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)

sample1.7s (32.6%)

Results

863.0ms	2222×	body	2048	valid
354.0ms	4249×	body	128	valid
285.0ms	1010×	body	1024	valid
117.0ms	521×	body	512	valid
39.0ms	254×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify11.0ms (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

15.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(hypot.f64 1 x)
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	2.1b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series21.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(hypot.f64 1 x)
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))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
24×	`sqrt-prod_binary64`
21×	`prod-diff_binary64`

Counts

4 → 110

Calls

4 calls:

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

simplify137.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
463×	`fma-neg_binary64`
398×	`times-frac_binary64`
372×	`associate-l_binary64`
332×	`associate-r_binary64`

Counts

158 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	3244
1	653	2896
2	1804	2575
3	4560	2539
4	4860	2539
5	5266	2539

prune193.0ms (3.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	194	3	197

Error

0.0b

Counts

197 → 3

Alt Table

Status	Error	Program
	15.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
	28.0b	(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 8) -1843/32768 (.f64 (pow.f64 x 4) -11/128))))
▶	15.3b	(/.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))))))

Compiler

Compiled 4439 to 3940 computations (11.2% saved)

localize8.0ms (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))))
✓	0.0b	(/.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	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	1.7b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series33.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

25.0ms

(/.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)))

rewrite44.0ms (0.8%)

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:

15.0ms

(/.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))))))

8.0ms

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

6.0ms

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

simplify160.0ms (3.1%)

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

prune332.0ms (6.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	269	3	272
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	272	3	275

Error

Counts

275 → 3

Alt Table

Status	Error	Program
	15.3b	(/.f64 (log.f64 (exp.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))))))
▶	15.3b	(/.f64 (log.f64 (/.f64 (exp.f64 1/2) (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	27.7b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128)))

Compiler

Compiled 10113 to 9043 computations (10.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (log.f64 (/.f64 (exp.f64 1/2) (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	0.0b	(/.f64 (exp.f64 1/2) (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	1.7b	(log.f64 (/.f64 (exp.f64 1/2) (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))

series40.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

26.0ms

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

10.0ms

(log.f64 (/.f64 (exp.f64 1/2) (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))

4.0ms

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

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`*-un-lft-identity_binary64`
54×	`times-frac_binary64`
46×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
28×	`distribute-lft-out_binary64`

Counts

3 → 124

Calls

3 calls:

14.0ms

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

6.0ms

(log.f64 (/.f64 (exp.f64 1/2) (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))

5.0ms

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

simplify154.0ms (3%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
561×	`times-frac_binary64`
220×	`fma-neg_binary64`
214×	`cancel-sign-sub-inv_binary64`
184×	`associate-/r*_binary64`

Counts

160 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	354	5310
1	924	4923
2	2806	4854
3	4599	4854
4	5317	4854

prune306.0ms (5.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	272	0	272
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	272	3	275

Error

Counts

275 → 3

Alt Table

Status	Error	Program
▶	15.3b	(/.f64 (log.f64 (exp.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))))))
✓	15.3b	(/.f64 (log.f64 (/.f64 (exp.f64 1/2) (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	27.7b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128)))

Compiler

Compiled 9125 to 8231 computations (9.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (log.f64 (exp.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	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	1.7b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	1.7b	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series28.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

24.0ms	(/.f64 (log.f64 (exp.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))))))
3.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite61.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`*-un-lft-identity_binary64`
132×	`add-sqr-sqrt_binary64`
104×	`times-frac_binary64`
70×	`add-cube-cbrt_binary64`
56×	`log-prod_binary64`

Counts

2 → 167

Calls

2 calls:

20.0ms	(/.f64 (log.f64 (exp.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))))))
11.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify263.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

495×	`times-frac_binary64`
288×	`exp-prod_binary64`
222×	`fma-def_binary64`
199×	`log-pow_binary64`
189×	`fma-neg_binary64`

Counts

191 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	563	7634
1	1198	6424
2	3316	6040
3	4550	6040
4	4900	6040
5	4746	6040

prune510.0ms (9.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	385	0	385
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	385	3	388

Error

Counts

388 → 3

Alt Table

Status	Error	Program
✓	15.3b	(/.f64 (log.f64 (exp.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))))))
✓	15.3b	(/.f64 (log.f64 (/.f64 (exp.f64 1/2) (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	27.7b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128)))

Compiler

Compiled 15533 to 13977 computations (10% saved)

regimes940.0ms (18.2%)

Accuracy

Total 0.2b remaining (82%)

Threshold costs 0.2b (82%)

Counts

119 → 3

Compiler

Compiled 14635 to 13235 computations (9.6% saved)

bsearch43.0ms (0.8%)

Steps

Iters	Range		Point
11	1.3245244896681527e-12	50115910.61651929	1.3900848933172312
10	-25839770606.22214	-0.00030729904005259695	-0.010110969448982569

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (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	37	95
1	45	95
2	51	95
3	53	95
4	54	95
5	52	95

end110.0ms (2.1%)

Compiler: Compiled 187 to 159 computations (15% saved)

Details

analyze1.0ms (0%)

sample1.7s (32.6%)

simplify11.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series21.0ms (0.4%)

rewrite24.0ms (0.5%)

simplify137.0ms (2.6%)

prune193.0ms (3.7%)

localize8.0ms (0.2%)

series33.0ms (0.6%)

rewrite44.0ms (0.8%)

simplify160.0ms (3.1%)

prune332.0ms (6.4%)

localize12.0ms (0.2%)

series40.0ms (0.8%)

rewrite36.0ms (0.7%)

simplify154.0ms (3%)

prune306.0ms (5.9%)

localize11.0ms (0.2%)

series28.0ms (0.5%)

rewrite61.0ms (1.2%)

simplify263.0ms (5.1%)

prune510.0ms (9.9%)

regimes940.0ms (18.2%)

bsearch43.0ms (0.8%)

simplify4.0ms (0.1%)

end110.0ms (2.1%)

Profiling