Details

analyze1.2s (26.2%)

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
2.7%	90.9%	6.4%	9
4.1%	86.4%	9.5%	10
4.4%	86.1%	9.5%	11
19.7%	65.3%	15%	12
21.9%	60.4%	17.7%	13
22.7%	59.6%	17.7%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample138.0ms (2.9%)

Algorithm

1×

intervals

Results

20.0ms	36×	body	1024	valid
15.0ms	192×	body	128	valid
6.0ms	17×	body	512	valid
3.0ms	13×	body	512	invalid
2.0ms	35×	body	128	nan
2.0ms	11×	body	256	valid
1.0ms	14×	body	128	invalid
1.0ms	4×	body	256	invalid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify53.0ms (1.1%)

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

prune4.0ms (0.1%)

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

4.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.0b	(+.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	0.0b	(/.f64 y (+.f64 y z))
✓	4.4b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series144.0ms (3%)

Counts

3 → 84

Calls

3 calls:

99.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
35.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
9.0ms	(/.f64 y (+.f64 y z))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`unpow-prod-down_binary64`

Counts

3 → 87

Calls

3 calls:

15.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
7.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
3.0ms	(/.f64 y (+.f64 y z))

simplify90.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

310×	`fma-def_binary64`
259×	`times-frac_binary64`
255×	`associate-+r+_binary64`
246×	`associate-r_binary64`
205×	`associate-+l+_binary64`

Counts

171 → 225

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	432	5061
1	1307	4883
2	5052	4883

prune176.0ms (3.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	223	3	226

Error

Counts

226 → 3

Alt Table

Status	Error	Program
▶	1.3b	(+.f64 x (/.f64 1 y))
	33.5b	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (sqrt.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))
	8.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))

Compiler

Compiled 6581 to 2875 computations (56.3% saved)

localize3.0ms (0.1%)

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))

simplify95.0ms (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

prune15.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	28	3	31

Error

Counts

31 → 3

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 x (/.f64 1 y))
	32.7b	(*.f64 (sqrt.f64 (+.f64 x (/.f64 1 y))) (sqrt.f64 (+.f64 x (/.f64 1 y))))
▶	8.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))

Compiler

Compiled 352 to 240 computations (31.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	0.0b	(/.f64 (exp.f64 (neg.f64 z)) y)

series19.0ms (0.4%)

Counts

2 → 44

Calls

2 calls:

10.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
8.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 48

Calls

2 calls:

5.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)
5.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))

simplify91.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

559×	`associate-/l*_binary64`
517×	`fma-neg_binary64`
466×	`fma-def_binary64`
340×	`associate-/l/_binary64`
311×	`associate-*l/_binary64`

Counts

92 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	1172
1	240	1134
2	585	1126
3	1543	1124
4	4396	1117
5	4890	1117
6	4978	1117

prune42.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	82	2	84

Error

Counts

84 → 2

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 x (/.f64 1 y))
▶	35.0b	(+.f64 x (/.f64 (/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)))

Compiler

Compiled 1151 to 387 computations (66.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)))
✓	0.1b	(/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y))
✓	0.1b	(/.f64 (/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y)) (sqrt.f64 y))

series64.0ms (1.4%)

Counts

3 → 64

Calls

3 calls:

24.0ms	(/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y))
22.0ms	(+.f64 x (/.f64 (/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)))
18.0ms	(/.f64 (/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y)) (sqrt.f64 y))

rewrite74.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
158×	`*-un-lft-identity_binary64`
156×	`add-sqr-sqrt_binary64`
156×	`add-cube-cbrt_binary64`
144×	`sqrt-prod_binary64`

Counts

3 → 237

Calls

3 calls:

34.0ms	(+.f64 x (/.f64 (/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)))
9.0ms	(/.f64 (/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y)) (sqrt.f64 y))
5.0ms	(/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y))

simplify256.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l/_binary64`
548×	`fma-neg_binary64`
527×	`times-frac_binary64`
361×	`associate-/r*_binary64`
346×	`associate-/l*_binary64`

Counts

301 → 303

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	7520
1	620	7004
2	1377	6682
3	4023	6624
4	4896	6624
5	4950	6624

prune118.0ms (2.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	303	0	303
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	303	2	305

Error

Counts

305 → 2

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 x (/.f64 1 y))
✓	35.0b	(+.f64 x (/.f64 (/.f64 (exp.f64 (neg.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)))

Compiler

Compiled 6490 to 1536 computations (76.3% saved)

regimes185.0ms (3.9%)

Accuracy

Total 0.2b remaining (20.2%)

Threshold costs 0.2b (20.2%)

Counts

31 → 2

Compiler

Compiled 2012 to 1397 computations (30.6% saved)

bsearch26.0ms (0.5%)

Steps

Iters	Range		Point
8	1.2734016891189084e-31	2.7684294473975427e-27	2.6774126192942535e-27

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	24	24
2	26	24
3	27	24
4	26	24

end1.0ms (0%)

Compiler: Compiled 19 to 13 computations (31.6% saved)

sample1.8s (38.7%)

Algorithm

1×

intervals

Results

486.0ms	6117×	body	128	valid
450.0ms	984×	body	1024	valid
162.0ms	574×	body	512	valid
80.0ms	191×	body	1024	invalid
69.0ms	260×	body	512	invalid
60.0ms	1025×	body	128	nan
56.0ms	316×	body	256	valid
37.0ms	429×	body	128	invalid
29.0ms	150×	body	256	invalid
6.0ms	9×	body	2048	valid

Compiler

Compiled 61 to 42 computations (31.1% saved)

Details

analyze1.2s (26.2%)

sample138.0ms (2.9%)

simplify53.0ms (1.1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series144.0ms (3%)

rewrite31.0ms (0.6%)

simplify90.0ms (1.9%)

prune176.0ms (3.7%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify95.0ms (2%)

prune15.0ms (0.3%)

localize5.0ms (0.1%)

series19.0ms (0.4%)

rewrite12.0ms (0.3%)

simplify91.0ms (1.9%)

prune42.0ms (0.9%)

localize7.0ms (0.1%)

series64.0ms (1.4%)

rewrite74.0ms (1.6%)

simplify256.0ms (5.4%)

prune118.0ms (2.5%)

regimes185.0ms (3.9%)

bsearch26.0ms (0.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.8s (38.7%)

Profiling