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)

sample2.2s (74.9%)

Results

965.0ms	2093×	body	1024	valid
568.0ms	4384×	body	128	valid
326.0ms	1029×	body	512	valid
159.0ms	246×	body	2048	valid
104.0ms	504×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.4%)

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

prune6.0ms (0.2%)

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

23.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	23.6b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize4.0ms (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 (3.6%)

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

prune33.0ms (1.1%)

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

0.1b

Counts

57 → 3

Alt Table

Status	Error	Program
✓	23.6b	(-.f64 (log1p.f64 N) (log.f64 N))
▶	23.3b	(log.f64 (/.f64 (+.f64 1 N) N))
	38.0b	(-.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))))

Compiler

Compiled 894 to 317 computations (64.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 N) N)
✓	2.4b	(log.f64 (/.f64 (+.f64 1 N) N))

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (/.f64 (+.f64 1 N) N))
2.0ms	(/.f64 (+.f64 1 N) N)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
16×	`log-prod_binary64`

Counts

2 → 64

Calls

2 calls:

5.0ms	(/.f64 (+.f64 1 N) N)
3.0ms	(log.f64 (/.f64 (+.f64 1 N) N))

simplify77.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
443×	`distribute-rgt-in_binary64`
395×	`associate-/l/_binary64`
394×	`fma-neg_binary64`
377×	`distribute-lft-in_binary64`

Counts

88 → 116

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	1207
1	263	1146
2	664	1124
3	1868	1117
4	4464	1079
5	4932	1079

prune52.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	116	3	119

Error

Counts

119 → 3

Alt Table

Status	Error	Program
▶	0.7b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
✓	23.3b	(log.f64 (/.f64 (+.f64 1 N) N))
	15.7b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))

Compiler

Compiled 1502 to 1038 computations (30.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 1 N))
✓	0.1b	(log1p.f64 (log1p.f64 (/.f64 1 N)))
✓	0.7b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))

series9.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log1p.f64 (log1p.f64 (/.f64 1 N)))
3.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
2.0ms	(log1p.f64 (/.f64 1 N))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 33

Calls

3 calls:

5.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
0.0ms	(log1p.f64 (log1p.f64 (/.f64 1 N)))
0.0ms	(log1p.f64 (/.f64 1 N))

simplify90.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

535×	`cancel-sign-sub-inv_binary64`
456×	`fma-neg_binary64`
329×	`div-sub_binary64`
311×	`associate-/l/_binary64`
261×	`associate-/r/_binary64`

Counts

69 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	1024
1	219	973
2	620	951
3	2236	940
4	4515	940
5	5083	940

prune29.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	62	3	65

Error

Counts

65 → 3

Alt Table

Status	Error	Program
✓	0.7b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
✓	23.3b	(log.f64 (/.f64 (+.f64 1 N) N))
▶	15.7b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))

Compiler

Compiled 874 to 661 computations (24.4% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (/.f64 1 N))
✓	0.5b	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
✓	15.7b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))

series8.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
4.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

2.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
2.0ms	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)

simplify81.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

965×	`fma-neg_binary64`
450×	`associate-l_binary64`
368×	`associate-r_binary64`
326×	`fma-def_binary64`
318×	`log-prod_binary64`

Counts

72 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	1104
1	286	1019
2	873	991
3	3301	986
4	4849	986
5	4930	986

prune43.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	88	3	91

Error

Counts

91 → 3

Alt Table

Status	Error	Program
✓	0.7b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
✓	23.3b	(log.f64 (/.f64 (+.f64 1 N) N))
✓	15.7b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))

Compiler

Compiled 1245 to 1001 computations (19.6% saved)

regimes71.0ms (2.5%)

Accuracy

Total 0.0b remaining (16.3%)

Threshold costs 0.0b (16.3%)

Counts

23 → 1

Compiler

Compiled 544 to 398 computations (26.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6
2	6	6

end50.0ms (1.7%)

Compiler: Compiled 32 to 26 computations (18.8% 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%)

sample2.2s (74.9%)

simplify10.0ms (0.4%)

prune6.0ms (0.2%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite6.0ms (0.2%)

simplify104.0ms (3.6%)

prune33.0ms (1.1%)

localize4.0ms (0.1%)

series4.0ms (0.2%)

rewrite12.0ms (0.4%)

simplify77.0ms (2.7%)

prune52.0ms (1.8%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite7.0ms (0.2%)

simplify90.0ms (3.1%)

prune29.0ms (1%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify81.0ms (2.8%)

prune43.0ms (1.5%)

regimes71.0ms (2.5%)

simplify2.0ms (0.1%)

end50.0ms (1.7%)

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