Details

sample141.0ms

Algorithm

intervals

Results

81.0ms	92×	body	1280	valid
33.0ms	84×	body	640	valid
10.0ms	53×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	160	valid
0.0ms	8×	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

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.1b	(log (- 1.0 x))
6.1b	(log (+ 1.0 x))

rewrite27.0ms

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:

16.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.0ms	(log (- 1.0 x))
5.0ms	(log (+ 1.0 x))

series210.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms	(log (- 1.0 x))
43.0ms	(log (+ 1.0 x))

simplify41.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (35.0ms)

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

prune195.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.3b

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)))
6.1b	(log (- 1.0 x))

rewrite111.0ms

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:

58.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
36.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
8.0ms	(log (- 1.0 x))

series231.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
49.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
48.0ms	(log (- 1.0 x))

simplify99.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (21.0ms)

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

prune471.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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)))))

rewrite178.0ms

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:

37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
36.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
91.0ms	(/ (- (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:

56.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
118.0ms	(/ (- (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)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (75.0ms)

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

prune749.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.7b	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
0.7b	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
0.7b	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

58×	`cbrt-prod`
52×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
22×	`pow1` `distribute-lft-out--`
18×	`cbrt-div`
15×	`add-cube-cbrt` `swap-sqr`
11×	`log-pow`
9×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 111

Calls

4 calls:

112.0ms	(* (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
12.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
12.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
13.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series910.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(* (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
221.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
219.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
219.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	507	2897
1	1877	2747
2	5001	2437

prune405.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes27.0ms

Accuracy

0% (0.5b remaining)

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

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

2.9s	3418×	body	1280	valid
1.0s	2537×	body	640	valid
235.0ms	1228×	body	320	valid
96.0ms	8000×	pre	80	true
63.0ms	585×	body	160	valid
10.0ms	232×	body	80	valid