Details

sample79.0ms

Algorithm

intervals

Results

40.0ms	64×	body	1280	valid
18.0ms	61×	body	640	valid
4.0ms	27×	body	320	valid
4.0ms	91×	body	80	valid
2.0ms	93×	body	80	nan
1.0ms	13×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	2
1	5	2

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize4.0ms

Local error

Found 1 expressions with local error:

3.3b	(log (+ 1.0 x))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-prod` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-div`
1×	`expm1-log1p-u` `flip3-+` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

1 → 17

Calls

1 calls:

3.0ms

(log (+ 1.0 x))

series44.0ms

Counts

1 → 3

Calls

1 calls:

44.0ms

(log (+ 1.0 x))

simplify39.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	131	99
1	363	89
2	1292	86
3	5002	81

prune43.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
69×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`add-exp-log` `unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 112

Calls

1 calls:

27.0ms

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

series53.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	535	648
1	2311	536
2	5001	535

prune238.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (log (+ 1.0 x))) (cbrt (log (+ 1.0 x))))
3.3b	(log (+ 1.0 x))
3.3b	(log (+ 1.0 x))
3.3b	(log (+ 1.0 x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
23×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`pow1`
15×	`add-cube-cbrt`
12×	`log-prod`
9×	`add-exp-log` `swap-sqr` `log-pow`
7×	`associate-r` `associate-l`
6×	`log-div` `pow1/3`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

7.0ms	(* (cbrt (log (+ 1.0 x))) (cbrt (log (+ 1.0 x))))
2.0ms	(log (+ 1.0 x))
2.0ms	(log (+ 1.0 x))
3.0ms	(log (+ 1.0 x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt (log (+ 1.0 x))) (cbrt (log (+ 1.0 x))))
44.0ms	(log (+ 1.0 x))
38.0ms	(log (+ 1.0 x))
44.0ms	(log (+ 1.0 x))

simplify54.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	458	860
1	1768	793
2	5001	696

prune238.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.3b	(log (+ 1.0 x))
3.3b	(log (+ 1.0 x))
13.3b	(log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
15.2b	(log (+ (pow 1.0 3) (pow x 3)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`log-prod`
8×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-div`
7×	`distribute-lft-out`
4×	`expm1-log1p-u` `unpow-prod-down` `flip3-+` `cube-prod` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
1×	`sum-cubes`

Counts

4 → 72

Calls

4 calls:

2.0ms	(log (+ 1.0 x))
2.0ms	(log (+ 1.0 x))
7.0ms	(log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
13.0ms	(log (+ (pow 1.0 3) (pow x 3)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(log (+ 1.0 x))
40.0ms	(log (+ 1.0 x))
70.0ms	(log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
255.0ms	(log (+ (pow 1.0 3) (pow x 3)))

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	357	585
1	1284	523
2	5001	514

prune336.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes237.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.6b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	2261×	body	1280	valid
405.0ms	1689×	body	640	valid
110.0ms	831×	body	320	valid
103.0ms	2810×	body	80	valid
60.0ms	2758×	body	80	nan
39.0ms	409×	body	160	valid