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 (76.1%)

Results

840.0ms	1989×	body	1024	valid
523.0ms	4418×	body	128	valid
306.0ms	1057×	body	512	valid
170.0ms	271×	body	2048	valid
102.0ms	521×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess19.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	164	8
9	200	8
10	226	8
11	228	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 8 to 6 computations (25% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	164	8
9	200	8
10	226	8
11	228	8

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (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

29.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.5b	(-.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

3 calls:

1.0ms	(-.f64 (log1p.f64 N) (log.f64 N))	N	-inf
1.0ms	(-.f64 (log1p.f64 N) (log.f64 N))	N	inf
1.0ms	(-.f64 (log1p.f64 N) (log.f64 N))	N	0

rewrite38.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

541×	`expm1-log1p-u_binary64`
540×	`log1p-expm1-u_binary64`
394×	`prod-diff_binary64`
252×	`log-prod_binary64`
168×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	106	8
2	1431	8

Stop Event

1×	node limit

Counts

1 → 85

simplify26.0ms (1%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
511×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`
223×	`fma-def_binary64`
191×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	186
1	94	184
2	235	184
3	685	181
4	2172	181

Stop Event

1×	node limit

Counts

97 → 99

prune43.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	3	100

Error

0.0b

Counts

100 → 3

Alt Table

Status	Error	Program
▶	29.4b	(log.f64 (/.f64 (+.f64 N 1) N))
	32.0b	(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
	30.8b	(/.f64 1 N)

Compiler

Compiled 1519 to 601 computations (60.4% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	2.8b	(log.f64 (/.f64 (+.f64 N 1) N))

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(log.f64 (/.f64 (+.f64 N 1) N))	N	-inf
1.0ms	(log.f64 (/.f64 (+.f64 N 1) N))	N	inf
1.0ms	(log.f64 (/.f64 (+.f64 N 1) N))	N	0
1.0ms	(/.f64 (+.f64 N 1) N)	N	-inf
0.0ms	(/.f64 (+.f64 N 1) N)	N	inf

rewrite41.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`log1p-expm1-u_binary64`
635×	`expm1-log1p-u_binary64`
115×	`fma-def_binary64`
108×	`log1p-udef_binary64`
107×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	127	15
2	1684	15

Stop Event

1×	node limit

Counts

2 → 88

simplify24.0ms (1%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
511×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`
223×	`fma-def_binary64`
191×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	255
1	96	253
2	237	253
3	689	250
4	2177	250

Stop Event

1×	node limit

Counts

112 → 104

prune40.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	104	3	107

Error

0.0b

Counts

107 → 3

Alt Table

Status	Error	Program
▶	30.8b	(/.f64 1 N)
✓	29.4b	(log.f64 (/.f64 (+.f64 N 1) N))
	31.9b	(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (*.f64 N N)) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))))

Compiler

Compiled 1304 to 713 computations (45.3% saved)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

0.0b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	30.8b	(/.f64 1 N)
✓	29.4b	(log.f64 (/.f64 (+.f64 N 1) N))
▶	31.9b	(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (*.f64 N N)) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))))

Compiler

Compiled 55 to 42 computations (23.6% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 -1/4 (pow.f64 N 4))
✓	0.5b	(/.f64 1/3 (pow.f64 N 3))
✓	0.8b	(/.f64 -1/2 (*.f64 N N))
✓	21.5b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))

series11.0ms (0.4%)

Counts

4 → 24

Calls

12 calls:

1.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))	N	0
1.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))	N	inf
1.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))	N	-inf
1.0ms	(/.f64 -1/4 (pow.f64 N 4))	N	0
1.0ms	(/.f64 1/3 (pow.f64 N 3))	N	0

rewrite71.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

938×	`prod-diff_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`
148×	`add-sqr-sqrt_binary64`
147×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	327	35
2	4136	35

Stop Event

1×	node limit

Counts

4 → 125

simplify31.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

388×	`distribute-neg-frac_binary64`
375×	`times-frac_binary64`
340×	`fma-def_binary64`
315×	`associate-l_binary64`
242×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	249
1	47	249
2	95	249
3	216	249
4	772	249
5	3566	249

Stop Event

1×	node limit

Counts

149 → 131

prune96.0ms (3.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	131	3	134

Error

0.0b

Counts

134 → 3

Alt Table

Status	Error	Program
✓	30.8b	(/.f64 1 N)
✓	29.4b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	31.9b	(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (*.f64 N N)) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))))

Compiler

Compiled 3482 to 2640 computations (24.2% saved)

regimes52.0ms (2%)

Accuracy

Total 0.0b remaining (1.5%)

Threshold costs 0.0b (1.5%)

Counts

21 → 2

Compiler

Compiled 594 to 452 computations (23.9% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Steps

Iters	Point		Range
0.00037743709491433464	∈ [	0.00037743709491433464	,	1.1257989073736718	]

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	54
1	35	54
2	39	54
3	41	54
4	42	54

Stop Event

1×

saturated

end73.0ms (2.8%)

Stop Event

1×

done

Compiler

Compiled 107 to 81 computations (24.3% saved)

Details

analyze1.0ms (0%)

sample2.0s (76.1%)

preprocess19.0ms (0.7%)

simplify9.0ms (0.3%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite38.0ms (1.5%)

simplify26.0ms (1%)

prune43.0ms (1.7%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite41.0ms (1.6%)

simplify24.0ms (1%)

prune40.0ms (1.6%)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

localize12.0ms (0.5%)

series11.0ms (0.4%)

rewrite71.0ms (2.8%)

simplify31.0ms (1.2%)

prune96.0ms (3.7%)

regimes52.0ms (2%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end73.0ms (2.8%)

Profiling