Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	66×	body	1280	valid
3.0ms	132×	body	80	valid
3.0ms	33×	body	640	valid
1.0ms	19×	body	320	valid
0.0ms	6×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite47.0ms

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:

5.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
31.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series227.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ x (+ x 1.0))
36.0ms	(/ (+ x 1.0) (- x 1.0))
155.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

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

prune198.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
2.0b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

1123×	`*-un-lft-identity`
759×	`times-frac`
571×	`add-sqr-sqrt`
318×	`unpow-prod-down` `cube-prod`
265×	`distribute-lft-out--`
184×	`distribute-lft-out`
180×	`difference-of-squares`
139×	`add-cube-cbrt`
77×	`associate-/l*`
61×	`sqr-pow`
35×	`associate-/r/`
27×	`frac-add`
24×	`swap-sqr`
21×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
17×	`frac-times` `associate-*r/`
13×	`flip3-+` `flip-+`
12×	`pow1`
11×	`associate-*l/`
7×	`div-inv`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`difference-cubes` `cube-div`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`pow-unpow` `associate-/r*` `associate-/l/`
2×	`flip3--` `pow-exp` `frac-sub` `flip--` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 581

Calls

4 calls:

150.0ms	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
16.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
7.0ms	(pow (/ x (+ x 1.0)) 3)
98.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series965.0ms

Counts

4 → 12

Calls

4 calls:

568.0ms	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
45.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
58.0ms	(pow (/ x (+ x 1.0)) 3)
293.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify190.0ms

Algorithm

egg-herbie

Counts

593 → 593

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1706	17407
1	5001	17140

prune1.1s

Filtered

593 candidates to 226 candidates (38.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

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)))
6.0b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite37.0ms

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 → 141

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
5.0ms	(/ 1 (- x 1.0))
12.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
9.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series227.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ x (+ x 1.0))
27.0ms	(/ 1 (- x 1.0))
37.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
129.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify71.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	576	950
1	2837	862
2	5001	820

prune233.0ms

Filtered

153 candidates to 99 candidates (64.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
5.9b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (* (+ x 1.0) (/ 1 (- x 1.0))) (* (+ x 1.0) (/ 1 (- x 1.0)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

246×	`frac-times`
156×	`associate-*l/`
144×	`frac-sub`
111×	`associate-*r/`
90×	`flip3-+` `flip-+`
73×	`add-sqr-sqrt`
63×	`associate-r`
61×	`*-un-lft-identity`
51×	`times-frac`
45×	`un-div-inv`
34×	`add-cube-cbrt`
31×	`add-exp-log`
19×	`add-cbrt-cube`
12×	`associate-l` `prod-exp`
10×	`pow1` `difference-of-squares`
9×	`distribute-lft-out--` `unswap-sqr`
6×	`div-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `flip--`
3×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv` `distribute-lft-out`
1×	`sub-neg` `diff-log`

Counts

4 → 304

Calls

4 calls:

13.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
13.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
15.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
22.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (* (+ x 1.0) (/ 1 (- x 1.0))) (* (+ x 1.0) (/ 1 (- x 1.0)))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
39.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
37.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
205.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (* (+ x 1.0) (/ 1 (- x 1.0))) (* (+ x 1.0) (/ 1 (- x 1.0)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1774	5364
1	5002	5221

prune486.0ms

Filtered

316 candidates to 155 candidates (49.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.4b

bsearch86.0ms

Steps

Iters	Range		Point
8	136.14768989527596	4873390.516357292	11016.298428452052
8	-21754618.13974568	-2693.2368339428763	-12043.949500294897

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	71
1	50	71

end0.0ms

sample533.0ms

Algorithm

intervals

Results

186.0ms	1725×	body	1280	valid
110.0ms	1273×	body	640	valid
96.0ms	4100×	body	80	valid
41.0ms	602×	body	320	valid
13.0ms	300×	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