Details

Time bar (total: 17.6s)

sample175.0ms

Algorithm
intervals
Results
37.0ms35×body2560valid
33.0ms86×body80nan
33.0ms184×body80valid
26.0ms28×body1280valid
11.0ms15×body640valid
5.0ms4×body5120valid
4.0ms8×body320valid
2.0ms5×body160valid

simplify107.0ms

Counts
1 → 1
Iterations
IterNodes
done98
798
697
595
487
370
243
124
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite170.0ms

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) (* (* c a) 4))) b) a)
15.0ms
(- (* b b) (* (* c a) 4))
59.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
57.0ms
(- (* b b) (* (* c a) 4))
127.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
78.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.5s

Counts
100 → 100
Iterations
IterNodes
done2001
32001
21108
1400
0161

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

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:
14.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
8.0ms
(- (* b b) (* (* c a) 4))
73.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
81.0ms
(- (* b b) (* (* c a) 4))
133.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
119.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.1s

Counts
109 → 109
Iterations
IterNodes
done2006
32006
21177
1413
0179

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

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:
53.0ms
(* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a))
20.0ms
(- (* b b) (* (* c a) 4))
46.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a)) (/ b a))
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a))
61.0ms
(- (* b b) (* (* c a) 4))
126.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a)) (/ b a))
92.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.0s

Counts
110 → 110
Iterations
IterNodes
done2002
32002
21525
1526
0199

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* c a) 4))
16.0b
(- (* (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) 1) (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) a)) (/ b a))
24.6b
(sqrt (- (* b b) (* (* c a) 4)))
24.6b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
3×frac-sub
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-*r/
1×frac-times associate-*l/ sub-div
Counts
4 → 62
Calls
4 calls:
15.0ms
(- (* b b) (* (* c a) 4))
37.0ms
(- (* (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) 1) (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) a)) (/ b a))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* (* c a) 4))
143.0ms
(- (* (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) 1) (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) a)) (/ b a))
113.0ms
(sqrt (- (* b b) (* (* c a) 4)))
123.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.0s

Counts
74 → 74
Iterations
IterNodes
done2004
32004
21076
1344
0118

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

regimes329.0ms

Accuracy

84.7% (4.4b remaining)

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

bsearch266.0ms

Steps
ItersRangePoint
10
8.296670056881522e-85
2.5972983117194536e-74
2.326372645943808e-74
7
-1.8217288728729631e+111
-6.606823090402082e+109
-5.148407540792454e+110

simplify10.0ms

Iterations
IterNodes
done36
136
029

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.4s5836×body80valid
1.3s1126×body2560valid
708.0ms915×body1280valid
396.0ms2976×body80nan
219.0ms417×body640valid
117.0ms236×body320valid
117.0ms119×body5120valid
53.0ms115×body160valid