Details

Time bar (total: 15.9s)

sample110.0ms

Algorithm
intervals
Results
23.0ms152×body160valid
20.0ms270×body80nan
18.0ms526×pre80true
8.0ms104×body80valid

simplify110.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize20.0ms

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))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite122.0ms

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:
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series341.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
53.0ms
(- (* b b) (* (* 4.0 a) c))
121.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify957.0ms

Counts
82 → 82
Iterations

Useful iterations: done (954.0ms)

IterNodesCost
01541565
14011461
213421245
done50011233

prune204.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

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)))))

rewrite197.0ms

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:
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
89.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
68.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series607.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
193.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
258.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.2s

Counts
163 → 163
Iterations

Useful iterations: 2 (495.0ms)

IterNodesCost
02475048
16124510
224984166
done50014166

prune430.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b
(* (/ (* (* a c) 4.0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite378.0ms

Algorithm
rewrite-expression-head
Rules
338×times-frac
263×add-sqr-sqrt
252×*-un-lft-identity
151×add-cube-cbrt
107×add-exp-log
85×associate-*r*
65×add-cbrt-cube
50×distribute-lft-out-- difference-of-squares
47×div-exp
35×prod-exp
30×associate-/l*
25×cbrt-undiv distribute-rgt-neg-in sqrt-prod
21×cbrt-unprod
16×associate-/r/
11×div-inv
10×associate-/r*
9×flip3-- flip--
7×pow1 associate-*l*
6×rec-exp 1-exp add-log-exp
4×unswap-sqr
2×frac-2neg clear-num
1×frac-times sub-neg pow-flip diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/ inv-pow
Counts
4 → 329
Calls
4 calls:
48.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
184.0ms
(* (/ (* (* a c) 4.0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series541.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
56.0ms
(- (* b b) (* (* 4.0 a) c))
162.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
182.0ms
(* (/ (* (* a c) 4.0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify2.8s

Counts
341 → 341
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
043510074
112189067
242058096
done50018096

prune964.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite214.0ms

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:
86.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series679.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
147.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(- (* b b) (* (* 4.0 a) c))
266.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.6s

Counts
97 → 97
Iterations

Useful iterations: 2 (556.0ms)

IterNodesCost
01762262
14932066
225591750
done50011750

prune428.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes177.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01925
12625
done2625

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.1s16291×pre80true
768.0ms8291×body80nan
695.0ms4450×body160valid
440.0ms3550×body80valid