Details

sample75.0ms

Algorithm

intervals

Results

16.0ms	36×	body	2560	valid
15.0ms	190×	body	80	valid
10.0ms	28×	body	1280	valid
6.0ms	92×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	5120	valid

simplify138.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize27.0ms

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))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite156.0ms

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:

98.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms	(- (* b b) (* (* 4.0 a) c))
29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
73.0ms	(- (* b b) (* (* 4.0 a) c))
116.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

82 → 82

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	154	1565
1	401	1461
2	1353	1245
done	5001	1233

prune375.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.4b	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.2b	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite364.0ms

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:

44.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
156.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
128.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
256.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
232.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

166 → 166

Iterations

Useful iterations: 2 (728.0ms)

Iter	Nodes	Cost
0	257	5113
1	634	4541
2	2639	4211
done	5001	4211

prune654.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite186.0ms

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×	`div-exp` `associate-/r*`
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` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 118

Calls

4 calls:

90.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
18.0ms	(- (* b b) (* (* 4.0 a) c))
63.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
97.0ms	(- (* b b) (* (* 4.0 a) c))
145.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

130 → 130

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	220	3137
1	497	2801
2	1461	2561
done	5000	2481

prune374.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
143.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
27.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* (* 4.0 a) c))
186.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
99.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

92 → 92

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	181	1881
1	465	1671
2	1663	1400
done	5001	1376

prune320.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.5b

regimes232.0ms

Accuracy

83.5% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 33.2b

bsearch249.0ms

Steps

Iters	Range		Point
11	1.5906747666251227e-34	6.100620313640196e-08	1.611450844781215e-34
9	-6.354265220965125e+156	-1.769171722317776e+149	-1.5501620157466267e+150

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample3.2s

Algorithm

intervals

Results

703.0ms	2915×	body	80	nan
664.0ms	5882×	body	80	valid
630.0ms	1076×	body	2560	valid
439.0ms	848×	body	1280	valid
162.0ms	468×	body	640	valid
62.0ms	107×	body	5120	valid
45.0ms	212×	body	320	valid
18.0ms	122×	body	160	valid