Details

Time bar (total: 18.5s)

sample59.0ms

Algorithm
intervals
Results
12.0ms41×body2560valid
10.0ms178×body80valid
7.0ms29×body1280valid
4.0ms93×body80nan
3.0ms17×body640valid
1.0ms5×body160valid
0.0ms1×body5120valid
0.0ms2×body320valid

simplify151.0ms

Counts
1 → 1
Iterations
IterNodes
done94
794
693
591
483
368
239
121
012

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
1.7b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
2.0b
(- (* b b) (* (* 3.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
97.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
64.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
11.0ms
(- (* b b) (* (* 3.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
102.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
72.0ms
(- (* b b) (* (* 3.0 a) c))
100.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts
84 → 84
Iterations
IterNodes
done5000
21253
1391
0154

prune628.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
1.7b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
2.0b
(- (* b b) (* (* 3.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×associate-/r* times-frac sqrt-prod difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
41.0ms
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
36.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms
(- (* b b) (* (* 3.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
109.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
57.0ms
(- (* b b) (* (* 3.0 a) c))
116.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.7s

Counts
83 → 83
Iterations
IterNodes
done5003
21233
1376
0147

prune661.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.7b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
2.0b
(- (* b b) (* (* 3.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
25.0ms
(* (* 3.0 a) c)
69.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms
(- (* b b) (* (* 3.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (* 3.0 a) c)
113.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
67.0ms
(- (* b b) (* (* 3.0 a) c))
107.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.0s

Counts
72 → 72
Iterations
IterNodes
done5000
33541
2911
1293
0120

prune454.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* 3.0 a))
1.7b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
2.0b
(- (* b b) (* (* 3.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
12×add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube
8×pow1 add-log-exp
7×add-cube-cbrt
4×div-exp sqrt-prod
3×times-frac flip3-- prod-exp flip-- associate-/l*
2×cbrt-undiv rec-exp sub-neg sqrt-div diff-log 1-exp pow-flip difference-of-squares
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow-prod-down cbrt-unprod div-inv distribute-lft-out-- inv-pow
Counts
4 → 70
Calls
4 calls:
9.0ms
(/ 1 (* 3.0 a))
48.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms
(- (* b b) (* (* 3.0 a) c))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ 1 (* 3.0 a))
122.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
82.0ms
(- (* b b) (* (* 3.0 a) c))
102.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.4s

Counts
82 → 82
Iterations
IterNodes
done5000
34899
21065
1321
0137

prune461.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.0b

regimes647.0ms

Accuracy

85.2% (4.3b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 34.9b

bsearch165.0ms

Steps
ItersRangePoint
10
8.767897341253802e-114
4.657027509742155e-104
4.6129908231112306e-104
9
-6.117539429929052e+154
-3.6285784997486435e+148
-3.2516568688411723e+152

simplify5.0ms

Iterations
IterNodes
done35
135
028

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.1s1115×body2560valid
797.0ms2954×body80nan
494.0ms5808×body80valid
414.0ms901×body1280valid
190.0ms455×body640valid
58.0ms105×body5120valid
45.0ms213×body320valid
16.0ms124×body160valid