Details

Time bar (total: 4.0m)

sample125.0ms

Algorithm
intervals
Results
24.0ms538×pre80true
24.0ms147×body160valid
22.0ms282×body80nan
12.0ms45×body320valid
5.0ms64×body80valid

simplify142.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
01417
12717
26816
310516
411616
done11616

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(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))
39.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite152.0ms

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))
85.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms
(- (* b b) (* (* 4.0 a) c))
171.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
109.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.7s

Counts
82 → 82
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01541565
19611436
done50011290

prune326.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

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))
0.2b
(/ (/ (+ 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)))))

rewrite310.0ms

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:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
141.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
91.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series684.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms
(- (* b b) (* (* 4.0 a) c))
205.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
307.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.0m

Counts
163 → 163
Iterations

Useful iterations: done (2.0m)

IterNodesCost
02475048
done50014497

prune872.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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

rewrite254.0ms

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:
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
90.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series542.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms
(- (* b b) (* (* 4.0 a) c))
165.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
197.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.8m

Counts
97 → 97
Iterations

Useful iterations: done (1.8m)

IterNodesCost
01762262
142522051
done50001766

prune371.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite440.0ms

Algorithm
rewrite-expression-head
Rules
389×times-frac
281×add-sqr-sqrt
255×*-un-lft-identity
169×add-cube-cbrt
117×add-exp-log
85×associate-*r*
77×add-cbrt-cube
62×div-exp
42×distribute-lft-out-- difference-of-squares
37×cbrt-undiv
33×associate-/l*
27×prod-exp
26×associate-*l*
21×distribute-rgt-neg-in sqrt-prod
19×div-inv
17×cbrt-unprod
16×associate-/r/
11×associate-/r*
8×unswap-sqr
7×flip3-- flip--
6×pow1
5×rec-exp 1-exp
4×add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 360
Calls
4 calls:
88.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
16.0ms
(/ 2.0 (* a c))
25.0ms
(/ 4.0 (/ 2.0 (* a c)))
266.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series496.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
43.0ms
(/ 2.0 (* a c))
37.0ms
(/ 4.0 (/ 2.0 (* a c)))
230.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify798.0ms

Counts
372 → 372
Iterations

Useful iterations: done (779.0ms)

IterNodesCost
048610218
done50009555

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes216.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
01925
12623
done2623

end0.0ms

sample4.0s

Algorithm
intervals
Results
917.0ms4786×body160valid
775.0ms8502×body80nan
696.0ms16502×pre80true
599.0ms1865×body80valid
283.0ms1349×body320valid