Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
87.5%	12.5%	0%	4
93.7%	6.2%	0%	5
96.8%	3.1%	0%	6
98.4%	1.6%	0%	7
99.2%	0.8%	0%	8
99.6%	0.4%	0%	9
99.8%	0.2%	0%	10
99.9%	0.1%	0%	11
99.9%	0%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample723.0ms (58.6%)

Results

710.0ms

8256×

body

128

valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess36.0ms (2.9%)

Algorithm

2×	egg-herbie

Rules

468×	`fma-def_binary64`
327×	`fma-neg_binary64`
233×	`div-sub_binary64`
156×	`times-frac_binary64`
137×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	11	10
2	15	10
3	21	10
4	29	10
5	39	10
6	52	10
7	69	10
8	88	10
9	120	10
10	153	10
11	195	10
12	287	10
13	417	10
14	669	10
15	1292	10
16	1949	10
17	2469	10
18	2644	10
19	2780	10
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 8 to 6 computations (25% saved)

simplify30.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

468×	`fma-def_binary64`
327×	`fma-neg_binary64`
233×	`div-sub_binary64`
156×	`times-frac_binary64`
137×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	11	10
2	15	10
3	21	10
4	29	10
5	39	10
6	52	10
7	69	10
8	88	10
9	120	10
10	153	10
11	195	10
12	287	10
13	417	10
14	669	10
15	1292	10
16	1949	10
17	2469	10
18	2644	10
19	2780	10

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))

series2.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(/.f64 (+.f64 x 1) (-.f64 1 x))	x	0
1.0ms	(/.f64 (+.f64 x 1) (-.f64 1 x))	x	inf
1.0ms	(/.f64 (+.f64 x 1) (-.f64 1 x))	x	-inf

rewrite38.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

737×	`log1p-expm1-u_binary64`
737×	`expm1-log1p-u_binary64`
241×	`prod-diff_binary64`
69×	`add-sqr-sqrt_binary64`
65×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	138	10
2	1948	10

Stop Event

1×	node limit

Counts

1 → 35

simplify45.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-neg_binary64`
601×	`fma-def_binary64`
418×	`cancel-sign-sub-inv_binary64`
303×	`associate-/l/_binary64`
291×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	151
1	102	130
2	299	128
3	890	128
4	2653	124

Stop Event

1×	node limit

Counts

47 → 49

prune41.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	3	50

Error

Counts

50 → 3

Alt Table

Status	Error	Program
	32.3b	(fma.f64 2 x 1)
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))
▶	0.0b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))))

Compiler

Compiled 626 to 490 computations (21.7% saved)

localize9.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))
✓	0.5b	(expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
✓	0.5b	(+.f64 1 (expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))

series7.0ms (0.5%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(+.f64 1 (expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))	x	-inf
1.0ms	(expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))	x	inf
1.0ms	(+.f64 1 (expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))	x	inf
1.0ms	(expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))	x	-inf
1.0ms	(+.f64 1 (expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))	x	0

rewrite48.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

423×	`log-prod_binary64`
368×	`prod-diff_binary64`
306×	`fma-def_binary64`
165×	`fma-neg_binary64`
157×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	185	24
2	2600	24

Stop Event

1×	node limit

Counts

2 → 76

simplify40.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-def_binary64`
247×	`associate-l_binary64`
237×	`distribute-rgt-out_binary64`
235×	`sub-neg_binary64`
187×	`associate-+l+_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	478
1	176	462
2	447	430
3	1350	402
4	3672	396

Stop Event

1×	node limit

Counts

100 → 107

prune115.0ms (9.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	156	3	159

Error

Counts

159 → 3

Alt Table

Status	Error	Program
▶	32.3b	(fma.f64 2 x 1)
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))
✓	0.0b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))))

Compiler

Compiled 2741 to 2292 computations (16.4% saved)

localize2.0ms (0.2%)

prune1.0ms (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

Counts

3 → 3

Alt Table

Status	Error	Program
✓	32.3b	(fma.f64 2 x 1)
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))
✓	0.0b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))))

Compiler

Compiled 25 to 20 computations (20% saved)

regimes33.0ms (2.7%)

Accuracy

Total 0.0b remaining (77.6%)

Threshold costs 0.0b (77.6%)

Counts

15 → 1

Compiler

Compiled 313 to 263 computations (16% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	15	16
2	19	16
3	21	16
4	22	16

Stop Event

1×

saturated

end54.0ms (4.3%)

Stop Event

1×

done

Compiler

Compiled 47 to 38 computations (19.1% saved)

Details

analyze3.0ms (0.2%)

sample723.0ms (58.6%)

preprocess36.0ms (2.9%)

simplify30.0ms (2.5%)

prune1.0ms (0.1%)

localize4.0ms (0.3%)

series2.0ms (0.2%)

rewrite38.0ms (3.1%)

simplify45.0ms (3.6%)

prune41.0ms (3.3%)

localize9.0ms (0.7%)

series7.0ms (0.5%)

rewrite48.0ms (3.9%)

simplify40.0ms (3.3%)

prune115.0ms (9.3%)

localize2.0ms (0.2%)

prune1.0ms (0.1%)

regimes33.0ms (2.7%)

simplify2.0ms (0.2%)

end54.0ms (4.3%)

Profiling