Details

Time bar (total: 16.0s)

sample96.0ms

Algorithm
intervals
Results
30.0ms33×body2560valid
14.0ms181×body80valid
12.0ms27×body1280valid
7.0ms92×body80nan
4.0ms14×body640valid
2.0ms4×body5120valid
2.0ms8×body320valid
1.0ms6×body160valid

simplify84.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01217
12117
24116
37616
49616
510416
done10416

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite142.0ms

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:
86.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
17.0ms
(- (* b b) (* (* 3.0 a) c))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
64.0ms
(- (* b b) (* (* 3.0 a) c))
100.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
99.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01541565
14141463
218791247
done50011241

prune418.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.2b
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
112.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
104.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series656.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
219.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
230.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
104.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.2s

Counts
166 → 166
Iterations

Useful iterations: 2 (732.0ms)

IterNodesCost
02535113
16574543
237264211
done50004211

prune576.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b
(/ (* (+ 0 (* (* 3.0 a) c)) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
9.2b
(* (+ 0 (* (* 3.0 a) c)) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
41×add-sqr-sqrt
34×*-un-lft-identity
30×add-cbrt-cube
27×associate-*r*
24×times-frac
17×add-cube-cbrt prod-exp
16×div-exp
9×cbrt-undiv cbrt-unprod
8×distribute-lft-out-- add-log-exp difference-of-squares
7×pow1 sqrt-prod
6×associate-/l/
4×frac-times distribute-rgt-neg-in flip3-+ associate-*l/ flip-+
3×rec-exp flip3-- 1-exp associate-*l* flip-- unswap-sqr
2×sqrt-div diff-log associate-*r/ associate-/r/ un-div-inv div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 122
Calls
4 calls:
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
59.0ms
(/ (* (+ 0 (* (* 3.0 a) c)) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
137.0ms
(* (+ 0 (* (* 3.0 a) c)) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series612.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
195.0ms
(/ (* (+ 0 (* (* 3.0 a) c)) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
208.0ms
(* (+ 0 (* (* 3.0 a) c)) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
90.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify494.0ms

Counts
134 → 134
Iterations

Useful iterations: done (488.0ms)

IterNodesCost
02463608
17342983
done50002543

prune488.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b
(/ (/ (* c (* 3.0 a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.2b
(/ (* c (* 3.0 a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
32×add-sqr-sqrt
31×*-un-lft-identity
17×cbrt-undiv div-exp
14×associate-/l*
13×prod-exp cbrt-unprod
11×add-cube-cbrt
10×distribute-lft-out-- difference-of-squares
8×associate-/r* sqrt-prod add-log-exp
6×associate-/r/
5×pow1 flip3-- distribute-rgt-neg-in flip--
4×div-inv
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 120
Calls
4 calls:
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
90.0ms
(/ (/ (* c (* 3.0 a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
66.0ms
(/ (* c (* 3.0 a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series740.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
286.0ms
(/ (/ (* c (* 3.0 a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
237.0ms
(/ (* c (* 3.0 a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
83.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.7s

Counts
132 → 132
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02263596
16453416
238292666
done50012600

prune400.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.2b

regimes601.0ms

Accuracy

91.9% (2.0b remaining)

Error of 7.4b against oracle of 5.5b and baseline of 29.8b

bsearch257.0ms

Steps
ItersRangePoint
10
1.3113650301339767e-12
0.01077406869848718
0.010648423176581222
9
-8.356775273780836e-234
-1.6460056981104342e-242
-2.0956679509109807e-241
9
-1.3908068482385633e+114
-9.803349624800032e+108
-4.137767488706159e+113

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03564
14460
24660
done4660

end0.0ms

sample3.1s

Algorithm
intervals
Results
940.0ms1092×body2560valid
924.0ms5891×body80valid
309.0ms846×body1280valid
209.0ms3046×body80nan
111.0ms465×body640valid
71.0ms96×body5120valid
40.0ms236×body320valid
12.0ms105×body160valid