Details

sample90.0ms

Algorithm

intervals

Results

19.0ms	36×	body	2560	valid
17.0ms	190×	body	80	valid
12.0ms	28×	body	1280	valid
8.0ms	92×	body	80	nan
6.0ms	16×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	3×	body	160	valid

simplify124.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize21.0ms

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)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

123.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms	(- (* b b) (* (* 4.0 a) c))
48.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
76.0ms	(- (* b b) (* (* 4.0 a) c))
148.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	167	1697
1	433	1584
2	1488	1361
done	5000	1347

prune434.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize30.0ms

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)))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 232

Calls

4 calls:

41.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
128.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
120.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series740.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
251.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
271.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts

244 → 244

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	338	10067
1	811	7605
2	3063	6508
done	5000	6422

prune786.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.5b

localize15.0ms

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)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 152

Calls

4 calls:

114.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
18.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
69.0ms	(- (* b b) (* (* 4.0 a) c))
152.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
126.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

164 → 164

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	261	4025
1	587	3484
2	1656	3082
done	5001	2938

prune426.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.5b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite419.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
55×	`prod-diff`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-cbrt-cube`
10×	`prod-exp`
8×	`add-log-exp`
7×	`pow1` `fma-neg` `associate-l`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`times-frac`
2×	`cbrt-undiv` `frac-times` `rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 154

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
276.0ms	(* (/ 1 (* a 2.0)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
105.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* (* 4.0 a) c))
197.0ms	(* (/ 1 (* a 2.0)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
125.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

166 → 166

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	248	4732
1	610	3916
2	1978	3120
done	5000	2922

prune445.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.5b

regimes276.0ms

Accuracy

83.5% (4.6b remaining)

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

bsearch240.0ms

Steps

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

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

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

end0.0ms

sample3.3s

Algorithm

intervals

Results

766.0ms	5882×	body	80	valid
651.0ms	1076×	body	2560	valid
445.0ms	212×	body	320	valid
403.0ms	848×	body	1280	valid
272.0ms	2915×	body	80	nan
158.0ms	107×	body	5120	valid
145.0ms	468×	body	640	valid
19.0ms	122×	body	160	valid