Details

analyze19.0ms (0.5%)

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)

sample2.9s (79%)

Results

1.8s	3982×	body	1024	valid
550.0ms	1956×	body	512	valid
221.0ms	433×	body	2048	valid
192.0ms	1068×	body	256	valid
85.0ms	817×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 30 to 16 computations (46.7% saved)

preprocess31.0ms (0.9%)

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)

simplify21.0ms (0.6%)

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

prune3.0ms (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

58.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	58.2b	(/.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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	6.9b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series14.0ms (0.4%)

Counts

2 → 16

Calls

6 calls:

6.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))	x	inf
5.0ms	(/.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
0.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))	x	-inf

rewrite84.0ms (2.3%)

Algorithm

2×	egg-rewrite-iter-limit
2×	egg-rewrite
1×	batch-egg-rewrite

Rules

99×	`add-sqr-sqrt_binary64`
99×	`add-sqr-sqrt_binary64`
95×	`*-un-lft-identity_binary64`
95×	`pow1_binary64`
95×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	186	12
2	3690	12
0	6	6
1	130	6
2	2149	6
0	6	6
0	8	3
1	186	3
2	3690	3
0	8	3

Stop Event

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

Counts

2 → 25

simplify31.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

495×	`fma-neg_binary64`
484×	`fma-def_binary64`
421×	`distribute-rgt-neg-in_binary64`
377×	`cancel-sign-sub-inv_binary64`
314×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	238
1	100	238
2	253	234
3	793	232
4	2098	232
5	3959	232

Stop Event

1×	node limit

Counts

41 → 43

prune31.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	3	44

Error

Counts

44 → 3

Alt Table

Status	Error	Program
▶	0.0b	(tanh.f64 x)
	0.8b	(/.f64 (*.f64 2 (sinh.f64 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	0.9b	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))

Compiler

Compiled 631 to 306 computations (51.5% saved)

localize1.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 x)

series22.0ms (0.6%)

Counts

1 → 12

Calls

3 calls:

9.0ms	(tanh.f64 x)	x	-inf
9.0ms	(tanh.f64 x)	x	inf
4.0ms	(tanh.f64 x)	x	0

rewrite32.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

465×	`pow1_binary64`
437×	`add-log-exp_binary64`
435×	`log1p-expm1-u_binary64`
435×	`expm1-log1p-u_binary64`
428×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	75	3
2	1079	3

Stop Event

1×	node limit

Counts

1 → 31

simplify38.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-neg_binary64`
404×	`distribute-rgt-neg-in_binary64`
367×	`cancel-sign-sub-inv_binary64`
299×	`distribute-lft-neg-in_binary64`
281×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	228
1	73	228
2	179	224
3	535	222
4	1589	222
5	3314	222
6	4744	222

Stop Event

1×	node limit

Counts

43 → 40

prune22.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	40	3	43

Error

Counts

43 → 3

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (.f64 2 (sinh.f64 x)) (.f64 2 (cosh.f64 x)))
✓	0.0b	(tanh.f64 x)
	0.9b	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))

Compiler

Compiled 440 to 307 computations (30.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 x)
✓	0.8b	(/.f64 (.f64 2 (sinh.f64 x)) (.f64 2 (cosh.f64 x)))

series34.0ms (1%)

Counts

2 → 24

Calls

6 calls:

13.0ms	(/.f64 (.f64 2 (sinh.f64 x)) (.f64 2 (cosh.f64 x)))	x	-inf
13.0ms	(/.f64 (.f64 2 (sinh.f64 x)) (.f64 2 (cosh.f64 x)))	x	inf
3.0ms	(sinh.f64 x)	x	-inf
3.0ms	(sinh.f64 x)	x	inf
1.0ms	(/.f64 (.f64 2 (sinh.f64 x)) (.f64 2 (cosh.f64 x)))	x	0

rewrite48.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

890×	`log1p-expm1-u_binary64`
890×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
88×	`*-un-lft-identity_binary64`
88×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	177	11
2	2439	11

Stop Event

1×	node limit

Counts

2 → 88

simplify34.0ms (1%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-neg_binary64`
468×	`fma-def_binary64`
406×	`distribute-rgt-neg-in_binary64`
367×	`cancel-sign-sub-inv_binary64`
301×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	378
1	103	378
2	271	366
3	807	364
4	2108	364
5	3928	364

Stop Event

1×	node limit

Counts

112 → 105

prune55.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	105	3	108

Error

Counts

108 → 3

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (.f64 2 (sinh.f64 x)) (.f64 2 (cosh.f64 x)))
✓	0.0b	(tanh.f64 x)
▶	0.9b	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))

Compiler

Compiled 1402 to 823 computations (41.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

2.0ms	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))	x	inf
1.0ms	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))	x	-inf
1.0ms	(fma.f64 (pow.f64 x 3) -1/3 x)	x	-inf
1.0ms	(fma.f64 (pow.f64 x 3) -1/3 x)	x	inf
1.0ms	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))	x	0

rewrite39.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`log1p-expm1-u_binary64`
835×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
97×	`add-log-exp_binary64`
95×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	218	23
2	2258	23

Stop Event

1×	node limit

Counts

2 → 47

simplify31.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-neg_binary64`
416×	`unswap-sqr_binary64`
405×	`cancel-sign-sub-inv_binary64`
333×	`associate-l_binary64`
304×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	264
1	43	260
2	102	228
3	309	228
4	735	228
5	2023	228
6	3560	228

Stop Event

1×	node limit

Counts

71 → 57

prune36.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	57	3	60

Error

Counts

60 → 3

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (.f64 2 (sinh.f64 x)) (.f64 2 (cosh.f64 x)))
✓	0.0b	(tanh.f64 x)
✓	0.9b	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))

Compiler

Compiled 907 to 703 computations (22.5% saved)

regimes64.0ms (1.8%)

Accuracy

Total 0.0b remaining (85.8%)

Threshold costs 0.0b (85.8%)

Counts

35 → 1

Compiler

Compiled 730 to 528 computations (27.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3

Stop Event

1×

saturated

end43.0ms (1.2%)

Stop Event

1×

done

Compiler

Compiled 31 to 23 computations (25.8% saved)

Details

analyze19.0ms (0.5%)

sample2.9s (79%)

preprocess31.0ms (0.9%)

simplify21.0ms (0.6%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series14.0ms (0.4%)

rewrite84.0ms (2.3%)

simplify31.0ms (0.9%)

prune31.0ms (0.8%)

localize1.0ms (0%)

series22.0ms (0.6%)

rewrite32.0ms (0.9%)

simplify38.0ms (1.1%)

prune22.0ms (0.6%)

localize5.0ms (0.1%)

series34.0ms (1%)

rewrite48.0ms (1.3%)

simplify34.0ms (1%)

prune55.0ms (1.5%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite39.0ms (1.1%)

simplify31.0ms (0.9%)

prune36.0ms (1%)

regimes64.0ms (1.8%)

simplify2.0ms (0%)

end43.0ms (1.2%)

Profiling