Details

analyze775.0ms (11.9%)

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 (17.4%)

Results

972.0ms	8256×	body	128	valid
62.0ms	603×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify113.0ms (1.7%)

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

3.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.1b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	2.9b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series50.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
19.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite25.0ms (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)
8.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify124.0ms (1.9%)

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

prune138.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	6	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	187	7	194

Error

Counts

194 → 7

Alt Table

Status	Error	Program
	16.8b	(.f64 (cbrt.f64 (.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (/.f64 (-.f64 x y) (-.f64 z y))) (/.f64 (-.f64 x y) (-.f64 z y)))) t)
	10.5b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	32.9b	(.f64 (.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y))) t)
✓	3.1b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
▶	4.2b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	11.1b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	11.2b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))

Compiler

Compiled 4626 to 1321 computations (71.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.6b	(cbrt.f64 t)
✓	0.9b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	2.3b	(.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))

series316.0ms (4.8%)

Counts

4 → 120

Calls

4 calls:

202.0ms	(.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
47.0ms	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
37.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
30.0ms	(cbrt.f64 t)

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
38×	`associate-l_binary64`
36×	`add-exp-log_binary64`
26×	`times-frac_binary64`

Counts

4 → 141

Calls

4 calls:

20.0ms	(.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
13.0ms	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
6.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)

simplify189.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

475×	`associate-r_binary64`
467×	`fma-neg_binary64`
350×	`associate-l_binary64`
206×	`*-commutative_binary64`
203×	`associate-/l*_binary64`

Counts

261 → 272

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	6368
1	1013	5556
2	4210	5079
3	4796	5079
4	4954	5079
5	4915	5079

prune162.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	308	0	308
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	308	7	315

Error

Counts

315 → 7

Alt Table

Status	Error	Program
	16.8b	(.f64 (cbrt.f64 (.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (/.f64 (-.f64 x y) (-.f64 z y))) (/.f64 (-.f64 x y) (-.f64 z y)))) t)
▶	10.5b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	32.9b	(.f64 (.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y))) t)
✓	3.1b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
✓	4.2b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	11.1b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	11.2b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))

Compiler

Compiled 8167 to 2450 computations (70% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	5.3b	(/.f64 (*.f64 t x) (-.f64 z y))
✓	10.4b	(/.f64 (*.f64 y t) (-.f64 z y))

series84.0ms (1.3%)

Counts

3 → 87

Calls

3 calls:

40.0ms	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
27.0ms	(/.f64 (*.f64 t x) (-.f64 z y))
17.0ms	(/.f64 (*.f64 y t) (-.f64 z y))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`times-frac_binary64`
121×	`prod-diff_binary64`
113×	`*-un-lft-identity_binary64`
113×	`add-sqr-sqrt_binary64`
56×	`associate-/r/_binary64`

Counts

3 → 221

Calls

3 calls:

15.0ms	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
4.0ms	(/.f64 (*.f64 y t) (-.f64 z y))
4.0ms	(/.f64 (*.f64 t x) (-.f64 z y))

simplify276.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

435×	`fma-neg_binary64`
321×	`sub-neg_binary64`
215×	`associate-/l*_binary64`
197×	`unsub-neg_binary64`
172×	`associate-l_binary64`

Counts

308 → 343

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	386	12003
1	994	10068
2	3722	8341
3	4484	8341
4	4970	8341
5	4868	8341

prune282.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	341	2	343
Fresh	2	2	4
Picked	0	1	1
Done	1	1	2
Total	344	6	350

Error

Counts

350 → 6

Alt Table

Status	Error	Program
	16.8b	(.f64 (cbrt.f64 (.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (/.f64 (-.f64 x y) (-.f64 z y))) (/.f64 (-.f64 x y) (-.f64 z y)))) t)
✓	10.5b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	3.1b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	10.6b	(.f64 (/.f64 1 (-.f64 z y)) (.f64 t (-.f64 x y)))
	11.1b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
▶	9.8b	(-.f64 (/.f64 t (/.f64 (-.f64 z y) x)) (/.f64 (*.f64 y t) (-.f64 z y)))

Compiler

Compiled 12923 to 2274 computations (82.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z y) x)
✓	0.0b	(-.f64 (/.f64 t (/.f64 (-.f64 z y) x)) (/.f64 (*.f64 y t) (-.f64 z y)))
✓	6.1b	(/.f64 t (/.f64 (-.f64 z y) x))
	10.4b	(/.f64 (*.f64 y t) (-.f64 z y))

series87.0ms (1.3%)

Counts

3 → 124

Calls

3 calls:

47.0ms	(-.f64 (/.f64 t (/.f64 (-.f64 z y) x)) (/.f64 (*.f64 y t) (-.f64 z y)))
30.0ms	(/.f64 t (/.f64 (-.f64 z y) x))
10.0ms	(/.f64 (-.f64 z y) x)

rewrite303.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

1674×	`times-frac_binary64`
1142×	`add-sqr-sqrt_binary64`
1135×	`*-un-lft-identity_binary64`
759×	`add-cube-cbrt_binary64`
682×	`prod-diff_binary64`

Counts

3 → 909

Calls

3 calls:

45.0ms	(-.f64 (/.f64 t (/.f64 (-.f64 z y) x)) (/.f64 (*.f64 y t) (-.f64 z y)))
6.0ms	(/.f64 t (/.f64 (-.f64 z y) x))
4.0ms	(/.f64 (-.f64 z y) x)

simplify1.0s (15.6%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-neg_binary64`
500×	`fma-udef_binary64`
347×	`unsub-neg_binary64`
271×	`associate-*l/_binary64`
225×	`associate-/r/_binary64`

Counts

1033 → 1181

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	895	64934
1	1800	52048
2	4762	52048
3	5350	52048

prune633.0ms (9.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1236	0	1236
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1236	6	1242

Error

Counts

1242 → 6

Alt Table

Status	Error	Program
	16.8b	(.f64 (cbrt.f64 (.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (/.f64 (-.f64 x y) (-.f64 z y))) (/.f64 (-.f64 x y) (-.f64 z y)))) t)
✓	10.5b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	3.1b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	10.6b	(.f64 (/.f64 1 (-.f64 z y)) (.f64 t (-.f64 x y)))
	11.1b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	9.8b	(-.f64 (/.f64 t (/.f64 (-.f64 z y) x)) (/.f64 (*.f64 y t) (-.f64 z y)))

Compiler

Compiled 63030 to 8538 computations (86.5% saved)

regimes595.0ms (9.1%)

Accuracy

Total 1.1b remaining (98.3%)

Threshold costs 0b (0%)

Counts

93 → 1

Compiler

Compiled 11583 to 6521 computations (43.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	49
1	20	49
2	26	49
3	28	49
4	29	49
5	29	49

end72.0ms (1.1%)

Compiler: Compiled 179 to 85 computations (52.5% saved)

Details

analyze775.0ms (11.9%)

sample1.1s (17.4%)

simplify113.0ms (1.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series50.0ms (0.8%)

rewrite25.0ms (0.4%)

simplify124.0ms (1.9%)

prune138.0ms (2.1%)

localize19.0ms (0.3%)

series316.0ms (4.8%)

rewrite51.0ms (0.8%)

simplify189.0ms (2.9%)

prune162.0ms (2.5%)

localize9.0ms (0.1%)

series84.0ms (1.3%)

rewrite55.0ms (0.8%)

simplify276.0ms (4.2%)

prune282.0ms (4.3%)

localize8.0ms (0.1%)

series87.0ms (1.3%)

rewrite303.0ms (4.7%)

simplify1.0s (15.6%)

prune633.0ms (9.7%)

regimes595.0ms (9.1%)

simplify3.0ms (0%)

end72.0ms (1.1%)

Profiling