Details

sample39.0ms

Algorithm

intervals

Results

14.0ms	285×	body	80	valid
4.0ms	82×	body	80	nan

simplify87.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	103
6	103
5	97
4	70
3	53
2	36
1	21
0	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
5.0b	(* (* x y) z)
8.3b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

13.0ms	(- (* z z) (* t a))
27.0ms	(* (* x y) z)
57.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
16.0ms	(sqrt (- (* z z) (* t a)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* z z) (* t a))
37.0ms	(* (* x y) z)
151.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
127.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1403
1	359
0	134

prune477.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.8b	(- (* z z) (* t a))
2.2b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

18.0ms	(/ (sqrt (- (* z z) (* t a))) z)
7.0ms	(- (* z z) (* t a))
19.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
8.0ms	(sqrt (- (* z z) (* t a)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (sqrt (- (* z z) (* t a))) z)
58.0ms	(- (* z z) (* t a))
207.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
103.0ms	(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1895
1	557
0	210

prune929.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.5b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.7b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

263×	`times-frac`
157×	`add-sqr-sqrt`
143×	`*-un-lft-identity` `add-cube-cbrt`
71×	`associate-r`
67×	`sqrt-prod`
22×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
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×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 227

Calls

4 calls:

12.0ms	(- (* z z) (* t a))
58.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
20.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* z z) (* t a))
161.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
110.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
101.0ms	(sqrt (- (* z z) (* t a)))

simplify2.3s

Counts

239 → 239

Iterations

Iter	Nodes
done	5013
2	3144
1	932
0	330

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.7b	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
2.0b	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 433

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
21.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
47.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
16.0ms	(sqrt (- (* z z) (* t a)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* z z) (* t a))
125.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
180.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
115.0ms	(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts

445 → 445

Iterations

Iter	Nodes
done	5002
1	1785
0	655

prune3.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.8b

regimes1.3s

Accuracy

77.7% (4.3b remaining)

Error of 7.7b against oracle of 3.4b and baseline of 22.9b

bsearch141.0ms

Steps

Iters	Range		Point
8	6.89875157706557e+88	4.6365785633703446e+92	5.930939844067446e+90
9	-6.325039929345352e+73	-7.299257252973953e+68	-2.8854075548046605e+71

simplify10.0ms

Iterations

Iter	Nodes
done	30
2	30
1	28
0	21

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.3s	8854×	body	80	valid
231.0ms	2985×	body	80	nan