Details

analyze547.0ms (10%)

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)

sample1.3s (24.4%)

Results

1.0s	8256×	body	128	valid
147.0ms	1186×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify62.0ms (1.1%)

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

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	2.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

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 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	3.8b	(*.f64 (/.f64 x y) z)

series42.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

20.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
16.0ms	(*.f64 (/.f64 x y) z)
6.0ms	(/.f64 (+.f64 x 4) y)

rewrite26.0ms (0.5%)

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

simplify122.0ms (2.2%)

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

prune104.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	175	4	179

Error

0.0b

Counts

179 → 4

Alt Table

Status	Error	Program
	2.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
▶	2.1b	(fabs.f64 (-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z)))
	30.4b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 3632 to 1704 computations (53.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z))
✓	0.0b	(/.f64 y (+.f64 x 4))
✓	0.1b	(/.f64 1 (/.f64 y (+.f64 x 4)))
	3.8b	(*.f64 (/.f64 x y) z)

series40.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

23.0ms	(-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z))
11.0ms	(/.f64 y (+.f64 x 4))
6.0ms	(/.f64 1 (/.f64 y (+.f64 x 4)))

rewrite64.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

294×	`times-frac_binary64`
217×	`*-un-lft-identity_binary64`
149×	`add-sqr-sqrt_binary64`
149×	`add-cube-cbrt_binary64`
59×	`fma-neg_binary64`

Counts

3 → 266

Calls

3 calls:

21.0ms	(-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z))
9.0ms	(/.f64 1 (/.f64 y (+.f64 x 4)))
4.0ms	(/.f64 y (+.f64 x 4))

simplify210.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

623×	`times-frac_binary64`
573×	`fma-def_binary64`
483×	`fma-neg_binary64`
228×	`distribute-rgt-in_binary64`
213×	`associate-/r/_binary64`

Counts

350 → 344

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	225	6846
1	524	6023
2	1718	5222
3	4254	5141
4	4693	5082
5	4868	5082

prune262.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	400	0	400
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	400	4	404

Error

0.0b

Counts

404 → 4

Alt Table

Status	Error	Program
▶	2.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
✓	2.1b	(fabs.f64 (-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z)))
	30.4b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 9982 to 5398 computations (45.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 z)
✓	0.6b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	1.3b	(.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
✓	2.8b	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))

series896.0ms (16.4%)

Counts

4 → 96

Calls

4 calls:

802.0ms	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms	(cbrt.f64 z)
27.0ms	(.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

9.0ms	(.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
9.0ms	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
6.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify118.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

807×	`unswap-sqr_binary64`
622×	`associate-*l/_binary64`
554×	`*-commutative_binary64`
396×	`associate-*r/_binary64`
354×	`associate-/l*_binary64`

Counts

219 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	2506
1	333	2092
2	1282	1957
3	3491	1929
4	4944	1929
5	4942	1929

prune224.0ms (4.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	218	5	223

Error

Counts

223 → 5

Alt Table

Status	Error	Program
▶	3.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))))
✓	2.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
✓	2.1b	(fabs.f64 (-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z)))
	30.4b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 5327 to 2149 computations (59.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 z)
	0.6b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	1.3b	(.f64 (/.f64 (.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))
✓	4.7b	(/.f64 (.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y)

series748.0ms (13.7%)

Counts

2 → 72

Calls

2 calls:

671.0ms	(/.f64 (.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y)
76.0ms	(.f64 (/.f64 (.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64`
10×	`prod-exp_binary64`

Counts

2 → 60

Calls

2 calls:

10.0ms	(.f64 (/.f64 (.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))
6.0ms	(/.f64 (.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) y)

simplify110.0ms (2%)

Algorithm

1×	egg-herbie

Rules

843×	`associate-/l*_binary64`
769×	`times-frac_binary64`
497×	`associate-*r/_binary64`
260×	`associate-/r*_binary64`
240×	`associate-/l/_binary64`

Counts

132 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	2167
1	282	1585
2	958	1509
3	4311	1509
4	4731	1509
5	4966	1509
6	4959	1509

prune157.0ms (2.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	216	5	221

Error

Counts

221 → 5

Alt Table

Status	Error	Program
✓	3.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 x (*.f64 (cbrt.f64 z) (cbrt.f64 z))) y) (cbrt.f64 z))))
✓	2.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
✓	2.1b	(fabs.f64 (-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z)))
	30.4b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 5215 to 2064 computations (60.4% saved)

regimes198.0ms (3.6%)

Accuracy

Total 0.8b remaining (97.7%)

Threshold costs 0.8b (97.7%)

Counts

24 → 3

Compiler

Compiled 2017 to 1351 computations (33% saved)

bsearch26.0ms (0.5%)

Steps

Iters	Range		Point
1	-3.7882663614506026e-278	-4.009638615065686e-282	-3.864679112187972e-280
8	-1.2097608397976797e+35	-1.387662742264533e+31	-1.6209712599203426e+31

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
13×	`sub-neg_binary64`
9×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	55
1	49	55
2	74	55
3	92	55
4	107	55
5	112	55
6	113	55
7	110	55

end83.0ms (1.5%)

Compiler: Compiled 166 to 105 computations (36.7% saved)

Details

analyze547.0ms (10%)

sample1.3s (24.4%)

simplify62.0ms (1.1%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series42.0ms (0.8%)

rewrite26.0ms (0.5%)

simplify122.0ms (2.2%)

prune104.0ms (1.9%)

localize11.0ms (0.2%)

series40.0ms (0.7%)

rewrite64.0ms (1.2%)

simplify210.0ms (3.8%)

prune262.0ms (4.8%)

localize11.0ms (0.2%)

series896.0ms (16.4%)

rewrite32.0ms (0.6%)

simplify118.0ms (2.2%)

prune224.0ms (4.1%)

localize11.0ms (0.2%)

series748.0ms (13.7%)

rewrite21.0ms (0.4%)

simplify110.0ms (2%)

prune157.0ms (2.9%)

regimes198.0ms (3.6%)

bsearch26.0ms (0.5%)

simplify4.0ms (0.1%)

end83.0ms (1.5%)

Profiling