Details

sample37.0ms

Algorithm

intervals

Results

16.0ms	362×	body	80	valid
5.0ms	140×	body	80	nan

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
2.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`div-exp` `add-log-exp`
3×	`fma-def` `times-frac` `prod-exp` `associate-/r*`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 43

Calls

2 calls:

5.0ms	(+ 1.0 (* 10.0 k))
31.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series138.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ 1.0 (* 10.0 k))
105.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify48.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	380	404
1	1771	347
2	5001	327

prune216.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.2b	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
2.5b	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
102×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`unpow-prod-down`
32×	`associate-/r*`
18×	`add-exp-log`
16×	`sqr-pow`
10×	`div-exp` `add-cbrt-cube`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `associate-/r/`

Counts

3 → 187

Calls

3 calls:

5.0ms	(+ 1.0 (* 10.0 k))
64.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
34.0ms	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ 1.0 (* 10.0 k))
64.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
108.0ms	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

simplify108.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	866	2564
1	4150	2370
2	5001	2347

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
15.0b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.0b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `hypot-def`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt k)
1.0ms	(cbrt k)
23.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
25.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt k)
171.0ms	(cbrt k)
43.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
47.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify69.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	188	398
1	635	378
2	2448	366
3	5002	362

prune639.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma k 10.0 (- 1.0 (* 1.0 (* m (log k)))))
0.2b	(* m (log k))
0.4b	(/ a (fma k 10.0 (- 1.0 (* 1.0 (* m (log k))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `log-prod`
4×	`associate-r`
3×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

3 → 66

Calls

3 calls:

0.0ms	(fma k 10.0 (- 1.0 (* 1.0 (* m (log k)))))
8.0ms	(* m (log k))
5.0ms	(/ a (fma k 10.0 (- 1.0 (* 1.0 (* m (log k))))))

series157.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma k 10.0 (- 1.0 (* 1.0 (* m (log k)))))
34.0ms	(* m (log k))
80.0ms	(/ a (fma k 10.0 (- 1.0 (* 1.0 (* m (log k))))))

simplify82.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	260	535
1	928	480
2	3180	471
3	5001	470

prune254.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes106.0ms

Accuracy

95.2% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.0b

bsearch120.0ms

Steps

Iters	Range		Point
7	2.8125274282717296e+115	1.6013341253949209e+117	6.973265254892905e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	47
1	59	47
2	59	47

end0.0ms

sample1.1s

Algorithm

intervals

Results

551.0ms	11920×	body	80	valid
168.0ms	4264×	body	80	nan