Details

sample45.0ms

Algorithm

intervals

Results

18.0ms	273×	body	80	valid
4.0ms	93×	body	80	nan

simplify73.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
11.1b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite83.0ms

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:

10.0ms	(- (* z z) (* t a))
19.0ms	(* (* x y) z)
39.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms	(sqrt (- (* z z) (* t a)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* z z) (* t a))
41.0ms	(* (* x y) z)
118.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
75.0ms	(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts

98 → 98

Iterations

Useful iterations: done (1.4s)

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

prune348.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize22.0ms

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))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite86.0ms

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:

24.0ms	(/ (sqrt (- (* z z) (* t a))) z)
10.0ms	(- (* z z) (* t a))
23.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
19.0ms	(sqrt (- (* z z) (* t a)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (sqrt (- (* z z) (* t a))) z)
57.0ms	(- (* z z) (* t a))
134.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
113.0ms	(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts

154 → 154

Iterations

Useful iterations: done (1.6s)

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

prune653.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

1.8b	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
24.6b	(sqrt (- (* z z) (* t a)))
24.6b	(sqrt (- (* z z) (* t a)))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`cbrt-prod`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
7×	`pow1`
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-div` `pow1/3` `div-inv`

Counts

4 → 84

Calls

4 calls:

7.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
16.0ms	(sqrt (- (* z z) (* t a)))
20.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
85.0ms	(sqrt (- (* z z) (* t a)))
95.0ms	(sqrt (- (* z z) (* t a)))
90.0ms	(sqrt (- (* z z) (* t a)))

simplify3.9s

Counts

96 → 96

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	147	1536
1	287	1394
2	675	1320
3	1617	1310
4	3884	1303
done	5000	1301

prune623.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
1.0b	(- (* z z) (* t a))
2.6b	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite162.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/r/` `associate-/l/`

Counts

4 → 443

Calls

4 calls:

31.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
10.0ms	(- (* z z) (* t a))
60.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
15.0ms	(sqrt (- (* z z) (* t a)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
50.0ms	(- (* z z) (* t a))
126.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
81.0ms	(sqrt (- (* z z) (* t a)))

simplify2.9s

Counts

455 → 455

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	668	12395
1	1540	11376
2	4792	10963
done	5002	10962

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

regimes458.0ms

Accuracy

84.2% (3.0b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 22.0b

bsearch99.0ms

Steps

Iters	Range		Point
8	7.3012733596749945e+62	1.421506626309928e+66	1.1880731543996549e+66
4	-5.8187113216689725e+144	-3.7837750553294994e+144	-5.373569013407213e+144

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	57
1	32	57
2	34	57
done	34	57

end0.0ms

sample2.0s

Algorithm

intervals

Results

725.0ms	8880×	body	80	valid
225.0ms	2902×	body	80	nan