3.4%)

prune322.0ms (5.2%)

regimes1.0s (16.7%)

simplify2.0ms (0%)

end92.0ms (1.5%)

Profiling