Details

analyze60.0ms (1.3%)

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
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)

sample2.3s (49.4%)

Symmetry

(sort a x)

Results

833.0ms	1510×	body	2048	valid
685.0ms	1818×	body	1024	valid
296.0ms	3142×	body	128	valid
292.0ms	1151×	body	512	valid
104.0ms	635×	body	256	valid
13.0ms	143×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify73.0ms (1.6%)

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 (0.1%)

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))

simplify70.0ms (1.5%)

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 (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	16	3	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	4	20

Error

0.0b

Counts

20 → 4

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))))
	22.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
	21.5b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 335 to 167 computations (50.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(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))))
✓	0.3b	(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	10.4b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series1.2s (24.8%)

Counts

3 → 72

Calls

3 calls:

695.0ms

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

455.0ms

(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))))

rewrite21.0ms (0.4%)

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:

10.0ms

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

5.0ms

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

1.0ms

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

simplify135.0ms (2.9%)

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

prune159.0ms (3.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	263	3	266
Fresh	0	2	2
Picked	1	0	1
Done	1	0	1
Total	265	5	270

Error

0.0b

Counts

270 → 5

Alt Table

Status	Error	Program
	40.2b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))) (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	21.5b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
▶	20.1b	(fma.f64 a x (.f64 (pow.f64 (.f64 a x) 2) 1/2))
	30.6b	(.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 (.f64 a x)) 1) 2) 1/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	22.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Compiler

Compiled 6991 to 1991 computations (71.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a x (.f64 (pow.f64 (.f64 a x) 2) 1/2))
✓	0.2b	(pow.f64 (*.f64 a x) 2)

series23.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(fma.f64 a x (.f64 (pow.f64 (.f64 a x) 2) 1/2))
9.0ms	(pow.f64 (*.f64 a x) 2)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-exp-log_binary64`
5×	`pow1_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`pow-unpow_binary64`

Counts

2 → 30

Calls

2 calls:

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

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

576×	`distribute-rgt-in_binary64`
550×	`distribute-lft-in_binary64`
367×	`unswap-sqr_binary64`
296×	`*-commutative_binary64`
294×	`exp-prod_binary64`

Counts

78 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	963
1	80	790
2	180	790
3	761	787
4	2197	787
5	4910	787
6	4938	787

prune35.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Error

0.0b

Counts

49 → 5

Alt Table

Status	Error	Program
	40.2b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))) (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
▶	21.5b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	20.1b	(fma.f64 a x (.f64 (pow.f64 (.f64 a x) 2) 1/2))
	30.6b	(.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 (.f64 a x)) 1) 2) 1/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	22.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Compiler

Compiled 832 to 480 computations (42.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 a x) 4)
✓	0.2b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	4.5b	(fma.f64 x (.f64 1/2 (.f64 a a)) a)
✓	10.8b	(fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4)))

series84.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

36.0ms	(fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4)))
19.0ms	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
18.0ms	(pow.f64 (*.f64 a x) 4)
12.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

4 → 49

Calls

4 calls:

2.0ms	(pow.f64 (*.f64 a x) 4)
0.0ms	(fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4)))
0.0ms	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
0.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

581×	`exp-prod_binary64`
519×	`associate-l_binary64`
435×	`associate-r_binary64`
337×	`distribute-rgt-out_binary64`
324×	`swap-sqr_binary64`

Counts

145 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	2650
1	176	2274
2	475	2252
3	2536	2220
4	5284	2220

prune88.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	96	5	101

Error

0.0b

Counts

101 → 5

Alt Table

Status	Error	Program
	40.2b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))) (.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	21.5b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	20.1b	(fma.f64 a x (.f64 (pow.f64 (.f64 a x) 2) 1/2))
	30.6b	(.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 (.f64 a x)) 1) 2) 1/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	22.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Compiler

Compiled 2914 to 1583 computations (45.7% saved)

regimes138.0ms (3%)

Accuracy

Total 0.0b remaining (5.9%)

Threshold costs 0.0b (5.9%)

Counts

32 → 1

Compiler

Compiled 2875 to 1494 computations (48% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	10	6
2	9	6

end87.0ms (1.9%)

Remove: (sort a x)
Compiler: Compiled 124 to 70 computations (43.5% saved)

Details

analyze60.0ms (1.3%)

sample2.3s (49.4%)

simplify73.0ms (1.6%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite1.0ms (0%)

simplify70.0ms (1.5%)

prune15.0ms (0.3%)

localize7.0ms (0.1%)

series1.2s (24.8%)

rewrite21.0ms (0.4%)

simplify135.0ms (2.9%)

prune159.0ms (3.4%)

localize6.0ms (0.1%)

series23.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify76.0ms (1.6%)

prune35.0ms (0.7%)

localize14.0ms (0.3%)

series84.0ms (1.8%)

rewrite5.0ms (0.1%)

simplify89.0ms (1.9%)

prune88.0ms (1.9%)

regimes138.0ms (3%)

simplify2.0ms (0%)

end87.0ms (1.9%)

Profiling