Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample63.0ms (2.1%)

Algorithm

1×

intervals

Results

15.0ms	57×	body	1024	valid
13.0ms	142×	body	128	valid
5.0ms	31×	body	512	valid
3.0ms	8×	body	2048	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify15.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

prune2.0ms (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

27.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.1b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.3b	(-.f64 (log1p.f64 N) (log.f64 N))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(-.f64 (log1p.f64 N) (log.f64 N))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
11×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`

Counts

1 → 39

Calls

1 calls:

4.0ms

(-.f64 (log1p.f64 N) (log.f64 N))

simplify104.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

435×	`fma-neg_binary64`
299×	`fma-def_binary64`
276×	`associate-l_binary64`
252×	`associate-/r*_binary64`
244×	`cancel-sign-sub-inv_binary64`

Counts

51 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	928
1	214	635
2	600	575
3	2045	572
4	4184	572
5	4526	572
6	4942	572
7	4836	572

prune28.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	2	57

Error

0.0b

Counts

57 → 2

Alt Table

Status	Error	Program
▶	35.1b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
✓	27.1b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 880 to 307 computations (65.1% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/4 (pow.f64 N 4))
✓	0.3b	(/.f64 1/3 (pow.f64 N 3))
✓	0.7b	(/.f64 1/2 (*.f64 N N))
✓	24.6b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))

series12.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

4.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
3.0ms	(/.f64 1/3 (pow.f64 N 3))
3.0ms	(/.f64 1/4 (pow.f64 N 4))
2.0ms	(/.f64 1/2 (*.f64 N N))

rewrite64.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

125×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
61×	`add-sqr-sqrt_binary64`
59×	`add-cube-cbrt_binary64`
29×	`distribute-lft-out_binary64`

Counts

4 → 205

Calls

4 calls:

38.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
5.0ms	(/.f64 1/4 (pow.f64 N 4))
4.0ms	(/.f64 1/3 (pow.f64 N 3))
3.0ms	(/.f64 1/2 (*.f64 N N))

simplify174.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

442×	`fma-neg_binary64`
342×	`associate-l_binary64`
306×	`associate-r_binary64`
245×	`associate-/r*_binary64`
169×	`distribute-rgt-in_binary64`

Counts

229 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	355	5972
1	837	5274
2	3831	5213
3	4942	5213
4	4915	5213

prune331.0ms (10.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	247	3	250

Error

Counts

250 → 3

Alt Table

Status	Error	Program
✓	35.1b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
✓	27.1b	(-.f64 (log1p.f64 N) (log.f64 N))
▶	35.3b	(fma.f64 (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 1/2 (*.f64 N N))))

Compiler

Compiled 9037 to 6623 computations (26.7% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1/3 (pow.f64 N 3))
	0.7b	(/.f64 1/2 (*.f64 N N))
✓	11.5b	(sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))))
✓	12.5b	(fma.f64 (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 1/2 (*.f64 N N))))

series71.0ms (2.3%)

Counts

2 → 1

Calls

2 calls:

63.0ms

(fma.f64 (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 1/2 (*.f64 N N))))

8.0ms

(sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))))

rewrite57.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
15×	`hypot-def_binary64`
15×	`*-un-lft-identity_binary64`
6×	`sqrt-prod_binary64`

Counts

2 → 46

Calls

2 calls:

53.0ms

(sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))))

0.0ms

(fma.f64 (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 1/2 (*.f64 N N))))

simplify62.0ms (2%)

Algorithm

1×	egg-herbie

Rules

573×	`fma-def_binary64`
536×	`fma-neg_binary64`
448×	`distribute-rgt-in_binary64`
438×	`distribute-lft-in_binary64`
281×	`associate-/r/_binary64`

Counts

47 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	855
1	138	764
2	373	754
3	1520	752
4	4360	752
5	5002	752

prune333.0ms (11%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	258	0	258
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	258	3	261

Error

Counts

261 → 3

Alt Table

Status	Error	Program
✓	35.1b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
✓	27.1b	(-.f64 (log1p.f64 N) (log.f64 N))
✓	35.3b	(fma.f64 (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 1/2 (*.f64 N N))))

Compiler

Compiled 10113 to 7636 computations (24.5% saved)

regimes88.0ms (2.9%)

Accuracy

Total 0.0b remaining (39.8%)

Threshold costs 0.0b (39.8%)

Counts

23 → 2

Compiler

Compiled 1544 to 1182 computations (23.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
7×	`sub-neg_binary64`
4×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	55
1	38	55
2	50	55
3	66	55
4	72	55
5	74	55
6	71	55

end1.0ms (0%)

Compiler: Compiled 37 to 27 computations (27% saved)

sample1.6s (52.2%)

Algorithm

1×

intervals

Results

653.0ms	1969×	body	1024	valid
300.0ms	4268×	body	128	valid
185.0ms	1025×	body	512	valid
112.0ms	253×	body	2048	valid
60.0ms	485×	body	256	valid

Compiler

Compiled 108 to 82 computations (24.1% saved)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Details

analyze2.0ms (0.1%)

sample63.0ms (2.1%)

simplify15.0ms (0.5%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite6.0ms (0.2%)

simplify104.0ms (3.4%)

prune28.0ms (0.9%)

localize14.0ms (0.5%)

series12.0ms (0.4%)

rewrite64.0ms (2.1%)

simplify174.0ms (5.7%)

prune331.0ms (10.9%)

localize14.0ms (0.5%)

series71.0ms (2.3%)

rewrite57.0ms (1.9%)

simplify62.0ms (2%)

prune333.0ms (11%)

regimes88.0ms (2.9%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (52.2%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8