Details

sample109.0ms

Algorithm

intervals

Results

33.0ms	188×	body	80	valid
25.0ms	39×	body	2560	valid
16.0ms	31×	body	1280	valid
9.0ms	87×	body	80	nan
5.0ms	13×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify114.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
0.4b	(- (* b b) (* (* 4 a) c))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`insert-posit16`
3×	`distribute-rgt-neg-in` `sqrt-prod`
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` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 74

Calls

4 calls:

45.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
7.0ms	(- (* b b) (* (* 4 a) c))
18.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
77.0ms	(- (* b b) (* (* 4 a) c))
130.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
112.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1358
1	406
0	153

prune512.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
0.4b	(- (* b b) (* (* 4 a) c))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
5×	`associate-l`
4×	`insert-posit16` `distribute-lft-out`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`frac-times` `sum-log` `distribute-rgt-neg-in` `flip3--` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `flip--` `unswap-sqr`
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-r/` `-commutative` `associate-+l-` `div-inv`

Counts

4 → 84

Calls

4 calls:

98.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
15.0ms	(- (* b b) (* (* 4 a) c))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
79.0ms	(- (* b b) (* (* 4 a) c))
122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
99.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1787
1	469
0	178

prune544.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (+ (* c (* -4 a)) (* b b))) b) 2) a)
0.4b	(+ (* c (* -4 a)) (* b b))
0.4b	(- (sqrt (+ (* c (* -4 a)) (* b b))) b)
23.1b	(sqrt (+ (* c (* -4 a)) (* b b)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`flip3-+` `sqrt-div` `div-sub` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `associate-/l/`

Counts

4 → 152

Calls

4 calls:

153.0ms	(/ (/ (- (sqrt (+ (* c (* -4 a)) (* b b))) b) 2) a)
21.0ms	(+ (* c (* -4 a)) (* b b))
86.0ms	(- (sqrt (+ (* c (* -4 a)) (* b b))) b)
15.0ms	(sqrt (+ (* c (* -4 a)) (* b b)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (/ (- (sqrt (+ (* c (* -4 a)) (* b b))) b) 2) a)
82.0ms	(+ (* c (* -4 a)) (* b b))
141.0ms	(- (sqrt (+ (* c (* -4 a)) (* b b))) b)
143.0ms	(sqrt (+ (* c (* -4 a)) (* b b)))

simplify2.2s

Counts

164 → 164

Iterations

Iter	Nodes
done	5001
2	1785
1	612
0	259

prune942.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (+ (* c (* -4 a)) (* b b))) b) (/ a 1/2))
0.4b	(+ (* c (* -4 a)) (* b b))
0.4b	(- (sqrt (+ (* c (* -4 a)) (* b b))) b)
23.1b	(sqrt (+ (* c (* -4 a)) (* b b)))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
129×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
68×	`add-cube-cbrt`
30×	`difference-of-squares`
18×	`sqrt-prod`
15×	`distribute-lft-out--`
13×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`div-inv` `add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`insert-posit16`
3×	`cbrt-undiv` `div-exp`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-/r/`

Counts

4 → 160

Calls

4 calls:

168.0ms	(/ (- (sqrt (+ (* c (* -4 a)) (* b b))) b) (/ a 1/2))
16.0ms	(+ (* c (* -4 a)) (* b b))
95.0ms	(- (sqrt (+ (* c (* -4 a)) (* b b))) b)
19.0ms	(sqrt (+ (* c (* -4 a)) (* b b)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (- (sqrt (+ (* c (* -4 a)) (* b b))) b) (/ a 1/2))
88.0ms	(+ (* c (* -4 a)) (* b b))
99.0ms	(- (sqrt (+ (* c (* -4 a)) (* b b))) b)
131.0ms	(sqrt (+ (* c (* -4 a)) (* b b)))

simplify2.0s

Counts

172 → 172

Iterations

Iter	Nodes
done	5002
2	2398
1	753
0	258

prune863.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

regimes446.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 33.7b

bsearch236.0ms

Steps

Iters	Range		Point
8	1.287554927770862e-68	8.304725640954512e-66	4.5810084990875205e-68
8	-3.370135567630554e+133	-1.481129451033522e+129	-2.1144981103869975e+131

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.1s	1064×	body	2560	valid
1.0s	5890×	body	80	valid
846.0ms	2854×	body	80	nan
724.0ms	901×	body	1280	valid
257.0ms	447×	body	640	valid
192.0ms	95×	body	5120	valid
86.0ms	207×	body	320	valid
35.0ms	133×	body	160	valid