Details

analyze1.2s (15.9%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
2.3%	91.3%	6.4%	9
3.5%	87%	9.5%	10
4.1%	86.4%	9.5%	11
18.4%	66.6%	15%	12
20.5%	61.8%	17.7%	13
21.9%	60.4%	17.7%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.6s (33.9%)

Results

952.0ms	6297×	body	128	valid
627.0ms	969×	body	1024	valid
280.0ms	620×	body	512	valid
218.0ms	1558×	body	128	invalid
128.0ms	195×	body	1024	invalid
121.0ms	276×	body	512	invalid
105.0ms	366×	body	256	valid
44.0ms	167×	body	256	invalid
4.0ms	4×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
522×	`unswap-sqr_binary64`
335×	`fma-neg_binary64`
256×	`associate-l_binary64`
216×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	19	16
2	28	16
3	56	16
4	119	16
5	280	16
6	672	16
7	2284	16
8	4398	16
9	4953	16

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

4.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.6b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

Compiler

Compiled 55 to 31 computations (43.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	0.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
✓	0.0b	(/.f64 y (+.f64 y z))
✓	5.4b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series167.0ms (2.2%)

Counts

4 → 108

Calls

4 calls:

91.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
43.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
25.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
7.0ms	(/.f64 y (+.f64 y z))

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
122×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
82×	`add-sqr-sqrt_binary64`
82×	`add-cube-cbrt_binary64`

Counts

4 → 195

Calls

4 calls:

18.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
9.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
5.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
3.0ms	(/.f64 y (+.f64 y z))

simplify157.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

385×	`fma-def_binary64`
358×	`times-frac_binary64`
355×	`associate-/l*_binary64`
264×	`associate-/r*_binary64`
248×	`associate-r_binary64`

Counts

303 → 427

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	612	9531
1	1653	9295
2	5034	9295

prune375.0ms (4.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	423	4	427
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	424	4	428

Error

0.0b

Counts

428 → 4

Alt Table

Status	Error	Program
	4.6b	(+.f64 x (/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y)) y))
	5.1b	(+.f64 x (.f64 (/.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (cbrt.f64 y))))
	13.0b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	3.1b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 12608 to 4734 computations (62.5% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 y))

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(+.f64 x (/.f64 1 y))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`distribute-lft-out_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

4.0ms

(+.f64 x (/.f64 1 y))

simplify91.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

572×	`unswap-sqr_binary64`
448×	`fma-neg_binary64`
321×	`fma-def_binary64`
284×	`distribute-rgt-in_binary64`
282×	`associate-+l+_binary64`

Counts

42 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	322
1	88	302
2	189	299
3	419	299
4	1068	299
5	2246	299
6	3475	299
7	4871	299
8	4894	299
9	4906	299

prune19.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Error

0.0b

Counts

32 → 4

Alt Table

Status	Error	Program
▶	4.6b	(+.f64 x (/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y)) y))
	5.1b	(+.f64 x (.f64 (/.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (cbrt.f64 y))))
	13.0b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.1b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 430 to 262 computations (39.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y))
	0.0b	(/.f64 y (+.f64 y z))
✓	0.8b	(pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y)
✓	4.8b	(sqrt.f64 (/.f64 y (+.f64 y z)))

series207.0ms (2.7%)

Counts

3 → 38

Calls

3 calls:

122.0ms	(*.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y))
63.0ms	(pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y)
21.0ms	(sqrt.f64 (/.f64 y (+.f64 y z)))

rewrite64.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`unpow-prod-down_binary64`
142×	`sqrt-prod_binary64`
122×	`add-sqr-sqrt_binary64`
119×	`*-un-lft-identity_binary64`
95×	`times-frac_binary64`

Counts

3 → 204

Calls

3 calls:

22.0ms	(*.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y))
10.0ms	(pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y)
4.0ms	(sqrt.f64 (/.f64 y (+.f64 y z)))

simplify229.0ms (3%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-def_binary64`
575×	`unswap-sqr_binary64`
283×	`associate-r_binary64`
242×	`associate-l_binary64`
193×	`sqr-pow_binary64`

Counts

242 → 300

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	334	6849
1	777	6529
2	3241	6431
3	4760	6415
4	4976	6415
5	4953	6415

prune468.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	561	0	561
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	561	4	565

Error

0.0b

Counts

565 → 4

Alt Table

Status	Error	Program
✓	4.6b	(+.f64 x (/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y)) y))
▶	5.1b	(+.f64 x (.f64 (/.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (cbrt.f64 y))))
	13.0b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.1b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 17778 to 4459 computations (74.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
	0.8b	(pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y)
	4.8b	(sqrt.f64 (/.f64 y (+.f64 y z)))

series71.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
33.0ms	(cbrt.f64 y)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune244.0ms (3.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	368	0	368
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	368	4	372

Error

0.0b

Counts

372 → 4

Alt Table

Status	Error	Program
✓	4.6b	(+.f64 x (/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y)) y))
✓	5.1b	(+.f64 x (.f64 (/.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (sqrt.f64 (/.f64 y (+.f64 y z))) y) (cbrt.f64 y))))
	13.0b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.1b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 13383 to 2781 computations (79.2% saved)

regimes1.4s (18.7%)

Accuracy

Total 1.4b remaining (99%)

Threshold costs 0b (0%)

Counts

166 → 2

Compiler

Compiled 16312 to 9607 computations (41.1% saved)

bsearch10.0ms (0.1%)

Steps

Iters	Range		Point
1	1.1848125928079478e-79	5.809399136760583e-75	2.6512083876927243e-77

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`fabs-div_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	49
1	32	49
2	31	49

end67.0ms (0.9%)

Compiler: Compiled 143 to 78 computations (45.5% saved)

Details

analyze1.2s (15.9%)

sample2.6s (33.9%)

simplify48.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series167.0ms (2.2%)

rewrite51.0ms (0.7%)

simplify157.0ms (2.1%)

prune375.0ms (4.9%)

localize3.0ms (0%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify91.0ms (1.2%)

prune19.0ms (0.2%)

localize9.0ms (0.1%)

series207.0ms (2.7%)

rewrite64.0ms (0.8%)

simplify229.0ms (3%)

prune468.0ms (6.2%)

localize12.0ms (0.2%)

series71.0ms (0.9%)

rewrite7.0ms (0.1%)

simplify65.0ms (0.9%)

prune244.0ms (3.2%)

regimes1.4s (18.7%)

bsearch10.0ms (0.1%)

simplify3.0ms (0%)

end67.0ms (0.9%)

Profiling