Details

analyze1.4s (10.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample9.6s (75.9%)

Results

4.5s	7967×	body	8192	exit
3.6s	4331×	body	2048	valid
954.0ms	2040×	body	1024	valid
296.0ms	1002×	body	512	valid
104.0ms	508×	body	256	valid
47.0ms	375×	body	128	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

819×	`div-sub_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	112	13
5	223	13
6	481	13
7	890	13
8	1570	13
9	4778	13
10	5815	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	4.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series5.0ms (0%)

Counts

2 → 16

Calls

2 calls:

3.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
2.0ms	(-.f64 (exp.f64 x) 2)

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-+l+_binary64`

Counts

2 → 69

Calls

2 calls:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
326×	`fma-def_binary64`
296×	`distribute-rgt-in_binary64`
282×	`distribute-lft-in_binary64`
268×	`distribute-rgt-out_binary64`

Counts

85 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1174
1	295	959
2	717	942
3	2801	932
4	4435	932
5	4838	932

prune95.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	3	115

Error

0.0b

Counts

115 → 3

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	0.5b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	27.9b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))

Compiler

Compiled 2120 to 1205 computations (43.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	0.0b	(*.f64 1/360 (pow.f64 x 6))

series8.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
3.0ms	(*.f64 1/360 (pow.f64 x 6))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 1/360 (pow.f64 x 6))
0.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

562×	`distribute-rgt-in_binary64`
557×	`distribute-lft-in_binary64`
385×	`fma-def_binary64`
384×	`unswap-sqr_binary64`
350×	`log-prod_binary64`

Counts

49 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	75	702
1	135	653
2	330	621
3	1413	621
4	4726	621
5	5066	621

prune64.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Error

Counts

57 → 4

Alt Table

Status	Error	Program
	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6)))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))
▶	0.5b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	0.4b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	27.9b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))

Compiler

Compiled 1139 to 833 computations (26.9% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	0.1b	(*.f64 1/12 (pow.f64 x 4))

series7.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
3.0ms	(*.f64 1/12 (pow.f64 x 4))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 1/12 (pow.f64 x 4))
0.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
562×	`unswap-sqr_binary64`
352×	`*-commutative_binary64`
333×	`distribute-rgt-out_binary64`
291×	`distribute-lft-out_binary64`

Counts

49 → 49

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	66	570
1	110	535
2	240	517
3	668	517
4	1295	511
5	3475	506
6	4962	506
7	4950	506

prune52.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	49	4	53

Error

Counts

53 → 4

Alt Table

Status	Error	Program
▶	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6)))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))
✓	0.5b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	0.4b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	27.9b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))

Compiler

Compiled 817 to 567 computations (30.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 1/360 (pow.f64 x 6))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6)))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))
✓	31.7b	(cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))))

series24.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))

8.0ms

(cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))))

5.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))

rewrite22.0ms (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:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))

5.0ms

(*.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))

1.0ms

(cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))))

simplify153.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

461×	`associate-l_binary64`
397×	`associate-r_binary64`
314×	`fma-def_binary64`
220×	`distribute-rgt-in_binary64`
216×	`distribute-lft-in_binary64`

Counts

129 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	4767
1	444	4276
2	1151	3511
3	4052	3280
4	4853	3280
5	4904	3280

prune622.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	385	0	385
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	385	4	389

Error

Counts

389 → 4

Alt Table

Status	Error	Program
✓	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6)))))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))
✓	0.5b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	0.4b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	27.9b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))

Compiler

Compiled 19614 to 14683 computations (25.1% saved)

regimes158.0ms (1.3%)

Accuracy

Total 0.5b remaining (85.9%)

Threshold costs 0.5b (85.9%)

Counts

87 → 1

Compiler

Compiled 3068 to 2316 computations (24.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	12	18
2	12	18

end95.0ms (0.8%)

Compiler: Compiled 125 to 87 computations (30.4% saved)

Details

analyze1.4s (10.9%)

sample9.6s (75.9%)

simplify57.0ms (0.5%)

prune2.0ms (0%)

localize6.0ms (0%)

series5.0ms (0%)

rewrite17.0ms (0.1%)

simplify81.0ms (0.6%)

prune95.0ms (0.8%)

localize8.0ms (0.1%)

series8.0ms (0.1%)

rewrite12.0ms (0.1%)

simplify74.0ms (0.6%)

prune64.0ms (0.5%)

localize6.0ms (0%)

series7.0ms (0.1%)

rewrite6.0ms (0%)

simplify80.0ms (0.6%)

prune52.0ms (0.4%)

localize11.0ms (0.1%)

series24.0ms (0.2%)

rewrite22.0ms (0.2%)

simplify153.0ms (1.2%)

prune622.0ms (4.9%)

regimes158.0ms (1.3%)

simplify2.0ms (0%)

end95.0ms (0.8%)

Profiling