Details

Time bar (total: 21.2s)

sample247.0ms

Algorithm
intervals
Results
25.0ms111×body320valid
20.0ms285×body80nan
17.0ms541×pre80true
17.0ms94×body160valid
4.0ms17×body640valid
2.0ms34×body80valid

simplify276.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
01417
12417
24416
37816
410216
511116
done11116

prune72.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite196.0ms

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:
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(- (* b b) (* (* 4.0 a) c))
124.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
42.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series609.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(- (* b b) (* (* 4.0 a) c))
245.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
147.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify992.0ms

Counts
82 → 82
Iterations

Useful iterations: done (989.0ms)

IterNodesCost
01541565
14191461
219081245
done50001239

prune397.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-cbrt-cube add-exp-log
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×clear-num sub-neg frac-2neg prod-exp cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
6.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
59.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series718.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (* b b) (* (* 4.0 a) c))
142.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
223.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
269.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.7s

Counts
163 → 163
Iterations

Useful iterations: 2 (613.0ms)

IterNodesCost
02475048
16584512
238034174
done50004174

prune898.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0))))))
0.5b
(* (* (* a c) 4.0) (* (* a c) 4.0))
0.5b
(/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0)))

rewrite566.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-cbrt-cube add-exp-log
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp associate-/r/
5×div-inv associate-/l/
4×unpow-prod-down flip3-- flip-- add-log-exp sqr-pow
3×clear-num frac-2neg pow-plus
2×flip3-+ flip-+
1×pow2 div-sub swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 235
Calls
4 calls:
260.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0)))))) (* 2.0 a))
122.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0))))))
119.0ms
(* (* (* a c) 4.0) (* (* a c) 4.0))
44.0ms
(/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0)))

series886.0ms

Counts
4 → 12
Calls
4 calls:
281.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0)))))) (* 2.0 a))
395.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0))))))
55.0ms
(* (* (* a c) 4.0) (* (* a c) 4.0))
155.0ms
(/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0)))

simplify525.0ms

Counts
247 → 247
Iterations

Useful iterations: done (506.0ms)

IterNodesCost
037710404
110339560
done50008838

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (sqrt (+ (* b b) (* (* a c) 4.0)))) (sqrt (+ (* b b) (* (* a c) 4.0)))))))
0.3b
(/ (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (sqrt (+ (* b b) (* (* a c) 4.0)))) (sqrt (+ (* b b) (* (* a c) 4.0))))
0.3b
(/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (sqrt (+ (* b b) (* (* a c) 4.0))))
0.5b
(* (* (* a c) 4.0) (* (* a c) 4.0))

rewrite810.0ms

Algorithm
rewrite-expression-head
Rules
619×times-frac
464×add-sqr-sqrt
324×sqrt-prod
278×*-un-lft-identity
262×add-cube-cbrt
179×difference-of-squares
118×pow1
66×pow-prod-down
51×associate-/l*
49×unpow-prod-down add-cbrt-cube add-exp-log sqr-pow
27×prod-exp cbrt-unprod
25×associate-/r*
20×associate-/r/
18×sqrt-div
10×flip3-+ flip-+ div-inv
9×pow-sqr pow-prod-up
8×distribute-lft-out--
5×cbrt-undiv div-exp associate-/l/
4×distribute-rgt-neg-in add-log-exp
3×clear-num frac-2neg pow-plus div-sub
2×flip3-- flip--
1×pow2 swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 514
Calls
4 calls:
570.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (sqrt (+ (* b b) (* (* a c) 4.0)))) (sqrt (+ (* b b) (* (* a c) 4.0)))))))
69.0ms
(/ (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (sqrt (+ (* b b) (* (* a c) 4.0)))) (sqrt (+ (* b b) (* (* a c) 4.0))))
40.0ms
(/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (sqrt (+ (* b b) (* (* a c) 4.0))))
98.0ms
(* (* (* a c) 4.0) (* (* a c) 4.0))

series741.0ms

Counts
4 → 12
Calls
4 calls:
376.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (sqrt (+ (* b b) (* (* a c) 4.0)))) (sqrt (+ (* b b) (* (* a c) 4.0)))))))
110.0ms
(/ (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (sqrt (+ (* b b) (* (* a c) 4.0)))) (sqrt (+ (* b b) (* (* a c) 4.0))))
192.0ms
(/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (sqrt (+ (* b b) (* (* a c) 4.0))))
62.0ms
(* (* (* a c) 4.0) (* (* a c) 4.0))

simplify1.2s

Counts
526 → 526
Iterations

Useful iterations: done (1.1s)

IterNodesCost
065730882
1166927333
done500125741

prune3.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes299.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02653
13351
23451
done3451

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.5s3696×body320valid
1.2s16178×pre80true
721.0ms8178×body80nan
525.0ms2870×body160valid
201.0ms525×body640valid
69.0ms909×body80valid