Details

sample127.0ms

Algorithm

intervals

Results

36.0ms	183×	body	80	valid
30.0ms	41×	body	2560	valid
20.0ms	31×	body	1280	valid
11.0ms	84×	body	80	nan
6.0ms	12×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify132.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.8b	(- (* b b) (* 4 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
20.7b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

205×	`add-sqr-sqrt`
114×	`*-un-lft-identity`
84×	`times-frac`
58×	`difference-of-squares`
44×	`unswap-sqr`
42×	`add-cube-cbrt`
36×	`sqrt-prod` `distribute-lft-out--`
32×	`associate-l`
24×	`associate-r`
14×	`distribute-rgt-neg-in` `*-commutative`
12×	`associate-/r*`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/l*`
6×	`swap-sqr`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`diff-log`
2×	`associate--l-` `neg-sub0` `cbrt-undiv` `sub-neg` `sqrt-div` `div-sub` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 208

Calls

4 calls:

633.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
73.0ms	(- (* b b) (* 4 (* a c)))
224.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
156.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
68.0ms	(- (* b b) (* 4 (* a c)))
142.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
105.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.1s

Counts

220 → 220

Iterations

Iter	Nodes
done	5002
2	2392
1	785
0	295

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b b) (* (* a c) 4))) b)
4.9b	(/ (/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b)) (* 2 a))
8.6b	(/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b))
20.7b	(sqrt (- (* b b) (* (* a c) 4)))

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

1021×	`*-un-lft-identity`
1008×	`times-frac`
799×	`add-sqr-sqrt`
396×	`associate-l`
319×	`add-cube-cbrt`
258×	`distribute-lft-out`
189×	`difference-of-squares`
129×	`associate-r`
111×	`sqrt-prod`
93×	`distribute-lft-out--`
61×	`unswap-sqr`
54×	`associate-/l*`
46×	`*-commutative`
28×	`associate-/r/`
24×	`associate-/r*`
21×	`associate-/l/`
18×	`add-cbrt-cube` `add-exp-log`
16×	`flip3--` `flip--`
15×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg` `swap-sqr`
2×	`flip3-+` `sqrt-div` `prod-exp` `cbrt-unprod` `flip-+`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 712

Calls

4 calls:

669.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
1.4s	(/ (/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b)) (* 2 a))
892.0ms	(/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b))
133.0ms	(sqrt (- (* b b) (* (* a c) 4)))

series797.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
268.0ms	(/ (/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b)) (* 2 a))
280.0ms	(/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b))
112.0ms	(sqrt (- (* b b) (* (* a c) 4)))

simplify2.3s

Counts

724 → 724

Iterations

Iter	Nodes
done	5001
1	1845
0	649

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize36.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b b) (* (* a c) 4))) b)
5.0b	(* (/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b)) (/ 1/2 a))
8.6b	(/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b))
20.7b	(sqrt (- (* b b) (* (* a c) 4)))

rewrite4.3s

Algorithm

rewrite-expression-head

Rules

294×	`*-un-lft-identity`
249×	`add-sqr-sqrt`
153×	`frac-times`
121×	`associate-/l*`
120×	`associate-/r` `associate-l*`
95×	`add-cube-cbrt`
85×	`times-frac`
69×	`distribute-lft-out`
63×	`difference-of-squares`
48×	`sqrt-prod`
30×	`clear-num` `distribute-lft-out--`
29×	`frac-2neg`
22×	`unswap-sqr` `associate-/l/`
18×	`add-cbrt-cube` `add-exp-log`
17×	`associate-*l/`
13×	`associate-r`
11×	`flip3-+` `flip-+`
9×	`associate-*r/`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`flip3--` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `insert-posit16` `flip--`
3×	`swap-sqr` `div-inv`
2×	`sqrt-div` `un-div-inv`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down`

Counts

4 → 376

Calls

4 calls:

738.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
2.6s	(* (/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b)) (/ 1/2 a))
748.0ms	(/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b))
169.0ms	(sqrt (- (* b b) (* (* a c) 4)))

series762.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
247.0ms	(* (/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b)) (/ 1/2 a))
297.0ms	(/ (+ 0 (* (* a c) 4)) (- (sqrt (- (* b b) (* (* a c) 4))) b))
103.0ms	(sqrt (- (* b b) (* (* a c) 4)))

simplify1.9s

Counts

388 → 388

Iterations

Iter	Nodes
done	5001
1	1477
0	477

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* a c) 4))
1.0b	(- (sqrt (- (* b b) (* (* a c) 4))) b)
13.5b	(/ (* (* a c) (* 4 1/2)) a)
20.7b	(sqrt (- (* b b) (* (* a c) 4)))

rewrite925.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
99×	`times-frac`
93×	`*-un-lft-identity`
90×	`associate-l`
76×	`unswap-sqr`
72×	`associate-r`
67×	`add-cube-cbrt`
33×	`associate-/l*`
32×	`difference-of-squares`
25×	`sqrt-prod`
22×	`add-cbrt-cube` `add-exp-log`
18×	`*-commutative`
13×	`distribute-lft-out--`
8×	`prod-exp` `cbrt-unprod` `add-log-exp`
6×	`swap-sqr`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`insert-posit16`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 243

Calls

4 calls:

76.0ms	(- (* b b) (* (* a c) 4))
623.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
91.0ms	(/ (* (* a c) (* 4 1/2)) a)
114.0ms	(sqrt (- (* b b) (* (* a c) 4)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b b) (* (* a c) 4))
119.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
21.0ms	(/ (* (* a c) (* 4 1/2)) a)
83.0ms	(sqrt (- (* b b) (* (* a c) 4)))

simplify3.1s

Counts

255 → 255

Iterations

Iter	Nodes
done	5000
2	4788
1	1154
0	440

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

regimes283.0ms

Accuracy

87.1% (3.3b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 31.1b

bsearch327.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	9.19242293018462e+63
8	-1.062177424076527e-128	-2.2311151369229123e-133	-4.726535681060057e-132
7	-9.460060253608456e+39	-2.573022393154551e+38	-9.877342284320474e+38

simplify9.0ms

Iterations

Iter	Nodes
done	46
1	46
0	38

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.5s	1101×	body	2560	valid
1.0s	5893×	body	80	valid
794.0ms	856×	body	1280	valid
440.0ms	3007×	body	80	nan
309.0ms	463×	body	640	valid
115.0ms	216×	body	320	valid
95.0ms	98×	body	5120	valid
34.0ms	119×	body	160	valid