Details

analyze360.0ms (6.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample145.0ms (2.5%)

Algorithm

1×

intervals

Results

37.0ms	65×	body	1024	valid
15.0ms	137×	body	128	valid
9.0ms	30×	body	512	valid
5.0ms	6×	body	2048	valid
4.0ms	18×	body	256	valid
1.0ms	11×	body	128	invalid
1.0ms	7×	body	128	overflowed
0.0ms	1×	body	512	invalid

Compiler

Compiled 65 to 53 computations (18.5% saved)

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
577×	`div-sub_binary64`
534×	`cancel-sign-sub-inv_binary64`
519×	`fma-neg_binary64`
467×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	57	45
2	153	37
3	394	37
4	1347	37
5	4048	37
6	4614	37
7	5259	37

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

28.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.9b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
	43.0b	(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))

Status

Error

Program

▶

28.9b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

43.0b

(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))

Compiler

Compiled 172 to 133 computations (22.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
✓	0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
✓	0.0b	(*.f64 (-.f64 1 eps) x)
✓	2.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series90.0ms (1.5%)

Counts

4 → 84

Calls

4 calls:

48.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
19.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
19.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
4.0ms	(*.f64 (-.f64 1 eps) x)

rewrite90.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64`
80×	`exp-neg_binary64`
80×	`frac-times_binary64`
60×	`exp-diff_binary64`
60×	`neg-sub0_binary64`

Counts

4 → 193

Calls

4 calls:

18.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
15.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
9.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
5.0ms	(*.f64 (-.f64 1 eps) x)

simplify285.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

542×	`fma-neg_binary64`
537×	`associate-l_binary64`
533×	`associate-r_binary64`
512×	`fma-def_binary64`
249×	`distribute-rgt-in_binary64`

Counts

277 → 341

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	577	12527
1	1526	11719
2	4683	11719
3	5028	11719

prune445.0ms (7.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	339	2	341
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	340	3	343

Error

0.0b

Counts

343 → 3

Alt Table

Status	Error	Program
✓	28.9b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
	16.4b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)
▶	0.3b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Compiler

Compiled 17524 to 13113 computations (25.2% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 2 x) 2))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`frac-times_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`

Counts

1 → 30

Calls

1 calls:

10.0ms

(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 2 x) 2))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-neg_binary64`
438×	`associate-*l/_binary64`
360×	`associate-/l*_binary64`
273×	`fma-def_binary64`
266×	`distribute-rgt-in_binary64`

Counts

42 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	671
1	244	543
2	771	537
3	2084	533
4	4357	533
5	4922	533

prune81.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	61	3	64

Error

Counts

64 → 3

Alt Table

Status	Error	Program
✓	28.9b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
▶	13.1b	(/.f64 (/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (pow.f64 (.f64 2 x) 3) (pow.f64 2 3))) (+.f64 (.f64 (.f64 2 x) (.f64 2 x)) (-.f64 (.f64 2 2) (.f64 (.f64 2 x) 2)))) 2)
	16.4b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)

Compiler

Compiled 1238 to 873 computations (29.5% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (pow.f64 (.f64 2 x) 3) (pow.f64 2 3))) (+.f64 (.f64 (.f64 2 x) (.f64 2 x)) (-.f64 (.f64 2 2) (.f64 (.f64 2 x) 2))))
✓	0.0b	(+.f64 (.f64 (.f64 2 x) (.f64 2 x)) (-.f64 (.f64 2 2) (.f64 (.f64 2 x) 2)))
✓	12.6b	(.f64 (exp.f64 (neg.f64 x)) (+.f64 (pow.f64 (.f64 2 x) 3) (pow.f64 2 3)))

series16.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

7.0ms

(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (pow.f64 (*.f64 2 x) 3) (pow.f64 2 3)))

6.0ms

(/.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (pow.f64 (*.f64 2 x) 3) (pow.f64 2 3))) (+.f64 (*.f64 (*.f64 2 x) (*.f64 2 x)) (-.f64 (*.f64 2 2) (*.f64 (*.f64 2 x) 2))))

3.0ms

(+.f64 (*.f64 (*.f64 2 x) (*.f64 2 x)) (-.f64 (*.f64 2 2) (*.f64 (*.f64 2 x) 2)))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`associate-/l/_binary64`
8×	`flip-+_binary64`

Counts

3 → 84

Calls

3 calls:

22.0ms

(/.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (pow.f64 (*.f64 2 x) 3) (pow.f64 2 3))) (+.f64 (*.f64 (*.f64 2 x) (*.f64 2 x)) (-.f64 (*.f64 2 2) (*.f64 (*.f64 2 x) 2))))

14.0ms

(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (pow.f64 (*.f64 2 x) 3) (pow.f64 2 3)))

12.0ms

(+.f64 (*.f64 (*.f64 2 x) (*.f64 2 x)) (-.f64 (*.f64 2 2) (*.f64 (*.f64 2 x) 2)))

simplify107.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

832×	`times-frac_binary64`
347×	`fma-neg_binary64`
259×	`cancel-sign-sub-inv_binary64`
191×	`associate-l_binary64`
190×	`associate-r_binary64`

Counts

120 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	2914
1	531	2329
2	2402	2193
3	4804	2193
4	4952	2193

prune251.0ms (4.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	176	3	179

Error

Counts

179 → 3

Alt Table

Status	Error	Program
✓	28.9b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
✓	13.1b	(/.f64 (/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (pow.f64 (.f64 2 x) 3) (pow.f64 2 3))) (+.f64 (.f64 (.f64 2 x) (.f64 2 x)) (-.f64 (.f64 2 2) (.f64 (.f64 2 x) 2)))) 2)
▶	16.4b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)

Compiler

Compiled 7032 to 5593 computations (20.5% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.4b	(.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))
✓	8.2b	(.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2)))
✓	8.7b	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))
✓	12.6b	(*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x)))

series65.0ms (1.1%)

Counts

4 → 40

Calls

4 calls:

32.0ms	(.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))
23.0ms	(.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2)))
5.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))
5.0ms	(*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`prod-exp_binary64`
42×	`add-exp-log_binary64`
31×	`associate-l_binary64`
28×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`

Counts

4 → 138

Calls

4 calls:

11.0ms	(.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2)))
10.0ms	(.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))
9.0ms	(*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x)))
7.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))

simplify109.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-neg_binary64`
392×	`associate-r_binary64`
378×	`cancel-sign-sub-inv_binary64`
376×	`unswap-sqr_binary64`
361×	`log-prod_binary64`

Counts

178 → 225

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	2948
1	485	2453
2	1939	2356
3	3999	2330
4	4965	2330

prune291.0ms (4.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	225	3	228

Error

Counts

228 → 3

Alt Table

Status	Error	Program
✓	28.9b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
✓	13.1b	(/.f64 (/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (pow.f64 (.f64 2 x) 3) (pow.f64 2 3))) (+.f64 (.f64 (.f64 2 x) (.f64 2 x)) (-.f64 (.f64 2 2) (.f64 (.f64 2 x) 2)))) 2)
✓	16.4b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)

Compiler

Compiled 10521 to 5942 computations (43.5% saved)

regimes719.0ms (12.1%)

Accuracy

Total 0.6b remaining (95.2%)

Threshold costs 0.6b (95.2%)

Counts

164 → 1

Compiler

Compiled 18220 to 14332 computations (21.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	18	24
2	20	24
3	21	24
4	21	24

end1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

sample2.5s (43%)

Algorithm

1×

intervals

Results

1.0s	1958×	body	1024	valid
482.0ms	4378×	body	128	valid
324.0ms	1016×	body	512	valid
186.0ms	207×	body	2048	valid
92.0ms	441×	body	256	valid
25.0ms	207×	body	128	invalid
17.0ms	170×	body	128	overflowed
10.0ms	21×	body	1024	invalid
4.0ms	12×	body	512	invalid
1.0ms	5×	body	256	invalid

Compiler

Compiled 160 to 123 computations (23.1% saved)

Details

analyze360.0ms (6.1%)

sample145.0ms (2.5%)

simplify65.0ms (1.1%)

prune5.0ms (0.1%)

localize20.0ms (0.3%)

series90.0ms (1.5%)

rewrite90.0ms (1.5%)

simplify285.0ms (4.8%)

prune445.0ms (7.5%)

localize7.0ms (0.1%)

series4.0ms (0.1%)

rewrite12.0ms (0.2%)

simplify67.0ms (1.1%)

prune81.0ms (1.4%)

localize17.0ms (0.3%)

series16.0ms (0.3%)

rewrite53.0ms (0.9%)

simplify107.0ms (1.8%)

prune251.0ms (4.2%)

localize20.0ms (0.3%)

series65.0ms (1.1%)

rewrite43.0ms (0.7%)

simplify109.0ms (1.8%)

prune291.0ms (4.9%)

regimes719.0ms (12.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.5s (43%)

Profiling