Details

Time bar (total: 22.3s)

sample92.0ms

Algorithm
intervals
Results
21.0ms35×body2560valid
18.0ms184×body80valid
13.0ms28×body1280valid
12.0ms86×body80nan
5.0ms15×body640valid
3.0ms4×body5120valid
3.0ms8×body320valid
1.0ms5×body160valid

simplify135.0ms

Counts
1 → 1
Iterations
IterNodes
895
795
694
592
484
367
243
124
014

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
0.6b
(- (* b b) (* (* 4 a) c))
1.7b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
24.6b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
86.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
13.0ms
(- (* b b) (* (* 4 a) c))
65.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
76.0ms
(- (* b b) (* (* 4 a) c))
118.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
127.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
100 → 100
Iterations
IterNodes
33816
21126
1392
0161

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
0.6b
(- (* b b) (* (* 4 a) c))
8.4b
(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
24.6b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
31×times-frac
30×*-un-lft-identity
22×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div insert-posit16 flip-- distribute-lft-out--
3×associate-/r* div-inv
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 97
Calls
4 calls:
13.0ms
(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
7.0ms
(- (* b b) (* (* 4 a) c))
61.0ms
(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series569.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
70.0ms
(- (* b b) (* (* 4 a) c))
155.0ms
(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
131.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts
109 → 109
Iterations
IterNodes
33407
21131
1408
0179

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a))
0.6b
(- (* b b) (* (* 4 a) c))
12.6b
(- (* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a)) (/ b a))
24.6b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac associate-*r* add-exp-log
10×sqrt-div
9×add-cbrt-cube sqrt-prod
8×add-log-exp
7×pow1 flip3-- flip--
6×associate-*l* frac-sub unswap-sqr
4×frac-times associate-*l/ prod-exp insert-posit16
3×associate-*r/ un-div-inv
2×sub-neg diff-log div-exp cbrt-unprod div-inv sub-div
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 distribute-rgt-out-- pow1/2 1-exp pow-prod-down *-commutative
Counts
4 → 98
Calls
4 calls:
54.0ms
(* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a))
8.0ms
(- (* b b) (* (* 4 a) c))
29.0ms
(- (* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a)) (/ b a))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series519.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a))
86.0ms
(- (* b b) (* (* 4 a) c))
145.0ms
(- (* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a)) (/ b a))
106.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify4.5s

Counts
110 → 110
Iterations
IterNodes
34298
21540
1519
0199

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4 a) c))
16.0b
(- (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (/ (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) a)) (/ b a))
24.6b
(sqrt (- (* b b) (* (* 4 a) c)))
24.6b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-div
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity flip3-- add-cube-cbrt sqrt-prod flip--
5×frac-sub
4×add-cbrt-cube add-exp-log insert-posit16
2×frac-times rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-*l/ associate-*r/
1×sub-div
Counts
4 → 64
Calls
4 calls:
15.0ms
(- (* b b) (* (* 4 a) c))
59.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (/ (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) a)) (/ b a))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* b b) (* (* 4 a) c))
135.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (/ (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) a)) (/ b a))
124.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
112.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.4s

Counts
76 → 76
Iterations
IterNodes
33173
2982
1337
0131

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

regimes336.0ms

Accuracy

84.7% (4.4b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 34.1b

bsearch204.0ms

Steps
ItersRangePoint
10
8.296670056881522e-85
2.5972983117194536e-74
2.326372645943808e-74
7
-1.8217288728729631e+111
-6.606823090402082e+109
-1.0027271082217074e+110

simplify5.0ms

Iterations
IterNodes
234
134
029

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.3s5836×body80valid
1.2s915×body1280valid
1.1s1126×body2560valid
502.0ms2976×body80nan
276.0ms417×body640valid
155.0ms119×body5120valid
103.0ms236×body320valid
30.0ms115×body160valid