Details

analyze1.0ms (0%)

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)

sample2.0s (56.4%)

Results

905.0ms	2084×	body	1024	valid
521.0ms	4385×	body	128	valid
308.0ms	996×	body	512	valid
153.0ms	264×	body	2048	valid
97.0ms	527×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.3%)

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

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

29.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.2b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.7b	(-.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))

rewrite5.0ms (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))

simplify102.0ms (2.8%)

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

prune31.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	3	57

Error

0.0b

Counts

57 → 3

Alt Table

Status	Error	Program
	32.4b	(-.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))))
▶	31.2b	(-.f64 (+.f64 N (.f64 1/3 (pow.f64 N 3))) (+.f64 (.f64 1/2 (pow.f64 N 2)) (log.f64 N)))
✓	29.2b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 914 to 333 computations (63.6% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/3 (pow.f64 N 3))
✓	0.2b	(*.f64 1/2 (pow.f64 N 2))
✓	12.6b	(-.f64 (+.f64 N (.f64 1/3 (pow.f64 N 3))) (+.f64 (.f64 1/2 (pow.f64 N 2)) (log.f64 N)))

series10.0ms (0.3%)

Counts

3 → 11

Calls

3 calls:

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

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`

Counts

3 → 101

Calls

3 calls:

8.0ms	(-.f64 (+.f64 N (.f64 1/3 (pow.f64 N 3))) (+.f64 (.f64 1/2 (pow.f64 N 2)) (log.f64 N)))
4.0ms	(*.f64 1/3 (pow.f64 N 3))
4.0ms	(*.f64 1/2 (pow.f64 N 2))

simplify91.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

293×	`cancel-sign-sub-inv_binary64`
224×	`exp-prod_binary64`
211×	`fma-neg_binary64`
203×	`distribute-rgt-neg-in_binary64`
190×	`associate-l_binary64`

Counts

112 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2433
1	571	2028
2	2062	1852
3	4582	1852
4	4924	1852

prune117.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	158	3	161

Error

0.0b

Counts

161 → 3

Alt Table

Status	Error	Program
▶	32.4b	(-.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))))
✓	31.2b	(-.f64 (+.f64 N (.f64 1/3 (pow.f64 N 3))) (+.f64 (.f64 1/2 (pow.f64 N 2)) (log.f64 N)))
✓	29.2b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 4484 to 3087 computations (31.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1/4 (pow.f64 N 4))
✓	0.5b	(/.f64 1/3 (pow.f64 N 3))
✓	0.9b	(/.f64 1/2 (*.f64 N N))
✓	20.3b	(-.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))))

series13.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

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

rewrite60.0ms (1.7%)

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:

34.0ms	(-.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))
3.0ms	(/.f64 1/2 (*.f64 N N))

simplify168.0ms (4.7%)

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

prune299.0ms (8.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	247	4	251

Error

Counts

251 → 4

Alt Table

Status	Error	Program
▶	32.6b	(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))))
✓	32.4b	(-.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))))
✓	31.2b	(-.f64 (+.f64 N (.f64 1/3 (pow.f64 N 3))) (+.f64 (.f64 1/2 (pow.f64 N 2)) (log.f64 N)))
✓	29.2b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 9054 to 6636 computations (26.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(/.f64 1/3 (pow.f64 N 3))
	0.9b	(/.f64 1/2 (*.f64 N N))
✓	7.3b	(sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))))
✓	12.7b	(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))))

series30.0ms (0.8%)

Counts

2 → 1

Calls

2 calls:

18.0ms

(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))))

12.0ms

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

rewrite26.0ms (0.7%)

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:

22.0ms

(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 (1.7%)

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

prune298.0ms (8.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	258	0	258
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	258	4	262

Error

Counts

262 → 4

Alt Table

Status	Error	Program
✓	32.6b	(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))))
✓	32.4b	(-.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))))
✓	31.2b	(-.f64 (+.f64 N (.f64 1/3 (pow.f64 N 3))) (+.f64 (.f64 1/2 (pow.f64 N 2)) (log.f64 N)))
✓	29.2b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 10130 to 7649 computations (24.5% saved)

regimes71.0ms (2%)

Accuracy

Total 0.0b remaining (27.8%)

Threshold costs 0.0b (27.8%)

Counts

23 → 2

Compiler

Compiled 1248 to 930 computations (25.5% saved)

bsearch1.0ms (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

end92.0ms (2.6%)

Compiler: Compiled 152 to 114 computations (25% 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

analyze1.0ms (0%)

sample2.0s (56.4%)

simplify10.0ms (0.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify102.0ms (2.8%)

prune31.0ms (0.9%)

localize10.0ms (0.3%)

series10.0ms (0.3%)

rewrite21.0ms (0.6%)

simplify91.0ms (2.5%)

prune117.0ms (3.3%)

localize11.0ms (0.3%)

series13.0ms (0.4%)

rewrite60.0ms (1.7%)

simplify168.0ms (4.7%)

prune299.0ms (8.4%)

localize14.0ms (0.4%)

series30.0ms (0.8%)

rewrite26.0ms (0.7%)

simplify62.0ms (1.7%)

prune298.0ms (8.3%)

regimes71.0ms (2%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end92.0ms (2.6%)

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