Details

sample22.0ms

Algorithm

intervals

Results

9.0ms	57×	body	1280	valid
3.0ms	40×	body	640	valid
3.0ms	131×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	13×	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: 29.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
40×	`times-frac`
35×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`add-cube-cbrt`
9×	`difference-of-squares`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

2 → 71

Calls

2 calls:

10.0ms	(/ (+ x 1.0) (- x 1.0))
53.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series166.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (+ x 1.0) (- x 1.0))
125.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify144.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	317	591
1	1003	565
2	4508	559
3	5003	559

prune141.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
2.5b	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

153×	`*-un-lft-identity`
136×	`add-sqr-sqrt`
111×	`times-frac`
70×	`cbrt-prod`
57×	`add-cube-cbrt`
56×	`unpow-prod-down` `cube-prod`
35×	`difference-of-squares`
26×	`distribute-lft-out`
22×	`distribute-lft-out--`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--` `add-log-exp`
5×	`pow1` `associate-/r*` `div-inv`
4×	`associate-/l*` `sqr-pow`
3×	`cube-div` `pow-unpow`
2×	`cbrt-undiv` `cube-mult` `cbrt-div` `unpow3` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `clear-num` `frac-sub` `rem-cbrt-cube` `flip-+`

Counts

4 → 213

Calls

4 calls:

13.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
10.0ms	(/ (+ x 1.0) (- x 1.0))
14.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
291.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
36.0ms	(/ (+ x 1.0) (- x 1.0))
61.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
136.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

simplify87.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	721	1953
1	3047	1816
2	5001	1796

prune295.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
0.5b	(/ 1 (pow x 3))
0.6b	(/ (- 1.0) (pow x 2))
7.6b	(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

131×	`times-frac`
101×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
45×	`unpow-prod-down`
27×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
20×	`add-exp-log` `associate-/r*`
16×	`associate-r`
15×	`sqr-pow`
13×	`associate-/l*`
12×	`cube-prod`
11×	`unpow2`
10×	`unpow3` `add-cbrt-cube`
9×	`neg-mul-1` `div-exp`
7×	`div-inv` `distribute-lft-out`
6×	`pow1` `associate-*r/` `add-log-exp`
5×	`distribute-rgt-out`
4×	`cube-mult` `pow-to-exp` `pow-exp`
3×	`rec-exp` `1-exp` `associate-l` `frac-sub`
2×	`cbrt-undiv` `neg-sub0` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `div-sub` `frac-add` `clear-num` `flip-+` `associate--r+`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `pow-prod-down` `distribute-rgt1-in` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 241

Calls

4 calls:

119.0ms	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
4.0ms	(/ 1 (pow x 3))
6.0ms	(/ (- 1.0) (pow x 2))
52.0ms	(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

series162.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
36.0ms	(/ 1 (pow x 3))
24.0ms	(/ (- 1.0) (pow x 2))
32.0ms	(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

simplify139.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	792	1535
1	4669	1275
2	5001	1275

prune397.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (pow x 3)) 3.0)
0.5b	(/ 1 (pow x 3))
0.6b	(/ 1.0 (pow x 2))
7.6b	(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* (/ 1 (pow x 3)) 3.0))

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac`
89×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
69×	`add-cube-cbrt`
40×	`associate-l`
38×	`add-exp-log`
35×	`unpow-prod-down`
23×	`cube-prod`
20×	`associate-/r*`
15×	`div-exp`
13×	`add-cbrt-cube` `sqr-pow`
11×	`add-log-exp`
10×	`prod-exp`
9×	`unswap-sqr`
7×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`
6×	`pow1` `rec-exp` `1-exp` `associate-/l*`
4×	`associate-*l/` `unpow2`
3×	`cbrt-undiv` `diff-log` `associate-r` `frac-sub` `div-inv` `distribute-neg-frac`
2×	`frac-2neg` `neg-log` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-neg-in` `flip3--` `pow-flip` `flip3-+` `pow-prod-down` `frac-add` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `inv-pow`

Counts

4 → 215

Calls

4 calls:

18.0ms	(* (/ 1 (pow x 3)) 3.0)
4.0ms	(/ 1 (pow x 3))
4.0ms	(/ 1.0 (pow x 2))
455.0ms	(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* (/ 1 (pow x 3)) 3.0))

series128.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (/ 1 (pow x 3)) 3.0)
30.0ms	(/ 1 (pow x 3))
24.0ms	(/ 1.0 (pow x 2))
35.0ms	(- (- (+ (/ 1.0 (pow x 2)) (/ 3.0 x))) (* (/ 1 (pow x 3)) 3.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	691	1196
1	3707	947
2	5001	918

prune355.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes43.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.1b

bsearch60.0ms

Steps

Iters	Range		Point
6	7065.8830381017015	33294.97377914132	9605.386656004559
9	-14674.600957416102	-0.00012459925560949148	-12747.116603779426

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	17
1	44	17
2	44	17

end0.0ms

sample516.0ms

Algorithm

intervals

Results

180.0ms	1709×	body	1280	valid
110.0ms	1325×	body	640	valid
85.0ms	3994×	body	80	valid
41.0ms	636×	body	320	valid
14.0ms	336×	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