Details

sample49.0ms

Algorithm

intervals

Results

16.0ms	283×	body	80	valid
6.0ms	98×	body	80	nan

simplify126.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
3.9b	(* (* x y) z)
10.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.2b	(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×	`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:

10.0ms	(- (* z z) (* t a))
37.0ms	(* (* x y) z)
69.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
19.0ms	(sqrt (- (* z z) (* t a)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* z z) (* t a))
42.0ms	(* (* x y) z)
142.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
68.0ms	(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts

88 → 88

Iterations

Useful iterations: done (1.4s)

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

prune341.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
2.4b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

19.0ms	(/ z (sqrt (- (* z z) (* t a))))
8.0ms	(- (* z z) (* t a))
54.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
9.0ms	(sqrt (- (* z z) (* t a)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ z (sqrt (- (* z z) (* t a))))
58.0ms	(- (* z z) (* t a))
128.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
93.0ms	(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts

124 → 124

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	166	2031
1	418	1847
2	1521	1643
done	5000	1642

prune431.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
0.8b	(- (* z z) (* t a))
1.5b	(* y (/ z (sqrt (- (* z z) (* t a)))))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

65.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
8.0ms	(- (* z z) (* t a))
78.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
18.0ms	(sqrt (- (* z z) (* t a)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
37.0ms	(- (* z z) (* t a))
77.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
78.0ms	(sqrt (- (* z z) (* t a)))

simplify2.3s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	161	1572
1	395	1453
2	1147	1241
3	3863	1240
done	5000	1240

prune345.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.8b

localize32.0ms

Local error

Found 4 expressions with local error:

12.7b	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
26.2b	(sqrt (- (* z z) (* t a)))
26.2b	(sqrt (- (* z z) (* t a)))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite72.0ms

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` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`associate-*r/`
1×	`cbrt-prod` `cbrt-div` `pow1/3`

Counts

4 → 55

Calls

4 calls:

43.0ms	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
9.0ms	(sqrt (- (* z z) (* t a)))
9.0ms	(sqrt (- (* z z) (* t a)))
9.0ms	(sqrt (- (* z z) (* t a)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt (* x (* y (/ z (sqrt (- (* z z) (* t a)))))))
67.0ms	(sqrt (- (* z z) (* t a)))
64.0ms	(sqrt (- (* z z) (* t a)))
68.0ms	(sqrt (- (* z z) (* t a)))

simplify2.9s

Counts

67 → 67

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	113	979
1	266	892
2	700	806
3	1895	800
4	4898	782
done	5001	782

prune364.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.8b

regimes496.0ms

Accuracy

87.3% (2.5b remaining)

Error of 6.0b against oracle of 3.5b and baseline of 23.0b

bsearch55.0ms

Steps

Iters	Range		Point
1	2.7753413219507016e+156	2.949286285521596e+156	2.818827562843425e+156
9	-3.285142281572991e+120	-3.2249995708726854e+115	-5.1997141694493184e+116

simplify6.0ms

Iterations

Useful iterations: 2 (3.0ms)

Iter	Nodes	Cost
0	21	30
1	26	30
2	27	29
3	33	29
done	33	29

end0.0ms

sample1.9s

Algorithm

intervals

Results

631.0ms	8864×	body	80	valid
151.0ms	2951×	body	80	nan