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 (76.5%)

Results

1.0s	2025×	body	1024	valid
549.0ms	4424×	body	128	valid
315.0ms	1036×	body	512	valid
182.0ms	278×	body	2048	valid
99.0ms	493×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify11.0ms (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

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

27.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.6b	(-.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
✓	2.9b	(-.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))

rewrite7.0ms (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))

simplify105.0ms (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

prune29.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	2	57

Error

0.0b

Counts

57 → 2

Alt Table

Status	Error	Program
▶	27.5b	(log.f64 (/.f64 (+.f64 1 N) N))
	33.2b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))

Compiler

Compiled 876 to 303 computations (65.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 N) N)
✓	3.1b	(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)

rewrite10.0ms (0.3%)

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	(/.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	0	0	0
Total	115	3	118

Error

0.0b

Counts

118 → 3

Alt Table

Status	Error	Program
	3.3b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))
▶	0.6b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
✓	27.5b	(log.f64 (/.f64 (+.f64 1 N) N))

Compiler

Compiled 1500 to 1036 computations (30.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (log1p.f64 (/.f64 1 N)))
✓	0.0b	(log1p.f64 (/.f64 1 N))
✓	0.6b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))

series14.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

8.0ms	(log1p.f64 (log1p.f64 (/.f64 1 N)))
3.0ms	(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	(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))

simplify72.0ms (2.5%)

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

prune32.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	61	4	65

Error

Counts

65 → 4

Alt Table

Status	Error	Program
▶	3.3b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))
✓	0.6b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
✓	27.5b	(log.f64 (/.f64 (+.f64 1 N) N))
	33.4b	(expm1.f64 (-.f64 (/.f64 1 N) (/.f64 1 (pow.f64 N 2))))

Compiler

Compiled 894 to 677 computations (24.3% saved)

localize12.0ms (0.4%)

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)))
✓	3.3b	(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)))

simplify88.0ms (3%)

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 (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	76	4	80

Error

Counts

80 → 4

Alt Table

Status	Error	Program
✓	3.3b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))
✓	0.6b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
✓	27.5b	(log.f64 (/.f64 (+.f64 1 N) N))
	33.4b	(expm1.f64 (-.f64 (/.f64 1 N) (/.f64 1 (pow.f64 N 2))))

Compiler

Compiled 1043 to 791 computations (24.2% saved)

regimes32.0ms (1.1%)

Accuracy

Total 0.0b remaining (48.7%)

Threshold costs 0.0b (48.7%)

Counts

18 → 1

Compiler

Compiled 314 to 244 computations (22.3% 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

end60.0ms (2.1%)

Compiler: Compiled 42 to 34 computations (19% 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 (76.5%)

simplify11.0ms (0.4%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite7.0ms (0.2%)

simplify105.0ms (3.6%)

prune29.0ms (1%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite10.0ms (0.3%)

simplify77.0ms (2.7%)

prune52.0ms (1.8%)

localize6.0ms (0.2%)

series14.0ms (0.5%)

rewrite2.0ms (0.1%)

simplify72.0ms (2.5%)

prune32.0ms (1.1%)

localize12.0ms (0.4%)

series8.0ms (0.3%)

rewrite3.0ms (0.1%)

simplify88.0ms (3%)

prune36.0ms (1.2%)

regimes32.0ms (1.1%)

simplify2.0ms (0.1%)

end60.0ms (2.1%)

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