Details

sample78.0ms

Algorithm

intervals

Results

40.0ms	281×	body	80	valid
21.0ms	82×	body	80	nan

simplify125.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	152
7	152
6	151
5	144
4	132
3	101
2	62
1	35
0	20

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize121.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4 a) c))
2.7b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `sub-neg` `distribute-rgt-neg-in` `flip3-+` `diff-log` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 61

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4 a) c))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* b b) (* (* 4 a) c))
131.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
121.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
117.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts

73 → 73

Iterations

Iter	Nodes
3	2749
2	795
1	247
0	95

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize141.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4 a) c))
3.4b	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
5.1b	(/ a (/ b c))
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
21×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `associate-/l*`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-*r/` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 124

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4 a) c))
74.0ms	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
10.0ms	(/ a (/ b c))
15.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* (* 4 a) c))
81.0ms	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
41.0ms	(/ a (/ b c))
103.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts

136 → 136

Iterations

Iter	Nodes
2	2425
1	689
0	260

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize168.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
1.1b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.2b	(- (* b b) (* (* 4 a) c))
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*` `times-frac` `add-cube-cbrt`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

61.0ms	(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.0ms	(- (* b b) (* (* 4 a) c))
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
107.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
60.0ms	(- (* b b) (* (* 4 a) c))
97.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.3s

Counts

92 → 92

Iterations

Iter	Nodes
3	4317
2	1201
1	378
0	152

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize151.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) c))
1.1b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.2b	(- (* b b) (* (* 4 a) c))
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
128×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
75×	`add-cube-cbrt`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/r*`
16×	`sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/r/`

Counts

4 → 167

Calls

4 calls:

36.0ms	(/ 2 (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) c))
33.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
8.0ms	(- (* b b) (* (* 4 a) c))
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ 2 (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) c))
131.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
72.0ms	(- (* b b) (* (* 4 a) c))
114.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify759.0ms

Counts

179 → 179

Iterations

Iter	Nodes
2	2179
1	708
0	280

prune2.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.1b

regimes509.0ms

Accuracy

93.4% (1.0b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 21.6b

bsearch354.0ms

Steps

Iters	Range		Point
6	1.890398075878753e+149	8.723340275486535e+149	4.69567004969582e+149
10	-9.368128875810715e+107	-4.5624341740005415e+97	-4.427569081900357e+107

simplify21.0ms

Iterations

Iter	Nodes
2	55
1	55
0	47

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.9s	8793×	body	80	valid
1.0s	2880×	body	80	nan