Details

sample19.0ms

Algorithm

intervals

Results

4.0ms	42×	body	1280	valid
3.0ms	42×	body	640	valid
3.0ms	140×	body	80	valid
1.0ms	17×	body	320	valid
1.0ms	15×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite122.0ms

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 → 104

Calls

3 calls:

10.0ms	(/ x (+ x 1.0))
24.0ms	(/ (+ x 1.0) (- x 1.0))
84.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
126.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5001	716

prune202.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ x (+ x 1.0)) (/ (+ 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)))
4.7b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

342×	`*-un-lft-identity`
208×	`times-frac`
152×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
73×	`distribute-lft-out`
72×	`swap-sqr`
44×	`associate-r` `associate-l`
36×	`distribute-lft-out--`
28×	`add-exp-log` `add-cbrt-cube`
21×	`difference-of-squares`
18×	`pow1`
16×	`associate-/r/`
9×	`frac-sub`
8×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
5×	`flip3--` `flip3-+` `flip--` `flip-+`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `sub-neg` `diff-log` `frac-add` `sum-log`

Counts

4 → 259

Calls

4 calls:

71.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
80.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
49.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
22.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
51.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
39.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
190.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1145	2720
1	5002	2529

prune397.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
4.7b	(log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
4.7b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

298×	`*-un-lft-identity`
192×	`times-frac`
154×	`add-sqr-sqrt`
90×	`add-cube-cbrt`
72×	`swap-sqr`
56×	`distribute-lft-out`
44×	`associate-r` `associate-l`
32×	`distribute-lft-out--`
28×	`add-exp-log` `add-cbrt-cube`
22×	`difference-of-squares`
19×	`pow1`
16×	`associate-/r/`
9×	`frac-sub`
8×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
6×	`add-log-exp`
5×	`log-prod` `flip3--` `log-pow` `flip--`
4×	`exp-prod` `flip3-+` `flip-+`
2×	`pow2` `sub-neg` `pow-plus` `exp-sum` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp`

Counts

4 → 257

Calls

4 calls:

80.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
48.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
61.0ms	(log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
20.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
44.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
193.0ms	(log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
195.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1118	2930
1	5001	2676

prune470.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
5.1b	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
10.3b	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
12.7b	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

287×	`add-sqr-sqrt`
258×	`*-un-lft-identity`
201×	`times-frac`
144×	`difference-of-squares`
108×	`unpow-prod-down` `cube-prod`
106×	`associate-l`
72×	`sqr-pow`
66×	`add-cube-cbrt`
51×	`distribute-lft-out`
45×	`distribute-lft-out--`
25×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
9×	`difference-cubes`
6×	`pow1` `flip3-+` `flip-+`
5×	`frac-sub`
4×	`frac-times` `associate-r/` `associate-/r/` `associate-/l`
3×	`flip3--` `associate-r` `sum-log` `flip--`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `associate--r+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 308

Calls

4 calls:

19.0ms	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
49.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
57.0ms	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
165.0ms	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
51.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
163.0ms	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
72.0ms	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1183	3828
1	5001	3694

prune645.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch75.0ms

Steps

Iters	Range		Point
10	0.43775957865898985	3845520655822.575	10654.135862899073
7	-245561.44084452273	-3096.4512561506854	-14119.488100805922

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	30
1	37	30

end0.0ms

sample524.0ms

Algorithm

intervals

Results

168.0ms	1703×	body	1280	valid
98.0ms	1237×	body	640	valid
90.0ms	4103×	body	80	valid
39.0ms	642×	body	320	valid
12.0ms	315×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6