Details

sample134.0ms

Algorithm

intervals

Results

78.0ms	306×	body	80	valid
25.0ms	110×	body	80	nan

simplify201.0ms

Calls

1 calls:

Slowest

201.0ms

(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize32.0ms

Local error

Found 4 expressions with local error:

9.7b	(* (/ h l) (/ (* M D) (* 2 d)))
5.4b	(/ (* M D) (* 2 d))
5.4b	(/ (* M D) (* 2 d))
4.7b	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

1355×	`add-sqr-sqrt`
672×	`times-frac`
492×	`unswap-sqr`
436×	`associate-r`
421×	`*-un-lft-identity`
357×	`add-cube-cbrt`
305×	`associate-l`
243×	`frac-times`
230×	`associate-/l*`
228×	`associate-/r*`
118×	`sqrt-prod`
112×	`difference-of-squares`
97×	`*-commutative`
69×	`add-cbrt-cube` `add-exp-log`
41×	`clear-num`
40×	`frac-2neg`
27×	`associate-*r/`
26×	`prod-exp` `cbrt-unprod`
21×	`cbrt-undiv` `div-exp`
9×	`associate-*l/`
7×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`un-div-inv` `distribute-lft-out--`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `flip--`

Calls

4 calls:

Slowest

1.3s	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
86.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
29.0ms	(/ (* M D) (* 2 d))
27.0ms	(/ (* M D) (* 2 d))

series403.0ms

Calls

4 calls:

Slowest

197.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
103.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
52.0ms	(/ (* M D) (* 2 d))
51.0ms	(/ (* M D) (* 2 d))

simplify2.9m

Calls

1482 calls:

Slowest

10.9s	(* (/ h (* (cbrt l) (cbrt l))) (/ (* M D) 1))
10.2s	(sqrt (+ 1 (* (sqrt (* (/ h l) (/ (* M D) (* 2 d)))) (/ (sqrt (* M D)) (* (sqrt 2) (sqrt d))))))
1.4s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.4s	(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune16.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.5b

localize47.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ (* 2 d) (* M D))
5.4b	(/ (* M D) (* 2 d))
4.8b	(/ h (* l (/ (* 2 d) (* M D))))
4.7b	(sqrt (- 1 (* (/ h (* l (/ (* 2 d) (* M D)))) (/ (* M D) (* 2 d)))))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

1519×	`times-frac`
1482×	`add-sqr-sqrt`
1042×	`associate-r`
671×	`*-un-lft-identity`
629×	`add-cube-cbrt`
464×	`associate-l`
402×	`unswap-sqr`
197×	`associate-/r*`
154×	`*-commutative`
77×	`sqrt-prod`
72×	`difference-of-squares`
53×	`add-cbrt-cube` `add-exp-log`
41×	`associate-/l*`
30×	`associate-/r/`
27×	`associate-*r/`
18×	`cbrt-undiv` `div-exp`
17×	`prod-exp` `cbrt-unprod`
7×	`div-inv`
5×	`pow1` `clear-num`
4×	`expm1-log1p-u` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv`
2×	`sqrt-div` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Calls

4 calls:

Slowest

2.1s	(sqrt (- 1 (* (/ h (* l (/ (* 2 d) (* M D)))) (/ (* M D) (* 2 d)))))
80.0ms	(/ h (* l (/ (* 2 d) (* M D))))
25.0ms	(/ (* M D) (* 2 d))
22.0ms	(/ (* 2 d) (* M D))

series425.0ms

Calls

4 calls:

Slowest

249.0ms	(sqrt (- 1 (* (/ h (* l (/ (* 2 d) (* M D)))) (/ (* M D) (* 2 d)))))
105.0ms	(/ h (* l (/ (* 2 d) (* M D))))
39.0ms	(/ (* 2 d) (* M D))
32.0ms	(/ (* M D) (* 2 d))

simplify4.2m

Calls

1886 calls:

Slowest

10.9s	(/ 1 (* l (/ (sqrt (* 2 d)) (* (sqrt M) (sqrt D)))))
10.7s	(/ (cbrt h) (/ (* (sqrt 2) (sqrt d)) D))
1.6s	(/ (* (* h h) h) (* (* (* l l) l) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* (* M D) (* M D)) (* M D)))))
1.5s	(/ (* (* h h) h) (* (* (* l l) l) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* (* M D) (* M D)) (* M D)))))
1.5s	(/ (* (* h h) h) (* (* (* l l) l) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* (* M M) M) (* (* D D) D)))))

prune19.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.5b

localize42.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ (* 2 d) (* D M))
5.4b	(/ (* 2 d) (* D M))
4.8b	(/ h (* l (/ (* 2 d) (* D M))))
4.7b	(pow (- 1 (/ (/ h (* l (/ (* 2 d) (* D M)))) (/ (* 2 d) (* D M)))) (/ 1 2))

rewrite16.9s

Algorithm

rewrite-expression-head

Rules

1598×	`times-frac`
1488×	`add-sqr-sqrt`
1042×	`associate-r`
676×	`*-un-lft-identity`
636×	`add-cube-cbrt`
463×	`associate-l`
332×	`unswap-sqr`
197×	`associate-/r*`
154×	`*-commutative`
76×	`unpow-prod-down`
72×	`difference-of-squares`
54×	`add-exp-log`
53×	`add-cbrt-cube`
41×	`associate-/l*`
30×	`associate-/r/`
27×	`associate-*r/`
18×	`cbrt-undiv` `div-exp`
17×	`prod-exp` `cbrt-unprod`
13×	`pow-unpow`
8×	`div-inv`
5×	`pow1` `clear-num`
4×	`expm1-log1p-u` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out--` `sqr-pow`

Calls

4 calls:

Slowest

16.7s	(pow (- 1 (/ (/ h (* l (/ (* 2 d) (* D M)))) (/ (* 2 d) (* D M)))) (/ 1 2))
85.0ms	(/ h (* l (/ (* 2 d) (* D M))))
28.0ms	(/ (* 2 d) (* D M))
18.0ms	(/ (* 2 d) (* D M))

series608.0ms

Calls

4 calls:

Slowest

418.0ms	(pow (- 1 (/ (/ h (* l (/ (* 2 d) (* D M)))) (/ (* 2 d) (* D M)))) (/ 1 2))
98.0ms	(/ h (* l (/ (* 2 d) (* D M))))
47.0ms	(/ (* 2 d) (* D M))
44.0ms	(/ (* 2 d) (* D M))