Details

sample97.0ms

Algorithm

intervals

Results

42.0ms	210×	body	80	valid
15.0ms	23×	body	2560	valid
11.0ms	25×	body	1280	valid
7.0ms	84×	body	80	nan
3.0ms	8×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify86.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
0.8b	(- (* b b) (* (* 4 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

139×	`add-sqr-sqrt`
116×	`*-un-lft-identity`
60×	`times-frac`
42×	`unswap-sqr`
36×	`associate-l` `add-cube-cbrt`
30×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`sqrt-prod`
18×	`associate-r`
14×	`distribute-rgt-neg-in`
12×	`associate-/r` `-commutative` `distribute-lft-out--`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`swap-sqr`
5×	`pow1` `associate-/l*`
4×	`insert-posit16`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 182

Calls

4 calls:

726.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
82.0ms	(- (* b b) (* (* 4 a) c))
229.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
119.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
70.0ms	(- (* b b) (* (* 4 a) c))
131.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
130.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts

194 → 194

Iterations

Iter	Nodes
done	5001
2	2178
1	677
0	272

prune840.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (- (* b b) (* 4 (* a c)))) b) a)
0.8b	(- (* b b) (* 4 (* a c)))
1.0b	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
20.8b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

127×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`difference-of-squares`
36×	`unswap-sqr`
27×	`sqrt-prod`
18×	`times-frac`
16×	`add-cube-cbrt`
13×	`distribute-lft-out--`
8×	`associate-l` `add-log-exp`
6×	`add-cbrt-cube` `swap-sqr` `add-exp-log` `-commutative` `associate-/l`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 126

Calls

4 calls:

1.2s	(/ (- (sqrt (- (* b b) (* 4 (* a c)))) b) a)
85.0ms	(- (* b b) (* 4 (* a c)))
754.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
170.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- (sqrt (- (* b b) (* 4 (* a c)))) b) a)
52.0ms	(- (* b b) (* 4 (* a c)))
108.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
80.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify974.0ms

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
2	1348
1	488
0	204

prune535.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ a (- (sqrt (- (* b b) (* 4 (* a c)))) b))
0.8b	(- (* b b) (* 4 (* a c)))
1.0b	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
20.8b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

127×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`difference-of-squares`
36×	`unswap-sqr`
27×	`sqrt-prod`
18×	`times-frac`
16×	`add-cube-cbrt`
13×	`distribute-lft-out--`
8×	`associate-l` `add-log-exp`
6×	`associate-/r` `add-cbrt-cube` `swap-sqr` `add-exp-log` `-commutative`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 125

Calls

4 calls:

446.0ms	(/ a (- (sqrt (- (* b b) (* 4 (* a c)))) b))
69.0ms	(- (* b b) (* 4 (* a c)))
536.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
111.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(/ a (- (sqrt (- (* b b) (* 4 (* a c)))) b))
53.0ms	(- (* b b) (* 4 (* a c)))
96.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
87.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.1s

Counts

137 → 137

Iterations

Iter	Nodes
done	5001
3	4489
2	1224
1	440
0	199

prune529.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
0.8b	(- (* b b) (* (* 4 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
38×	`unswap-sqr`
30×	`difference-of-squares`
24×	`sqrt-prod`
23×	`associate-l`
19×	`add-cube-cbrt`
18×	`frac-times`
13×	`associate-r`
12×	`distribute-lft-out--`
11×	`flip3-+` `flip-+`
10×	`times-frac` `associate-/l*` `add-log-exp`
9×	`associate-/r` `add-cbrt-cube` `associate-r/` `add-exp-log`
7×	`pow1` `*-commutative`
6×	`swap-sqr`
4×	`clear-num` `insert-posit16` `distribute-lft-out`
3×	`frac-2neg`
2×	`sum-log` `distribute-rgt-neg-in` `flip3--` `sqrt-div` `associate-*l/` `prod-exp` `un-div-inv` `cbrt-unprod` `flip--`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `neg-log` `associate-+l-` `div-inv`

Counts

4 → 152

Calls

4 calls:

726.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
70.0ms	(- (* b b) (* (* 4 a) c))
180.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
113.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
53.0ms	(- (* b b) (* (* 4 a) c))
97.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
89.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.4s

Counts

164 → 164

Iterations

Iter	Nodes
done	5002
2	2481
1	676
0	264

prune579.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.5b

regimes319.0ms

Accuracy

81.2% (5.2b remaining)

Error of 10.8b against oracle of 5.7b and baseline of 33.0b

bsearch332.0ms

Steps

Iters	Range		Point
8	5.451909898538592e-70	5.081728108716245e-67	1.546013236023957e-67
7	6.366271362828677e-80	2.0474353944207673e-78	1.6168702840263923e-79
8	1.9015403840268286e-125	4.787339246176752e-121	1.3353078790738604e-121
7	-9.460060253608456e+39	-2.573022393154551e+38	-9.348931433494438e+39

simplify26.0ms

Iterations

Iter	Nodes
done	42
1	42
0	35

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	1084×	body	2560	valid
706.0ms	5870×	body	80	valid
456.0ms	907×	body	1280	valid
429.0ms	232×	body	320	valid
308.0ms	3007×	body	80	nan
206.0ms	447×	body	640	valid
66.0ms	101×	body	5120	valid
44.0ms	109×	body	160	valid