Details

sample33.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
6.0ms	109×	body	80	overflowed

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	5
1	7	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp a) (exp b))
1.0b	(/ (exp a) (+ (exp a) (exp b)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 45

Calls

2 calls:

4.0ms	(+ (exp a) (exp b))
9.0ms	(/ (exp a) (+ (exp a) (exp b)))

series53.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(+ (exp a) (exp b))
36.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify86.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	163	384
1	486	357
2	1239	355
3	4158	355
4	5001	355

prune107.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp a))
0.0b	(+ (exp a) (exp b))
0.5b	(/ (sqrt (exp a)) (/ (+ (exp a) (exp b)) (sqrt (exp a))))
0.8b	(/ (+ (exp a) (exp b)) (sqrt (exp a)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

360×	`times-frac`
286×	`*-un-lft-identity`
189×	`sqrt-prod`
187×	`add-sqr-sqrt`
186×	`add-cube-cbrt`
50×	`distribute-lft-out`
34×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `sqrt-pow1` `div-exp`
3×	`exp-prod`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `pow1/2` `sum-log` `associate-/r/`

Counts

4 → 293

Calls

4 calls:

1.0ms	(sqrt (exp a))
4.0ms	(+ (exp a) (exp b))
17.0ms	(/ (sqrt (exp a)) (/ (+ (exp a) (exp b)) (sqrt (exp a))))
17.0ms	(/ (+ (exp a) (exp b)) (sqrt (exp a)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (exp a))
18.0ms	(+ (exp a) (exp b))
30.0ms	(/ (sqrt (exp a)) (/ (+ (exp a) (exp b)) (sqrt (exp a))))
51.0ms	(/ (+ (exp a) (exp b)) (sqrt (exp a)))

simplify97.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	653	4694
1	3302	4233
2	5002	4196

prune468.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (/ (sqrt (exp a)) (/ (+ (exp a) (exp b)) (sqrt (exp a))))))
0.0b	(+ (exp a) (exp b))
0.5b	(/ (sqrt (exp a)) (/ (+ (exp a) (exp b)) (sqrt (exp a))))
0.8b	(/ (+ (exp a) (exp b)) (sqrt (exp a)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

672×	`times-frac`
504×	`*-un-lft-identity`
342×	`sqrt-prod`
332×	`add-sqr-sqrt` `add-cube-cbrt`
174×	`log-pow`
173×	`exp-prod`
86×	`distribute-lft-out`
34×	`associate-/r*`
16×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`log-prod`
2×	`frac-2neg` `flip3-+` `clear-num` `associate-/r/` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-log-exp` `sum-log`

Counts

4 → 462

Calls

4 calls:

60.0ms	(log (exp (/ (sqrt (exp a)) (/ (+ (exp a) (exp b)) (sqrt (exp a))))))
4.0ms	(+ (exp a) (exp b))
18.0ms	(/ (sqrt (exp a)) (/ (+ (exp a) (exp b)) (sqrt (exp a))))
17.0ms	(/ (+ (exp a) (exp b)) (sqrt (exp a)))

series141.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(log (exp (/ (sqrt (exp a)) (/ (+ (exp a) (exp b)) (sqrt (exp a))))))
18.0ms	(+ (exp a) (exp b))
31.0ms	(/ (sqrt (exp a)) (/ (+ (exp a) (exp b)) (sqrt (exp a))))
54.0ms	(/ (+ (exp a) (exp b)) (sqrt (exp a)))

simplify110.0ms

Algorithm

egg-herbie

Counts

474 → 474

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	855	6579
1	3707	5919
2	5001	5891

prune774.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/4 (pow a 2))
0.0b	(sqrt (exp a))
0.0b	(/ (sqrt (exp a)) (+ (* 1/4 (pow a 2)) (+ b 2)))
1.0b	(log (exp (/ (sqrt (exp a)) (+ (* 1/4 (pow a 2)) (+ b 2)))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
27×	`exp-prod`
25×	`log-pow`
24×	`sqrt-prod`
11×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`unpow-prod-down` `sqrt-pow1` `associate-/r/` `add-log-exp` `unswap-sqr`
3×	`log-prod` `associate-l` `prod-exp` `associate-/r*`
2×	`flip3-+` `flip-+` `div-inv` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `pow1/2` `div-exp` `rem-log-exp` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

6.0ms	(* 1/4 (pow a 2))
1.0ms	(sqrt (exp a))
18.0ms	(/ (sqrt (exp a)) (+ (* 1/4 (pow a 2)) (+ b 2)))
41.0ms	(log (exp (/ (sqrt (exp a)) (+ (* 1/4 (pow a 2)) (+ b 2)))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 1/4 (pow a 2))
18.0ms	(sqrt (exp a))
56.0ms	(/ (sqrt (exp a)) (+ (* 1/4 (pow a 2)) (+ b 2)))
65.0ms	(log (exp (/ (sqrt (exp a)) (+ (* 1/4 (pow a 2)) (+ b 2)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	343	1043
1	1122	972
2	5001	964

prune380.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes84.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

end0.0ms

sample615.0ms

Algorithm

intervals

Results

298.0ms	8000×	body	80	valid
139.0ms	3514×	body	80	overflowed