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)

sample86.0ms (3.6%)

Algorithm

1×

intervals

Results

18.0ms	60×	body	1024	valid
9.0ms	135×	body	128	valid
7.0ms	40×	body	512	valid
4.0ms	9×	body	2048	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% 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

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

29.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.7b	(-.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
✓	3.0b	(-.f64 (log1p.f64 N) (log.f64 N))

series6.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

6.0ms

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

rewrite6.0ms (0.3%)

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 (4.4%)

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

prune35.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Error

0.0b

Counts

57 → 5

Alt Table

Status	Error	Program
▶	29.6b	(log.f64 (/.f64 (+.f64 1 N) N))
	29.7b	(+.f64 (log1p.f64 N) (*.f64 (neg.f64 1) (log.f64 N)))
	61.6b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
	32.1b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
	30.6b	(/.f64 1 N)

Compiler

Compiled 922 to 329 computations (64.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 N) N)
✓	2.9b	(log.f64 (/.f64 (+.f64 1 N) N))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite11.0ms (0.5%)

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:

4.0ms	(log.f64 (/.f64 (+.f64 1 N) N))
4.0ms	(/.f64 (+.f64 1 N) N)

simplify80.0ms (3.4%)

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

prune59.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	116	5	121

Error

Counts

121 → 5

Alt Table

Status	Error	Program
✓	29.6b	(log.f64 (/.f64 (+.f64 1 N) N))
	3.5b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))
	29.7b	(-.f64 (log.f64 (+.f64 1 N)) (log.f64 N))
▶	0.5b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
	30.6b	(/.f64 1 N)

Compiler

Compiled 1524 to 1054 computations (30.8% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 1 N))
✓	0.0b	(log1p.f64 (log1p.f64 (/.f64 1 N)))
✓	0.5b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))

series12.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(log1p.f64 (log1p.f64 (/.f64 1 N)))
4.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
3.0ms	(log1p.f64 (/.f64 1 N))

rewrite2.0ms (0.1%)

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:

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

simplify70.0ms (2.9%)

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

prune34.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	62	5	67

Error

Counts

67 → 5

Alt Table

Status	Error	Program
✓	29.6b	(log.f64 (/.f64 (+.f64 1 N) N))
▶	3.5b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))
	29.7b	(-.f64 (log.f64 (+.f64 1 N)) (log.f64 N))
✓	0.5b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
	30.6b	(/.f64 1 N)

Compiler

Compiled 896 to 677 computations (24.4% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (/.f64 1 N))
✓	0.0b	(log.f64 (log1p.f64 (/.f64 1 N)))
✓	3.5b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))

series8.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(log.f64 (log1p.f64 (/.f64 1 N)))
3.0ms	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))
1.0ms	(log.f64 (log1p.f64 (/.f64 1 N)))

simplify87.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-neg_binary64`
432×	`sub-neg_binary64`
233×	`fma-def_binary64`
218×	`distribute-neg-frac_binary64`
196×	`div-sub_binary64`

Counts

55 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	830
1	269	773
2	761	758
3	2802	743
4	4819	743
5	4946	743
6	5059	743

prune36.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	76	5	81

Error

Counts

81 → 5

Alt Table

Status	Error	Program
✓	29.6b	(log.f64 (/.f64 (+.f64 1 N) N))
✓	3.5b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))
	29.7b	(-.f64 (log.f64 (+.f64 1 N)) (log.f64 N))
✓	0.5b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
	30.6b	(/.f64 1 N)

Compiler

Compiled 1044 to 791 computations (24.2% saved)

regimes43.0ms (1.8%)

Accuracy

Total 0.0b remaining (80.7%)

Threshold costs 0.0b (80.7%)

Counts

25 → 1

Compiler

Compiled 566 to 360 computations (36.4% 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

end0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

sample1.7s (69.6%)

Algorithm

1×

intervals

Results

666.0ms	2024×	body	1024	valid
310.0ms	4243×	body	128	valid
175.0ms	970×	body	512	valid
127.0ms	230×	body	2048	valid
55.0ms	533×	body	256	valid

Compiler

Compiled 48 to 38 computations (20.8% 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

analyze2.0ms (0.1%)

sample86.0ms (3.6%)

simplify10.0ms (0.4%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite6.0ms (0.3%)

simplify104.0ms (4.4%)

prune35.0ms (1.5%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite11.0ms (0.5%)

simplify80.0ms (3.4%)

prune59.0ms (2.5%)

localize5.0ms (0.2%)

series12.0ms (0.5%)

rewrite2.0ms (0.1%)

simplify70.0ms (2.9%)

prune34.0ms (1.4%)

localize6.0ms (0.3%)

series8.0ms (0.3%)

rewrite3.0ms (0.1%)

simplify87.0ms (3.6%)

prune36.0ms (1.5%)

regimes43.0ms (1.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (69.6%)

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