Details

analyze19.0ms (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)

sample3.1s (69.5%)

Results

1.8s	3996×	body	1024	valid
554.0ms	2018×	body	512	valid
298.0ms	1027×	body	256	valid
201.0ms	400×	body	2048	valid
87.0ms	815×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 44 to 23 computations (47.7% saved)

simplify65.0ms (1.5%)

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%)

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

58.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	58.7b	(/.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)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	2.2b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	5.4b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series18.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

14.0ms	(/.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)))

rewrite69.0ms (1.6%)

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:

49.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
8.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
3.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify108.0ms (2.5%)

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

prune68.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	3	153

Error

Counts

153 → 3

Alt Table

Status	Error	Program
	2.9b	(-.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)))
▶	0.0b	(tanh.f64 x)
	58.7b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))

Compiler

Compiled 3428 to 760 computations (77.8% saved)

localize1.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 x)

series21.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

21.0ms

(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)

simplify51.0ms (1.2%)

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 (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Error

Counts

27 → 3

Alt Table

Status	Error	Program
✓	0.0b	(tanh.f64 x)
	39.6b	(cbrt.f64 (.f64 (.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x)))
▶	2.9b	(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))

Compiler

Compiled 266 to 168 computations (36.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series11.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 30

Calls

3 calls:

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

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-def_binary64`
381×	`unsub-neg_binary64`
357×	`exp-prod_binary64`
319×	`fma-neg_binary64`
294×	`*-commutative_binary64`

Counts

66 → 56

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	1071
1	109	950
2	260	942
3	1117	942
4	2874	942
5	4681	942
6	4975	942
7	4886	942

prune45.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

59 → 3

Alt Table

Status	Error	Program
✓	0.0b	(tanh.f64 x)
▶	39.6b	(cbrt.f64 (.f64 (.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x)))
✓	2.9b	(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))

Compiler

Compiled 1193 to 917 computations (23.1% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(tanh.f64 x)
✓	0.0b	(*.f64 (tanh.f64 x) (tanh.f64 x))
✓	0.1b	(.f64 (.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x))
✓	39.6b	(cbrt.f64 (.f64 (.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x)))

series114.0ms (2.6%)

Counts

3 → 36

Calls

3 calls:

58.0ms	(*.f64 (tanh.f64 x) (tanh.f64 x))
34.0ms	(.f64 (.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x))
21.0ms	(cbrt.f64 (.f64 (.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x)))

rewrite47.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`frac-times_binary64`
104×	`tanh-def-a_binary64`
104×	`tanh-def-b_binary64`
104×	`tanh-def-c_binary64`
63×	`cbrt-div_binary64`

Counts

3 → 211

Calls

3 calls:

9.0ms	(cbrt.f64 (.f64 (.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x)))
8.0ms	(.f64 (.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x))
4.0ms	(*.f64 (tanh.f64 x) (tanh.f64 x))

simplify223.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

684×	`fma-def_binary64`
573×	`times-frac_binary64`
533×	`log-prod_binary64`
344×	`associate-/l*_binary64`
319×	`log-div_binary64`

Counts

247 → 306

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	8029
1	596	7026
2	2007	6217
3	4385	6217
4	5573	6217

prune190.0ms (4.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	378	0	378
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	378	3	381

Error

Counts

381 → 3

Alt Table

Status	Error	Program
✓	0.0b	(tanh.f64 x)
✓	39.6b	(cbrt.f64 (.f64 (.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x)))
✓	2.9b	(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))

Compiler

Compiled 8849 to 4703 computations (46.9% saved)

regimes110.0ms (2.5%)

Accuracy

Total 0.0b remaining (86.1%)

Threshold costs 0.0b (86.1%)

Counts

60 → 1

Compiler

Compiled 2044 to 1192 computations (41.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	3	3

end49.0ms (1.1%)

Compiler: Compiled 36 to 24 computations (33.3% saved)

Details

analyze19.0ms (0.4%)

sample3.1s (69.5%)

simplify65.0ms (1.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series18.0ms (0.4%)

rewrite69.0ms (1.6%)

simplify108.0ms (2.5%)

prune68.0ms (1.6%)

localize1.0ms (0%)

series21.0ms (0.5%)

rewrite1.0ms (0%)

simplify51.0ms (1.2%)

prune15.0ms (0.3%)

localize10.0ms (0.2%)

series11.0ms (0.3%)

rewrite2.0ms (0%)

simplify91.0ms (2.1%)

prune45.0ms (1%)

localize5.0ms (0.1%)

series114.0ms (2.6%)

rewrite47.0ms (1.1%)

simplify223.0ms (5.1%)

prune190.0ms (4.3%)

regimes110.0ms (2.5%)

simplify2.0ms (0%)

end49.0ms (1.1%)

Profiling