Details

sample77.0ms

Algorithm

intervals

Results

25.0ms	273×	body	80	valid
8.0ms	93×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize18.0ms

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)))

rewrite94.0ms

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:

9.0ms	(- (* z z) (* t a))
21.0ms	(* (* x y) z)
52.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms	(sqrt (- (* z z) (* t a)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* z z) (* t a))
33.0ms	(* (* x y) z)
138.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
103.0ms	(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts

88 → 88

Iterations

Useful iterations: done (1.5s)

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

prune378.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize13.0ms

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×	`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)
14.0ms	(- (* z z) (* t a))
36.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
10.0ms	(sqrt (- (* z z) (* t a)))

series758.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (sqrt (- (* z z) (* t a))) z)
42.0ms	(- (* z z) (* t a))
122.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
480.0ms	(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

prune456.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize29.0ms

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)))

rewrite48.0ms

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` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 76

Calls

4 calls:

9.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
14.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))
10.0ms	(sqrt (- (* z z) (* t a)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
66.0ms	(sqrt (- (* z z) (* t a)))
71.0ms	(sqrt (- (* z z) (* t a)))
78.0ms	(sqrt (- (* z z) (* t a)))

simplify2.7s

Counts

88 → 88

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	143	1458
1	274	1328
2	627	1252
3	1441	1246
4	3407	1238
done	5001	1236

prune562.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize19.0ms

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)))

rewrite141.0ms

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`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`

Counts

4 → 433

Calls

4 calls:

33.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
9.0ms	(- (* z z) (* t a))
51.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
10.0ms	(sqrt (- (* z z) (* t a)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
59.0ms	(- (* z z) (* t a))
147.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
115.0ms	(sqrt (- (* z z) (* t a)))

simplify3.1s

Counts

445 → 445

Iterations

Useful iterations: 2 (2.0s)

Iter	Nodes	Cost
0	656	12287
1	1519	11278
2	4751	10862
done	5002	10862

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

regimes505.0ms

Accuracy

84.2% (3.0b remaining)

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

bsearch73.0ms

Steps

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

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	57
1	32	57
2	34	57
done	34	57

end0.0ms

sample2.0s

Algorithm

intervals

Results

607.0ms	8880×	body	80	valid
151.0ms	2902×	body	80	nan