Details

sample103.0ms

Algorithm

intervals

Results

18.0ms	186×	body	80	valid
17.0ms	29×	body	2560	valid
11.0ms	24×	body	1280	valid
10.0ms	102×	body	80	nan
5.0ms	14×	body	640	valid
4.0ms	5×	body	5120	valid
3.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	102	16
5	111	16
done	111	16

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite103.0ms

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*`
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 → 70

Calls

4 calls:

72.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
6.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
61.0ms	(- (* b b) (* (* 4.0 a) c))
128.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify952.0ms

Counts

82 → 82

Iterations

Useful iterations: done (949.0ms)

Iter	Nodes	Cost
0	154	1565
1	421	1461
2	1926	1245
done	5001	1239

prune555.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize47.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.9b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `diff-log` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

33.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
60.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series654.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
180.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
273.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

166 → 166

Iterations

Useful iterations: 2 (646.0ms)

Iter	Nodes	Cost
0	254	5113
1	659	4543
2	3736	4219
done	5000	4219

prune993.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize35.0ms

Local error

Found 4 expressions with local error:

10.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.1b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

9.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
54.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
238.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

92 → 92

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	160	3048
1	411	1909
2	2161	1783
done	5000	1763

prune638.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
47×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 118

Calls

4 calls:

52.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
17.0ms	(- (* b b) (* (* 4.0 a) c))
38.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
76.0ms	(- (* b b) (* (* 4.0 a) c))
116.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

130 → 130

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	220	3137
1	571	2809
2	2710	2613
done	5001	2611

prune508.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

regimes487.0ms

Accuracy

85.6% (3.9b remaining)

Error of 9.4b against oracle of 5.5b and baseline of 32.7b

bsearch310.0ms

Steps

Iters	Range		Point
7	1.9371672431899034e+133	5.16149553175908e+134	2.1254018088008333e+133
9	1.657231371314425e-305	1.760208242016082e-296	1.495170435206392e-301
9	-3.792961868720521e+75	-7.261872368850313e+67	-3.5695008721667037e+75

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	37	69
1	44	67
2	45	67
done	45	67

end0.0ms

sample3.6s

Algorithm

intervals

Results

963.0ms	5961×	body	80	valid
719.0ms	1054×	body	2560	valid
594.0ms	455×	body	640	valid
426.0ms	877×	body	1280	valid
207.0ms	2946×	body	80	nan
113.0ms	97×	body	5120	valid
44.0ms	214×	body	320	valid
16.0ms	111×	body	160	valid