Details

Time bar (total: 9.9s)

sample34.0ms

Algorithm
intervals
Results
15.0ms278×body80valid
4.0ms76×body80nan

simplify83.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13538
26537
311437
413637
514837
614937
done14937

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize114.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
72 → 72
Iterations

Useful iterations: 3 (480.0ms)

IterNodesCost
0971211
12281091
27651009
33087998
done5001998

prune297.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

localize124.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.7b
(/ (* a c) b)
5.0b
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt
8×times-frac add-log-exp
6×associate-/l*
5×pow1
4×cbrt-undiv div-exp associate-/r* sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in
2×neg-sub0 flip3-- frac-2neg sqrt-div diff-log div-sub prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- associate-+l- associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 83
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(/ (* a c) b)
61.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(/ (* a c) b)
56.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify616.0ms

Counts
95 → 95
Iterations

Useful iterations: done (614.0ms)

IterNodesCost
01871588
14771449
217221285
done50001284

prune359.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize245.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.4b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 associate-*l* neg-log *-commutative
Counts
4 → 63
Calls
4 calls:
6.0ms
(* (* 4.0 a) c)
6.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 4.0 a) c)
46.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
75 → 75
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01261083
1298989
21071899
34573889
done5000889

prune270.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize122.0ms

Local error

Found 4 expressions with local error:

15.6b
(cbrt (* (* 4.0 a) c))
15.6b
(cbrt (* (* 4.0 a) c))
15.6b
(cbrt (* (* 4.0 a) c))
24.7b
(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 42
Calls
4 calls:
5.0ms
(cbrt (* (* 4.0 a) c))
5.0ms
(cbrt (* (* 4.0 a) c))
5.0ms
(cbrt (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(cbrt (* (* 4.0 a) c))
95.0ms
(cbrt (* (* 4.0 a) c))
97.0ms
(cbrt (* (* 4.0 a) c))
135.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

simplify690.0ms

Counts
54 → 54
Iterations

Useful iterations: done (689.0ms)

IterNodesCost
088981
1206897
2512529
31684514
done5000513

prune254.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

regimes199.0ms

Accuracy

92.2% (1.1b remaining)

Error of 7.9b against oracle of 6.8b and baseline of 21.1b

bsearch193.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.047592289682709e+46
11
-1.829086240692416e+154
-2.187052964502477e+134
-8.555281377770497e+140

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
051140
162140
done62140

end0.0ms

sample836.0ms

Algorithm
intervals
Results
454.0ms8732×body80valid
135.0ms2861×body80nan