Details

sample142.0ms

Algorithm

intervals

Results

81.0ms	92×	body	1280	valid
33.0ms	84×	body	640	valid
10.0ms	53×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	160	valid
0.0ms	8×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.1b	(log (- 1.0 x))
6.1b	(log (+ 1.0 x))

rewrite29.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 75

Calls

3 calls:

16.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.0ms	(log (- 1.0 x))
5.0ms	(log (+ 1.0 x))

series203.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
40.0ms	(log (- 1.0 x))
43.0ms	(log (+ 1.0 x))

simplify45.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	452	686
1	1669	638
2	5002	623

prune207.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.3b

localize14.0ms

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)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
6.1b	(log (- 1.0 x))

rewrite66.0ms

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-/l*`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `div-sub` `flip--` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 165

Calls

3 calls:

37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
15.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
6.0ms	(log (- 1.0 x))

series238.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
142.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
41.0ms	(log (- 1.0 x))

simplify87.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	928	1522
1	4312	1284
2	5001	1284

prune468.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

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

rewrite141.0ms

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×	`log-pow` `cbrt-unprod` `difference-of-squares`
3×	`cbrt-undiv` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `clear-num` `flip--`

Counts

3 → 268

Calls

3 calls:

34.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
36.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
55.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series221.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
119.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify85.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	753	2429
1	3174	2138
2	5001	2135

prune749.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

58×	`cbrt-prod`
52×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
22×	`pow1` `distribute-lft-out--`
18×	`cbrt-div`
15×	`add-cube-cbrt` `swap-sqr`
11×	`log-pow`
9×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 119

Calls

4 calls:

105.0ms	(* (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
12.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
15.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
12.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series892.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(* (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
215.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
218.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
211.0ms	(cbrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	527	2984
1	1975	2830
2	5001	2530

prune468.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes19.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	16
1	18	16

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.9s	3418×	body	1280	valid
983.0ms	2537×	body	640	valid
231.0ms	1228×	body	320	valid
93.0ms	8000×	pre	80	true
61.0ms	585×	body	160	valid
10.0ms	232×	body	80	valid