Details

sample42.0ms

Algorithm

intervals

Results

17.0ms	291×	body	80	valid
4.0ms	79×	body	80	nan

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	178	9
3	446	9
4	1530	9
5	5001	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.9b	(/ (* M D) (* 2.0 d))
10.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

8.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms	(/ (* M D) (* 2.0 d))
15.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

407.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
372.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms	(/ (* M D) (* 2.0 d))
693.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify77.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	609	1075
1	2742	997
2	5003	994

prune392.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

3.0b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
3.5b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.9b	(/ (* M D) (* 2.0 d))
6.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
26×	`prod-exp`
23×	`add-cbrt-cube`
20×	`div-exp`
18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `pow-exp`
9×	`associate-l`
6×	`cbrt-undiv` `unpow-prod-down` `cbrt-unprod`
5×	`pow1` `times-frac` `sqrt-prod`
4×	`associate-/r*` `add-log-exp`
3×	`associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

7.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.8s

Counts

4 → 12

Calls

4 calls:

368.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
703.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
35.0ms	(/ (* M D) (* 2.0 d))
742.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify62.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	560	829
1	2559	746
2	5001	744

prune338.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.3b

localize16.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.9b	(/ (* M D) (* 2.0 d))
5.9b	(/ (* M D) (* 2.0 d))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
184×	`prod-exp`
129×	`div-exp`
80×	`pow-exp`
39×	`add-cbrt-cube`
16×	`pow-to-exp`
14×	`add-sqr-sqrt`
12×	`cbrt-unprod`
11×	`cbrt-undiv`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`unpow-prod-down` `times-frac`
5×	`associate-/r*`
4×	`pow1` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*` `unswap-sqr`
2×	`sqr-pow`
1×	`*-commutative`

Counts

4 → 150

Calls

4 calls:

16.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
9.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))

series1.7s

Counts

4 → 12

Calls

4 calls:

914.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
731.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
28.0ms	(/ (* M D) (* 2.0 d))
34.0ms	(/ (* M D) (* 2.0 d))

simplify79.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	836	1701
1	3118	1278
2	5001	1274

prune353.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.3b

localize20.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.9b	(/ (* M D) (* 2.0 d))
6.0b	(* (* M D) (/ 1 (* 2.0 d)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

970×	`add-exp-log`
581×	`prod-exp`
285×	`div-exp`
210×	`pow-exp`
48×	`add-cbrt-cube`
36×	`rec-exp` `1-exp`
26×	`pow-to-exp`
19×	`cbrt-unprod`
16×	`add-sqr-sqrt`
11×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r` `associate-l`
9×	`pow1`
8×	`times-frac`
6×	`unpow-prod-down`
4×	`associate-/r*` `div-inv` `add-log-exp`
3×	`pow-prod-down` `unswap-sqr`
2×	`frac-2neg` `clear-num` `-commutative` `associate-/l` `sqr-pow`
1×	`associate-*r/` `un-div-inv`

Counts

4 → 249

Calls

4 calls:

35.0ms	(/ (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
17.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
7.0ms	(/ (* M D) (* 2.0 d))
25.0ms	(* (* M D) (/ 1 (* 2.0 d)))

series1.5s

Counts

4 → 12

Calls

4 calls:

671.0ms	(/ (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
702.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
37.0ms	(/ (* M D) (* 2.0 d))
43.0ms	(* (* M D) (/ 1 (* 2.0 d)))

simplify127.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1570	3106
1	4928	2306
2	5002	2306

prune394.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.3b

regimes656.0ms

Accuracy

0% (1.5b remaining)

Error of 8.9b against oracle of 7.4b and baseline of 8.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	17
1	32	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

484.0ms	9453×	body	80	valid
163.0ms	3018×	body	80	nan