Details

analyze583.0ms (9.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
45.2%	53.8%	0.9%	9
50.3%	47.8%	1.9%	10
54%	43.6%	2.4%	11
61.7%	32.9%	5.4%	12
64.1%	28.3%	7.6%	13
66.2%	24.7%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (21.8%)

Results

1.1s	8256×	body	128	valid
143.0ms	1204×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1167×	`fma-def_binary64`
1073×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	43	18
3	75	18
4	123	16
5	213	16
6	302	16
7	472	16
8	1009	13
9	1328	13
10	1542	13
11	1559	13
12	1556	13
13	1556	13
14	1453	13

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	2.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	3.6b	(*.f64 (/.f64 x y) z)

series43.0ms (0.7%)

Counts

3 → 96

Calls

3 calls:

22.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
15.0ms	(*.f64 (/.f64 x y) z)
6.0ms	(/.f64 (+.f64 x 4) y)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

3 → 117

Calls

3 calls:

8.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
6.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

simplify127.0ms (2%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-l_binary64`
381×	`fma-def_binary64`
379×	`associate-*l/_binary64`
369×	`associate-r_binary64`
310×	`fma-neg_binary64`

Counts

213 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	187	3147
1	457	2896
2	1229	2394
3	3977	2382
4	4927	2330
5	4911	2330

prune140.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	172	7	179

Error

Counts

179 → 7

Alt Table

Status	Error	Program
	3.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
	23.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (.f64 (/.f64 x y) z)) (sqrt.f64 (*.f64 (/.f64 x y) z)))))
▶	2.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 x y) z)) (cbrt.f64 (.f64 (/.f64 x y) z))) (cbrt.f64 (*.f64 (/.f64 x y) z)))))
	30.1b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	28.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
✓	2.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	2.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 3733 to 1759 computations (52.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 x y) z)) (cbrt.f64 (.f64 (/.f64 x y) z))) (cbrt.f64 (*.f64 (/.f64 x y) z)))
✓	0.4b	(.f64 (cbrt.f64 (.f64 (/.f64 x y) z)) (cbrt.f64 (*.f64 (/.f64 x y) z)))
	3.6b	(*.f64 (/.f64 x y) z)
✓	12.2b	(cbrt.f64 (*.f64 (/.f64 x y) z))

series2.6s (42%)

Counts

3 → 108

Calls

3 calls:

1.6s

(*.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) (cbrt.f64 (*.f64 (/.f64 x y) z)))

941.0ms

(cbrt.f64 (*.f64 (/.f64 x y) z))

63.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) (cbrt.f64 (*.f64 (/.f64 x y) z))) (cbrt.f64 (*.f64 (/.f64 x y) z)))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
23×	`associate-*l/_binary64`
17×	`cbrt-div_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`

Counts

3 → 90

Calls

3 calls:

7.0ms

(*.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) (cbrt.f64 (*.f64 (/.f64 x y) z)))

7.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) (cbrt.f64 (*.f64 (/.f64 x y) z))) (cbrt.f64 (*.f64 (/.f64 x y) z)))

3.0ms

(cbrt.f64 (*.f64 (/.f64 x y) z))

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
406×	`fma-neg_binary64`
285×	`associate-*l/_binary64`
224×	`associate-*r/_binary64`
208×	`*-commutative_binary64`

Counts

198 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3329
1	402	3109
2	969	2609
3	3716	2609
4	4917	2609
5	4991	2609

prune330.0ms (5.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	384	0	384
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	384	7	391

Error

Counts

391 → 7

Alt Table

Status	Error	Program
	3.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
	23.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (.f64 (/.f64 x y) z)) (sqrt.f64 (*.f64 (/.f64 x y) z)))))
✓	2.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 x y) z)) (cbrt.f64 (.f64 (/.f64 x y) z))) (cbrt.f64 (*.f64 (/.f64 x y) z)))))
	30.1b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	28.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
✓	2.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	2.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 12470 to 3690 computations (70.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.4b	(/.f64 (-.f64 x (fma.f64 x z -4)) y)

series18.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

18.0ms

(/.f64 (-.f64 x (fma.f64 x z -4)) y)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

1 → 40

Calls

1 calls:

5.0ms

(/.f64 (-.f64 x (fma.f64 x z -4)) y)

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

552×	`distribute-rgt-in_binary64`
532×	`distribute-lft-in_binary64`
426×	`fma-def_binary64`
406×	`times-frac_binary64`
357×	`div-sub_binary64`

Counts

76 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1438
1	224	1392
2	495	1134
3	1230	1134
4	4511	1134
5	4991	1134

prune62.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	72	5	77

Error

Counts

77 → 5

Alt Table

Status	Error	Program
	23.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (.f64 (/.f64 x y) z)) (sqrt.f64 (*.f64 (/.f64 x y) z)))))
▶	2.6b	(fabs.f64 (*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y)))
✓	2.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 x y) z)) (cbrt.f64 (.f64 (/.f64 x y) z))) (cbrt.f64 (*.f64 (/.f64 x y) z)))))
	30.1b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	2.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 1364 to 814 computations (40.3% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.5b	(*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y))

series18.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

18.0ms

(*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 44

Calls

1 calls:

8.0ms

(*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y))

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

845×	`fma-def_binary64`
306×	`fma-neg_binary64`
290×	`associate-/l*_binary64`
272×	`associate-l_binary64`
230×	`div-sub_binary64`

Counts

80 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1400
1	243	1310
2	689	1046
3	2012	1046
4	4555	1046
5	4996	1046
6	4951	1046

prune62.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	80	5	85

Error

Counts

85 → 5

Alt Table

Status	Error	Program
	23.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (.f64 (/.f64 x y) z)) (sqrt.f64 (*.f64 (/.f64 x y) z)))))
✓	2.6b	(fabs.f64 (*.f64 (-.f64 x (fma.f64 x z -4)) (/.f64 1 y)))
✓	2.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 x y) z)) (cbrt.f64 (.f64 (/.f64 x y) z))) (cbrt.f64 (*.f64 (/.f64 x y) z)))))
	30.1b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	2.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 1555 to 997 computations (35.9% saved)

regimes316.0ms (5.1%)

Accuracy

Total 0.1b remaining (80.2%)

Threshold costs 0.1b (80.2%)

Counts

45 → 2

Compiler

Compiled 4057 to 2686 computations (33.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
11×	`sub-neg_binary64`
8×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	54
1	38	54
2	58	54
3	74	54
4	89	54
5	95	54
6	96	54
7	93	54

end83.0ms (1.3%)

Compiler: Compiled 173 to 100 computations (42.2% saved)

Details

analyze583.0ms (9.4%)

sample1.4s (21.8%)

simplify63.0ms (1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series43.0ms (0.7%)

rewrite26.0ms (0.4%)

simplify127.0ms (2%)

prune140.0ms (2.2%)

localize12.0ms (0.2%)

series2.6s (42%)

rewrite26.0ms (0.4%)

simplify125.0ms (2%)

prune330.0ms (5.3%)

localize6.0ms (0.1%)

series18.0ms (0.3%)

rewrite8.0ms (0.1%)

simplify73.0ms (1.2%)

prune62.0ms (1%)

localize11.0ms (0.2%)

series18.0ms (0.3%)

rewrite12.0ms (0.2%)

simplify88.0ms (1.4%)

prune62.0ms (1%)

regimes316.0ms (5.1%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end83.0ms (1.3%)

Profiling