Details

sample118.0ms

Algorithm

intervals

Results

66.0ms	115×	body	1280	valid
23.0ms	79×	body	640	valid
7.0ms	249×	body	80	nan
7.0ms	41×	body	320	valid
2.0ms	16×	body	160	valid
0.0ms	5×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	4
1	20	4
2	23	4
3	23	4

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: 58.9b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- 1.0 eps) (+ 1.0 eps))
4.7b	(log (/ (- 1.0 eps) (+ 1.0 eps)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
40×	`times-frac`
26×	`log-prod`
23×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
5×	`associate-/l*`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1`
2×	`expm1-log1p-u` `flip3-+` `div-exp` `rem-log-exp` `flip-+` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-sub` `clear-num` `log-pow` `flip--`

Counts

2 → 87

Calls

2 calls:

8.0ms	(/ (- 1.0 eps) (+ 1.0 eps))
7.0ms	(log (/ (- 1.0 eps) (+ 1.0 eps)))

series153.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (- 1.0 eps) (+ 1.0 eps))
121.0ms	(log (/ (- 1.0 eps) (+ 1.0 eps)))

simplify135.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	354	672
1	1096	638
2	4786	623
3	5001	622

prune171.0ms

Filtered

93 candidates to 63 candidates (67.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	3	94

Merged error: 0.1b

Counts

94 → 3

localize9.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune3.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Merged error: 0.1b

Counts

3 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (+ 1.0 eps)) (cbrt (+ 1.0 eps)))
3.8b	(+ (log (/ (+ (sqrt 1.0) (sqrt eps)) (* (cbrt (+ 1.0 eps)) (cbrt (+ 1.0 eps))))) (log (/ (- (sqrt 1.0) (sqrt eps)) (cbrt (+ 1.0 eps)))))
5.9b	(log (/ (- (sqrt 1.0) (sqrt eps)) (cbrt (+ 1.0 eps))))
5.9b	(log (/ (+ (sqrt 1.0) (sqrt eps)) (* (cbrt (+ 1.0 eps)) (cbrt (+ 1.0 eps)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

189×	`add-sqr-sqrt`
187×	`*-un-lft-identity`
172×	`log-prod`
136×	`times-frac`
96×	`cbrt-prod`
88×	`sqrt-prod`
69×	`add-cube-cbrt` `associate-+r+`
56×	`difference-of-squares`
40×	`cbrt-div`
32×	`distribute-lft-out`
28×	`distribute-lft-out--`
21×	`flip3-+` `flip-+`
20×	`associate-/r/`
18×	`pow1`
17×	`associate-+l+`
15×	`add-exp-log`
12×	`frac-times`
9×	`swap-sqr`
7×	`associate-r` `associate-l` `log-pow`
6×	`pow1/3` `associate-r/` `associate-l/`
5×	`rem-log-exp`
4×	`expm1-log1p-u` `log-div` `fma-def` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`div-exp`
2×	`pow-prod-down` `prod-exp` `pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `associate-+l-` `associate-+r-` `pow-plus` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 277

Calls

4 calls:

10.0ms	(* (cbrt (+ 1.0 eps)) (cbrt (+ 1.0 eps)))
30.0ms	(+ (log (/ (+ (sqrt 1.0) (sqrt eps)) (* (cbrt (+ 1.0 eps)) (cbrt (+ 1.0 eps))))) (log (/ (- (sqrt 1.0) (sqrt eps)) (cbrt (+ 1.0 eps)))))
14.0ms	(log (/ (- (sqrt 1.0) (sqrt eps)) (cbrt (+ 1.0 eps))))
14.0ms	(log (/ (+ (sqrt 1.0) (sqrt eps)) (* (cbrt (+ 1.0 eps)) (cbrt (+ 1.0 eps)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (cbrt (+ 1.0 eps)) (cbrt (+ 1.0 eps)))
901.0ms	(+ (log (/ (+ (sqrt 1.0) (sqrt eps)) (* (cbrt (+ 1.0 eps)) (cbrt (+ 1.0 eps))))) (log (/ (- (sqrt 1.0) (sqrt eps)) (cbrt (+ 1.0 eps)))))
436.0ms	(log (/ (- (sqrt 1.0) (sqrt eps)) (cbrt (+ 1.0 eps))))
414.0ms	(log (/ (+ (sqrt 1.0) (sqrt eps)) (* (cbrt (+ 1.0 eps)) (cbrt (+ 1.0 eps)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1527	5637
1	5002	5226

prune857.0ms

Filtered

289 candidates to 168 candidates (58.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	287	2	289
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	287	5	292

Merged error: 0.1b

Counts

292 → 5

localize38.0ms

Local error

Found 4 expressions with local error:

4.6b	(log (cbrt (+ 1.0 eps)))
4.8b	(log (cbrt (+ (* 1.0 1.0) (- (* eps eps) (* 1.0 eps)))))
5.9b	(log (- (sqrt 1.0) (sqrt eps)))
5.9b	(log (/ (+ (sqrt 1.0) (sqrt eps)) (* (cbrt (+ (pow 1.0 3) (pow eps 3))) (cbrt (+ (pow 1.0 3) (pow eps 3))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

39×	`log-prod`
21×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
16×	`cbrt-div`
13×	`add-exp-log`
11×	`add-cube-cbrt`
8×	`pow1` `flip3-+` `sqrt-prod` `associate-/r/` `flip-+`
7×	`cbrt-prod` `log-div`
6×	`rem-log-exp` `log-pow`
5×	`times-frac`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`distribute-lft-out`
2×	`pow1/3` `associate-r/` `div-exp` `associate-l/` `distribute-lft-out--`
1×	`flip3--` `prod-exp` `flip--` `div-inv`

Counts

4 → 94

Calls

4 calls:

4.0ms	(log (cbrt (+ 1.0 eps)))
6.0ms	(log (cbrt (+ (* 1.0 1.0) (- (* eps eps) (* 1.0 eps)))))
8.0ms	(log (- (sqrt 1.0) (sqrt eps)))
30.0ms	(log (/ (+ (sqrt 1.0) (sqrt eps)) (* (cbrt (+ (pow 1.0 3) (pow eps 3))) (cbrt (+ (pow 1.0 3) (pow eps 3))))))

series637.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(log (cbrt (+ 1.0 eps)))
140.0ms	(log (cbrt (+ (* 1.0 1.0) (- (* eps eps) (* 1.0 eps)))))
158.0ms	(log (- (sqrt 1.0) (sqrt eps)))
217.0ms	(log (/ (+ (sqrt 1.0) (sqrt eps)) (* (cbrt (+ (pow 1.0 3) (pow eps 3))) (cbrt (+ (pow 1.0 3) (pow eps 3))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	684	1462
1	2246	1323
2	5001	1316

prune631.0ms

Filtered

106 candidates to 83 candidates (78.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	106	5	111

Merged error: 0.1b

Counts

111 → 5

regimes88.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	8
1	13	8

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	3472×	body	1280	valid
521.0ms	2442×	body	640	valid
169.0ms	8139×	body	80	nan
152.0ms	1228×	body	320	valid
49.0ms	647×	body	160	valid
7.0ms	211×	body	80	valid