Details

sample62.0ms

Algorithm

intervals

Results

36.0ms	84×	body	1280	valid
11.0ms	61×	body	640	valid
2.0ms	82×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	101×	body	80	nan
1.0ms	16×	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: 40.8b

localize4.0ms

Local error

Found 1 expressions with local error:

4.2b	(log (+ 1.0 x))

rewrite5.0ms

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:

4.0ms

(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 (37.0ms)

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

prune46.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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)))))

rewrite45.0ms

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:

38.0ms	(* 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)))))

series91.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
39.0ms	(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	832
1	2867	631
2	5002	630

prune296.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(sqrt (+ 1.0 x))
4.3b	(log (sqrt (+ 1.0 x)))
4.3b	(log (sqrt (+ 1.0 x)))

rewrite30.0ms

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:

7.0ms	(sqrt (+ 1.0 x))
10.0ms	(sqrt (+ 1.0 x))
5.0ms	(log (sqrt (+ 1.0 x)))
5.0ms	(log (sqrt (+ 1.0 x)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (+ 1.0 x))
28.0ms	(sqrt (+ 1.0 x))
79.0ms	(log (sqrt (+ 1.0 x)))
80.0ms	(log (sqrt (+ 1.0 x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	187	508
1	531	462
2	2062	442
3	5002	428

prune204.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (pow (log (sqrt (+ 1.0 x))) 3))
0.3b	(pow (log (sqrt (+ 1.0 x))) 3)
4.3b	(log (sqrt (+ 1.0 x)))
4.3b	(log (sqrt (+ 1.0 x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod` `*-un-lft-identity` `log-pow`
17×	`pow1`
14×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
12×	`unpow-prod-down` `cube-prod`
8×	`sqrt-prod`
7×	`add-exp-log`
6×	`sqrt-pow1` `pow1/2`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log-div` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `flip3-+` `unpow3` `rem-log-exp` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 104

Calls

4 calls:

3.0ms	(cbrt (pow (log (sqrt (+ 1.0 x))) 3))
4.0ms	(pow (log (sqrt (+ 1.0 x))) 3)
6.0ms	(log (sqrt (+ 1.0 x)))
5.0ms	(log (sqrt (+ 1.0 x)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(cbrt (pow (log (sqrt (+ 1.0 x))) 3))
181.0ms	(pow (log (sqrt (+ 1.0 x))) 3)
79.0ms	(log (sqrt (+ 1.0 x)))
79.0ms	(log (sqrt (+ 1.0 x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	339	726
1	1245	668
2	5001	633

prune221.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.4b 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	18	10
1	18	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

989.0ms	2276×	body	1280	valid
345.0ms	1702×	body	640	valid
81.0ms	807×	body	320	valid
57.0ms	2813×	body	80	valid
32.0ms	2609×	body	80	nan
24.0ms	402×	body	160	valid