Details

Time bar (total: 7.2s)

sample53.0ms

Algorithm
intervals
Results
9.0ms292×body80nan
9.0ms548×pre80true
9.0ms134×body160valid
4.0ms122×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059
done1059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite106.0ms

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:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
64.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify45.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25002674
done5002674

prune198.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

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-exp-log add-cbrt-cube
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×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series471.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
187.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify113.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06422664
131752400
250032388
done50032388

prune435.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite439.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
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×frac-2neg pow-plus clear-num
2×flip3-+ flip-+
1×pow2 div-sub swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 235
Calls
4 calls:
182.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
122.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
39.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
80.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series555.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
230.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
96.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
37.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify70.0ms

Counts
247 → 247
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09935284
150024705
done50024705

prune712.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ 1 (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))))
0.4b
(* (/ 1 (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
130×times-frac
120×pow1
90×*-un-lft-identity
68×add-cube-cbrt
67×pow-prod-down
66×add-exp-log
59×sqrt-prod
56×add-cbrt-cube
43×associate-*r* difference-of-squares
35×prod-exp
31×cbrt-unprod
25×associate-*l*
15×unswap-sqr
13×unpow-prod-down sqr-pow
12×associate-/r*
10×div-exp
9×pow-sqr pow-prod-up associate-/l*
8×associate-/r/ distribute-lft-out--
6×cbrt-undiv sqrt-div
4×distribute-rgt-neg-in flip3-+ flip-+ div-inv associate-/l/ add-log-exp
3×pow-plus
2×rec-exp flip3-- frac-2neg 1-exp clear-num *-commutative flip--
1×pow2 frac-times div-sub associate-*r/ swap-sqr associate-*l/
Counts
4 → 273
Calls
4 calls:
41.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
36.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ 1 (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))))
102.0ms
(* (/ 1 (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))
78.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
229.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ 1 (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))))
94.0ms
(* (/ 1 (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))
42.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify78.0ms

Counts
285 → 285
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011606132
150015632
done50015632

prune955.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes139.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03438
13738
23738
done3738

end0.0ms

sample1.5s

Algorithm
intervals
Results
303.0ms4496×body160valid
284.0ms16759×pre80true
281.0ms8759×body80nan
118.0ms3504×body80valid