Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample4.9s (64.5%)

Results

3.4s	4383×	body	2048	valid
898.0ms	2024×	body	1024	valid
323.0ms	1035×	body	512	valid
94.0ms	479×	body	256	valid
38.0ms	335×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify58.0ms (0.8%)

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

27.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	3.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series4.0ms (0.1%)

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)

rewrite22.0ms (0.3%)

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:

8.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(-.f64 (exp.f64 x) 2)

simplify87.0ms (1.1%)

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

prune79.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	3	115

Error

0.0b

Counts

115 → 3

Alt Table

Status	Error	Program
▶	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	27.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
	27.0b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (-.f64 (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (*.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))

Compiler

Compiled 2143 to 1218 computations (43.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))

series16.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

10.0ms

(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

3.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

3.0ms

(*.f64 1/20160 (pow.f64 x 8))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms

(*.f64 1/20160 (pow.f64 x 8))

0.0ms

(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

0.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
562×	`associate-+l+_binary64`
546×	`associate-+r+_binary64`
247×	`associate-l_binary64`
214×	`associate-r_binary64`

Counts

71 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1228
1	162	1128
2	390	1110
3	1598	1110
4	5154	1110

prune92.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	77	3	80

Error

0.0b

Counts

80 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	27.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	27.0b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (-.f64 (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (*.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))

Compiler

Compiled 1900 to 1416 computations (25.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))
✓	0.0b	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
✓	0.0b	(pow.f64 (exp.f64 (neg.f64 x)) 3)
✓	3.5b	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3))

series33.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

16.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3))
7.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
6.0ms	(pow.f64 (exp.f64 (neg.f64 x)) 3)
3.0ms	(*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`exp-prod_binary64`
82×	`*-un-lft-identity_binary64`
48×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`
27×	`distribute-rgt-neg-in_binary64`

Counts

4 → 185

Calls

4 calls:

13.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3))
11.0ms	(*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))
4.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
3.0ms	(pow.f64 (exp.f64 (neg.f64 x)) 3)

simplify155.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-neg_binary64`
513×	`cancel-sign-sub-inv_binary64`
298×	`exp-prod_binary64`
265×	`log-prod_binary64`
188×	`associate-r_binary64`

Counts

221 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	2744
1	601	2389
2	2219	2348
3	3928	2348
4	4965	2348
5	4989	2348
6	4918	2348

prune320.0ms (4.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	244	4	248

Error

0.0b

Counts

248 → 4

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	27.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	27.0b	(/.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 (neg.f64 x)) 3) 3)) (+.f64 (.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (-.f64 (exp.f64 x) 2) 3)) (-.f64 (.f64 (pow.f64 (exp.f64 (neg.f64 x)) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3))))) (+.f64 (.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (-.f64 (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))
✓	27.0b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (-.f64 (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (*.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))

Compiler

Compiled 11206 to 5690 computations (49.2% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
	0.0b	(pow.f64 (exp.f64 (neg.f64 x)) 3)
✓	0.0b	(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3)
✓	3.4b	(+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 (neg.f64 x)) 3) 3))

series114.0ms (1.5%)

Counts

2 → 24

Calls

2 calls:

100.0ms	(+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 (neg.f64 x)) 3) 3))
13.0ms	(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3)

rewrite66.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`*-un-lft-identity_binary64`
120×	`cube-prod_binary64`
120×	`unpow-prod-down_binary64`
38×	`fma-def_binary64`
37×	`distribute-lft-out_binary64`

Counts

2 → 148

Calls

2 calls:

45.0ms	(+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 (neg.f64 x)) 3) 3))
7.0ms	(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3)

simplify127.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
391×	`fma-neg_binary64`
384×	`cancel-sign-sub-inv_binary64`
244×	`log-prod_binary64`
201×	`associate-r_binary64`

Counts

172 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	3641
1	576	3566
2	2277	3418
3	4577	3418
4	4931	3418

prune1.1s (15.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	499	1	500
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	500	4	504

Error

Counts

504 → 4

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	27.1b	(/.f64 (/.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 (neg.f64 x)) 3) 3)))) (+.f64 (.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (-.f64 (exp.f64 x) 2) 3)) (-.f64 (.f64 (pow.f64 (exp.f64 (neg.f64 x)) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3))))) (+.f64 (.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (-.f64 (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))
✓	27.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	27.0b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (-.f64 (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (*.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))

Compiler

Compiled 44296 to 25404 computations (42.6% saved)

regimes85.0ms (1.1%)

Accuracy

Total 0.5b remaining (97.6%)

Threshold costs 0.5b (97.6%)

Counts

39 → 1

Compiler

Compiled 2354 to 1564 computations (33.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	16	25
2	16	25

end113.0ms (1.5%)

Compiler: Compiled 191 to 125 computations (34.6% saved)

Details

analyze5.0ms (0.1%)

sample4.9s (64.5%)

simplify58.0ms (0.8%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite22.0ms (0.3%)

simplify87.0ms (1.1%)

prune79.0ms (1%)

localize11.0ms (0.1%)

series16.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify50.0ms (0.7%)

prune92.0ms (1.2%)

localize15.0ms (0.2%)

series33.0ms (0.4%)

rewrite43.0ms (0.6%)

simplify155.0ms (2.1%)

prune320.0ms (4.2%)

localize24.0ms (0.3%)

series114.0ms (1.5%)

rewrite66.0ms (0.9%)

simplify127.0ms (1.7%)

prune1.1s (15.2%)

regimes85.0ms (1.1%)

simplify2.0ms (0%)

end113.0ms (1.5%)

Profiling