Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
3.0ms	41×	body	640	valid
3.0ms	128×	body	80	valid
1.0ms	22×	body	320	valid
0.0ms	9×	body	160	valid

simplify21.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite75.0ms

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 1.0) (- x 1.0))
7.0ms	(/ x (+ x 1.0))
53.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (+ x 1.0) (- x 1.0))
37.0ms	(/ x (+ x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5002	716

prune214.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
6.0b	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
9.6b	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
14.9b	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

296×	`add-sqr-sqrt`
275×	`*-un-lft-identity`
213×	`times-frac`
144×	`difference-of-squares`
108×	`unpow-prod-down` `cube-prod`
106×	`associate-l`
75×	`add-cube-cbrt`
72×	`sqr-pow`
55×	`distribute-lft-out`
45×	`distribute-lft-out--`
29×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
9×	`difference-cubes`
7×	`associate-/l*`
6×	`pow1` `flip3-+` `associate-/r/` `flip-+` `add-log-exp`
5×	`frac-sub`
4×	`frac-times` `associate-*r/`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `flip--` `div-inv`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/` `associate--r+` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 328

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
32.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
32.0ms	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
110.0ms	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ x (+ x 1.0))
55.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
172.0ms	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
69.0ms	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1230	3877
1	5001	3757

prune752.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
6.0b	(/ x (+ (pow x 3) (pow 1.0 3)))
9.6b	(- (* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
14.9b	(* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

135×	`*-un-lft-identity`
75×	`times-frac`
58×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
41×	`distribute-lft-out`
33×	`associate-l`
28×	`unpow-prod-down` `cube-prod`
14×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `sum-cubes` `flip-+` `associate-/l*`
6×	`pow1` `associate-/r/` `add-log-exp`
5×	`frac-sub` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times` `associate-*r/`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `associate-*l/` `prod-exp` `associate--l+` `clear-num` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 175

Calls

4 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
27.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
34.0ms	(- (* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
86.0ms	(* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (+ x 1.0) (- x 1.0))
98.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
201.0ms	(- (* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
77.0ms	(* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

simplify115.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	891	1901
1	4528	1763
2	5002	1763

prune500.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.2b	(/ (- 1.0) (pow x 2))
0.3b	(/ 3.0 (pow x 3))
6.0b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite727.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
120×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
78×	`add-cube-cbrt`
48×	`unpow-prod-down`
29×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`sqr-pow`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`cube-prod` `associate-/l*` `unpow2`
11×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`neg-mul-1`
8×	`add-cbrt-cube`
6×	`div-exp`
5×	`frac-sub`
4×	`pow1` `cube-mult` `diff-log` `unpow3`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `frac-2neg` `div-sub` `pow-exp` `associate--l+` `clear-num` `div-inv`
1×	`distribute-frac-neg`

Counts

4 → 234

Calls

4 calls:

82.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
6.0ms	(/ (- 1.0) (pow x 2))
4.0ms	(/ 3.0 (pow x 3))
622.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
33.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(/ 3.0 (pow x 3))
34.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify91.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	741	1813
1	3530	1605
2	5001	1602

prune416.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.8b

bsearch107.0ms

Steps

Iters	Range		Point
10	488.5072251079851	29561296481055.625	12590.693041910416
10	-146662999352.95746	-3.9934486818618	-9657.022981435695

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	28
1	47	28

end0.0ms

sample541.0ms

Algorithm

intervals

Results

197.0ms	1735×	body	1280	valid
104.0ms	1251×	body	640	valid
92.0ms	4040×	body	80	valid
44.0ms	656×	body	320	valid
14.0ms	318×	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