Details

analyze55.0ms (1.7%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample92.0ms (2.9%)

Algorithm

1×

intervals

Symmetry

(sort a x)

Results

25.0ms	58×	body	2048	valid
8.0ms	45×	body	1024	valid
4.0ms	35×	body	512	valid
3.0ms	93×	body	128	valid
2.0ms	25×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify64.0ms (2%)

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 (0.1%)

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

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))

series6.0ms (0.2%)

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))

simplify61.0ms (1.9%)

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

prune11.0ms (0.3%)

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
✓	0.0b	(expm1.f64 (*.f64 a x))
	35.8b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
▶	24.1b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))

Compiler

Compiled 277 to 133 computations (52% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (.f64 a a))
✓	1.0b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
✓	3.8b	(fma.f64 x (.f64 1/2 (.f64 a a)) a)

series28.0ms (0.9%)

Counts

3 → 60

Calls

3 calls:

14.0ms	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
11.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)
2.0ms	(.f64 1/2 (.f64 a a))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 53

Calls

3 calls:

6.0ms	(.f64 1/2 (.f64 a a))
3.0ms	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
0.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)

simplify52.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

975×	`distribute-rgt-in_binary64`
973×	`distribute-lft-in_binary64`
511×	`fma-def_binary64`
440×	`associate-l_binary64`
338×	`associate-r_binary64`

Counts

113 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	86	1516
1	165	1339
2	468	1329
3	1415	1329
4	5555	1329

prune48.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	90	3	93

Error

0.0b

Counts

93 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	35.8b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
✓	24.1b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))

Compiler

Compiled 1432 to 672 computations (53.1% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
✓	12.3b	(sqrt.f64 (expm1.f64 (*.f64 a x)))

series36.0ms (1.1%)

Counts

2 → 40

Calls

2 calls:

29.0ms	(sqrt.f64 (expm1.f64 (*.f64 a x)))
6.0ms	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
1.0ms	(sqrt.f64 (expm1.f64 (*.f64 a x)))

simplify97.0ms (3%)

Algorithm

1×	egg-herbie

Rules

501×	`fma-neg_binary64`
462×	`unswap-sqr_binary64`
338×	`associate-l_binary64`
279×	`associate-r_binary64`
264×	`difference-of-squares_binary64`

Counts

108 → 85

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	76	1213
1	148	1154
2	421	1125
3	1479	1077
4	3607	999
5	4448	993
6	4981	993
7	5027	993

prune58.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	141	4	145

Error

Counts

145 → 4

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	35.8b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
✓	24.1b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
▶	35.9b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))

Compiler

Compiled 2394 to 611 computations (74.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))
✓	0.2b	(cbrt.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))
	12.3b	(sqrt.f64 (expm1.f64 (*.f64 a x)))
✓	12.4b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series923.0ms (28.9%)

Counts

3 → 72

Calls

3 calls:

462.0ms

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

453.0ms

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

7.0ms

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

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-exp-log_binary64`

Counts

3 → 52

Calls

3 calls:

6.0ms

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

1.0ms

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

1.0ms

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

simplify89.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
564×	`distribute-lft-out_binary64`
478×	`*-commutative_binary64`
264×	`distribute-rgt-in_binary64`
258×	`distribute-lft-in_binary64`

Counts

124 → 106

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	157	2497
1	380	2304
2	1111	1926
3	2580	1578
4	3667	1517
5	4905	1517

prune60.0ms (1.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	144	4	148

Error

Counts

148 → 4

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	35.8b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
✓	24.1b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
✓	35.9b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))

Compiler

Compiled 3697 to 920 computations (75.1% saved)

regimes54.0ms (1.7%)

Accuracy

Total 0.0b remaining (21%)

Threshold costs 0.0b (21%)

Counts

13 → 1

Compiler

Compiled 730 to 489 computations (33% saved)

simplify2.0ms (0.1%)

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

end5.0ms (0.2%)

Remove: (sort a x)
Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.4s (43.7%)

Algorithm

1×

intervals

Results

475.0ms	1449×	body	2048	valid
328.0ms	1733×	body	1024	valid
132.0ms	3090×	body	128	valid
125.0ms	1121×	body	512	valid
41.0ms	607×	body	256	valid
5.0ms	160×	body	128	invalid

Compiler

Compiled 68 to 39 computations (42.6% saved)

Details

analyze55.0ms (1.7%)

sample92.0ms (2.9%)

simplify64.0ms (2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite1.0ms (0%)

simplify61.0ms (1.9%)

prune11.0ms (0.3%)

localize6.0ms (0.2%)

series28.0ms (0.9%)

rewrite11.0ms (0.3%)

simplify52.0ms (1.6%)

prune48.0ms (1.5%)

localize5.0ms (0.2%)

series36.0ms (1.1%)

rewrite12.0ms (0.4%)

simplify97.0ms (3%)

prune58.0ms (1.8%)

localize8.0ms (0.3%)

series923.0ms (28.9%)

rewrite11.0ms (0.3%)

simplify89.0ms (2.8%)

prune60.0ms (1.9%)

regimes54.0ms (1.7%)

simplify2.0ms (0.1%)

end5.0ms (0.2%)

sample1.4s (43.7%)

Profiling