Details

analyze21.0ms (0.4%)

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)

sample49.0ms (1%)

Algorithm

1×

intervals

Results

23.0ms	64×	body	1024	valid
9.0ms	134×	body	128	valid
6.0ms	34×	body	512	valid
2.0ms	5×	body	2048	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify15.0ms (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

prune2.0ms (0%)

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

30.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.3b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.3b	(-.f64 (log1p.f64 N) (log.f64 N))

rewrite6.0ms (0.1%)

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))

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

simplify144.0ms (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 → 86

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 (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	4	87

Error

0.0b

Counts

87 → 4

Alt Table

Status	Error	Program
▶	30.4b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 3) (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (log1p.f64 N) (log1p.f64 N)) (+.f64 (.f64 (log.f64 N) (log.f64 N)) (*.f64 (log1p.f64 N) (log.f64 N)))))
	30.8b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
	31.2b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
✓	30.3b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 944 to 339 computations (64.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (log1p.f64 N) (log.f64 N))
✓	0.5b	(*.f64 (log.f64 N) (log.f64 N))
✓	0.8b	(pow.f64 (log.f64 N) 3)
✓	3.2b	(-.f64 (pow.f64 (log1p.f64 N) 3) (pow.f64 (log.f64 N) 3))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

168×	`prod-diff_binary64`
129×	`add-sqr-sqrt_binary64`
117×	`cube-prod_binary64`
117×	`*-un-lft-identity_binary64`
117×	`unpow-prod-down_binary64`

Counts

4 → 325

Calls

4 calls:

15.0ms	(-.f64 (pow.f64 (log1p.f64 N) 3) (pow.f64 (log.f64 N) 3))
6.0ms	(*.f64 (log.f64 N) (log.f64 N))
3.0ms	(*.f64 (log1p.f64 N) (log.f64 N))
2.0ms	(pow.f64 (log.f64 N) 3)

series498.0ms (9.7%)

Counts

4 → 44

Calls

4 calls:

241.0ms	(*.f64 (log.f64 N) (log.f64 N))
227.0ms	(pow.f64 (log.f64 N) 3)
23.0ms	(-.f64 (pow.f64 (log1p.f64 N) 3) (pow.f64 (log.f64 N) 3))
6.0ms	(*.f64 (log1p.f64 N) (log.f64 N))

simplify240.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

435×	`fma-neg_binary64`
340×	`associate-r_binary64`
324×	`fma-def_binary64`
304×	`associate-l_binary64`
207×	`+-commutative_binary64`

Counts

369 → 674

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	454	8825
1	1006	7476
2	4233	7407
3	5007	7407

prune243.0ms (4.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	673	1	674
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	674	4	678

Error

Counts

678 → 4

Alt Table

Status	Error	Program
	30.9b	(/.f64 (-.f64 (fma.f64 3 (/.f64 (neg.f64 (log.f64 N)) (pow.f64 N 3)) (fma.f64 3 (/.f64 (pow.f64 (log.f64 N) 2) N) (+.f64 (/.f64 (pow.f64 (log.f64 N) 2) (pow.f64 N 3)) (/.f64 1 (pow.f64 N 3))))) (fma.f64 3/2 (/.f64 (pow.f64 (log.f64 N) 2) (.f64 N N)) (/.f64 (.f64 -3 (log.f64 N)) (.f64 N N)))) (+.f64 (.f64 (log1p.f64 N) (log1p.f64 N)) (+.f64 (.f64 (log.f64 N) (log.f64 N)) (.f64 (log1p.f64 N) (log.f64 N)))))
✓	30.4b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 3) (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (log1p.f64 N) (log1p.f64 N)) (+.f64 (.f64 (log.f64 N) (log.f64 N)) (*.f64 (log1p.f64 N) (log.f64 N)))))
▶	30.8b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
✓	30.3b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 13820 to 5618 computations (59.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
✓	0.1b	(/.f64 1/2 (*.f64 N N))
✓	0.3b	(/.f64 1/3 (pow.f64 N 3))
✓	12.0b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))

rewrite93.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

272×	`times-frac_binary64`
221×	`add-sqr-sqrt_binary64`
210×	`*-un-lft-identity_binary64`
193×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

4 → 354

Calls

4 calls:

40.0ms	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
13.0ms	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
4.0ms	(/.f64 1/3 (pow.f64 N 3))
3.0ms	(/.f64 1/2 (*.f64 N N))

series39.0ms (0.8%)

Counts

4 → 36

Calls

4 calls:

14.0ms	(/.f64 1/3 (pow.f64 N 3))
10.0ms	(/.f64 1/2 (*.f64 N N))
8.0ms	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
7.0ms	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))

simplify287.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

484×	`unswap-sqr_binary64`
422×	`cancel-sign-sub-inv_binary64`
401×	`fma-neg_binary64`
306×	`log-prod_binary64`
230×	`associate-/r*_binary64`

Counts

390 → 719

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	313	6283
1	609	5641
2	2431	4805
3	4524	4747
4	4712	4747
5	4897	4747

prune471.0ms (9.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	719	0	719
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	719	4	723

Error

Counts

723 → 4

Alt Table

Status	Error	Program
▶	30.9b	(/.f64 (-.f64 (fma.f64 3 (/.f64 (neg.f64 (log.f64 N)) (pow.f64 N 3)) (fma.f64 3 (/.f64 (pow.f64 (log.f64 N) 2) N) (+.f64 (/.f64 (pow.f64 (log.f64 N) 2) (pow.f64 N 3)) (/.f64 1 (pow.f64 N 3))))) (fma.f64 3/2 (/.f64 (pow.f64 (log.f64 N) 2) (.f64 N N)) (/.f64 (.f64 -3 (log.f64 N)) (.f64 N N)))) (+.f64 (.f64 (log1p.f64 N) (log1p.f64 N)) (+.f64 (.f64 (log.f64 N) (log.f64 N)) (.f64 (log1p.f64 N) (log.f64 N)))))
✓	30.4b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 3) (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (log1p.f64 N) (log1p.f64 N)) (+.f64 (.f64 (log.f64 N) (log.f64 N)) (*.f64 (log1p.f64 N) (log.f64 N)))))
✓	30.8b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
✓	30.3b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 16424 to 11414 computations (30.5% saved)

localize32.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (log.f64 N) 2)
	0.5b	(pow.f64 (log.f64 N) 2)
✓	0.5b	(pow.f64 (log.f64 N) 2)
✓	12.4b	(-.f64 (fma.f64 3 (/.f64 (neg.f64 (log.f64 N)) (pow.f64 N 3)) (fma.f64 3 (/.f64 (pow.f64 (log.f64 N) 2) N) (+.f64 (/.f64 (pow.f64 (log.f64 N) 2) (pow.f64 N 3)) (/.f64 1 (pow.f64 N 3))))) (fma.f64 3/2 (/.f64 (pow.f64 (log.f64 N) 2) (.f64 N N)) (/.f64 (.f64 -3 (log.f64 N)) (*.f64 N N))))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`unpow-prod-down_binary64`

Counts

2 → 53

Calls

2 calls:

3.0ms

(-.f64 (fma.f64 3 (/.f64 (neg.f64 (log.f64 N)) (pow.f64 N 3)) (fma.f64 3 (/.f64 (pow.f64 (log.f64 N) 2) N) (+.f64 (/.f64 (pow.f64 (log.f64 N) 2) (pow.f64 N 3)) (/.f64 1 (pow.f64 N 3))))) (fma.f64 3/2 (/.f64 (pow.f64 (log.f64 N) 2) (*.f64 N N)) (/.f64 (*.f64 -3 (log.f64 N)) (*.f64 N N))))

2.0ms

(pow.f64 (log.f64 N) 2)

series303.0ms (5.9%)

Counts

2 → 20

Calls

2 calls:

235.0ms

(pow.f64 (log.f64 N) 2)

68.0ms

(-.f64 (fma.f64 3 (/.f64 (neg.f64 (log.f64 N)) (pow.f64 N 3)) (fma.f64 3 (/.f64 (pow.f64 (log.f64 N) 2) N) (+.f64 (/.f64 (pow.f64 (log.f64 N) 2) (pow.f64 N 3)) (/.f64 1 (pow.f64 N 3))))) (fma.f64 3/2 (/.f64 (pow.f64 (log.f64 N) 2) (*.f64 N N)) (/.f64 (*.f64 -3 (log.f64 N)) (*.f64 N N))))

simplify110.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

879×	`fma-def_binary64`
409×	`distribute-rgt-in_binary64`
407×	`times-frac_binary64`
292×	`cancel-sign-sub-inv_binary64`
135×	`sub-neg_binary64`

Counts

73 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	4599
1	528	4099
2	1788	3518
3	4963	3518

prune208.0ms (4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	286	4	290

Error

Counts

290 → 4

Alt Table

Status	Error	Program
✓	30.9b	(/.f64 (-.f64 (fma.f64 3 (/.f64 (neg.f64 (log.f64 N)) (pow.f64 N 3)) (fma.f64 3 (/.f64 (pow.f64 (log.f64 N) 2) N) (+.f64 (/.f64 (pow.f64 (log.f64 N) 2) (pow.f64 N 3)) (/.f64 1 (pow.f64 N 3))))) (fma.f64 3/2 (/.f64 (pow.f64 (log.f64 N) 2) (.f64 N N)) (/.f64 (.f64 -3 (log.f64 N)) (.f64 N N)))) (+.f64 (.f64 (log1p.f64 N) (log1p.f64 N)) (+.f64 (.f64 (log.f64 N) (log.f64 N)) (.f64 (log1p.f64 N) (log.f64 N)))))
✓	30.4b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 3) (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (log1p.f64 N) (log1p.f64 N)) (+.f64 (.f64 (log.f64 N) (log.f64 N)) (*.f64 (log1p.f64 N) (log.f64 N)))))
✓	30.8b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
✓	30.3b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 12955 to 6375 computations (50.8% saved)

regimes770.0ms (15%)

Accuracy

Total 0.1b remaining (44.7%)

Threshold costs 0.1b (44.7%)

Compiler

Compiled 16188 to 11708 computations (27.7% saved)

bsearch13.0ms (0.2%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	46
1	32	46
2	43	46
3	47	46
4	49	46
5	47	46

end1.0ms (0%)

Compiler: Compiled 31 to 22 computations (29% saved)

sample1.5s (28.5%)

Algorithm

1×

intervals

Results

537.0ms	1983×	body	1024	valid
287.0ms	4264×	body	128	valid
174.0ms	988×	body	512	valid
109.0ms	271×	body	2048	valid
51.0ms	494×	body	256	valid

Compiler

Compiled 160 to 100 computations (37.5% 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

analyze21.0ms (0.4%)

sample49.0ms (1%)

simplify15.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite6.0ms (0.1%)

series5.0ms (0.1%)

simplify144.0ms (2.8%)

prune29.0ms (0.6%)

localize14.0ms (0.3%)

rewrite50.0ms (1%)

series498.0ms (9.7%)

simplify240.0ms (4.7%)

prune243.0ms (4.7%)

localize9.0ms (0.2%)

rewrite93.0ms (1.8%)

series39.0ms (0.8%)

simplify287.0ms (5.6%)

prune471.0ms (9.2%)

localize32.0ms (0.6%)

rewrite13.0ms (0.3%)

series303.0ms (5.9%)

simplify110.0ms (2.1%)

prune208.0ms (4%)

regimes770.0ms (15%)

bsearch13.0ms (0.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.5s (28.5%)

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