Details

analyze966.0ms (12.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.7%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.9%	0.1%	8
16.4%	83.5%	0.1%	9
19.1%	80.8%	0.1%	10
20.5%	79.4%	0.1%	11
22%	78%	0.1%	12
22.7%	77.2%	0.1%	13
23.4%	76.5%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample3.8s (48.2%)

Symmetry

(sort a x)

Results

1.5s	2880×	body	8192	exit
836.0ms	1543×	body	2048	valid
653.0ms	1831×	body	1024	valid
324.0ms	3175×	body	128	valid
318.0ms	1098×	body	512	valid
129.0ms	609×	body	256	valid

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
455×	`*-commutative_binary64`
440×	`unswap-sqr_binary64`
344×	`associate-l_binary64`
274×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	16	6
2	23	6
3	35	6
4	70	6
5	160	6
6	432	6
7	1564	6
8	3490	6
9	4954	6
10	4993	6
11	4874	6

prune3.0ms (0%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (*.f64 a x))

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(expm1.f64 (*.f64 a x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`log1p-expm1-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (*.f64 a x))

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
844×	`distribute-lft-out_binary64`
785×	`fma-neg_binary64`
383×	`*-commutative_binary64`
308×	`unswap-sqr_binary64`

Counts

35 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	382
1	96	369
2	262	363
3	966	347
4	2376	333
5	3696	333
6	4842	333
7	5375	333

prune15.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	3	20

Error

0.0b

Counts

20 → 3

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	0.1b	(expm1.f64 (*.f64 a x))
	19.9b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))))

Compiler

Compiled 299 to 135 computations (54.8% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(expm1.f64 (*.f64 a x))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	0.4b	(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	8.9b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series1.0s (13%)

Counts

3 → 72

Calls

3 calls:

568.0ms

(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

449.0ms

(cbrt.f64 (expm1.f64 (*.f64 a x)))

7.0ms

(*.f64 (*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

4.0ms

(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

1.0ms

(cbrt.f64 (expm1.f64 (*.f64 a x)))

simplify130.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
437×	`*-commutative_binary64`
358×	`distribute-rgt-in_binary64`
343×	`distribute-lft-in_binary64`
260×	`unswap-sqr_binary64`

Counts

165 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	2948
1	409	2621
2	1154	2203
3	2637	2016
4	4849	1965
5	4962	1965
6	4932	1965

prune129.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	264	2	266
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	265	4	269

Error

0.0b

Counts

269 → 4

Alt Table

Status	Error	Program
	47.5b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)
▶	19.9b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))))
✓	0.1b	(expm1.f64 (*.f64 a x))
	40.9b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (pow.f64 (expm1.f64 (.f64 a x)) 1/6)) (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (pow.f64 (expm1.f64 (.f64 a x)) 1/6))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 6921 to 1947 computations (71.9% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(expm1.f64 (*.f64 a x))
✓	0.1b	(.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x)))
✓	0.2b	(.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (*.f64 a x)))
✓	19.9b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))))

series41.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

21.0ms

(*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))

12.0ms

(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))

7.0ms

(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 70

Calls

3 calls:

4.0ms

(*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))

3.0ms

(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))))

3.0ms

(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))

simplify107.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-neg_binary64`
445×	`fma-def_binary64`
248×	`distribute-neg-in_binary64`
237×	`*-commutative_binary64`
233×	`sqr-pow_binary64`

Counts

142 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	107	1870
1	246	1686
2	778	1664
3	2126	1610
4	2909	1543
5	4766	1543
6	5251	1543

prune101.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	169	4	173

Error

0.0b

Counts

173 → 4

Alt Table

Status	Error	Program
	47.5b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)
✓	19.9b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))))
✓	0.1b	(expm1.f64 (*.f64 a x))
▶	40.9b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (pow.f64 (expm1.f64 (.f64 a x)) 1/6)) (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (pow.f64 (expm1.f64 (.f64 a x)) 1/6))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 3569 to 1125 computations (68.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))
✓	8.5b	(sqrt.f64 (expm1.f64 (*.f64 a x)))
	8.9b	(cbrt.f64 (expm1.f64 (*.f64 a x)))
✓	9.5b	(pow.f64 (expm1.f64 (*.f64 a x)) 1/6)

series910.0ms (11.5%)

Counts

3 → 64

Calls

3 calls:

444.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 1/6)
441.0ms	(cbrt.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))
25.0ms	(sqrt.f64 (expm1.f64 (*.f64 a x)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cbrt-prod_binary64`
6×	`sqrt-prod_binary64`

Counts

3 → 50

Calls

3 calls:

2.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 1/6)
1.0ms	(cbrt.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))
1.0ms	(sqrt.f64 (expm1.f64 (*.f64 a x)))

simplify108.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

621×	`unswap-sqr_binary64`
380×	`associate-l_binary64`
321×	`associate-r_binary64`
258×	`log-prod_binary64`
237×	`fma-def_binary64`

Counts

114 → 73

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	107	1903
1	207	1898
2	497	1631
3	1800	1443
4	3927	1431
5	4561	1383
6	5127	1383

prune100.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	175	4	179

Error

0.0b

Counts

179 → 4

Alt Table

Status	Error	Program
✓	0.1b	(expm1.f64 (*.f64 a x))
	40.9b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (pow.f64 (expm1.f64 (.f64 a x)) 1/6)) (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (.f64 (pow.f64 (expm1.f64 (.f64 a x)) 1/12) (pow.f64 (expm1.f64 (.f64 a x)) 1/12)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	47.5b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)
✓	19.9b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))))

Compiler

Compiled 7451 to 2288 computations (69.3% saved)

regimes170.0ms (2.2%)

Accuracy

Total 0.0b remaining (28.2%)

Threshold costs 0.0b (28.2%)

Counts

41 → 1

Compiler

Compiled 3270 to 1924 computations (41.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
2	6	6

end64.0ms (0.8%)

Remove: (sort a x)
Compiler: Compiled 99 to 53 computations (46.5% saved)

Details

analyze966.0ms (12.3%)

sample3.8s (48.2%)

simplify72.0ms (0.9%)

prune3.0ms (0%)

localize3.0ms (0%)

series6.0ms (0.1%)

rewrite1.0ms (0%)

simplify65.0ms (0.8%)

prune15.0ms (0.2%)

localize6.0ms (0.1%)

series1.0s (13%)

rewrite19.0ms (0.2%)

simplify130.0ms (1.6%)

prune129.0ms (1.6%)

localize6.0ms (0.1%)

series41.0ms (0.5%)

rewrite13.0ms (0.2%)

simplify107.0ms (1.4%)

prune101.0ms (1.3%)

localize11.0ms (0.1%)

series910.0ms (11.5%)

rewrite5.0ms (0.1%)

simplify108.0ms (1.4%)

prune100.0ms (1.3%)

regimes170.0ms (2.2%)

simplify2.0ms (0%)

end64.0ms (0.8%)

Profiling