Details

sample149.0ms

Algorithm

intervals

Results

88.0ms	102×	body	1280	valid
37.0ms	90×	body	640	valid
7.0ms	36×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	21×	body	160	valid
0.0ms	7×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.2b	(log (- 1.0 x))
6.2b	(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:

8.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
2.0ms	(log (- 1.0 x))
2.0ms	(log (+ 1.0 x))

series400.0ms

Counts

3 → 9

Calls

3 calls:

310.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
48.0ms	(log (- 1.0 x))
42.0ms	(log (+ 1.0 x))

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	425	668
1	1561	624
2	5001	599

prune181.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 59.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
6.2b	(log (- 1.0 x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
83×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`pow1` `div-exp` `prod-exp` `add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
5×	`log-prod` `log-pow`
4×	`log-div` `associate-/r/` `associate-/l*`
3×	`flip3--` `associate-r/` `associate-l` `associate-/r` `flip--` `add-log-exp`
2×	`cbrt-undiv` `div-sub` `frac-sub` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `flip3-+` `rem-log-exp` `pow-prod-down` `clear-num` `*-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 163

Calls

3 calls:

30.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
26.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
3.0ms	(log (- 1.0 x))

series229.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
131.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
47.0ms	(log (- 1.0 x))

simplify104.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	995	1550
1	4213	1389
2	5001	1389

prune459.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

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)))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
158×	`add-sqr-sqrt`
136×	`associate-r`
112×	`unpow-prod-down`
94×	`*-un-lft-identity`
82×	`add-cube-cbrt`
51×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
20×	`prod-exp`
19×	`div-exp`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
8×	`distribute-lft-out--`
6×	`associate-l` `associate-/l*`
4×	`associate-*r/` `associate-/r/` `log-pow` `cbrt-unprod` `difference-of-squares`
3×	`cbrt-undiv` `associate-/r*` `div-inv` `add-log-exp`
2×	`flip3--` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `associate-/l/`
1×	`frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+`

Counts

3 → 266

Calls

3 calls:

30.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
41.0ms	(/ (- (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)))))

series229.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
123.0ms	(/ (- (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)))))

simplify102.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	855	2669
1	4152	2250
2	5001	2250

prune705.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
0.7b	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.7b	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.7b	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`cbrt-div`
11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`associate-*r/` `frac-sub`
5×	`pow1`
4×	`add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`distribute-lft-out--`
1×	`log-pow` `difference-of-squares`

Counts

4 → 61

Calls

4 calls:

6.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
13.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
10.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
10.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series888.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
228.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
217.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
217.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	456	1688
1	1646	1607
2	5002	1504

prune399.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes21.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	59
1	26	59

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.9s	3359×	body	1280	valid
1.1s	2591×	body	640	valid
246.0ms	1236×	body	320	valid
106.0ms	8000×	pre	80	true
70.0ms	595×	body	160	valid
10.0ms	219×	body	80	valid