Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample29.0ms

Algorithm

intervals

Results

7.0ms	49×	body	1280	valid
5.0ms	38×	body	640	valid
5.0ms	141×	body	80	valid
2.0ms	22×	body	320	valid
0.0ms	6×	body	160	valid

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	1001	13
1	1001	13

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 27.2b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.4b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 103

Calls

3 calls:

7.0ms	(/ x (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
33.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4955	1404
1	4955	1404

prune172.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	4	113

Merged error: 0.2b

Counts

113 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
2.4b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

329×	`*-un-lft-identity`
212×	`times-frac`
173×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
72×	`swap-sqr`
62×	`distribute-lft-out`
44×	`associate-r` `associate-l`
37×	`distribute-lft-out--`
30×	`add-exp-log` `add-cbrt-cube`
26×	`difference-of-squares`
18×	`pow1` `associate-/r/`
9×	`cbrt-undiv` `div-exp` `frac-sub` `div-inv`
8×	`frac-times` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `associate-/r*` `flip-+`
4×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num`

Counts

4 → 282

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
30.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
19.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
13.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series20.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
3.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
11.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify95.0ms

Algorithm

egg-herbie

Counts

294 → 294

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4996	4340
1	4996	4340

prune504.0ms

Filtered

164 candidates to 294 candidates (-79.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	293	1	294
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	293	5	298

Merged error: 0.0b

Counts

298 → 5

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (- x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.7b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
44×	`times-frac`
33×	`add-cube-cbrt`
21×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/r*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `frac-sub` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `flip-+` `distribute-lft-out`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp`
3×	`cbrt-undiv` `flip3--` `flip--` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `un-div-inv` `cbrt-unprod`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 140

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
6.0ms	(/ 1 (- x 1.0))
14.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
11.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series15.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ x (+ x 1.0))
2.0ms	(/ 1 (- x 1.0))
3.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5312	1602

prune172.0ms

Filtered

99 candidates to 152 candidates (-53.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	151	6	157

Merged error: 0.0b

Counts

157 → 6

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* x (+ (* x 1.0) 3.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `add-log-exp` `unswap-sqr`

Counts

1 → 22

Calls

1 calls:

6.0ms

(* x (+ (* x 1.0) 3.0))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(* x (+ (* x 1.0) 3.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4957	216
1	4957	216

prune23.0ms

Filtered

16 candidates to 25 candidates (-56.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	25	6	31

Merged error: 0.0b

Counts

31 → 6

regimes51.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch29.0ms

Steps

Iters	Range		Point
10	3.537211321013767e-06	30485921977313.348	15879.946460749441
9	-26770.030102508103	-0.2871834512418839	-12213.433285445302

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	197	95
1	197	95

end0.0ms

sample742.0ms

Algorithm

intervals

Results

280.0ms	1783×	body	1280	valid
153.0ms	1183×	body	640	valid
135.0ms	4109×	body	80	valid
59.0ms	615×	body	320	valid
19.0ms	310×	body	160	valid

Details

analyze4.0ms

sample29.0ms

simplify83.0ms

prune4.0ms

localize6.0ms

rewrite52.0ms

series12.0ms

simplify55.0ms

prune172.0ms

localize13.0ms

rewrite88.0ms

series20.0ms

simplify95.0ms

prune504.0ms

localize7.0ms

rewrite40.0ms

series15.0ms

simplify53.0ms

prune172.0ms

localize5.0ms

rewrite7.0ms

series6.0ms

simplify53.0ms

prune23.0ms

regimes51.0ms

bsearch29.0ms

simplify3.0ms

end0.0ms

sample742.0ms

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