Details

sample60.0ms

Algorithm

intervals

Results

35.0ms	77×	body	1280	valid
10.0ms	52×	body	640	valid
2.0ms	22×	body	320	valid
2.0ms	89×	body	80	valid
1.0ms	93×	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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize4.0ms

Local error

Found 1 expressions with local error:

4.3b	(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))

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

(log (+ 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (39.0ms)

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

prune46.0ms

Filtered

20 candidates to 15 candidates (75.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

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:

0.0ms	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
29.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))

series102.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
57.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))

simplify65.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (49.0ms)

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

prune300.0ms

Filtered

128 candidates to 81 candidates (63.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
12.7b	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
12.7b	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
12.7b	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

6.0ms	(* (cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.0ms	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
1.0ms	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
1.0ms	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series976.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(* (cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
236.0ms	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
239.0ms	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
236.0ms	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	450	1824
1	1681	1697
2	5002	1501

prune338.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

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

series172.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(log (sqrt (+ 1.0 x)))
87.0ms	(log (sqrt (+ 1.0 x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	143	314
1	362	284
2	1284	272
3	5002	264

prune107.0ms

Filtered

50 candidates to 36 candidates (72.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes102.0ms

Accuracy

99% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.2b

bsearch1.0ms

simplify1.0ms

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

976.0ms	2255×	body	1280	valid
356.0ms	1726×	body	640	valid
84.0ms	818×	body	320	valid
63.0ms	2775×	body	80	valid
35.0ms	2706×	body	80	nan
28.0ms	426×	body	160	valid