Details

analyze20.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	1.6%	48.5%	9
50.4%	1.2%	48.5%	10
50.4%	1.2%	48.5%	11
50.4%	1.1%	48.6%	12
50.4%	1%	48.6%	13
50.5%	0.9%	48.6%	14

Compiler

Compiled 15 to 8 computations (46.7% saved)

sample2.8s (64.1%)

Results

1.8s	4074×	body	1024	valid
557.0ms	1970×	body	512	valid
209.0ms	404×	body	2048	valid
193.0ms	972×	body	256	valid
84.0ms	836×	body	128	valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

preprocess33.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

720×	`fma-def_binary64`
478×	`fma-neg_binary64`
464×	`times-frac_binary64`
264×	`associate-l_binary64`
226×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	20	22
2	35	22
3	59	22
4	133	22
5	336	22
6	878	22
7	2569	22
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 14 to 7 computations (50% saved)

simplify20.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
478×	`fma-neg_binary64`
464×	`times-frac_binary64`
264×	`associate-l_binary64`
226×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	20	22
2	35	22
3	59	22
4	133	22
5	336	22
6	878	22
7	2569	22

Stop Event

1×	node limit

Counts

1 → 1

prune2.0ms (0%)

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

56.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	56.7b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 42 to 21 computations (50% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	0.3b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	5.6b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series18.0ms (0.4%)

Counts

3 → 24

Calls

9 calls:

7.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))	x	-inf
6.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))	x	inf
1.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))	x	0
1.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))	x	0
1.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))	x	0

rewrite98.0ms (2.2%)

Algorithm

6×	egg-rewrite
1×	batch-egg-rewrite

Rules

97×	`add-sqr-sqrt_binary64`
92×	`log1p-expm1-u_binary64`
92×	`expm1-log1p-u_binary64`
91×	`add-cbrt-cube_binary64`
91×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	186	18
2	3662	18
0	6	6
1	130	6
2	2131	6
0	6	6
0	8	3
1	186	3
2	3662	3
0	8	3
0	6	6
1	129	6
2	2130	6
0	6	6

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

3 → 37

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-def_binary64`
695×	`fma-neg_binary64`
507×	`unswap-sqr_binary64`
471×	`associate-l_binary64`
377×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	321
1	138	317
2	352	311
3	1114	309
4	3894	309

Stop Event

1×	node limit

Counts

61 → 64

prune44.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	4	65

Error

Counts

65 → 4

Alt Table

Status	Error	Program
	0.0b	(tanh.f64 x)
	1.4b	(/.f64 (fma.f64 x (fma.f64 x (.f64 x 1/3) 2) (fma.f64 1/60 (pow.f64 x 5) (.f64 1/2520 (pow.f64 x 7)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	1.8b	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))
▶	0.0b	(expm1.f64 (log1p.f64 (tanh.f64 x)))

Compiler

Compiled 1024 to 467 computations (54.4% saved)

localize3.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (tanh.f64 x)))
✓	0.0b	(tanh.f64 x)
✓	0.2b	(log1p.f64 (tanh.f64 x))

series504.0ms (11.3%)

Counts

3 → 36

Calls

9 calls:

233.0ms	(log1p.f64 (tanh.f64 x))	x	-inf
231.0ms	(log1p.f64 (tanh.f64 x))	x	inf
11.0ms	(expm1.f64 (log1p.f64 (tanh.f64 x)))	x	inf
9.0ms	(tanh.f64 x)	x	-inf
8.0ms	(expm1.f64 (log1p.f64 (tanh.f64 x)))	x	-inf

rewrite42.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`expm1-log1p-u_binary64`
508×	`log1p-expm1-u_binary64`
243×	`unpow-prod-down_binary64`
224×	`log-prod_binary64`
138×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	94	11
2	1291	11

Stop Event

1×	node limit

Counts

3 → 138

simplify44.0ms (1%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-def_binary64`
542×	`associate-l_binary64`
491×	`associate-r_binary64`
436×	`cancel-sign-sub-inv_binary64`
254×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	724
1	135	700
2	353	688
3	1152	682
4	4933	682

Stop Event

1×	node limit

Counts

174 → 101

prune60.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	103	2	105

Error

Counts

105 → 2

Alt Table

Status	Error	Program
	0.1b	(expm1.f64 (log1p.f64 (.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))
▶	0.0b	(tanh.f64 x)

Compiler

Compiled 1260 to 850 computations (32.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(tanh.f64 x)

prune33.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	63	2	65

Error

Counts

65 → 2

Alt Table

Status	Error	Program
▶	0.1b	(expm1.f64 (log1p.f64 (.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))
✓	0.0b	(tanh.f64 x)

Compiler

Compiled 713 to 491 computations (31.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
✓	0.0b	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
✓	0.0b	(pow.f64 (exp.f64 2) x)
✓	0.2b	(log1p.f64 (.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))

series318.0ms (7.2%)

Counts

4 → 48

Calls

12 calls:

149.0ms	(log1p.f64 (.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))	x	-inf
148.0ms	(log1p.f64 (.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))	x	inf
4.0ms	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))	x	-inf
4.0ms	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))	x	inf
3.0ms	(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))	x	-inf

rewrite51.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`prod-diff_binary64`
217×	`fma-def_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
115×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	251	54
2	2958	54

Stop Event

1×	node limit

Counts

4 → 96

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

508×	`cancel-sign-sub-inv_binary64`
359×	`fma-neg_binary64`
326×	`sub-neg_binary64`
272×	`unswap-sqr_binary64`
253×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	649
1	190	612
2	509	598
3	1710	598
4	4145	598

Stop Event

1×	node limit

Counts

144 → 131

prune81.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	131	2	133

Error

Counts

133 → 2

Alt Table

Status	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))
✓	0.0b	(tanh.f64 x)

Compiler

Compiled 2397 to 1657 computations (30.9% saved)

regimes86.0ms (1.9%)

Accuracy

Total 0.0b remaining (40%)

Threshold costs 0.0b (40%)

Counts

57 → 1

Compiler

Compiled 1524 to 1158 computations (24% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11

Stop Event

1×

saturated

end39.0ms (0.9%)

Stop Event

1×

done

Compiler

Compiled 33 to 28 computations (15.2% saved)

Details

analyze20.0ms (0.4%)

sample2.8s (64.1%)

preprocess33.0ms (0.7%)

simplify20.0ms (0.5%)

prune2.0ms (0%)

localize12.0ms (0.3%)

series18.0ms (0.4%)

rewrite98.0ms (2.2%)

simplify30.0ms (0.7%)

prune44.0ms (1%)

localize3.0ms (0.1%)

series504.0ms (11.3%)

rewrite42.0ms (0.9%)

simplify44.0ms (1%)

prune60.0ms (1.3%)

localize6.0ms (0.1%)

prune33.0ms (0.7%)

localize10.0ms (0.2%)

series318.0ms (7.2%)

rewrite51.0ms (1.2%)

simplify42.0ms (0.9%)

prune81.0ms (1.8%)

regimes86.0ms (1.9%)

simplify2.0ms (0%)

end39.0ms (0.9%)

Profiling