Details

sample131.0ms

Algorithm

intervals

Results

62.0ms	299×	body	80	valid
35.0ms	99×	body	80	nan

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	596
2	95
1	38
0	17

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize56.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))
3.5b	(sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))
6.5b	(/ (* M D) (* 2 d))
9.2b	(* (pow (/ (* M D) (* 2 d)) 2) (/ h l))

rewrite6.7s

Algorithm

rewrite-expression-head

Rules

572×	`add-sqr-sqrt`
377×	`times-frac`
308×	`associate-l`
212×	`*-un-lft-identity`
205×	`associate-r`
198×	`unpow-prod-down`
172×	`unswap-sqr`
169×	`add-cube-cbrt`
79×	`sqrt-prod`
68×	`difference-of-squares`
67×	`add-exp-log`
52×	`*-commutative`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp`
16×	`associate-/l*`
15×	`associate-/r*`
11×	`associate-*r/` `unpow2` `sqr-pow`
10×	`pow-exp`
9×	`pow1`
7×	`cbrt-unprod`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`clear-num` `div-inv`
2×	`pow-to-exp` `frac-2neg` `flip3--` `pow-prod-down` `un-div-inv` `flip--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 527

Calls

4 calls:

3.8s	(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))
2.4s	(sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))
42.0ms	(/ (* M D) (* 2 d))
358.0ms	(* (pow (/ (* M D) (* 2 d)) 2) (/ h l))

series721.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))
220.0ms	(sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))
37.0ms	(/ (* M D) (* 2 d))
138.0ms	(* (pow (/ (* M D) (* 2 d)) 2) (/ h l))

simplify2.1s

Counts

539 → 539

Iterations

Iter	Nodes
done	5004
1	2806
0	860

prune3.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize41.0ms

Local error

Found 4 expressions with local error:

4.6b	(* (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h) (/ 1 l))
5.2b	(* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)
6.5b	(/ (/ (* M D) 2) d)
6.5b	(/ (/ (* M D) 2) d)

rewrite24.1s

Algorithm

rewrite-expression-head

Rules

87188×	`associate-/l*`
83117×	`frac-times`
60771×	`add-sqr-sqrt`
54363×	`times-frac`
51452×	`associate-*l/`
48386×	`*-un-lft-identity`
48256×	`add-cube-cbrt`
25809×	`associate-/l/`
21282×	`associate-/r*`
19013×	`associate-l`
17721×	`associate-r`
7117×	`clear-num`
7094×	`frac-2neg`
6183×	`unswap-sqr`
5828×	`*-commutative`
1473×	`div-inv`
713×	`associate-*r/`
606×	`add-exp-log`
372×	`add-cbrt-cube`
304×	`swap-sqr`
279×	`prod-exp`
246×	`div-exp`
161×	`cbrt-unprod`
148×	`cbrt-undiv`
58×	`un-div-inv`
18×	`pow1` `rec-exp` `1-exp`
9×	`pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 48064

Calls

4 calls:

11.0s	(* (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h) (/ 1 l))
2.7s	(* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)
33.0ms	(/ (/ (* M D) 2) d)
44.0ms	(/ (/ (* M D) 2) d)

series312.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h) (/ 1 l))
107.0ms	(* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)
40.0ms	(/ (/ (* M D) 2) d)
50.0ms	(/ (/ (* M D) 2) d)

simplify1.2m

Counts

48076 → 48076

Iterations

Iter	Nodes
done	55261
0	55261

prune5.9m

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize49.0ms

Local error

Found 4 expressions with local error:

4.3b	(* (/ (/ (* M D) (sqrt 2)) d) h)
4.6b	(* (* (* (/ (/ (* M D) 2) d) (/ (/ 1 (sqrt 2)) 1)) (* (/ (/ (* M D) (sqrt 2)) d) h)) (/ 1 l))
6.5b	(/ (/ (* M D) 2) d)
6.6b	(/ (/ (* M D) (sqrt 2)) d)

rewrite2.2m

Algorithm

rewrite-expression-head

Calls

4 calls:

170.0ms	(* (/ (/ (* M D) (sqrt 2)) d) h)
1.7m	(* (* (* (/ (/ (* M D) 2) d) (/ (/ 1 (sqrt 2)) 1)) (* (/ (/ (* M D) (sqrt 2)) d) h)) (/ 1 l))
34.0ms	(/ (/ (* M D) 2) d)
48.0ms	(/ (/ (* M D) (sqrt 2)) d)