Details

analyze496.0ms (18.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.6s (59.3%)

Results

863.0ms	2775×	body	1024	valid
283.0ms	1332×	body	512	valid
261.0ms	3236×	body	128	valid
95.0ms	661×	body	256	valid
91.0ms	252×	body	2048	valid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8

Stop Event

1×

saturated

Counts

1 → 2

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 x)
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

series10.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
2.0ms	(expm1.f64 x)

rewrite38.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_binary64`
332×	`unpow-prod-down_binary64`
258×	`log-prod_binary64`
131×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	99	11
2	1299	11

Stop Event

1×	node limit

Counts

2 → 103

Calls

2 calls:

36.0ms	(expm1.f64 x)
36.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))

simplify35.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

803×	`unswap-sqr_binary64`
534×	`fma-def_binary64`
334×	`fma-neg_binary64`
288×	`*-commutative_binary64`
228×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	180
1	79	176
2	190	174
3	627	168
4	2150	168
5	3971	168

Stop Event

1×	node limit

Counts

127 → 120

prune60.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	3	121

Error

0.2b

Counts

121 → 3

Alt Table

Status	Error	Program
	21.5b	(+.f64 1/2 (/.f64 1 x))
	1.1b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) 2) -1) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
▶	0.3b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))

Compiler

Compiled 1526 to 701 computations (54.1% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 x)
✓	0.0b	(/.f64 1 (expm1.f64 x))
✓	0.2b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))

series17.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(/.f64 1 (expm1.f64 x))
8.0ms	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))

rewrite34.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

545×	`log1p-expm1-u_binary64`
545×	`expm1-log1p-u_binary64`
305×	`log-prod_binary64`
156×	`pow2_binary64`
111×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	135	14
2	1595	14

Stop Event

1×	node limit

Counts

2 → 59

Calls

2 calls:

33.0ms	(/.f64 1 (expm1.f64 x))
33.0ms	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))

simplify36.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary64`
297×	`fma-neg_binary64`
284×	`distribute-rgt-neg-in_binary64`
284×	`unswap-sqr_binary64`
232×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	204
1	63	194
2	149	192
3	449	192
4	1199	192
5	2845	192
6	4177	192

Stop Event

1×	node limit

Counts

83 → 75

prune59.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	120	3	123

Error

0.2b

Counts

123 → 3

Alt Table

Status	Error	Program
	21.5b	(+.f64 1/2 (/.f64 1 x))
▶	0.5b	(*.f64 (exp.f64 x) (/.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))))
✓	0.3b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))

Compiler

Compiled 1381 to 756 computations (45.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)))
✓	0.0b	(+.f64 (exp.f64 x) 1)
✓	0.2b	(*.f64 (exp.f64 x) (/.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))))
✓	0.4b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))

series33.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

12.0ms	(*.f64 (exp.f64 x) (/.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))))
10.0ms	(/.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)))
9.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))
1.0ms	(+.f64 (exp.f64 x) 1)

rewrite54.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

304×	`prod-diff_binary64`
173×	`fma-def_binary64`
168×	`expm1-udef_binary64`
168×	`log1p-udef_binary64`
157×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	56
1	221	23
2	3131	23

Stop Event

1×	node limit

Counts

4 → 157

Calls

4 calls:

52.0ms	(/.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)))
52.0ms	(+.f64 (exp.f64 x) 1)
52.0ms	(*.f64 (exp.f64 x) (/.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))))
52.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))

simplify35.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-def_binary64`
549×	`fma-neg_binary64`
424×	`cancel-sign-sub-inv_binary64`
407×	`times-frac_binary64`
245×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	596
1	130	586
2	314	584
3	991	573
4	3070	333

Stop Event

1×	node limit

Counts

205 → 188

prune87.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	188	3	191

Error

0.2b

Counts

191 → 3

Alt Table

Status	Error	Program
▶	21.5b	(+.f64 1/2 (/.f64 1 x))
✓	0.5b	(*.f64 (exp.f64 x) (/.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))))
✓	0.3b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))

Compiler

Compiled 2870 to 1808 computations (37% saved)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

0.2b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	21.5b	(+.f64 1/2 (/.f64 1 x))
✓	0.5b	(*.f64 (exp.f64 x) (/.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))))
✓	0.3b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))

Compiler

Compiled 29 to 21 computations (27.6% saved)

regimes35.0ms (1.3%)

Accuracy

Total 0.1b remaining (19.6%)

Threshold costs 0.1b (19.6%)

Counts

16 → 1

Compiler

Compiled 545 to 379 computations (30.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11

Stop Event

1×

saturated

end48.0ms (1.8%)

Compiler: Compiled 45 to 33 computations (26.7% saved)

Details

analyze496.0ms (18.1%)

sample1.6s (59.3%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series10.0ms (0.4%)

rewrite38.0ms (1.4%)

simplify35.0ms (1.3%)

prune60.0ms (2.2%)

localize5.0ms (0.2%)

series17.0ms (0.6%)

rewrite34.0ms (1.2%)

simplify36.0ms (1.3%)

prune59.0ms (2.2%)

localize12.0ms (0.4%)

series33.0ms (1.2%)

rewrite54.0ms (2%)

simplify35.0ms (1.3%)

prune87.0ms (3.2%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

regimes35.0ms (1.3%)

simplify2.0ms (0.1%)

end48.0ms (1.8%)

Profiling