Details

sample108.0ms

Algorithm

intervals

Results

27.0ms	24×	body	1280	valid
16.0ms	186×	body	80	valid
13.0ms	29×	body	2560	valid
9.0ms	102×	body	80	nan
5.0ms	14×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize19.0ms

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:

69.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
6.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
76.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify946.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1926
1	421
0	154

prune580.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize54.0ms

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)))

rewrite192.0ms

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:

18.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
102.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
51.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series708.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
230.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
245.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
2	3736
1	659
0	254

prune987.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize35.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.6b	(* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.5b	(/ (* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) a)
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-cbrt-cube` `add-exp-log`
42×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
28×	`times-frac`
27×	`associate-r`
21×	`cbrt-undiv` `div-exp`
20×	`add-cube-cbrt`
16×	`prod-exp` `cbrt-unprod`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `associate-l` `sqrt-prod`
4×	`distribute-rgt-neg-in`
3×	`associate-/r*` `flip3--` `div-inv` `flip--` `associate-/l/`
2×	`frac-times` `sqrt-div` `diff-log` `associate-l/` `associate-r/` `associate-/r/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `-commutative` `associate-/l`

Counts

4 → 127

Calls

4 calls:

38.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
114.0ms	(* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
35.0ms	(/ (* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) a)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series833.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
347.0ms	(* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
257.0ms	(/ (* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) a)
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify482.0ms

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
1	795
0	262

prune732.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize42.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.6b	(/ (/ a (/ 2.0 4.0)) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
3.5b	(/ a (/ (/ a (/ 2.0 4.0)) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

21772×	`times-frac`
10613×	`add-sqr-sqrt`
10612×	`*-un-lft-identity`
7956×	`add-cube-cbrt`
1328×	`distribute-lft-out--` `difference-of-squares`
1130×	`associate-/r*`
731×	`div-inv`
667×	`sqrt-prod`
664×	`distribute-rgt-neg-in`
132×	`associate-/r/`
54×	`add-cbrt-cube` `add-exp-log`
47×	`associate-/l*`
37×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1`
2×	`clear-num` `frac-2neg` `flip3--` `sqrt-div` `diff-log` `flip--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 5674

Calls

4 calls:

24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
146.0ms	(/ (/ a (/ 2.0 4.0)) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
344.0ms	(/ a (/ (/ a (/ 2.0 4.0)) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series673.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
299.0ms	(/ (/ a (/ 2.0 4.0)) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
190.0ms	(/ a (/ (/ a (/ 2.0 4.0)) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

5686 → 5686

Iterations

Iter	Nodes
done	6298
0	6298

prune39.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.4b

regimes420.0ms

Accuracy

80.2% (5.2b remaining)

Error of 10.7b against oracle of 5.5b and baseline of 31.9b

bsearch344.0ms

Steps

Iters	Range	Point
7	1.9371672431899034e+133	5.16149553175908e+134	1.958082194924451e+133
9	-3.471348648739332e-161	-2.9914105727278497e-167	-3.4362912587903164e-161
6	-1.745417689399421e+60	-1.2092396089946692e+59	-1.5543343806564732e+60

Iters

Range

Point

1.9371672431899034e+133

5.16149553175908e+134

1.958082194924451e+133

-3.471348648739332e-161

-2.9914105727278497e-167

-3.4362912587903164e-161

-1.745417689399421e+60

-1.2092396089946692e+59

-1.5543343806564732e+60

simplify8.0ms

Iterations

Iter	Nodes
done	50
1	50
0	41

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	5961×	body	80	valid
759.0ms	1054×	body	2560	valid
471.0ms	877×	body	1280	valid
313.0ms	2946×	body	80	nan
145.0ms	455×	body	640	valid
57.0ms	97×	body	5120	valid
57.0ms	214×	body	320	valid
17.0ms	111×	body	160	valid