Details

analyze104.0ms (2%)

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)

sample131.0ms (2.6%)

Algorithm

1×

intervals

Results

94.0ms	139×	body	2048	valid
19.0ms	58×	body	1024	valid
5.0ms	28×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	17×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify87.0ms (1.7%)

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

27.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	4.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series6.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

4.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
2.0ms	(-.f64 (exp.f64 x) 2)

rewrite15.0ms (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)

simplify115.0ms (2.2%)

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

prune82.0ms (1.6%)

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

Counts

115 → 3

Alt Table

Status	Error	Program
✓	27.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
	27.6b	(/.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)))
▶	1.4b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 2101 to 1192 computations (43.3% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

4.0ms

(*.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))

simplify95.0ms (1.8%)

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

prune31.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	34	3	37

Error

Counts

37 → 3

Alt Table

Status	Error	Program
✓	27.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	27.6b	(/.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)))
✓	1.4b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 547 to 379 computations (30.7% saved)

localize15.0ms (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))
✓	0.0b	(/.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)))
✓	0.1b	(pow.f64 (exp.f64 x) 3)
✓	4.3b	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8)))))

series110.0ms (2.1%)

Counts

4 → 40

Calls

4 calls:

78.0ms	(/.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))
8.0ms	(pow.f64 (exp.f64 x) 3)

rewrite21.0ms (0.4%)

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:

7.0ms	(/.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)))
4.0ms	(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
3.0ms	(pow.f64 (exp.f64 x) 3)
3.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8)))))

simplify172.0ms (3.4%)

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

prune163.0ms (3.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
✓	27.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	27.6b	(/.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)))
✓	1.4b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 5827 to 3460 computations (40.6% saved)

regimes76.0ms (1.5%)

Accuracy

Total 0.1b remaining (61.9%)

Threshold costs 0.1b (61.9%)

Counts

31 → 2

Compiler

Compiled 1270 to 840 computations (33.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	72
1	44	72
2	51	72
3	54	72
4	52	72

end2.0ms (0%)

Compiler: Compiled 46 to 36 computations (21.7% saved)

sample3.9s (75.4%)

Algorithm

1×

intervals

Results

2.6s	4201×	body	2048	valid
653.0ms	2027×	body	1024	valid
184.0ms	936×	body	512	valid
56.0ms	457×	body	256	valid
24.0ms	379×	body	128	valid

Compiler

Compiled 104 to 76 computations (26.9% saved)

Details

analyze104.0ms (2%)

sample131.0ms (2.6%)

simplify87.0ms (1.7%)

prune2.0ms (0%)

localize10.0ms (0.2%)

series6.0ms (0.1%)

rewrite15.0ms (0.3%)

simplify115.0ms (2.2%)

prune82.0ms (1.6%)

localize7.0ms (0.1%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify95.0ms (1.8%)

prune31.0ms (0.6%)

localize15.0ms (0.3%)

series110.0ms (2.1%)

rewrite21.0ms (0.4%)

simplify172.0ms (3.4%)

prune163.0ms (3.2%)

regimes76.0ms (1.5%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end2.0ms (0%)

sample3.9s (75.4%)

Profiling