Details

sample68.0ms

Algorithm

intervals

Results

37.0ms	72×	body	1280	valid
14.0ms	57×	body	640	valid
4.0ms	31×	body	320	valid
2.0ms	82×	body	80	valid
2.0ms	77×	body	80	nan
1.0ms	14×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize3.0ms

Local error

Found 1 expressions with local error:

3.9b	(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))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

(log (+ 1.0 x))

simplify44.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (37.0ms)

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

prune45.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 122

Calls

2 calls:

28.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0ms	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series95.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
47.0ms	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	560	763
1	2406	633
2	5001	632

prune298.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(sqrt (+ 1.0 x))
4.0b	(log (sqrt (+ 1.0 x)))
4.0b	(log (sqrt (+ 1.0 x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`log-prod`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `hypot-def`

Counts

4 → 82

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 x))
4.0ms	(sqrt (+ 1.0 x))
3.0ms	(log (sqrt (+ 1.0 x)))
3.0ms	(log (sqrt (+ 1.0 x)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ 1.0 x))
34.0ms	(sqrt (+ 1.0 x))
82.0ms	(log (sqrt (+ 1.0 x)))
80.0ms	(log (sqrt (+ 1.0 x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	187	510
1	521	462
2	1993	440
3	5002	428

prune211.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
3.9b	(log (+ 1.0 x))
4.0b	(log (sqrt (+ 1.0 x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
10×	`add-sqr-sqrt`
8×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt`
5×	`add-exp-log`
4×	`log-div` `sqrt-div` `log-pow`
3×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `rem-log-exp`
1×	`rem-sqrt-square` `hypot-def`

Counts

3 → 58

Calls

3 calls:

4.0ms	(sqrt (+ 1.0 x))
2.0ms	(log (+ 1.0 x))
3.0ms	(log (sqrt (+ 1.0 x)))

series158.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(sqrt (+ 1.0 x))
41.0ms	(log (+ 1.0 x))
82.0ms	(log (sqrt (+ 1.0 x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	261	353
1	763	320
2	3137	307
3	5003	299

prune152.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes71.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	21
1	32	21
2	32	21

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	2285×	body	1280	valid
410.0ms	1674×	body	640	valid
109.0ms	837×	body	320	valid
85.0ms	2792×	body	80	valid
59.0ms	2707×	body	80	nan
32.0ms	412×	body	160	valid