Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample103.0ms (5.3%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify81.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
366×	`fma-neg_binary64`
277×	`*-commutative_binary64`
262×	`exp-prod_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	20	13
3	27	13
4	46	13
5	78	13
6	146	13
7	274	13
8	670	13
9	1896	13
10	2692	13
11	3535	13
12	4713	13
13	4865	13
14	4794	13

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

series17.0ms (0.9%)

Counts

2 → 16

Calls

2 calls:

14.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 57

Calls

2 calls:

5.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
3.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify79.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-neg_binary64`
684×	`fma-def_binary64`
548×	`associate-l_binary64`
292×	`times-frac_binary64`
257×	`distribute-rgt-in_binary64`

Counts

73 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1210
1	248	1114
2	549	1101
3	1241	1099
4	4205	1099
5	4980	1099

prune62.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	3	106

Error

Counts

106 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))) 3))

Compiler

Compiled 1627 to 687 computations (57.8% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))) 3))
✓	0.0b	(pow.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))) 3)

series49.0ms (2.5%)

Counts

4 → 48

Calls

4 calls:

21.0ms	(pow.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))) 3)
13.0ms	(cbrt.f64 (pow.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))) 3))
12.0ms	(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
3.0ms	(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))

rewrite36.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
48×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`
42×	`cbrt-prod_binary64`

Counts

4 → 164

Calls

4 calls:

7.0ms	(cbrt.f64 (pow.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))) 3))
7.0ms	(pow.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))) 3)
6.0ms	(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
4.0ms	(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))

simplify108.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

662×	`associate-*l/_binary64`
354×	`times-frac_binary64`
287×	`associate-/l*_binary64`
273×	`associate-/r*_binary64`
247×	`fma-def_binary64`

Counts

212 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	4578
1	522	4110
2	1484	3997
3	5078	3997

prune132.0ms (6.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	205	3	208

Error

Counts

208 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))) 3))

Compiler

Compiled 3943 to 1978 computations (49.8% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 2) (cosh.f64 x))
✓	0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))

series58.0ms (3%)

Counts

2 → 24

Calls

2 calls:

34.0ms	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
24.0ms	(/.f64 (sqrt.f64 2) (cosh.f64 x))

rewrite28.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
66×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
36×	`sqrt-prod_binary64`

Counts

2 → 118

Calls

2 calls:

14.0ms	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
6.0ms	(/.f64 (sqrt.f64 2) (cosh.f64 x))

simplify93.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

640×	`associate-/l*_binary64`
573×	`fma-def_binary64`
363×	`*-commutative_binary64`
356×	`associate-/l/_binary64`
267×	`fma-neg_binary64`

Counts

142 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	2599
1	478	2383
2	1423	2028
3	3862	1982
4	4922	1982

prune122.0ms (6.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	177	3	180

Error

Counts

180 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))) 3))

Compiler

Compiled 3172 to 2509 computations (20.9% saved)

regimes70.0ms (3.6%)

Accuracy

Total 0.0b remaining (20.8%)

Threshold costs 0.0b (20.8%)

Counts

29 → 1

Compiler

Compiled 842 to 705 computations (16.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	9	6
2	8	6

end0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

sample851.0ms (44.2%)

Algorithm

1×

intervals

Results

644.0ms

8000×

body

128

valid

Compiler

Compiled 48 to 40 computations (16.7% saved)

Details

analyze1.0ms (0.1%)

sample103.0ms (5.3%)

simplify81.0ms (4.2%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series17.0ms (0.9%)

rewrite11.0ms (0.6%)

simplify79.0ms (4.1%)

prune62.0ms (3.2%)

localize8.0ms (0.4%)

series49.0ms (2.5%)

rewrite36.0ms (1.9%)

simplify108.0ms (5.6%)

prune132.0ms (6.8%)

localize6.0ms (0.3%)

series58.0ms (3%)

rewrite28.0ms (1.5%)

simplify93.0ms (4.8%)

prune122.0ms (6.3%)

regimes70.0ms (3.6%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample851.0ms (44.2%)

Profiling