Details

sample163.0ms

Algorithm

intervals

Results

100.0ms	110×	body	1280	valid
36.0ms	80×	body	640	valid
10.0ms	42×	body	320	valid
5.0ms	256×	pre	80	true
2.0ms	14×	body	160	valid
1.0ms	10×	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 (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: 61.3b

Counts

2 → 1

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:

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

series221.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms	(log (+ 1.0 x))
48.0ms	(log (- 1.0 x))

simplify47.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (38.0ms)

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

prune188.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	9	79

Merged error: 59.1b

Counts

79 → 9

localize14.0ms

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))

rewrite41.0ms

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:

20.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
11.0ms	(/ (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))

series443.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
345.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
49.0ms	(log (- 1.0 x))

simplify104.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	995	1618
1	4698	1387
2	5003	1387

prune384.0ms

Filtered

172 candidates to 114 candidates (66.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	177	4	181

Merged error: 0.0b

Counts

181 → 4

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)))))

rewrite67.0ms

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:

19.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
19.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
15.0ms	(/ (- (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)))))

series225.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
51.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
124.0ms	(/ (- (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)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (77.0ms)

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

prune602.0ms

Filtered

275 candidates to 171 candidates (62.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	271	4	275
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	272	7	279

Merged error: 0.0b

Counts

279 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ (- (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	(/ (- (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	(/ (- (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	(/ (- (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)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
77×	`add-sqr-sqrt`
72×	`times-frac`
47×	`add-cube-cbrt`
30×	`distribute-lft-out--`
26×	`cbrt-prod`
19×	`pow1`
18×	`associate-/l*`
16×	`associate-/r/`
15×	`log-pow` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
8×	`associate-*r/` `frac-sub`
7×	`flip3--` `flip--`
6×	`associate-/l/`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num`
1×	`cbrt-div` `pow1/3`

Counts

4 → 173

Calls

4 calls:

11.0ms	(cbrt (/ (- (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))))))
13.0ms	(/ (- (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)))))
14.0ms	(/ (- (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)))))
16.0ms	(/ (- (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)))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt (/ (- (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))))))
117.0ms	(/ (- (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)))))
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)))))
125.0ms	(/ (- (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)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	487	5034
1	1852	4780
2	5001	4775

prune580.0ms

Filtered

185 candidates to 134 candidates (72.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	185	7	192

Merged error: 0.0b

Counts

192 → 7

regimes61.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	56
1	23	56

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.0s	3318×	body	1280	valid
1.1s	2556×	body	640	valid
293.0ms	1270×	body	320	valid
131.0ms	8000×	pre	80	true
82.0ms	613×	body	160	valid
14.0ms	243×	body	80	valid