Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	46×	body	1280	valid
3.0ms	41×	body	640	valid
3.0ms	132×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 29.4b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
4.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

1097×	`*-un-lft-identity`
736×	`times-frac`
653×	`add-sqr-sqrt`
468×	`prod-diff`
467×	`add-cube-cbrt`
213×	`distribute-lft-out`
140×	`frac-sub`
115×	`associate-/r*`
100×	`distribute-lft-out--`
94×	`associate-/r/`
91×	`difference-of-squares`
89×	`associate-/l*`
47×	`div-inv`
39×	`flip3-+` `flip-+`
26×	`frac-2neg` `clear-num`
22×	`associate-/l/`
20×	`flip3--` `flip--`
18×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp`
1×	`sub-neg` `diff-log`

Counts

3 → 735

Calls

3 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
53.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (+ x 1.0) (- x 1.0))
33.0ms	(/ x (+ x 1.0))
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify207.0ms

Algorithm

egg-herbie

Counts

744 → 744

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2323	20311
1	5002	17909

prune1.0s

Filtered

744 candidates to 281 candidates (37.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	741	3	744
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	742	3	745

Merged error: 0.2b

Counts

745 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) x) (- (- x 1.0)))
0.0b	(/ (- (- (* 1 (- x 1.0)) (* (/ (+ x 1.0) x) (+ x 1.0)))) (* (/ (+ x 1.0) x) (- (- x 1.0))))
0.0b	(* (/ (+ x 1.0) x) (+ x 1.0))
4.3b	(- (* 1 (- x 1.0)) (* (/ (+ x 1.0) x) (+ x 1.0)))

rewrite653.0ms

Algorithm

rewrite-expression-head

Rules

3838×	`add-sqr-sqrt`
2605×	`*-un-lft-identity`
2465×	`times-frac`
1397×	`associate-l`
1096×	`unswap-sqr`
930×	`add-cube-cbrt`
894×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
805×	`difference-of-squares`
792×	`associate-r`
574×	`distribute-lft-out--`
441×	`prod-diff`
211×	`distribute-lft-out`
168×	`frac-times`
166×	`associate-*r/`
152×	`frac-sub`
130×	`distribute-neg-frac`
124×	`associate-/l*`
120×	`associate-/l/`
104×	`flip3--` `flip--`
100×	`associate-/r*`
86×	`flip3-+` `*-commutative` `flip-+`
84×	`associate-*l/`
80×	`neg-mul-1`
59×	`div-inv`
38×	`associate-/r/`
26×	`distribute-rgt-in` `distribute-lft-in`
23×	`add-exp-log` `add-cbrt-cube`
22×	`distribute-neg-in` `frac-2neg` `associate--l+` `clear-num`
15×	`fma-neg`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`sub-neg`
4×	`+-commutative` `expm1-log1p-u` `log1p-expm1-u` `associate--r+`
2×	`pow-prod-down`
1×	`neg-sub0` `diff-log` `div-sub` `distribute-frac-neg` `distribute-rgt-neg-out`

Counts

4 → 2431

Calls

4 calls:

18.0ms	(* (/ (+ x 1.0) x) (- (- x 1.0)))
290.0ms	(/ (- (- (* 1 (- x 1.0)) (* (/ (+ x 1.0) x) (+ x 1.0)))) (* (/ (+ x 1.0) x) (- (- x 1.0))))
14.0ms	(* (/ (+ x 1.0) x) (+ x 1.0))
54.0ms	(- (* 1 (- x 1.0)) (* (/ (+ x 1.0) x) (+ x 1.0)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (/ (+ x 1.0) x) (- (- x 1.0)))
79.0ms	(/ (- (- (* 1 (- x 1.0)) (* (/ (+ x 1.0) x) (+ x 1.0)))) (* (/ (+ x 1.0) x) (- (- x 1.0))))
34.0ms	(* (/ (+ x 1.0) x) (+ x 1.0))
42.0ms	(- (* 1 (- x 1.0)) (* (/ (+ x 1.0) x) (+ x 1.0)))

simplify544.0ms

Algorithm

egg-herbie

Counts

2443 → 2443

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5001	60753

prune4.0s

Filtered

2443 candidates to 1158 candidates (47.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	2441	2	2443
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	2443	3	2446

Merged error: 0b

Counts

2446 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) x)
0.0b	(* (/ (+ x 1.0) x) (- (- x 1.0)))
0.0b	(/ (- (- (+ 3.0 (* 1.0 (/ 1 x))))) (* (/ (+ x 1.0) x) (- (- x 1.0))))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

1677×	`*-un-lft-identity`
1638×	`times-frac`
1082×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
1015×	`add-sqr-sqrt`
709×	`add-cube-cbrt`
696×	`associate-l`
476×	`associate-r`
416×	`distribute-lft-out`
148×	`neg-mul-1`
68×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
60×	`associate-/l*`
58×	`associate-/r*`
56×	`distribute-neg-frac`
48×	`frac-times`
38×	`associate-/r/`
36×	`div-inv`
34×	`*-commutative`
26×	`flip3--` `flip--`
24×	`associate-*l/`
22×	`distribute-neg-in`
19×	`add-exp-log` `add-cbrt-cube`
18×	`prod-diff`
16×	`associate-/l/`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`associate-*r/` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`
1×	`neg-sub0` `div-sub` `distribute-frac-neg` `pow-prod-down` `distribute-rgt-neg-out`

Counts

3 → 1456

Calls

3 calls:

6.0ms	(/ (+ x 1.0) x)
18.0ms	(* (/ (+ x 1.0) x) (- (- x 1.0)))
61.0ms	(/ (- (- (+ 3.0 (* 1.0 (/ 1 x))))) (* (/ (+ x 1.0) x) (- (- x 1.0))))

series242.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (+ x 1.0) x)
112.0ms	(* (/ (+ x 1.0) x) (- (- x 1.0)))
85.0ms	(/ (- (- (+ 3.0 (* 1.0 (/ 1 x))))) (* (/ (+ x 1.0) x) (- (- x 1.0))))

simplify277.0ms

Algorithm

egg-herbie

Counts

1465 → 1465

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	3722	24142
1	5002	23970

prune1.6s

Filtered

1465 candidates to 528 candidates (36.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1463	2	1465
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	1466	2	1468

Merged error: 0b

Counts

1468 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* 1.0 (/ 1 x)) x)
0.0b	(/ (- (- (+ 3.0 (* 1.0 (/ 1 x))))) (- (* 1.0 (/ 1 x)) x))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

601×	`add-sqr-sqrt`
499×	`*-un-lft-identity`
400×	`times-frac`
240×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
165×	`add-cube-cbrt`
136×	`difference-of-squares`
114×	`unswap-sqr`
86×	`associate-l`
80×	`distribute-lft-out`
72×	`prod-diff`
68×	`distribute-lft-out--`
52×	`associate-r`
32×	`associate-/l*`
30×	`neg-mul-1`
24×	`fma-neg`
9×	`associate-/r*`
5×	`div-inv`
4×	`add-exp-log` `*-commutative` `add-cbrt-cube` `distribute-neg-frac` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `flip-+`

Counts

2 → 465

Calls

2 calls:

23.0ms	(- (* 1.0 (/ 1 x)) x)
34.0ms	(/ (- (- (+ 3.0 (* 1.0 (/ 1 x))))) (- (* 1.0 (/ 1 x)) x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (* 1.0 (/ 1 x)) x)
49.0ms	(/ (- (- (+ 3.0 (* 1.0 (/ 1 x))))) (- (* 1.0 (/ 1 x)) x))

simplify141.0ms

Algorithm

egg-herbie

Counts

471 → 471

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	1005	6980
1	3276	6275
2	5001	5931

prune446.0ms

Filtered

471 candidates to 158 candidates (33.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	471	0	471
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	471	2	473

Merged error: 0b

Counts

473 → 2

regimes21.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	9
1	32	9
2	48	9
3	65	9
4	78	9
5	80	9
6	80	9

end0.0ms

sample535.0ms

Algorithm

intervals

Results

177.0ms	1670×	body	1280	valid
100.0ms	4170×	body	80	valid
100.0ms	1219×	body	640	valid
42.0ms	618×	body	320	valid
14.0ms	323×	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