Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample1.7s (51.6%)

Results

759.0ms	1978×	body	1024	valid
435.0ms	4451×	body	128	valid
270.0ms	1028×	body	512	valid
119.0ms	242×	body	2048	valid
96.0ms	557×	body	256	valid

Compiler

Compiled 38 to 35 computations (7.9% saved)

simplify25.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

978×	`times-frac_binary64`
434×	`unswap-sqr_binary64`
374×	`associate-*l/_binary64`
342×	`associate-/l*_binary64`
228×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	19	15
2	25	15
3	34	15
4	59	15
5	124	15
6	311	15
7	972	15
8	2549	15
9	4189	15

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.8b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 46 to 42 computations (8.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
✓	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	3.0b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

series16.0ms (0.5%)

Counts

3 → 20

Calls

3 calls:

8.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
7.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
1.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

rewrite53.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

426×	`log-prod_binary64`
259×	`prod-diff_binary64`
227×	`fma-def_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	218	36
2	2665	36

Stop Event

1×	node limit

Counts

3 → 114

Calls

3 calls:

51.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))
51.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
51.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

simplify30.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
431×	`distribute-rgt-neg-in_binary64`
352×	`distribute-lft-neg-in_binary64`
349×	`cancel-sign-sub-inv_binary64`
277×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	257
1	126	252
2	325	238
3	1082	231
4	3632	231

Stop Event

1×	node limit

Counts

134 → 137

prune87.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	3	138

Error

0.0b

Counts

138 → 3

Alt Table

Status	Error	Program
	30.8b	(fma.f64 2 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
	30.8b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))
▶	30.5b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))

Compiler

Compiled 2345 to 2110 computations (10% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2/15 (pow.f64 x 5) x)
✓	17.6b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
3.0ms	(fma.f64 2/15 (pow.f64 x 5) x)

rewrite40.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`log1p-expm1-u_binary64`
835×	`expm1-log1p-u_binary64`
103×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
95×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	214	23
2	2284	23

Stop Event

1×	node limit

Counts

2 → 47

Calls

2 calls:

39.0ms	(fma.f64 2/15 (pow.f64 x 5) x)
39.0ms	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))

simplify32.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-neg_binary64`
416×	`unswap-sqr_binary64`
405×	`cancel-sign-sub-inv_binary64`
315×	`associate-l_binary64`
304×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	246
1	42	242
2	96	228
3	285	228
4	693	228
5	1942	228
6	3515	228

Stop Event

1×	node limit

Counts

71 → 56

prune31.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	56	3	59

Error

0.0b

Counts

59 → 3

Alt Table

Status	Error	Program
	30.8b	(fma.f64 2 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
▶	30.8b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))
✓	30.5b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))

Compiler

Compiled 935 to 731 computations (21.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 -2) x)
✓	0.7b	(log1p.f64 (pow.f64 (exp.f64 -2) x))
✓	3.3b	(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))

series310.0ms (9.2%)

Counts

3 → 36

Calls

3 calls:

177.0ms	(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))
130.0ms	(log1p.f64 (pow.f64 (exp.f64 -2) x))
2.0ms	(pow.f64 (exp.f64 -2) x)

rewrite51.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

826×	`expm1-log1p-u_binary64`
825×	`log1p-expm1-u_binary64`
415×	`prod-diff_binary64`
90×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	189	27
2	2250	27

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

50.0ms	(pow.f64 (exp.f64 -2) x)
50.0ms	(log1p.f64 (pow.f64 (exp.f64 -2) x))
50.0ms	(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))

simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary64`
530×	`associate-l_binary64`
490×	`cancel-sign-sub-inv_binary64`
480×	`associate-r_binary64`
302×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	361
1	119	352
2	329	343
3	1176	331

Stop Event

1×	node limit

Counts

118 → 107

prune67.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	108	2	110

Error

0.0b

Counts

110 → 2

Alt Table

Status	Error	Program
▶	30.8b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))
✓	30.5b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))

Compiler

Compiled 1840 to 1633 computations (11.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 x) -2)
✓	0.7b	(log1p.f64 (pow.f64 (exp.f64 x) -2))
✓	3.3b	(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))

series477.0ms (14.2%)

Counts

3 → 36

Calls

3 calls:

240.0ms	(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
231.0ms	(log1p.f64 (pow.f64 (exp.f64 x) -2))
7.0ms	(pow.f64 (exp.f64 x) -2)

rewrite53.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`expm1-log1p-u_binary64`
807×	`log1p-expm1-u_binary64`
408×	`prod-diff_binary64`
90×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	190	27
2	2229	27

Stop Event

1×	node limit

Counts

3 → 81

Calls

3 calls:

51.0ms	(pow.f64 (exp.f64 x) -2)
51.0ms	(log1p.f64 (pow.f64 (exp.f64 x) -2))
51.0ms	(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))

simplify24.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-def_binary64`
527×	`associate-l_binary64`
498×	`cancel-sign-sub-inv_binary64`
477×	`associate-r_binary64`
307×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	433
1	121	424
2	332	343
3	1176	331

Stop Event

1×	node limit

Counts

117 → 107

prune59.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	107	2	109

Error

0.0b

Counts

109 → 2

Alt Table

Status	Error	Program
✓	30.8b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))
✓	30.5b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))

Compiler

Compiled 1831 to 1475 computations (19.4% saved)

regimes135.0ms (4%)

Accuracy

Total 0.5b remaining (98.1%)

Threshold costs 0.5b (98.1%)

Counts

19 → 2

Compiler

Compiled 1613 to 1403 computations (13% saved)

bsearch1.0ms (0%)

Compiler: Compiled 10 to 9 computations (10% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	44
1	36	44
2	48	44
3	54	44
4	58	44
5	59	44

Stop Event

1×

saturated

end62.0ms (1.9%)

Compiler: Compiled 84 to 72 computations (14.3% saved)

Details

analyze1.0ms (0%)

sample1.7s (51.6%)

simplify25.0ms (0.8%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series16.0ms (0.5%)

rewrite53.0ms (1.6%)

simplify30.0ms (0.9%)

prune87.0ms (2.6%)

localize8.0ms (0.2%)

series6.0ms (0.2%)

rewrite40.0ms (1.2%)

simplify32.0ms (0.9%)

prune31.0ms (0.9%)

localize8.0ms (0.2%)

series310.0ms (9.2%)

rewrite51.0ms (1.5%)

simplify25.0ms (0.7%)

prune67.0ms (2%)

localize7.0ms (0.2%)

series477.0ms (14.2%)

rewrite53.0ms (1.6%)

simplify24.0ms (0.7%)

prune59.0ms (1.8%)

regimes135.0ms (4%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end62.0ms (1.9%)

Profiling