Details

sample166.0ms

Algorithm

intervals

Results

95.0ms	101×	body	1280	valid
43.0ms	97×	body	640	valid
8.0ms	33×	body	320	valid
5.0ms	256×	pre	80	true
2.0ms	16×	body	160	valid
1.0ms	9×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 61.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.7b	(log (- 1.0 x))
4.7b	(log (+ 1.0 x))

rewrite15.0ms

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:

8.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (- 1.0 x))
3.0ms	(log (+ 1.0 x))

series208.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms	(log (- 1.0 x))
44.0ms	(log (+ 1.0 x))

simplify48.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (40.0ms)

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

prune222.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 58.9b

localize13.0ms

Local error

Found 4 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)))
0.0b	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
4.7b	(log (- 1.0 x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
84×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
50×	`*-un-lft-identity`
48×	`add-cube-cbrt`
30×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
11×	`pow1` `add-cbrt-cube`
10×	`div-exp` `prod-exp`
6×	`pow-to-exp` `pow-exp`
5×	`log-prod` `log-pow`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-l` `associate-/r*`
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` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 175

Calls

4 calls:

0.0ms	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
30.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
7.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
3.0ms	(log (- 1.0 x))

series269.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
50.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
136.0ms	(/ (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))

simplify95.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	939	1568
1	3867	1383
2	5001	1383

prune543.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
159×	`add-sqr-sqrt`
136×	`associate-r`
112×	`unpow-prod-down`
95×	`*-un-lft-identity`
83×	`add-cube-cbrt`
52×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
20×	`prod-exp`
19×	`div-exp`
16×	`add-cbrt-cube`
12×	`pow1` `pow-to-exp` `pow-exp`
8×	`distribute-lft-out--`
6×	`associate-l` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log-pow` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-undiv` `associate-/r*` `div-inv`
2×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l/`
1×	`+-commutative` `flip3--` `fma-def` `frac-2neg` `flip3-+` `div-sub` `clear-num` `sum-log` `flip--` `flip-+`

Counts

4 → 282

Calls

4 calls:

3.0ms	(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
29.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
25.0ms	(/ (- (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))))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
51.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
50.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
121.0ms	(/ (- (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))))))

simplify100.0ms

Algorithm

egg-herbie

Counts

294 → 294

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	824	2553
1	3511	2263
2	5002	2260

prune841.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

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

rewrite12.0ms

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))))))

series930.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(* (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)))))))
227.0ms	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
227.0ms	(cbrt (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
222.0ms	(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

prune380.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes31.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	16
1	18	16

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.2s	3376×	body	1280	valid
1.2s	2515×	body	640	valid
312.0ms	1221×	body	320	valid
166.0ms	8000×	pre	80	true
104.0ms	646×	body	160	valid
23.0ms	242×	body	80	valid