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)

sample71.0ms (1.5%)

Algorithm

1×

intervals

Results

24.0ms	76×	body	2048	valid
9.0ms	38×	body	1024	valid
8.0ms	126×	body	128	valid
2.0ms	14×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 28 to 26 computations (7.1% saved)

simplify9.0ms (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

prune6.0ms (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

14.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.7b	(-.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series12.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

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

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`
20×	`sqrt-prod_binary64`

Counts

3 → 97

Calls

3 calls:

9.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
4.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
2.0ms	(/.f64 1/2 (hypot.f64 1 x))

simplify168.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-def_binary64`
469×	`associate-l_binary64`
393×	`associate-r_binary64`
375×	`fma-neg_binary64`
233×	`cancel-sign-sub-inv_binary64`

Counts

133 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	2882
1	570	2527
2	1556	2218
3	4471	2218
4	4836	2218

prune130.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	4	161

Error

0.0b

Counts

161 → 4

Alt Table

Status	Error	Program
	14.7b	(expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	30.7b	(*.f64 1/8 (pow.f64 x 2))
▶	14.2b	(/.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))))))
	14.7b	(/.f64 (-.f64 1 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 3754 to 3350 computations (10.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.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)))))
✓	0.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series33.0ms (0.7%)

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)))

rewrite44.0ms (0.9%)

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))))))

7.0ms

(+.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)))

simplify158.0ms (3.3%)

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

prune349.0ms (7.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	265	3	268
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	269	3	272

Error

Counts

272 → 3

Alt Table

Status	Error	Program
	31.2b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
▶	14.2b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	14.7b	(.f64 (.f64 (cbrt.f64 (/.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))))))) (cbrt.f64 (/.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)))))))) (cbrt.f64 (/.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 9941 to 8889 computations (10.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.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)))))
✓	0.0b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	0.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series37.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

24.0ms

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

12.0ms

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

rewrite76.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

337×	`times-frac_binary64`
328×	`*-un-lft-identity_binary64`
328×	`add-sqr-sqrt_binary64`
124×	`distribute-lft-out_binary64`
111×	`add-cube-cbrt_binary64`

Counts

2 → 260

Calls

2 calls:

19.0ms

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

12.0ms

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

simplify269.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

474×	`times-frac_binary64`
296×	`associate-+r+_binary64`
279×	`fma-def_binary64`
228×	`+-commutative_binary64`
217×	`associate-/r*_binary64`

Counts

284 → 278

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	388	13307
1	1060	12630
2	3836	12437
3	4941	12437

prune538.0ms (11.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	424	1	425
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	426	2	428

Error

Counts

428 → 2

Alt Table

Status	Error	Program
▶	31.2b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
	31.7b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 1 1/2 (neg.f64 (.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))))

Status

Error

Program

▶

31.2b

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

31.7b

(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 1 1/2 (neg.f64 (*.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (*.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))))

Compiler

Compiled 17374 to 15666 computations (9.8% 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 (0.1%)

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)

rewrite6.0ms (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))

simplify73.0ms (1.5%)

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

prune60.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	63	2	65

Error

Counts

65 → 2

Alt Table

Status	Error	Program
✓	31.2b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
	31.7b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 1 1/2 (neg.f64 (.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))))

Status

Error

Program

✓

31.2b

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

31.7b

(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 1 1/2 (neg.f64 (*.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (*.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))))

Compiler

Compiled 1054 to 774 computations (26.6% saved)

regimes992.0ms (20.7%)

Accuracy

Total 0.3b remaining (84.1%)

Threshold costs 0.3b (84.1%)

Counts

102 → 2

Compiler

Compiled 19760 to 17883 computations (9.5% saved)

bsearch4.0ms (0.1%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	113
1	42	113
2	46	113
3	48	113
4	47	113

end2.0ms (0%)

Compiler: Compiled 75 to 64 computations (14.7% saved)

sample1.7s (35.1%)

Algorithm

1×

intervals

Results

684.0ms	2103×	body	2048	valid
261.0ms	1017×	body	1024	valid
253.0ms	4133×	body	128	valid
101.0ms	500×	body	512	valid
28.0ms	247×	body	256	valid

Compiler

Compiled 160 to 138 computations (13.8% saved)

Details

analyze1.0ms (0%)

sample71.0ms (1.5%)

simplify9.0ms (0.2%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

series12.0ms (0.3%)

rewrite21.0ms (0.4%)

simplify168.0ms (3.5%)

prune130.0ms (2.7%)

localize9.0ms (0.2%)

series33.0ms (0.7%)

rewrite44.0ms (0.9%)

simplify158.0ms (3.3%)

prune349.0ms (7.3%)

localize9.0ms (0.2%)

series37.0ms (0.8%)

rewrite76.0ms (1.6%)

simplify269.0ms (5.6%)

prune538.0ms (11.3%)

localize6.0ms (0.1%)

series7.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify73.0ms (1.5%)

prune60.0ms (1.3%)

regimes992.0ms (20.7%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

end2.0ms (0%)

sample1.7s (35.1%)

Profiling