Details

Time bar (total: 5.6s)

sample54.0ms

Algorithm
intervals
Results
10.0ms144×body160valid
9.0ms535×pre80true
9.0ms279×body80nan
4.0ms112×body80valid

simplify10.0ms

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: 30.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
30.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite104.0ms

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:
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms
(- (* b b) (* (* 4.0 a) c))
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify44.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25002674
done5002674

prune193.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

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))))
83.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
50.0ms
(- (* b b) (* (* 4.0 a) c))
191.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify111.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06422664
131752400
250032388
done50032388

prune423.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
15×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
9×pow1
7×add-cube-cbrt associate-*r*
6×prod-exp cbrt-unprod
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down associate-/l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ associate-*l* neg-log clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 85
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
55.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
157.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify122.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
05221156
13447949
25002944
done5002944

prune256.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-*r*
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
5×distribute-rgt-neg-out distribute-lft-out
4×associate-/r*
3×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ associate-/l*
2×flip3-- sqrt-div associate-*r/ associate-/r/ flip-- associate-/l/ distribute-neg-frac
1×cbrt-undiv +-commutative neg-mul-1 sub-neg distribute-neg-out frac-2neg diff-log div-exp associate-*l* unsub-neg clear-num sum-log *-commutative div-inv
Counts
4 → 96
Calls
4 calls:
19.0ms
(+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms
(* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series523.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
93.0ms
(* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
266.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify119.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
05851518
132201294
250021276
done50021276

prune303.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes124.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02613
12813
22813
done2813

end0.0ms

sample1.5s

Algorithm
intervals
Results
305.0ms4452×body160valid
285.0ms8609×body80nan
278.0ms16609×pre80true
123.0ms3548×body80valid