Details

sample43.0ms

Algorithm

intervals

Results

15.0ms	282×	body	80	valid
4.0ms	91×	body	80	nan

simplify82.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	22	14
2	46	14
3	72	14
4	97	14
5	112	14
done	112	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
7.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite137.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-l` `prod-diff` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

19.0ms	(- (* z z) (* t a))
39.0ms	(* (* x y) z)
41.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
30.0ms	(sqrt (- (* z z) (* t a)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* z z) (* t a))
27.0ms	(* (* x y) z)
146.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
82.0ms	(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	146	1331
1	361	1220
2	1560	1062
done	5001	1060

prune428.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.4b	(- (* z z) (* t a))
4.1b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite111.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `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` `fma-neg` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 142

Calls

4 calls:

30.0ms	(/ (sqrt (- (* z z) (* t a))) z)
20.0ms	(- (* z z) (* t a))
33.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.0ms	(sqrt (- (* z z) (* t a)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (sqrt (- (* z z) (* t a))) z)
63.0ms	(- (* z z) (* t a))
151.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
97.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

154 → 154

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	222	2758
1	522	2513
2	1693	2314
done	5001	2309

prune633.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.3b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.2b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite162.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 237

Calls

4 calls:

13.0ms	(- (* z z) (* t a))
31.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
90.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
13.0ms	(sqrt (- (* z z) (* t a)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* z z) (* t a))
77.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
127.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
77.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

249 → 249

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	342	4983
1	802	4462
2	2341	4239
done	5001	4235

prune912.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

localize63.0ms

Local error

Found 4 expressions with local error:

9.4b	(cbrt (* x (/ y (/ (sqrt (- (* z z) (* t a))) z))))
22.9b	(sqrt (- (* z z) (* t a)))
22.9b	(sqrt (- (* z z) (* t a)))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*r/`

Counts

4 → 63

Calls

4 calls:

28.0ms	(cbrt (* x (/ y (/ (sqrt (- (* z z) (* t a))) z))))
24.0ms	(sqrt (- (* z z) (* t a)))
24.0ms	(sqrt (- (* z z) (* t a)))
25.0ms	(sqrt (- (* z z) (* t a)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt (* x (/ y (/ (sqrt (- (* z z) (* t a))) z))))
100.0ms	(sqrt (- (* z z) (* t a)))
122.0ms	(sqrt (- (* z z) (* t a)))
82.0ms	(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts

75 → 75

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	117	1065
1	274	966
2	740	882
3	2092	873
done	5001	856

prune451.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.4b

regimes589.0ms

Accuracy

86.1% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 23.0b

bsearch138.0ms

Steps

Iters	Range		Point
9	6.663579023451854e+147	9.351805393147033e+156	1.9720317117511606e+149
7	-7.495622944610967e+154	-1.314778648009767e+153	-1.6391293784153955e+153

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	29
1	27	29
2	29	29
done	29	29

end0.0ms

sample2.5s

Algorithm

intervals

Results

857.0ms	8845×	body	80	valid
226.0ms	3033×	body	80	nan