Details

Time bar (total: 15.9s)

sample78.0ms

Algorithm
intervals
Results
15.0ms196×body80valid
11.0ms27×body2560valid
11.0ms31×body1280valid
7.0ms92×body80nan
5.0ms16×body640valid
3.0ms5×body5120valid
1.0ms3×body320valid
1.0ms4×body160valid

simplify118.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite155.0ms

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:
94.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
32.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
145.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
56.0ms
(- (* b b) (* (* 4.0 a) c))
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01541565
14211461
219121245
done50001239

prune419.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 2.0 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) a)
0.9b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
24×*-un-lft-identity associate-*l*
19×times-frac
16×add-cube-cbrt
9×add-exp-log add-cbrt-cube
8×add-log-exp difference-of-squares
7×pow1 sqrt-prod
4×flip3-- flip-- distribute-lft-out--
3×associate-*r*
2×sub-neg sqrt-div diff-log prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 85
Calls
4 calls:
175.0ms
(* (/ 2.0 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) a)
73.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(* (/ 2.0 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) a)
148.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
75.0ms
(- (* b b) (* (* 4.0 a) c))
133.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
97 → 97
Iterations

Useful iterations: 2 (373.0ms)

IterNodesCost
01741773
14351675
220341509
done50021509

prune353.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (* b b) (* (* 4.0 a) c))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
66 → 66
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
0621010
1165930
2739834
34972834
done5001834

prune275.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.5b

localize33.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log
Counts
4 → 57
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts
69 → 69
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
0621075
1165969
2739881
34972881
done5001881

prune391.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 4.5b

regimes451.0ms

Accuracy

87.9% (3.5b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 34.4b

bsearch248.0ms

Steps
ItersRangePoint
8
6412590.878131424
2116652649.122401
683389336.5992492
10
7.683585266441067e-90
6.043928490067347e-79
7.752932492055354e-90
8
-1.5489453231745737e+155
-2.021963087226922e+151
-2.2976245343188767e+152

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03568
14266
24366
done4366

end0.0ms

sample2.4s

Algorithm
intervals
Results
788.0ms5754×body80valid
372.0ms917×body1280valid
335.0ms1069×body2560valid
208.0ms2912×body80nan
197.0ms488×body640valid
69.0ms109×body5120valid
35.0ms246×body320valid
9.0ms91×body160valid