Details

sample102.0ms

Algorithm

intervals

Results

62.0ms	290×	body	80	valid
16.0ms	96×	body	80	nan

simplify920.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2071
4	2071
3	592
2	95
1	38
0	17

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize37.0ms

Local error

Found 4 expressions with local error:

3.7b	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
7.4b	(/ (* M D) (* 2 d))
7.4b	(/ (* M D) (* 2 d))
13.5b	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

368×	`add-cbrt-cube` `add-exp-log`
190×	`prod-exp` `cbrt-unprod`
114×	`cbrt-undiv` `div-exp`
16×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
10×	`pow1`
5×	`frac-times` `associate-*l/`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `associate-*r/` `sqrt-prod` `div-inv`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-/l` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l` `*-commutative` `flip--`

Counts

4 → 198

Calls

4 calls:

8.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
21.0ms	(/ (* M D) (* 2 d))
22.0ms	(/ (* M D) (* 2 d))
223.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series353.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
47.0ms	(/ (* M D) (* 2 d))
52.0ms	(/ (* M D) (* 2 d))
91.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify1.1s

Counts

210 → 210

Iterations

Iter	Nodes
done	2000
2	2000
1	961
0	321

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize60.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
3.7b	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))) (/ (cbrt h) (cbrt l)))))
4.9b	(/ M (/ 2 (/ D d)))
4.9b	(/ M (/ 2 (/ D d)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

1204×	`times-frac`
637×	`add-sqr-sqrt`
550×	`*-un-lft-identity` `add-cube-cbrt`
137×	`associate-r`
88×	`associate-/r*`
54×	`add-exp-log`
52×	`cbrt-prod`
48×	`div-inv`
46×	`add-cbrt-cube`
40×	`associate-l`
28×	`cbrt-undiv` `div-exp`
20×	`unswap-sqr`
14×	`associate-/r/`
8×	`prod-exp` `cbrt-unprod`
7×	`pow1`
6×	`associate-/l*`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 636

Calls

4 calls:

36.0ms	(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
4.0ms	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))) (/ (cbrt h) (cbrt l)))))
9.0ms	(/ M (/ 2 (/ D d)))
8.0ms	(/ M (/ 2 (/ D d)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
183.0ms	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))) (/ (cbrt h) (cbrt l)))))
55.0ms	(/ M (/ 2 (/ D d)))
41.0ms	(/ M (/ 2 (/ D d)))

simplify1.6s

Counts

648 → 648

Iterations

Iter	Nodes
done	2000
1	2000
0	756

prune6.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize94.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))
3.2b	(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
3.7b	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))))
4.9b	(/ M (/ 2 (/ D d)))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

5897×	`add-exp-log`
3281×	`add-cbrt-cube`
2688×	`cbrt-undiv` `div-exp`
2670×	`prod-exp` `cbrt-unprod`
844×	`times-frac`
477×	`add-sqr-sqrt`
390×	`*-un-lft-identity` `add-cube-cbrt`
177×	`associate-r`
88×	`cbrt-prod`
50×	`frac-times`
44×	`associate-/r*`
41×	`associate-l`
38×	`associate-*l/`
32×	`div-inv`
25×	`pow1`
24×	`associate-*r/`
20×	`unswap-sqr`
14×	`pow-prod-down`
9×	`associate-/r/`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-prod` `associate-/l*`
2×	`sqrt-div` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 1573

Calls

4 calls:

1.7s	(* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))
46.0ms	(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
5.0ms	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))))
8.0ms	(/ M (/ 2 (/ D d)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))
264.0ms	(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
197.0ms	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))))
67.0ms	(/ M (/ 2 (/ D d)))

simplify4.0s

Counts

1585 → 1585

Iterations

Iter	Nodes
done	2614
0	2614

prune22.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize169.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (sqrt (- 1 (* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l))))) w0)
2.2b	(/ (cbrt M) (/ 2 (/ D (cbrt d))))
2.5b	(* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))
3.7b	(sqrt (- 1 (* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))))

rewrite13.9s

Algorithm

rewrite-expression-head

Rules

315835×	`add-exp-log`
157104×	`div-exp`
149615×	`prod-exp`
34071×	`add-cbrt-cube`
31920×	`cbrt-undiv`
30159×	`cbrt-unprod`
12064×	`rec-exp` `1-exp`
1302×	`times-frac`
616×	`add-sqr-sqrt`
611×	`*-un-lft-identity` `add-cube-cbrt`
441×	`cbrt-prod`
129×	`frac-times`
103×	`associate-*l/`
71×	`associate-/r*`
47×	`associate-*r/`
43×	`associate-r`
36×	`pow1`
30×	`div-inv`
23×	`pow-prod-down`
8×	`associate-/r/`
7×	`associate-l` `sqrt-prod`
6×	`associate-/l*`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`flip3--` `*-commutative` `flip--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 26322

Calls

4 calls:

13.0ms	(* (sqrt (- 1 (* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l))))) w0)
9.0ms	(/ (cbrt M) (/ 2 (/ D (cbrt d))))
5.6s	(* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))
4.0ms	(sqrt (- 1 (* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

384.0ms	(* (sqrt (- 1 (* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l))))) w0)
123.0ms	(/ (cbrt M) (/ 2 (/ D (cbrt d))))
269.0ms	(* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))
255.0ms	(sqrt (- 1 (* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))))

simplify1.5m

Counts

26334 → 26334

Iterations

Iter	Nodes
done	40504
0	40504

prune6.2m

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

regimes1.1s

Accuracy

0% (1.0b remaining)

Error of 7.5b against oracle of 6.6b and baseline of 7.5b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	45
1	45
0	36

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s	9348×	body	80	valid
341.0ms	2943×	body	80	nan