Details

sample170.0ms

Algorithm

intervals

Results

110.0ms	122×	body	1280	valid
32.0ms	68×	body	640	valid
10.0ms	42×	body	320	valid
5.0ms	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

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: 62.1b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.9b	(log (- 1.0 x))
5.9b	(log (+ 1.0 x))

rewrite15.0ms

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))

series213.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms	(log (- 1.0 x))
44.0ms	(log (+ 1.0 x))

simplify45.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (37.0ms)

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

prune181.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Merged error: 60.0b

Counts

79 → 6

localize17.0ms

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)))))
5.9b	(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:

21.0ms	(* 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))

series233.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
132.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
48.0ms	(log (- 1.0 x))

simplify100.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (25.0ms)

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

prune424.0ms

Filtered

172 candidates to 114 candidates (66.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	175	3	178

Merged error: 0.0b

Counts

178 → 3

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)))))

rewrite76.0ms

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:

22.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
25.0ms	(* 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)))))

series230.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
49.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
127.0ms	(/ (- (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)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (77.0ms)

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

prune660.0ms

Filtered

275 candidates to 171 candidates (62.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	274	1	275
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	274	4	278

Merged error: 0.0b

Counts

278 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-div`
30×	`associate-*r/`
26×	`frac-sub`
25×	`cbrt-prod`
23×	`add-sqr-sqrt`
16×	`frac-times`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`flip3--` `flip3-+` `flip--` `flip-+`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`associate-*l/` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

16.0ms	(* (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
6.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
6.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
6.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series925.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
218.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
224.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
226.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	601	3504
1	2269	3369
2	5001	3255

prune503.0ms

Filtered

121 candidates to 90 candidates (74.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	121	4	125

Merged error: 0.0b

Counts

125 → 4

regimes21.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b 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

sample4.8s

Algorithm

intervals

Results

3.1s	3402×	body	1280	valid
1.1s	2499×	body	640	valid
280.0ms	1237×	body	320	valid
141.0ms	8000×	pre	80	true
86.0ms	639×	body	160	valid
13.0ms	223×	body	80	valid