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 (80.8%)

Results

3.4s	4282×	body	2048	valid
934.0ms	2029×	body	1024	valid
307.0ms	1059×	body	512	valid
92.0ms	502×	body	256	valid
45.0ms	384×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify58.0ms (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

34.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	34.6b	(+.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)
✓	4.6b	(+.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)

rewrite17.0ms (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:

7.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
5.0ms	(-.f64 (exp.f64 x) 2)

simplify83.0ms (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

prune75.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	4	115

Error

0.0b

Counts

115 → 4

Alt Table

Status	Error	Program
▶	0.8b	(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)))))
	34.8b	(/.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)))
	1.1b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	34.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 2139 to 1220 computations (43% saved)

localize11.0ms (0.2%)

Local error

Found 4 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 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))

series18.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

5.0ms	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
5.0ms	(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)))))
4.0ms	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
3.0ms	(*.f64 1/20160 (pow.f64 x 8))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

4.0ms	(*.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)))))
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 x x (*.f64 1/20160 (pow.f64 x 8)))

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
610×	`associate-+r+_binary64`
610×	`associate-+l+_binary64`
262×	`associate-l_binary64`
230×	`associate-r_binary64`

Counts

93 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1505
1	172	1382
2	418	1364
3	1707	1364
4	5576	1364

prune82.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	84	4	88

Error

0.0b

Counts

88 → 4

Alt Table

Status	Error	Program
✓	0.8b	(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)))))
	34.8b	(/.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)))
▶	1.1b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	34.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 1995 to 1487 computations (25.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.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))

simplify58.0ms (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

prune34.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

0.0b

Counts

38 → 4

Alt Table

Status	Error	Program
✓	0.8b	(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)))))
▶	34.8b	(/.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)))
✓	1.1b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	34.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 566 to 393 computations (30.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
✓	0.1b	(pow.f64 (exp.f64 x) 3)
✓	0.3b	(/.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)))
✓	3.8b	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8)))))

series104.0ms (1.7%)

Counts

4 → 40

Calls

4 calls:

74.0ms	(/.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)))
14.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8)))))
9.0ms	(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
7.0ms	(pow.f64 (exp.f64 x) 3)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

6.0ms	(/.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)))
5.0ms	(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
3.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8)))))
2.0ms	(pow.f64 (exp.f64 x) 3)

simplify139.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-neg_binary64`
321×	`exp-prod_binary64`
317×	`unswap-sqr_binary64`
224×	`associate-l_binary64`
211×	`cancel-sign-sub-inv_binary64`

Counts

133 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	3661
1	495	3044
2	2254	2963
3	4026	2963
4	4925	2963
5	4942	2963

prune164.0ms (2.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	162	5	167

Error

Counts

167 → 5

Alt Table

Status	Error	Program
✓	0.8b	(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)))))
✓	34.8b	(/.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)))
✓	1.1b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	34.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
	34.5b	(/.f64 (/.f64 (fma.f64 (exp.f64 x) (+.f64 (+.f64 (exp.f64 x) (pow.f64 (exp.f64 x) 3)) -6) 4) (exp.f64 x)) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))

Compiler

Compiled 5872 to 3489 computations (40.6% saved)

regimes71.0ms (1.2%)

Accuracy

Total 0.5b remaining (97.9%)

Threshold costs 0.5b (97.9%)

Counts

32 → 1

Compiler

Compiled 1494 to 984 computations (34.1% 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

end104.0ms (1.7%)

Compiler: Compiled 130 to 88 computations (32.3% saved)

Details

analyze5.0ms (0.1%)

sample4.9s (80.8%)

simplify58.0ms (1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite17.0ms (0.3%)

simplify83.0ms (1.4%)

prune75.0ms (1.2%)

localize11.0ms (0.2%)

series18.0ms (0.3%)

rewrite8.0ms (0.1%)

simplify74.0ms (1.2%)

prune82.0ms (1.4%)

localize6.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify58.0ms (1%)

prune34.0ms (0.6%)

localize16.0ms (0.3%)

series104.0ms (1.7%)

rewrite20.0ms (0.3%)

simplify139.0ms (2.3%)

prune164.0ms (2.7%)

regimes71.0ms (1.2%)

simplify2.0ms (0%)

end104.0ms (1.7%)

Profiling