Details

Time bar (total: 17.1s)

sample71.0ms

Algorithm
intervals
Results
15.0ms162×body160valid
11.0ms242×body80nan
11.0ms498×pre80true
6.0ms42×body320valid
3.0ms52×body80valid

simplify95.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.2b

localize15.0ms

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))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite166.0ms

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))
101.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
60.0ms
(- (* b b) (* (* 4.0 a) c))
189.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
127.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.3s

Counts
82 → 82
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01541565
14191461
219261245
done50011239

prune310.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* 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)))))

rewrite279.0ms

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:
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
78.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series615.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms
(- (* b b) (* (* 4.0 a) c))
202.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
241.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.3s

Counts
163 → 163
Iterations

Useful iterations: 2 (657.0ms)

IterNodesCost
02475048
16594512
238214174
done50004174

prune683.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite350.0ms

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:
155.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
53.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
121.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series651.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
145.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
62.0ms
(- (* b b) (* (* 4.0 a) c))
272.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify3.0s

Counts
97 → 97
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
01762262
15432068
243581760
done50011760

prune364.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite619.0ms

Algorithm
rewrite-expression-head
Rules
132×pow1
75×pow-prod-down
72×add-exp-log add-cbrt-cube
44×prod-exp cbrt-unprod
14×add-sqr-sqrt
12×*-un-lft-identity
9×associate-*l* pow-sqr pow-prod-up
8×add-cube-cbrt associate-*r*
6×associate-*l/
5×cbrt-undiv div-exp
4×flip3-- times-frac associate-*r/ flip-- associate-/l* add-log-exp difference-of-squares
3×pow-plus *-commutative distribute-rgt-neg-out
2×distribute-rgt-neg-in associate-/r/ associate-/l/ distribute-lft-out--
1×pow2 distribute-lft-neg-in neg-mul-1 frac-2neg div-sub swap-sqr clear-num associate-/r* sqrt-prod div-inv unswap-sqr
Counts
4 → 147
Calls
4 calls:
212.0ms
(* (* a 2.0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 4.0 (* a c)))))
129.0ms
(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 4.0 (* a c))))
146.0ms
(/ (- (* 0 0) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (* (* a 2.0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 4.0 (* a c))))))
120.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

series641.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(* (* a 2.0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 4.0 (* a c)))))
139.0ms
(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 4.0 (* a c))))
200.0ms
(/ (- (* 0 0) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (* (* a 2.0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 4.0 (* a c))))))
66.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

simplify431.0ms

Counts
159 → 159
Iterations

Useful iterations: done (423.0ms)

IterNodesCost
02244408
17614079
done50013115

prune517.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes189.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify20.0ms

Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
02340
13638
25337
36237
47237
57637
done7637

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.2s16174×pre80true
832.0ms4827×body160valid
577.0ms8174×body80nan
272.0ms1363×body320valid
212.0ms1810×body80valid