Details

sample81.0ms

Algorithm

intervals

Results

48.0ms	285×	body	80	valid
15.0ms	91×	body	80	nan

simplify70.0ms

Calls

1 calls:

Slowest

69.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize30.0ms

Local error

Found 4 expressions with local error:

12.7b	(* (pow (/ (* M D) (* 2 d)) 2) (/ h l))
4.7b	(/ (* M D) (* 2 d))
2.8b	(sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))
1.9b	(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
10×	`associate-r`
10×	`*-un-lft-identity`
9×	`associate-l`
8×	`add-cbrt-cube`
6×	`sqrt-prod`
5×	`unpow-prod-down`
4×	`add-log-exp`
4×	`prod-exp`
4×	`sqrt-div`
4×	`pow1`
3×	`div-inv`
3×	`associate-*r/`
2×	`flip--`
2×	`*-commutative`
2×	`pow-exp`
2×	`div-exp`
2×	`flip3--`
2×	`times-frac`
1×	`unpow2`
1×	`associate-/l*`
1×	`cbrt-unprod`
1×	`pow1/2`
1×	`frac-2neg`
1×	`associate-/r*`
1×	`clear-num`
1×	`rem-sqrt-square`
1×	`cbrt-undiv`
1×	`pow-to-exp`

Calls

4 calls:

Slowest

8.0ms	(* (pow (/ (* M D) (* 2 d)) 2) (/ h l))
2.0ms	(/ (* M D) (* 2 d))
2.0ms	(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))
1.0ms	(sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))

series358.0ms

Calls

4 calls:

Slowest

167.0ms	(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))
117.0ms	(sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))
58.0ms	(* (pow (/ (* M D) (* 2 d)) 2) (/ h l))
15.0ms	(/ (* M D) (* 2 d))

simplify4.2s

Calls

47 calls:

Slowest

675.0ms	(sqrt (+ 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))
464.0ms	(sqrt (cbrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))
398.0ms	(+ (log (pow (/ (* M D) (* 2 d)) 2)) (log (/ h l)))
224.0ms	(+ (* (- (log (* M D)) (log (* 2 d))) 2) (log (/ h l)))
214.0ms	(* (cbrt (pow (/ (* M D) (* 2 d)) 2)) (cbrt (pow (/ (* M D) (* 2 d)) 2)))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize21.0ms

Local error

Found 4 expressions with local error:

5.2b	(* (pow (/ (* M D) (* 2 d)) 2) h)
4.7b	(/ (* M D) (* 2 d))
4.5b	(/ (* (pow (/ (* M D) (* 2 d)) 2) h) l)
2.8b	(sqrt (- 1 (/ (* (pow (/ (* M D) (* 2 d)) 2) h) l)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-l`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
7×	`*-un-lft-identity`
6×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`unpow-prod-down`
4×	`add-log-exp`
4×	`pow1`
3×	`div-inv`
3×	`sqrt-prod`
2×	`associate-/l*`
2×	`sqrt-div`
2×	`times-frac`
2×	`frac-2neg`
2×	`clear-num`
1×	`unpow2`
1×	`flip--`
1×	`*-commutative`
1×	`div-exp`
1×	`pow1/2`
1×	`flip3--`
1×	`associate-/r*`
1×	`rem-sqrt-square`
1×	`cbrt-undiv`

Calls

4 calls:

Slowest

6.0ms	(* (pow (/ (* M D) (* 2 d)) 2) h)
5.0ms	(/ (* (pow (/ (* M D) (* 2 d)) 2) h) l)
2.0ms	(/ (* M D) (* 2 d))
1.0ms	(sqrt (- 1 (/ (* (pow (/ (* M D) (* 2 d)) 2) h) l)))

series246.0ms

Calls

4 calls:

Slowest

96.0ms	(sqrt (- 1 (/ (* (pow (/ (* M D) (* 2 d)) 2) h) l)))
65.0ms	(/ (* (pow (/ (* M D) (* 2 d)) 2) h) l)
61.0ms	(* (pow (/ (* M D) (* 2 d)) 2) h)
25.0ms	(/ (* M D) (* 2 d))

simplify4.6s

Calls

31 calls:

Slowest

690.0ms	(sqrt (sqrt (- 1 (/ (* (pow (/ (* M D) (* 2 d)) 2) h) l))))
680.0ms	(sqrt (- 1 (/ (* (pow (/ (* M D) (* 2 d)) 2) h) l)))
623.0ms	(sqrt (* (cbrt (- 1 (/ (* (pow (/ (* M D) (* 2 d)) 2) h) l))) (cbrt (- 1 (/ (* (pow (/ (* M D) (* 2 d)) 2) h) l)))))
314.0ms	(* 1/4 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))
281.0ms	(* 1/4 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize18.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* M D) (* 2 d))
4.7b	(/ (* M D) (* 2 d))
4.5b	(/ (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h)) l)
4.4b	(* (/ (* M D) (* 2 d)) h)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log`
8×	`add-cbrt-cube`
5×	`add-cube-cbrt`
5×	`associate-l`
5×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`add-log-exp`
4×	`div-inv`
4×	`associate-*l/`
4×	`pow1`
3×	`associate-/l/`
3×	`associate-/l*`
3×	`times-frac`
3×	`frac-2neg`
3×	`clear-num`
2×	`div-exp`
2×	`associate-/r*`
2×	`cbrt-undiv`
1×	`*-commutative`
1×	`associate-*r/`
1×	`frac-times`

Calls

4 calls:

Slowest

12.0ms	(/ (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h)) l)
4.0ms	(* (/ (* M D) (* 2 d)) h)
3.0ms	(/ (* M D) (* 2 d))
3.0ms	(/ (* M D) (* 2 d))

series118.0ms

Calls

4 calls:

Slowest

55.0ms	(/ (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h)) l)
32.0ms	(* (/ (* M D) (* 2 d)) h)
16.0ms	(/ (* M D) (* 2 d))
15.0ms	(/ (* M D) (* 2 d))

simplify2.5s

Calls

29 calls:

Slowest

453.0ms	(* (* M D) (* (/ (* M D) (* 2 d)) h))
427.0ms	(* (/ (* M D) (* 2 d)) (* (* M D) h))
189.0ms	(* 1/2 (/ (* M (* D h)) d))
189.0ms	(* 1/2 (/ (* M (* D h)) d))
188.0ms	(* 1/2 (/ (* M (* D h)) d))

prune906.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize27.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* M D) (* 2 d))
4.7b	(/ (* M D) (* 2 d))
4.4b	(* (/ (* M D) (* 2 d)) h)
3.8b	(/ l (* (/ (* M D) (* 2 d)) h))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log`
8×	`add-cbrt-cube`
5×	`add-cube-cbrt`
5×	`associate-l`
5×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`add-log-exp`
4×	`div-inv`
4×	`pow1`
3×	`times-frac`
3×	`frac-2neg`
3×	`associate-/r*`
3×	`clear-num`
2×	`associate-/l*`
2×	`associate-*l/`
2×	`div-exp`
2×	`cbrt-undiv`
1×	`*-commutative`
1×	`associate-/r/`

Calls

4 calls:

Slowest

4.0ms	(/ (* M D) (* 2 d))
4.0ms	(* (/ (* M D) (* 2 d)) h)
2.0ms	(/ (* M D) (* 2 d))
1.0ms	(/ l (* (/ (* M D) (* 2 d)) h))

series129.0ms

Calls

4 calls:

Slowest

53.0ms	(/ l (* (/ (* M D) (* 2 d)) h))
34.0ms	(* (/ (* M D) (* 2 d)) h)
25.0ms	(/ (* M D) (* 2 d))
17.0ms	(/ (* M D) (* 2 d))

simplify2.4s

Calls

26 calls:

Slowest

355.0ms	(* 2 (/ (* l d) (* h (* M D))))
302.0ms	(* 2 (/ (* l d) (* h (* M D))))
294.0ms	(* 2 (/ (* l d) (* h (* M D))))
243.0ms	(* 1/2 (/ (* M (* D h)) d))
200.0ms	(* 1/2 (/ (* M (* D h)) d))

prune708.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

regimes1.5s

Accuracy

0% (1.3b remaining)

Error of 8.5b against oracle of 7.2b and baseline of 8.5b

bsearch2.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.1s	9263×	body	80	valid
521.0ms	3130×	body	80	nan