Details

sample146.0ms

Algorithm

intervals

Results

87.0ms	102×	body	1280	valid
33.0ms	82×	body	640	valid
9.0ms	44×	body	320	valid
3.0ms	256×	pre	80	true
3.0ms	24×	body	160	valid
0.0ms	4×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 62.1b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.7b	(log (+ 1.0 x))
6.9b	(log (- 1.0 x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 69

Calls

3 calls:

6.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (+ 1.0 x))
3.0ms	(log (- 1.0 x))

series232.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
49.0ms	(log (+ 1.0 x))
45.0ms	(log (- 1.0 x))

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	421	668
1	1543	624
2	5002	599

prune356.0ms

Filtered

78 candidates to 55 candidates (29.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 59.9b

Counts

79 → 8

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
6.9b	(log (- 1.0 x))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

388×	`add-sqr-sqrt`
284×	`times-frac`
212×	`*-un-lft-identity`
114×	`unpow-prod-down`
102×	`unswap-sqr`
91×	`difference-of-squares`
87×	`add-cube-cbrt`
70×	`unpow2` `sqr-pow`
68×	`associate-r`
58×	`pow1`
57×	`associate-*r/`
55×	`associate-/r*`
53×	`log-pow`
51×	`distribute-lft-out--`
48×	`associate-l`
44×	`associate-/r/`
42×	`frac-sub`
40×	`distribute-lft-out`
31×	`associate-/l*`
29×	`add-exp-log`
21×	`flip3-+` `flip-+`
10×	`div-exp` `prod-exp` `add-cbrt-cube`
7×	`clear-num`
6×	`pow-to-exp` `pow-exp` `un-div-inv`
5×	`log-prod`
4×	`log-div` `frac-2neg`
3×	`flip3--` `flip--` `add-log-exp`
2×	`cbrt-undiv` `div-sub` `cbrt-unprod` `div-inv`
1×	`rem-log-exp` `pow-prod-down` `*-commutative`

Counts

3 → 363

Calls

3 calls:

70.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
26.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
3.0ms	(log (- 1.0 x))

series245.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
50.0ms	(log (- 1.0 x))

simplify88.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1612	5342
1	5002	4993

prune706.0ms

Filtered

372 candidates to 192 candidates (48.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	371	1	372
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	374	6	380

Merged error: 0.0b

Counts

380 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

1234×	`*-un-lft-identity`
1061×	`add-sqr-sqrt`
834×	`times-frac`
470×	`distribute-lft-out--`
397×	`associate-l`
376×	`distribute-lft-out`
302×	`difference-of-squares`
289×	`unswap-sqr`
256×	`unpow-prod-down`
227×	`pow1`
220×	`log-pow`
176×	`unpow2` `sqr-pow`
136×	`associate-r`
134×	`add-cube-cbrt`
76×	`associate-*r/`
63×	`associate-/r*`
51×	`add-exp-log`
50×	`associate-/l*`
44×	`associate-/r/`
42×	`frac-sub`
21×	`flip3-+` `flip-+`
20×	`prod-exp`
19×	`div-exp`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `pow-exp`
9×	`clear-num`
8×	`un-div-inv`
5×	`frac-2neg`
4×	`cbrt-unprod`
3×	`cbrt-undiv` `div-sub` `div-inv` `add-log-exp`
2×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `associate-/l/` `associate--r+`
1×	`+-commutative`

Counts

3 → 800

Calls

3 calls:

23.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
23.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
142.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series242.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
133.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify195.0ms

Algorithm

egg-herbie

Counts

809 → 809

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1791	16272
1	5001	15455

prune1.0s

Filtered

809 candidates to 271 candidates (66.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	807	2	809
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	810	5	815

Merged error: 0.0b

Counts

815 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0b	(cbrt (pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
0.0b	(pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)

rewrite795.0ms

Algorithm

rewrite-expression-head

Rules

3409×	`*-un-lft-identity`
2708×	`add-sqr-sqrt`
2070×	`times-frac`
1406×	`unpow-prod-down`
1370×	`distribute-lft-out--`
1142×	`associate-l`
1096×	`distribute-lft-out`
868×	`difference-of-squares`
748×	`unswap-sqr`
649×	`pow1`
642×	`log-pow`
487×	`cbrt-prod`
384×	`sqr-pow`
382×	`unpow2`
207×	`add-cube-cbrt`
133×	`associate-*r/`
132×	`associate-/r/`
126×	`frac-sub`
87×	`associate-/r*`
77×	`associate-/l*`
68×	`associate-r`
63×	`flip3-+` `flip-+`
32×	`add-exp-log`
15×	`clear-num`
14×	`un-div-inv` `add-cbrt-cube`
11×	`div-exp`
10×	`prod-exp`
8×	`frac-2neg` `pow-exp`
7×	`pow-to-exp`
4×	`pow-unpow` `flip3--` `flip--` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `div-sub`
2×	`unpow3` `rem-cbrt-cube` `cbrt-unprod` `associate-/l/` `associate--r+` `rem-cube-cbrt`
1×	`+-commutative` `pow-pow` `pow1/3` `pow-prod-down` `*-commutative`

Counts

4 → 1667

Calls

4 calls:

23.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
140.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
189.0ms	(cbrt (pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
162.0ms	(pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)

series493.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
130.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
128.0ms	(cbrt (pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
178.0ms	(pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)

simplify495.0ms

Algorithm

egg-herbie

Counts

1679 → 1679

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3431	47269
1	5002	44221

prune1.6s

Filtered

1679 candidates to 343 candidates (79.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1679	0	1679
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	1679	5	1684

Merged error: 0.0b

Counts

1684 → 5

regimes23.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	19
1	22	19

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.0s	3384×	body	1280	valid
1.0s	2513×	body	640	valid
272.0ms	1285×	body	320	valid
109.0ms	8000×	pre	80	true
71.0ms	602×	body	160	valid
11.0ms	216×	body	80	valid