Details

analyze1.4s (31.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample108.0ms (2.5%)

Algorithm

1×

intervals

Results

82.0ms	97×	body	1024	valid
8.0ms	39×	body	512	valid
5.0ms	92×	body	128	valid
3.0ms	8×	body	2048	valid
2.0ms	20×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

667×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
380×	`fma-def_binary64`
279×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	123	11
5	318	8
6	1056	8
7	4350	8
8	4987	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
4×	`sqrt-prod_binary64`
2×	`sqrt-div_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 21

Calls

1 calls:

3.0ms

(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 193 to 132 computations (31.6% saved)

series16.0ms (0.4%)

Error

0.0b

Counts

1 → 6

Calls

1 calls:

9.0ms

(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 234 to 209 computations (10.7% saved)

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
661×	`associate-/l*_binary64`
283×	`fma-neg_binary64`
177×	`associate-/r/_binary64`
153×	`distribute-neg-frac_binary64`

Counts

27 → 10

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	373
1	170	349
2	478	325
3	1806	311
4	4964	311

prune7.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	9	1	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	9	2	11

Error

0.0b

Counts

11 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	19.3b	(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))

Compiler

Compiled 163 to 129 computations (20.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 x (sqrt.f64 2)) x)
0.1b	(.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)
0.5b	(/.f64 x (sqrt.f64 2))
0.5b	(/.f64 x (sqrt.f64 2))

rewrite130.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

57×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
49×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64`
34×	`sqrt-prod_binary64`

Counts

4 → 149

Calls

4 calls:

7.0ms	(*.f64 (/.f64 x (sqrt.f64 2)) x)
6.0ms	(.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)
3.0ms	(/.f64 x (sqrt.f64 2))
3.0ms	(/.f64 x (sqrt.f64 2))

Compiler

Compiled 3162 to 2519 computations (20.3% saved)

series38.0ms (0.9%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 x (sqrt.f64 2))
9.0ms	(*.f64 (/.f64 x (sqrt.f64 2)) x)
8.0ms	(.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)
7.0ms	(/.f64 x (sqrt.f64 2))

Compiler

Compiled 484 to 417 computations (13.8% saved)

simplify236.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

842×	`fma-neg_binary64`
494×	`associate-*l/_binary64`
483×	`fma-def_binary64`
394×	`*-commutative_binary64`
300×	`associate-/l*_binary64`

Counts

161 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	2145
1	270	1948
2	785	1936
3	2219	1922
4	2679	1922
5	3869	1922
6	4821	1922
7	4982	1922

prune147.0ms (3.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	93	2	95

Error

0.0b

Counts

95 → 2

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	19.3b	(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))

Compiler

Compiled 1411 to 1144 computations (18.9% saved)

regimes94.0ms (2.2%)

Accuracy

Total 0.0b remaining (9.3%)

Threshold costs 0.0b (9.3%)

Compiler

Compiled 616 to 510 computations (17.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	11	8
2	10	8

end1.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

sample2.1s (47.9%)

Algorithm

1×

intervals

Results

1.0s	2661×	body	1024	valid
272.0ms	1329×	body	512	valid
209.0ms	3059×	body	128	valid
188.0ms	673×	body	256	valid
113.0ms	278×	body	2048	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 45 to 38 computations (15.6% saved)

Details

analyze1.4s (31.1%)

sample108.0ms (2.5%)

simplify53.0ms (1.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

rewrite17.0ms (0.4%)

series16.0ms (0.4%)

simplify43.0ms (1%)

prune7.0ms (0.2%)

localize13.0ms (0.3%)

rewrite130.0ms (3%)

series38.0ms (0.9%)

simplify236.0ms (5.4%)

prune147.0ms (3.4%)

regimes94.0ms (2.2%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample2.1s (47.9%)

Profiling