Details

sample51.0ms

Algorithm

intervals

Results

25.0ms	279×	body	80	valid
5.0ms	90×	body	80	nan

simplify92.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	21	14
2	45	14
3	67	14
4	92	14
5	107	14
done	107	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
4.8b	(* (* x y) z)
10.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite117.0ms

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:

8.0ms	(- (* z z) (* t a))
28.0ms	(* (* x y) z)
62.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
17.0ms	(sqrt (- (* z z) (* t a)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* z z) (* t a))
41.0ms	(* (* x y) z)
148.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
102.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

88 → 88

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	134	1237
1	341	1135
2	1495	975
done	5001	974

prune367.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.6b	(- (* z z) (* t a))
2.5b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite100.0ms

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:

26.0ms	(/ (sqrt (- (* z z) (* t a))) z)
13.0ms	(- (* z z) (* t a))
38.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
13.0ms	(sqrt (- (* z z) (* t a)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (sqrt (- (* z z) (* t a))) z)
40.0ms	(- (* z z) (* t a))
109.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
88.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

144 → 144

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	210	2654
1	500	2421
2	1641	2221
done	5000	2218

prune418.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.1b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
2.1b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite148.0ms

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:

15.0ms	(- (* z z) (* t a))
58.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
29.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
17.0ms	(sqrt (- (* z z) (* t a)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* z z) (* t a))
137.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
97.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
117.0ms	(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts

239 → 239

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	330	4875
1	782	4362
2	2270	4138
done	5000	4135

prune857.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
2.5b	(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

671×	`times-frac`
275×	`add-sqr-sqrt`
274×	`add-cube-cbrt` `*-un-lft-identity`
267×	`sqrt-prod`
155×	`associate-/r*`
29×	`associate-/r/`
28×	`sqrt-div`
27×	`add-exp-log` `add-cbrt-cube`
16×	`div-inv`
15×	`flip3--` `flip--`
13×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`associate-/l*`
3×	`prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 390

Calls

4 calls:

28.0ms	(/ z (sqrt (- (* z z) (* t a))))
16.0ms	(- (* z z) (* t a))
81.0ms	(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
30.0ms	(sqrt (- (* z z) (* t a)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ z (sqrt (- (* z z) (* t a))))
52.0ms	(- (* z z) (* t a))
161.0ms	(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
103.0ms	(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts

402 → 402

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	632	10469
1	1514	7928
2	2983	7240
done	5001	7240

prune957.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.3b

regimes482.0ms

Accuracy

85% (2.9b remaining)

Error of 6.1b against oracle of 3.2b and baseline of 22.6b

bsearch118.0ms

Steps

Iters	Range		Point
10	4.3064310246787576e+110	1.1096282980114098e+126	2.811098440010323e+123
9	-5.269798588618117e+155	-1.769171722317776e+149	-1.3870375139541522e+152

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	33
1	29	30
done	29	30

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s	8818×	body	80	valid
291.0ms	3008×	body	80	nan