Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.2s (55.1%)

Results

1.1s	2143×	body	2048	valid
490.0ms	4318×	body	128	valid
422.0ms	1047×	body	1024	valid
149.0ms	494×	body	512	valid
52.0ms	254×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	35	15
4	42	15
5	52	15
6	60	15
7	69	15
8	72	15
9	53	15

prune3.0ms (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

17.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.1b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	3.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series18.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
4.0ms	(hypot.f64 1 x)
3.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
22×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

4 → 98

Calls

4 calls:

8.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
5.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0ms	(hypot.f64 1 x)

simplify106.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-def_binary64`
495×	`associate-l_binary64`
429×	`fma-neg_binary64`
427×	`associate-r_binary64`
268×	`cancel-sign-sub-inv_binary64`

Counts

146 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	3114
1	607	2734
2	1733	2412
3	4850	2412
4	4972	2412

prune141.0ms (3.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	3	182

Error

0.0b

Counts

182 → 3

Alt Table

Status	Error	Program
▶	16.6b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	32.2b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
	17.1b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 4130 to 3666 computations (11.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	2.7b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series33.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

24.0ms

(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

5.0ms

(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

3.0ms

(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite51.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
60×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

3 → 157

Calls

3 calls:

18.0ms

(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

10.0ms

(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

7.0ms

(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify185.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

565×	`times-frac_binary64`
260×	`fma-def_binary64`
206×	`associate-r_binary64`
200×	`associate-/r*_binary64`
184×	`fma-neg_binary64`

Counts

193 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	8251
1	1249	5965
2	3887	5923
3	5050	5923

prune293.0ms (7.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	271	3	274

Error

Counts

274 → 3

Alt Table

Status	Error	Program
✓	16.6b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	32.2b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
▶	17.1b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 10035 to 8974 computations (10.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.5b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	0.5b	(expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	3.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series22.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
6.0ms	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0ms	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

554×	`fma-def_binary64`
447×	`associate-/r*_binary64`
447×	`fma-neg_binary64`
370×	`times-frac_binary64`
298×	`associate-l_binary64`

Counts

46 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	1459
1	425	1327
2	1458	1228
3	4893	1228
4	5170	1228

prune152.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	181	3	184

Error

Counts

184 → 3

Alt Table

Status	Error	Program
✓	16.6b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
▶	32.2b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	17.1b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 4930 to 4441 computations (9.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	0.1b	(*.f64 (pow.f64 x 4) -11/128)

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
3.0ms	(*.f64 (pow.f64 x 4) -11/128)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-l_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 (pow.f64 x 4) -11/128)
0.0ms	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))

simplify77.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

461×	`unsub-neg_binary64`
423×	`*-commutative_binary64`
388×	`distribute-rgt-neg-in_binary64`
343×	`exp-prod_binary64`
304×	`log-prod_binary64`

Counts

61 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	724
1	123	683
2	317	665
3	1110	665
4	2628	659
5	4199	659
6	5084	659

prune37.0ms (0.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
✓	16.6b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	32.2b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	17.1b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 1027 to 751 computations (26.9% saved)

regimes469.0ms (11.5%)

Accuracy

Total 0.1b remaining (64.4%)

Threshold costs 0.1b (64.4%)

Counts

53 → 2

Compiler

Compiled 7108 to 6387 computations (10.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	50
1	30	50
2	37	50
3	39	50
4	40	50
5	38	50

end79.0ms (1.9%)

Compiler: Compiled 113 to 95 computations (15.9% saved)

Details

analyze1.0ms (0%)

sample2.2s (55.1%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series18.0ms (0.5%)

rewrite25.0ms (0.6%)

simplify106.0ms (2.6%)

prune141.0ms (3.5%)

localize9.0ms (0.2%)

series33.0ms (0.8%)

rewrite51.0ms (1.3%)

simplify185.0ms (4.5%)

prune293.0ms (7.2%)

localize10.0ms (0.2%)

series22.0ms (0.5%)

rewrite1.0ms (0%)

simplify76.0ms (1.9%)

prune152.0ms (3.7%)

localize6.0ms (0.1%)

series7.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify77.0ms (1.9%)

prune37.0ms (0.9%)

regimes469.0ms (11.5%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end79.0ms (1.9%)

Profiling