Details

sample32.0ms

Algorithm

intervals

Results

10.0ms	287×	body	80	valid
3.0ms	93×	body	80	nan

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7
done	115	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
8.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.8b	(sqrt (- (* z z) (* t a)))

rewrite66.0ms

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:

7.0ms	(- (* z z) (* t a))
16.0ms	(* (* x y) z)
32.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
8.0ms	(sqrt (- (* z z) (* t a)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* z z) (* t a))
24.0ms	(* (* x y) z)
92.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5002	510
done	5002	510

prune229.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.0b	(- (* z z) (* t a))
3.8b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.8b	(sqrt (- (* z z) (* t a)))

rewrite60.0ms

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:

19.0ms	(/ (sqrt (- (* z z) (* t a))) z)
8.0ms	(- (* z z) (* t a))
20.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
9.0ms	(sqrt (- (* z z) (* t a)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (sqrt (- (* z z) (* t a))) z)
38.0ms	(- (* z z) (* t a))
91.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify67.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	519	1327
1	2380	1230
2	5001	1214
done	5001	1214

prune542.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
1.5b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.0b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
24.8b	(sqrt (- (* z z) (* t a)))

rewrite98.0ms

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:

8.0ms	(- (* z z) (* t a))
17.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
50.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
9.0ms	(sqrt (- (* z z) (* t a)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* z z) (* t a))
61.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
91.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify100.0ms

Counts

239 → 239

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	817	2502
1	4005	2347
2	5002	2347
done	5002	2347

prune569.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* x y) (/ (sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a))))) z))
24.8b	(sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a)))))
24.8b	(sqrt (- (* z z) (* t a)))
24.8b	(sqrt (- (* z z) (* t a)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
24×	`add-sqr-sqrt` `sqrt-pow1` `sqrt-div`
22×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
13×	`sqrt-prod`
11×	`pow1/2`
8×	`flip3--` `flip--`
6×	`cbrt-undiv` `div-exp`
5×	`pow-prod-up`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square` `pow-prod-down` `pow-sqr` `div-inv`
2×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 114

Calls

4 calls:

25.0ms	(/ (* x y) (/ (sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a))))) z))
26.0ms	(sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a)))))
8.0ms	(sqrt (- (* z z) (* t a)))
9.0ms	(sqrt (- (* z z) (* t a)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (* x y) (/ (sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a))))) z))
60.0ms	(sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a)))))
64.0ms	(sqrt (- (* z z) (* t a)))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify66.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	508	1338
1	2187	1102
2	5002	1089
done	5002	1089

prune317.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.4b

regimes385.0ms

Accuracy

86% (2.8b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 23.2b

bsearch75.0ms

Steps

Iters	Range		Point
9	3.0509751148851044e+144	4.046094989899507e+150	1.874715117526438e+146
8	-1.693909364183909e+121	-1.1368421250931169e+117	-6.341587143310156e+119

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	32	10
2	32	10
done	32	10

end0.0ms

sample891.0ms

Algorithm

intervals

Results

322.0ms	8900×	body	80	valid
89.0ms	2959×	body	80	nan