Details

sample152.0ms

Algorithm

intervals

Results

86.0ms	308×	body	80	valid
29.0ms	123×	body	80	nan

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	592
2	95
1	38
0	17

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize54.0ms

Local error

Found 4 expressions with local error:

5.3b	(/ d (/ (* M D) 2))
5.3b	(/ d (/ (* M D) 2))
5.9b	(sqrt (- 1 (/ (/ (/ h l) (/ d (/ (* M D) 2))) (/ d (/ (* M D) 2)))))
10.4b	(/ (/ h l) (/ d (/ (* M D) 2)))

rewrite655.0ms

Algorithm

rewrite-expression-head

Rules

1129×	`times-frac`
518×	`add-sqr-sqrt`
435×	`*-un-lft-identity`
422×	`add-cube-cbrt`
94×	`div-inv`
54×	`add-cbrt-cube` `add-exp-log`
40×	`associate-/r*`
32×	`cbrt-undiv` `div-exp`
26×	`sqrt-prod`
22×	`difference-of-squares`
19×	`associate-/l*`
17×	`associate-/r/`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 543

Calls

4 calls:

7.0ms	(/ d (/ (* M D) 2))
7.0ms	(/ d (/ (* M D) 2))
598.0ms	(sqrt (- 1 (/ (/ (/ h l) (/ d (/ (* M D) 2))) (/ d (/ (* M D) 2)))))
24.0ms	(/ (/ h l) (/ d (/ (* M D) 2)))

series814.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ d (/ (* M D) 2))
47.0ms	(/ d (/ (* M D) 2))
596.0ms	(sqrt (- 1 (/ (/ (/ h l) (/ d (/ (* M D) 2))) (/ d (/ (* M D) 2)))))
120.0ms	(/ (/ h l) (/ d (/ (* M D) 2)))

simplify2.4s

Counts

555 → 555

Iterations

Iter	Nodes
done	5000
1	3158
0	989

prune5.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.8b

localize72.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))) (/ (/ d (/ (* M D) 2)) (/ (cbrt h) (cbrt l))))
5.3b	(/ d (/ (* M D) 2))
5.3b	(/ d (/ (* M D) 2))
5.9b	(sqrt (- 1 (/ (/ (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))) (/ (/ d (/ (* M D) 2)) (/ (cbrt h) (cbrt l)))) (/ d (/ (* M D) 2)))))

rewrite14.4s

Algorithm

rewrite-expression-head

Rules

25847×	`times-frac`
8857×	`add-sqr-sqrt`
8398×	`*-un-lft-identity`
8349×	`add-cube-cbrt`
5680×	`cbrt-prod`
2179×	`div-inv`
1059×	`associate-/r*`
304×	`add-exp-log`
249×	`associate-/r/`
201×	`cbrt-undiv` `div-exp`
192×	`add-cbrt-cube`
98×	`sqrt-prod`
94×	`difference-of-squares`
48×	`prod-exp` `cbrt-unprod`
11×	`associate-/l*`
5×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 6587

Calls

4 calls:

45.0ms	(/ (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))) (/ (/ d (/ (* M D) 2)) (/ (cbrt h) (cbrt l))))
7.0ms	(/ d (/ (* M D) 2))
7.0ms	(/ d (/ (* M D) 2))
13.9s	(sqrt (- 1 (/ (/ (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))) (/ (/ d (/ (* M D) 2)) (/ (cbrt h) (cbrt l)))) (/ d (/ (* M D) 2)))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))) (/ (/ d (/ (* M D) 2)) (/ (cbrt h) (cbrt l))))
31.0ms	(/ d (/ (* M D) 2))
29.0ms	(/ d (/ (* M D) 2))
202.0ms	(sqrt (- 1 (/ (/ (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))) (/ (/ d (/ (* M D) 2)) (/ (cbrt h) (cbrt l)))) (/ d (/ (* M D) 2)))))

simplify12.4s

Counts

6599 → 6599

Iterations

Iter	Nodes
done	10944
0	10944

prune1.5m

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.8b

localize115.0ms

Local error

Found 4 expressions with local error:

5.9b	(sqrt (- 1 (/ (* (/ (* (cbrt h) (cbrt h)) (/ (* (cbrt (/ d (/ (* M D) 2))) (cbrt (/ d (/ (* M D) 2)))) (* (cbrt (/ (cbrt h) (cbrt l))) (cbrt (/ (cbrt h) (cbrt l)))))) (/ (/ 1 (* (cbrt l) (cbrt l))) (/ (cbrt (/ d (/ (* M D) 2))) (cbrt (/ (cbrt h) (cbrt l)))))) (/ d (/ (* M D) 2)))))
17.1b	(cbrt (/ d (/ (* M D) 2)))
17.1b	(cbrt (/ d (/ (* M D) 2)))
17.1b	(cbrt (/ d (/ (* M D) 2)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
78×	`cbrt-prod`
51×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
47×	`add-cube-cbrt`
12×	`div-inv`
6×	`sqrt-prod`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-/r/`
2×	`sqrt-div` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--` `distribute-lft-out--`

Counts

4 → 127

Calls

4 calls:

31.0ms	(sqrt (- 1 (/ (* (/ (* (cbrt h) (cbrt h)) (/ (* (cbrt (/ d (/ (* M D) 2))) (cbrt (/ d (/ (* M D) 2)))) (* (cbrt (/ (cbrt h) (cbrt l))) (cbrt (/ (cbrt h) (cbrt l)))))) (/ (/ 1 (* (cbrt l) (cbrt l))) (/ (cbrt (/ d (/ (* M D) 2))) (cbrt (/ (cbrt h) (cbrt l)))))) (/ d (/ (* M D) 2)))))
6.0ms	(cbrt (/ d (/ (* M D) 2)))
15.0ms	(cbrt (/ d (/ (* M D) 2)))
6.0ms	(cbrt (/ d (/ (* M D) 2)))

series954.0ms

Counts

4 → 12

Calls

4 calls:

492.0ms	(sqrt (- 1 (/ (* (/ (* (cbrt h) (cbrt h)) (/ (* (cbrt (/ d (/ (* M D) 2))) (cbrt (/ d (/ (* M D) 2)))) (* (cbrt (/ (cbrt h) (cbrt l))) (cbrt (/ (cbrt h) (cbrt l)))))) (/ (/ 1 (* (cbrt l) (cbrt l))) (/ (cbrt (/ d (/ (* M D) 2))) (cbrt (/ (cbrt h) (cbrt l)))))) (/ d (/ (* M D) 2)))))
150.0ms	(cbrt (/ d (/ (* M D) 2)))
160.0ms	(cbrt (/ d (/ (* M D) 2)))
152.0ms	(cbrt (/ d (/ (* M D) 2)))

simplify3.4s

Counts

139 → 139

Iterations

Iter	Nodes
done	5003
2	1045
1	394
0	211

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.2b

localize117.0ms

Local error

Found 4 expressions with local error:

5.9b	(sqrt (- 1 (* (/ (/ (cbrt h) (/ (cbrt (* (/ d D) (/ 2 M))) (cbrt (/ (cbrt h) (cbrt l))))) (* (/ d D) (/ 2 M))) (/ (/ (cbrt h) (/ (cbrt (* (/ d D) (/ 2 M))) (cbrt (/ (cbrt h) (cbrt l))))) (* (/ (cbrt (* (/ d D) (/ 2 M))) (cbrt (/ (cbrt h) (cbrt l)))) (* (cbrt l) (cbrt l)))))))
17.1b	(cbrt (* (/ d D) (/ 2 M)))
17.1b	(cbrt (* (/ d D) (/ 2 M)))
17.1b	(cbrt (* (/ d D) (/ 2 M)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-div`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-l/` `associate-r/` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 55

Calls

4 calls:

4.0ms	(sqrt (- 1 (* (/ (/ (cbrt h) (/ (cbrt (* (/ d D) (/ 2 M))) (cbrt (/ (cbrt h) (cbrt l))))) (* (/ d D) (/ 2 M))) (/ (/ (cbrt h) (/ (cbrt (* (/ d D) (/ 2 M))) (cbrt (/ (cbrt h) (cbrt l))))) (* (/ (cbrt (* (/ d D) (/ 2 M))) (cbrt (/ (cbrt h) (cbrt l)))) (* (cbrt l) (cbrt l)))))))
5.0ms	(cbrt (* (/ d D) (/ 2 M)))
5.0ms	(cbrt (* (/ d D) (/ 2 M)))
6.0ms	(cbrt (* (/ d D) (/ 2 M)))

series916.0ms

Counts

4 → 12

Calls

4 calls:

437.0ms	(sqrt (- 1 (* (/ (/ (cbrt h) (/ (cbrt (* (/ d D) (/ 2 M))) (cbrt (/ (cbrt h) (cbrt l))))) (* (/ d D) (/ 2 M))) (/ (/ (cbrt h) (/ (cbrt (* (/ d D) (/ 2 M))) (cbrt (/ (cbrt h) (cbrt l))))) (* (/ (cbrt (* (/ d D) (/ 2 M))) (cbrt (/ (cbrt h) (cbrt l)))) (* (cbrt l) (cbrt l)))))))
155.0ms	(cbrt (* (/ d D) (/ 2 M)))
154.0ms	(cbrt (* (/ d D) (/ 2 M)))
170.0ms	(cbrt (* (/ d D) (/ 2 M)))

simplify2.9s

Counts

67 → 67

Iterations

Iter	Nodes
done	5005
2	694
1	214
0	109

prune771.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 9.2b

regimes1.5s

Accuracy

0% (1.2b remaining)

Error of 8.1b against oracle of 6.9b and baseline of 8.1b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	39
1	39
0	31

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.0s	9316×	body	80	valid
663.0ms	3118×	body	80	nan