Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	38×	body	2560	valid
10.0ms	190×	body	80	valid
8.0ms	36×	body	1280	valid
4.0ms	79×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify103.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	99	16
5	107	16
done	107	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite170.0ms

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:

114.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms	(- (* b b) (* (* 4.0 a) c))
27.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms	(- (* b b) (* (* 4.0 a) c))
114.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms	(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	421	1461
2	1932	1245
done	5000	1239

prune310.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.9b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
7.7b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite301.0ms

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-exp-log` `add-cbrt-cube`
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×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

38.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
91.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series748.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
221.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
307.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

166 → 166

Iterations

Useful iterations: 2 (599.0ms)

Iter	Nodes	Cost
0	254	5113
1	660	4543
2	3720	4219
done	5001	4219

prune540.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.9b	(/ (/ (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0) a)
7.7b	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

376×	`times-frac`
192×	`add-sqr-sqrt`
191×	`*-un-lft-identity`
131×	`add-cube-cbrt`
44×	`associate-/l*`
33×	`add-exp-log` `add-cbrt-cube`
30×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/r/`
18×	`sqrt-prod` `div-inv`
15×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `div-exp` `flip--`
10×	`associate-/r*`
8×	`add-log-exp`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 262

Calls

4 calls:

33.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
104.0ms	(/ (/ (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0) a)
71.0ms	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
206.0ms	(/ (/ (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0) a)
229.0ms	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify594.0ms

Counts

274 → 274

Iterations

Useful iterations: done (583.0ms)

Iter	Nodes	Cost
0	501	9706
1	1342	9049
done	5000	8631

prune982.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b	(* (* 4.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.9b	(/ (/ (* (* 4.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0) a)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
49×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
41×	`add-exp-log` `add-cbrt-cube`
32×	`add-cube-cbrt`
27×	`associate-r`
15×	`cbrt-undiv` `div-exp`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`sqrt-prod` `associate-/l*`
6×	`div-inv`
4×	`distribute-rgt-neg-in`
3×	`flip3--` `pow-prod-down` `associate-/r*` `flip--`
2×	`sqrt-div` `diff-log` `associate-/r/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `neg-log` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 134

Calls

4 calls:

39.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms	(* (* 4.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
52.0ms	(/ (/ (* (* 4.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0) a)
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
233.0ms	(* (* 4.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
216.0ms	(/ (/ (* (* 4.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0) a)
86.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify542.0ms

Counts

146 → 146

Iterations

Useful iterations: done (537.0ms)

Iter	Nodes	Cost
0	291	3760
1	842	3595
done	5001	3081

prune451.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes260.0ms

Accuracy

88.7% (2.9b remaining)

Error of 8.8b against oracle of 5.9b and baseline of 32.0b

bsearch256.0ms

Steps

Iters	Range	Point
6	2.941880788678857e-52	2.1089452572092024e-51	2.0795344158701052e-51
9	-7.152300718152866e-253	-1.7963911490351415e-262	-1.8359597498390082e-262
9	-7.561250615295736e+156	-1.350243324689865e+150	-4.919628179067154e+153

Iters

Range

Point

2.941880788678857e-52

2.1089452572092024e-51

2.0795344158701052e-51

-7.152300718152866e-253

-1.7963911490351415e-262

-1.8359597498390082e-262

-7.561250615295736e+156

-1.350243324689865e+150

-4.919628179067154e+153

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	66
1	42	66
done	42	66

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	906×	body	1280	valid
571.0ms	1053×	body	2560	valid
548.0ms	5922×	body	80	valid
202.0ms	2894×	body	80	nan
111.0ms	458×	body	640	valid
46.0ms	121×	body	160	valid
40.0ms	85×	body	5120	valid
39.0ms	220×	body	320	valid