Details

sample73.0ms

Algorithm

intervals

Results

14.0ms	45×	body	1280	valid
13.0ms	184×	body	80	valid
9.0ms	25×	body	2560	valid
7.0ms	2×	body	5120	valid
4.0ms	17×	body	640	valid
4.0ms	69×	body	80	nan
2.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify146.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

83.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
124.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

82 → 82

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	154	1565
1	401	1461
2	1342	1245
done	5001	1233

prune423.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
3.5b	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.2b	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
78.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series673.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
257.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
251.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
115.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

160 → 160

Iterations

Useful iterations: 2 (701.0ms)

Iter	Nodes	Cost
0	252	4912
1	623	4364
2	2681	4036
done	5000	4036

prune737.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
14.8b	(/ (* 2.0 a) (* 4.0 (* a c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

42.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(- (* b b) (* (* 4.0 a) c))
37.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

82 → 82

Iterations

Useful iterations: 2 (368.0ms)

Iter	Nodes	Cost
0	157	1330
1	412	1216
2	2082	994
done	5000	994

prune434.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-exp-log`
51×	`prod-exp`
44×	`div-exp`
29×	`add-cbrt-cube`
16×	`rec-exp` `1-exp`
14×	`associate-/r/`
12×	`add-sqr-sqrt`
11×	`pow1` `frac-times` `*-un-lft-identity`
10×	`cbrt-undiv` `add-log-exp`
9×	`cbrt-unprod`
8×	`flip3--` `flip--`
7×	`add-cube-cbrt` `associate-*l/`
5×	`associate-*r/`
4×	`sqrt-prod`
3×	`pow-flip` `times-frac` `diff-log` `pow-prod-down` `un-div-inv` `associate-/l*`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r*` `div-inv` `inv-pow`

Counts

4 → 116

Calls

4 calls:

215.0ms	(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
58.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
132.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms	(- (* b b) (* (* 4.0 a) c))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

128 → 128

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	254	3006
1	618	2576
2	2109	2143
done	5001	2104

prune414.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.2b

regimes311.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.7b

bsearch292.0ms

Steps

Iters	Range	Point
2	5.341589198600723e+134	5.967668210703041e+134	5.732888581164671e+134
10	-1.2529167750641135e-296	-2.859335985249397e-307	-3.1046203401759487e-300
9	-8.712513212907472e+114	-1.0414090820182828e+108	-2.463372194426505e+111

Iters

Range

Point

5.341589198600723e+134

5.967668210703041e+134

5.732888581164671e+134

-1.2529167750641135e-296

-2.859335985249397e-307

-3.1046203401759487e-300

-8.712513212907472e+114

-1.0414090820182828e+108

-2.463372194426505e+111

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	38	66
1	51	64
2	52	64
done	52	64

end0.0ms

sample3.5s

Algorithm

intervals

Results

761.0ms	1056×	body	2560	valid
627.0ms	5848×	body	80	valid
533.0ms	113×	body	5120	valid
420.0ms	922×	body	1280	valid
386.0ms	2941×	body	80	nan
292.0ms	479×	body	640	valid
54.0ms	208×	body	320	valid
20.0ms	109×	body	160	valid