Details

sample158.0ms

Algorithm

intervals

Results

99.0ms	112×	body	1280	valid
32.0ms	81×	body	640	valid
8.0ms	39×	body	320	valid
6.0ms	256×	pre	80	true
2.0ms	17×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.2b	(log (+ 1.0 x))
5.2b	(log (- 1.0 x))

rewrite14.0ms

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))
3.0ms	(log (- 1.0 x))

series219.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
42.0ms	(log (+ 1.0 x))
47.0ms	(log (- 1.0 x))

simplify45.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (36.0ms)

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

prune205.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 59.1b

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)))))
5.2b	(log (- 1.0 x))

rewrite94.0ms

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:

48.0ms	(* 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))

series234.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
139.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
44.0ms	(log (- 1.0 x))

simplify106.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (21.0ms)

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

prune489.0ms

Pruning

3 alts after pruning (2 fresh and 1 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)))))

rewrite109.0ms

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:

27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
29.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
39.0ms	(/ (- (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)))))

series439.0ms

Counts

3 → 9

Calls

3 calls:

254.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
52.0ms	(* 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)))))

simplify104.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	855	2533
1	3688	2254
2	5001	2253

prune744.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 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	(/ 1 (/ (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.0b	(/ (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

322×	`times-frac`
248×	`add-sqr-sqrt`
196×	`*-un-lft-identity`
148×	`add-cube-cbrt`
136×	`associate-r`
112×	`unpow-prod-down`
63×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
32×	`distribute-lft-out--`
30×	`associate-/r*`
26×	`div-exp`
25×	`pow1`
21×	`add-cbrt-cube`
20×	`prod-exp`
16×	`log-pow` `difference-of-squares`
12×	`pow-to-exp` `pow-exp`
11×	`associate-/r/`
8×	`div-inv`
6×	`cbrt-undiv` `flip3--` `associate-l` `flip--` `associate-/l*`
4×	`associate-*r/` `cbrt-unprod` `associate-/l/` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `clear-num` `*-commutative` `frac-sub`
1×	`pow-flip` `flip3-+` `div-sub` `flip-+` `inv-pow`

Counts

4 → 386

Calls

4 calls:

27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
37.0ms	(/ 1 (/ (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
56.0ms	(/ (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
51.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
129.0ms	(/ 1 (/ (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
123.0ms	(/ (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

398 → 398

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1136	6212
1	5001	5693

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	17
1	19	17

end0.0ms

sample4.5s

Algorithm

intervals

Results

3.0s	3437×	body	1280	valid
992.0ms	2477×	body	640	valid
250.0ms	1257×	body	320	valid
100.0ms	8000×	pre	80	true
70.0ms	625×	body	160	valid
10.0ms	204×	body	80	valid