Details

sample10.5s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 12.460327%

Results

107.0ms	119×	body	1280	valid
33.0ms	75×	body	640	valid
10.0ms	43×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	14×	body	160	valid
0.0ms	5×	body	80	valid

simplify4.0ms

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

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: 62.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.5b	(log (- 1.0 x))
5.5b	(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))

series20.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (- 1.0 x))
3.0ms	(log (+ 1.0 x))

simplify50.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	515	773
1	2021	724
2	5002	711

prune158.0ms

Filtered

56 candidates to 78 candidates (-39.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	5	79

Merged error: 59.8b

Counts

79 → 5

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)))))
5.5b	(log (- 1.0 x))

rewrite44.0ms

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:

23.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
10.0ms	(/ (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))

series19.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* 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))

simplify105.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1040	1572
1	4406	1408
2	5001	1408

prune374.0ms

Filtered

114 candidates to 172 candidates (-50.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	2	1	3
Picked	1	0	1
Done	1	0	1
Total	175	2	177

Merged error: 0.0b

Counts

177 → 2

localize15.0ms

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)))))

rewrite70.0ms

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:

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

series19.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
5.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
9.0ms	(/ (- (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)))))

simplify99.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	855	2533
1	3688	2253
2	5001	2252

prune820.0ms

Filtered

171 candidates to 275 candidates (-60.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	274	1	275
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	274	3	277

Merged error: 0b

Counts

277 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.1b	(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
0.1b	(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
29.8b	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

562×	`add-exp-log`
353×	`prod-exp`
209×	`div-exp`
138×	`pow-to-exp` `pow-exp`
129×	`times-frac`
119×	`add-sqr-sqrt`
106×	`associate-*r/`
89×	`*-un-lft-identity`
72×	`associate-r`
62×	`add-cube-cbrt`
58×	`associate-l`
56×	`pow1` `unpow-prod-down`
52×	`associate-/r/` `add-cbrt-cube`
48×	`frac-sub`
45×	`frac-times`
40×	`flip3-+` `flip-+`
30×	`associate-*l/`
25×	`cbrt-unprod`
24×	`unpow2` `sqr-pow`
22×	`difference-of-squares`
19×	`pow-prod-down` `unswap-sqr`
18×	`distribute-lft-out--`
9×	`cbrt-undiv` `log-pow`
6×	`associate-/l*`
4×	`frac-add` `associate-/r*` `pow-sqr` `pow-prod-up` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--` `div-inv`
2×	`pow-plus` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-sub` `swap-sqr` `clear-num`

Counts

4 → 427

Calls

4 calls:

20.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
25.0ms	(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
32.0ms	(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
21.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
7.0ms	(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
17.0ms	(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 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)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify117.0ms

Algorithm

egg-herbie

Counts

439 → 439

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2069	7797
1	5002	7330

prune2.6s

Filtered

203 candidates to 439 candidates (-116.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	439	0	439
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	439	3	442

Merged error: 0b

Counts

442 → 3

regimes32.0ms

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

sample15.6s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 12.460327%

Results

3.1s	3435×	body	1280	valid
1.1s	2484×	body	640	valid
276.0ms	1243×	body	320	valid
134.0ms	8000×	pre	80	true
85.0ms	641×	body	160	valid
11.0ms	197×	body	80	valid

Details

sample10.5s

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite14.0ms

series20.0ms

simplify50.0ms

prune158.0ms

localize13.0ms

rewrite44.0ms

series19.0ms

simplify105.0ms

prune374.0ms

localize15.0ms

rewrite70.0ms

series19.0ms

simplify99.0ms

prune820.0ms

localize17.0ms

rewrite136.0ms

series43.0ms

simplify117.0ms

prune2.6s

regimes32.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample15.6s

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