Details

analyze484.0ms (15%)

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%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample2.1s (65.6%)

Results

1.3s	2781×	body	1024	valid
307.0ms	3191×	body	128	valid
302.0ms	1340×	body	512	valid
106.0ms	269×	body	2048	valid
99.0ms	675×	body	256	valid
1.0ms	2×	body	2048	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

series8.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

7.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

simplify67.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
587×	`div-sub_binary64`
548×	`times-frac_binary64`
500×	`fma-neg_binary64`
317×	`distribute-rgt-in_binary64`

Counts

41 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	559
1	130	521
2	292	519
3	609	519
4	1403	519
5	4001	519
6	5294	519

prune21.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	2	41

Error

Counts

41 → 2

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 465 to 158 computations (66% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 x))
✓	0.0b	(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
✓	0.0b	(/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x)))

series20.0ms (0.6%)

Counts

3 → 28

Calls

3 calls:

9.0ms	(/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x)))
8.0ms	(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
2.0ms	(sqrt.f64 (exp.f64 x))

rewrite44.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
158×	`add-sqr-sqrt_binary64`
157×	`*-un-lft-identity_binary64`
157×	`add-cube-cbrt_binary64`
147×	`sqrt-prod_binary64`

Counts

3 → 237

Calls

3 calls:

15.0ms	(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
4.0ms	(/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x)))
1.0ms	(sqrt.f64 (exp.f64 x))

simplify229.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

858×	`fma-def_binary64`
457×	`associate-r_binary64`
453×	`associate-/r*_binary64`
388×	`*-commutative_binary64`
234×	`associate-/r/_binary64`

Counts

265 → 287

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	268	7418
1	552	6984
2	1765	6542
3	3431	6349
4	4614	6322
5	4946	6322

prune130.0ms (4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	314	2	316

Error

Counts

316 → 2

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6279 to 1273 computations (79.7% saved)

regimes38.0ms (1.2%)

Accuracy

Total 0.0b remaining (1.2%)

Threshold costs 0.0b (1.2%)

Counts

16 → 1

Compiler

Compiled 473 to 331 computations (30% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	9	11

end37.0ms (1.2%)

Compiler: Compiled 33 to 22 computations (33.3% saved)

Details

analyze484.0ms (15%)

sample2.1s (65.6%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series8.0ms (0.3%)

rewrite9.0ms (0.3%)

simplify67.0ms (2.1%)

prune21.0ms (0.6%)

localize5.0ms (0.2%)

series20.0ms (0.6%)

rewrite44.0ms (1.4%)

simplify229.0ms (7.1%)

prune130.0ms (4%)

regimes38.0ms (1.2%)

simplify4.0ms (0.1%)

end37.0ms (1.2%)

Profiling