Details

sample193.0ms

Algorithm

intervals

Results

22.0ms	35×	body	2560	valid
15.0ms	196×	body	80	valid
12.0ms	31×	body	1280	valid
7.0ms	89×	body	80	nan
3.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
0.0ms	2×	body	320	valid
0.0ms	3×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
4	44
3	41
2	32
1	18
0	10

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
36×	`times-frac`
31×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`neg-mul-1`
3×	`associate-/r*` `sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `distribute-frac-neg` `div-inv`

Counts

4 → 106

Calls

4 calls:

151.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
64.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
107.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify945.0ms

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1823
1	448
0	186

prune714.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ -1 (/ a (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
82×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
18×	`associate-/r*`
13×	`distribute-lft-out`
9×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
8×	`add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `div-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `flip--`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 129

Calls

4 calls:

47.0ms	(/ -1 (/ a (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
6.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ -1 (/ a (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
41.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	2801
1	623
0	241

prune912.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.7b	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
14.6b	(/ (- (+ 0 (* a c))) a)
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-/l*`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`neg-mul-1` `sqrt-prod`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `distribute-neg-frac` `difference-of-squares` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `distribute-frac-neg` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 101

Calls

4 calls:

18.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(/ (- (+ 0 (* a c))) a)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b_2 b_2) (* a c))
107.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(/ (- (+ 0 (* a c))) a)
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1976
1	422
0	185

prune649.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
3.8b	(/ (- (/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
10.6b	(/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

318×	`times-frac`
270×	`add-sqr-sqrt`
211×	`*-un-lft-identity`
153×	`add-cube-cbrt`
96×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
58×	`difference-of-squares`
55×	`associate-/l*`
32×	`sqrt-prod`
29×	`distribute-lft-out--`
18×	`associate-/r/`
11×	`flip3--` `flip--`
10×	`div-inv`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1`
4×	`neg-mul-1`
3×	`associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-div` `div-exp`
1×	`neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-sub` `distribute-frac-neg` `flip-+` `distribute-neg-frac`

Counts

4 → 299

Calls

4 calls:

22.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
137.0ms	(/ (- (/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
71.0ms	(/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
201.0ms	(/ (- (/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
266.0ms	(/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify539.0ms

Counts

311 → 311

Iterations

Iter	Nodes
done	5000
1	1185
0	473

prune1.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.4b

regimes293.0ms

Accuracy

87.1% (3.7b remaining)

Error of 9.1b against oracle of 5.4b and baseline of 33.9b

bsearch279.0ms

Steps

Iters	Range		Point
10	4.0721326822252617e+40	3.6590220876252264e+50	3.628799960716312e+50
8	7.211886341925621e-305	2.1257753989446086e-302	7.285221369089651e-305
8	-3.854198347822332e+69	-2.1688378611128307e+65	-1.09861951291665e+69

simplify8.0ms

Iterations

Iter	Nodes
done	63
3	63
2	59
1	42
0	32

end0.0ms

sample2.9s

Algorithm

intervals

Results

659.0ms	2815×	body	80	nan
501.0ms	5799×	body	80	valid
483.0ms	1136×	body	2560	valid
375.0ms	868×	body	1280	valid
127.0ms	446×	body	640	valid
84.0ms	109×	body	5120	valid
71.0ms	238×	body	320	valid
12.0ms	102×	body	160	valid