Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	280×	body	80	valid
3.0ms	93×	body	80	nan

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	14
1	21	14
2	44	14
3	65	14
4	89	14
5	102	14
done	102	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
4.0b	(* (* x y) z)
8.5b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.0b	(sqrt (- (* z z) (* t a)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

2.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
11.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
82.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify527.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (156.0ms)

Iter	Nodes	Cost
0	134	1237
1	343	1135
2	1586	975
done	5001	975

prune232.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.0b	(- (* z z) (* t a))
2.4b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.0b	(sqrt (- (* z z) (* t a)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

7.0ms	(/ (sqrt (- (* z z) (* t a))) z)
2.0ms	(- (* z z) (* t a))
12.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (sqrt (- (* z z) (* t a))) z)
36.0ms	(- (* z z) (* t a))
78.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify607.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (238.0ms)

Iter	Nodes	Cost
0	210	2654
1	517	2421
2	1729	2227
done	5001	2227

prune363.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.3b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
1.0b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.0b	(- (* z z) (* t a))
22.0b	(sqrt (- (* z z) (* t a)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

263×	`times-frac`
157×	`add-sqr-sqrt`
143×	`add-cube-cbrt` `*-un-lft-identity`
71×	`associate-r`
67×	`sqrt-prod`
22×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`unswap-sqr`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 227

Calls

4 calls:

11.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
33.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
2.0ms	(- (* z z) (* t a))
4.0ms	(sqrt (- (* z z) (* t a)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
81.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
37.0ms	(- (* z z) (* t a))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify972.0ms

Counts

239 → 239

Iterations

Useful iterations: 2 (318.0ms)

Iter	Nodes	Cost
0	330	4875
1	815	4362
2	2357	4138
done	5001	4138

prune564.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
1.0b	(- (* z z) (* t a))
1.3b	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
22.0b	(sqrt (- (* z z) (* t a)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

828×	`times-frac`
400×	`add-sqr-sqrt`
399×	`add-cube-cbrt` `*-un-lft-identity`
147×	`sqrt-prod`
73×	`associate-/r*`
25×	`associate-/l*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`

Counts

4 → 433

Calls

4 calls:

12.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
3.0ms	(- (* z z) (* t a))
20.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
4.0ms	(sqrt (- (* z z) (* t a)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
36.0ms	(- (* z z) (* t a))
83.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify1.2s

Counts

445 → 445

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	656	12287
1	1623	11278
done	5001	11030

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.3b

regimes344.0ms

Accuracy

84.6% (2.9b remaining)

Error of 6.2b against oracle of 3.3b and baseline of 22.3b

bsearch83.0ms

Steps

Iters	Range		Point
7	4.43464859477407e+147	1.5123157394476474e+149	6.926066888201142e+147
9	-2.7283838574175814e+156	-2.1161453073457986e+149	-8.618354790122042e+153

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	29
1	26	29
2	29	29
done	29	29

end0.0ms

sample811.0ms

Algorithm

intervals

Results

352.0ms	8864×	body	80	valid
106.0ms	2952×	body	80	nan