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)

sample5.1s (83.3%)

Results

3.7s	4358×	body	2048	valid
901.0ms	1997×	body	1024	valid
320.0ms	1033×	body	512	valid
98.0ms	536×	body	256	valid
39.0ms	332×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify60.0ms (1%)

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

31.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.1%)

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)))

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)

rewrite18.0ms (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:

10.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(-.f64 (exp.f64 x) 2)

simplify84.0ms (1.4%)

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

prune80.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	4	115

Error

0.0b

Counts

115 → 4

Alt Table

Status	Error	Program
	31.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	0.9b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	31.5b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
▶	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)))))

Compiler

Compiled 2130 to 1217 computations (42.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
✓	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)))))
✓	0.1b	(*.f64 1/20160 (pow.f64 x 8))

series15.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

6.0ms

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

4.0ms

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

4.0ms

(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)))))

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)))))

simplify52.0ms (0.8%)

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 → 71

Iterations

Useful iterations: 2 (0.0ms)

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

prune74.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	71	4	75

Error

0.0b

Counts

75 → 4

Alt Table

Status	Error	Program
	31.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
▶	0.9b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	31.5b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
✓	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)))))

Compiler

Compiled 1684 to 1262 computations (25.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

7.0ms

(*.f64 1/12 (pow.f64 x 4))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unpow-prod-down_binary64`
4×	`*-un-lft-identity_binary64`

Counts

1 → 27

Calls

1 calls:

4.0ms

(*.f64 1/12 (pow.f64 x 4))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-/l*_binary64`
527×	`unswap-sqr_binary64`
465×	`associate-/l/_binary64`
448×	`associate-/r/_binary64`
442×	`fma-def_binary64`

Counts

27 → 34

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	54	293
1	96	281
2	205	263
3	560	263
4	940	257
5	1988	252
6	4944	252
7	4866	252

prune32.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	34	4	38

Error

0.0b

Counts

38 → 4

Alt Table

Status	Error	Program
	31.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
✓	0.9b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
▶	31.5b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
✓	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)))))

Compiler

Compiled 557 to 390 computations (30% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 x) -3)
✓	0.0b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
✓	0.0b	(pow.f64 (exp.f64 x) 3)
✓	4.1b	(+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (*.f64 (exp.f64 x) -3)))

series46.0ms (0.7%)

Counts

4 → 40

Calls

4 calls:

29.0ms	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
8.0ms	(+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (*.f64 (exp.f64 x) -3)))
6.0ms	(pow.f64 (exp.f64 x) 3)
3.0ms	(*.f64 (exp.f64 x) -3)

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 96

Calls

4 calls:

21.0ms	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
8.0ms	(+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (*.f64 (exp.f64 x) -3)))
4.0ms	(*.f64 (exp.f64 x) -3)
2.0ms	(pow.f64 (exp.f64 x) 3)

simplify103.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

431×	`unswap-sqr_binary64`
383×	`fma-neg_binary64`
257×	`exp-prod_binary64`
249×	`log-prod_binary64`
243×	`associate-l_binary64`

Counts

136 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2619
1	523	2222
2	2309	2197
3	3913	2197
4	4960	2197

prune137.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	163	4	167

Error

Counts

167 → 4

Alt Table

Status	Error	Program
	31.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
✓	0.9b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	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)))))
	31.4b	(/.f64 (/.f64 (+.f64 8 (pow.f64 (fma.f64 (exp.f64 x) -3 (pow.f64 (exp.f64 x) 3)) 3)) (fma.f64 (fma.f64 (exp.f64 x) -3 (pow.f64 (exp.f64 x) 3)) (+.f64 (fma.f64 (exp.f64 x) -3 (pow.f64 (exp.f64 x) 3)) -2) 4)) (*.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))

Compiler

Compiled 4286 to 2645 computations (38.3% saved)

regimes53.0ms (0.9%)

Accuracy

Total 0.4b remaining (98.2%)

Threshold costs 0.4b (98.2%)

Counts

26 → 1

Compiler

Compiled 814 to 600 computations (26.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	25	31
2	25	31

end98.0ms (1.6%)

Compiler: Compiled 123 to 90 computations (26.8% saved)

Details

analyze5.0ms (0.1%)

sample5.1s (83.3%)

simplify60.0ms (1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite18.0ms (0.3%)

simplify84.0ms (1.4%)

prune80.0ms (1.3%)

localize11.0ms (0.2%)

series15.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify52.0ms (0.8%)

prune74.0ms (1.2%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify65.0ms (1.1%)

prune32.0ms (0.5%)

localize11.0ms (0.2%)

series46.0ms (0.7%)

rewrite42.0ms (0.7%)

simplify103.0ms (1.7%)

prune137.0ms (2.2%)

regimes53.0ms (0.9%)

simplify2.0ms (0%)

end98.0ms (1.6%)

Profiling