Details

analyze254.0ms

Algorithm

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

sample76.0ms

Algorithm

intervals

Results

33.0ms	54×	body	1280	valid
15.0ms	42×	body	640	valid
11.0ms	133×	body	80	valid
5.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid
1.0ms	7×	body	80	invalid
1.0ms	1×	body	1280	invalid
1.0ms	7×	body	80	overflowed

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5720	27

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 29.2b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- 1.0 eps) x)
1.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
76×	`exp-neg` `frac-times`
57×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
38×	`associate-*r/`
32×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
19×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `associate-r`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out`

Counts

4 → 165

Calls

4 calls:

14.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
6.0ms	(* (+ 1.0 eps) x)
6.0ms	(* (- 1.0 eps) x)
18.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
4.0ms	(* (+ 1.0 eps) x)
4.0ms	(* (- 1.0 eps) x)
48.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4979	6639
1	4979	6639

prune322.0ms

Filtered

94 candidates to 177 candidates (-88.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	177	2	179

Merged error: 0b

Counts

179 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 3) 0.6666666666666667)
5.4b	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-l`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-r` `prod-exp`
2×	`pow1` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 45

Calls

2 calls:

6.0ms	(* (pow x 3) 0.6666666666666667)
7.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

series8.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(* (pow x 3) 0.6666666666666667)
4.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

simplify55.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4959	458
1	4959	458

prune60.0ms

Filtered

33 candidates to 51 candidates (-54.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	51	2	53

Merged error: 0b

Counts

53 → 2

regimes157.0ms

Accuracy

97.1% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 17.1b

bsearch97.0ms

Steps

Iters	Range		Point
11	1.361516370113076e-13	3512449.7129801814	166.76597640670573

simplify9.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	455	47
1	455	47

end0.0ms

sample2.2s

Algorithm

intervals

Results

996.0ms	1746×	body	1280	valid
430.0ms	1190×	body	640	valid
343.0ms	4150×	body	80	valid
149.0ms	604×	body	320	valid
50.0ms	310×	body	160	valid
19.0ms	206×	body	80	invalid
14.0ms	180×	body	80	overflowed
11.0ms	19×	body	1280	invalid
8.0ms	16×	body	640	invalid
1.0ms	5×	body	320	invalid
1.0ms	3×	body	160	invalid

Details

analyze254.0ms

sample76.0ms

simplify43.0ms

prune12.0ms

localize21.0ms

rewrite55.0ms

series68.0ms

simplify68.0ms

prune322.0ms

localize9.0ms

rewrite14.0ms

series8.0ms

simplify55.0ms

prune60.0ms

regimes157.0ms

bsearch97.0ms

simplify9.0ms

end0.0ms

sample2.2s

Profiling