Details

analyze19.0ms (0.6%)

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)

sample141.0ms (4.6%)

Algorithm

1×

intervals

Results

44.0ms	138×	body	1024	valid
9.0ms	53×	body	512	valid
3.0ms	31×	body	256	valid
3.0ms	8×	body	2048	valid
1.0ms	26×	body	128	valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
658×	`unswap-sqr_binary64`
478×	`fma-neg_binary64`
464×	`times-frac_binary64`
388×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	20	22
2	34	22
3	58	22
4	125	22
5	288	22
6	624	22
7	1577	22
8	3798	22
9	4553	22
10	5023	22

prune2.0ms (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

58.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	58.3b	(/.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)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	1.3b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	5.9b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series20.0ms (0.7%)

Counts

3 → 24

Calls

3 calls:

15.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

3 → 110

Calls

3 calls:

10.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
4.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
3.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify118.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary64`
473×	`associate-l_binary64`
370×	`fma-neg_binary64`
327×	`times-frac_binary64`
203×	`associate-/l*_binary64`

Counts

134 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3081
1	434	2840
2	1282	2757
3	4252	2757
4	4850	2757

prune64.0ms (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	2	153

Error

Counts

153 → 2

Alt Table

Status	Error	Program
▶	0.0b	(tanh.f64 x)
	1.5b	(-.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315)))

Compiler

Compiled 3378 to 738 computations (78.2% saved)

localize1.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 x)

series22.0ms (0.7%)

Counts

1 → 12

Calls

1 calls:

22.0ms

(tanh.f64 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 12

Calls

1 calls:

1.0ms

(tanh.f64 x)

simplify53.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

748×	`times-frac_binary64`
602×	`fma-neg_binary64`
330×	`fma-def_binary64`
236×	`distribute-rgt-in_binary64`
234×	`distribute-lft-in_binary64`

Counts

24 → 24

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	189
1	111	182
2	266	178
3	751	175
4	3049	175
5	4950	175
6	5000	175

prune15.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	24	2	26

Error

Counts

26 → 2

Alt Table

Status	Error	Program
✓	0.0b	(tanh.f64 x)
▶	1.5b	(-.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315)))

Compiler

Compiled 248 to 160 computations (35.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 5) 2/15 x)
✓	0.0b	(-.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315)))
✓	0.1b	(*.f64 (pow.f64 x 7) 17/315)
✓	0.1b	(fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315))

series18.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315))
4.0ms	(fma.f64 (pow.f64 x 5) 2/15 x)
4.0ms	(-.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315)))
4.0ms	(*.f64 (pow.f64 x 7) 17/315)

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(*.f64 (pow.f64 x 7) 17/315)
4.0ms	(-.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315)))
0.0ms	(fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315))
0.0ms	(fma.f64 (pow.f64 x 5) 2/15 x)

simplify99.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

782×	`times-frac_binary64`
674×	`fma-neg_binary64`
409×	`fma-def_binary64`
340×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`

Counts

127 → 143

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	2314
1	263	2103
2	844	1916
3	2884	1859
4	4353	1844
5	5866	1844

prune138.0ms (4.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	143	2	145

Error

Counts

145 → 2

Alt Table

Status	Error	Program
✓	0.0b	(tanh.f64 x)
✓	1.5b	(-.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315)))

Compiler

Compiled 3920 to 3100 computations (20.9% saved)

regimes51.0ms (1.7%)

Accuracy

Total 0.0b remaining (72%)

Threshold costs 0.0b (72%)

Counts

29 → 1

Compiler

Compiled 738 to 544 computations (26.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	3	3

end0.0ms (0%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

sample2.1s (70.8%)

Algorithm

1×

intervals

Results

1.2s	3850×	body	1024	valid
341.0ms	1965×	body	512	valid
140.0ms	402×	body	2048	valid
107.0ms	1015×	body	256	valid
52.0ms	768×	body	128	valid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 40 to 27 computations (32.5% saved)

Details

analyze19.0ms (0.6%)

sample141.0ms (4.6%)

simplify67.0ms (2.2%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series20.0ms (0.7%)

rewrite26.0ms (0.9%)

simplify118.0ms (3.9%)

prune64.0ms (2.1%)

localize1.0ms (0%)

series22.0ms (0.7%)

rewrite1.0ms (0%)

simplify53.0ms (1.8%)

prune15.0ms (0.5%)

localize11.0ms (0.4%)

series18.0ms (0.6%)

rewrite13.0ms (0.4%)

simplify99.0ms (3.3%)

prune138.0ms (4.5%)

regimes51.0ms (1.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.1s (70.8%)

Profiling