Details

Time bar (total: 22.8s)

sample169.0ms

Algorithm
intervals
Results
60.0ms39×body2560valid
30.0ms180×body80valid
25.0ms29×body1280valid
16.0ms21×body640valid
11.0ms70×body80nan
4.0ms7×body320valid
0.0ms1×body160valid

simplify150.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.0b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
1.0b
(- (* b b) (* (* c a) 4))
19.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite166.0ms

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:
74.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
61.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms
(- (* b b) (* (* c a) 4))
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
133.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
77.0ms
(- (* b b) (* (* c a) 4))
115.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify2.9s

Counts
100 → 100
Iterations
IterNodes
done5011
34767
21107
1400
0161

prune570.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
1.0b
(- (* b b) (* (* c a) 4))
5.4b
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
19.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite132.0ms

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:
29.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
15.0ms
(- (* b b) (* (* c a) 4))
71.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
65.0ms
(- (* b b) (* (* c a) 4))
123.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
97.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify2.8s

Counts
109 → 109
Iterations
IterNodes
done5003
34532
21177
1413
0179

prune662.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4)))))
1.0b
(- (* b b) (* (* c a) 4))
10.1b
(- (/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4))))) (/ b a))
19.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
173×times-frac
132×add-sqr-sqrt
95×*-un-lft-identity
82×add-cube-cbrt
43×sqrt-prod
24×associate-/r*
15×add-exp-log
14×difference-of-squares
10×sqrt-div
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1 div-inv
4×insert-posit16
3×cbrt-undiv associate-/l* distribute-lft-out--
2×rec-exp sub-neg diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 frac-sub pow-flip inv-pow
Counts
4 → 181
Calls
4 calls:
17.0ms
(/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4)))))
15.0ms
(- (* b b) (* (* c a) 4))
115.0ms
(- (/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4))))) (/ b a))
19.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series792.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4)))))
79.0ms
(- (* b b) (* (* c a) 4))
504.0ms
(- (/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4))))) (/ b a))
89.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.8s

Counts
193 → 193
Iterations
IterNodes
done5000
21944
1746
0295

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize99.0ms

Local error

Found 4 expressions with local error:

15.2b
(- (/ (/ 1 (/ 1 (sqrt (* (cbrt (- (* b b) (* (* c a) 4))) (cbrt (- (* b b) (* (* c a) 4))))))) (/ a (sqrt (cbrt (- (* b b) (* (* c a) 4)))))) (/ b a))
19.9b
(cbrt (- (* b b) (* (* c a) 4)))
19.9b
(cbrt (- (* b b) (* (* c a) 4)))
19.9b
(cbrt (- (* b b) (* (* c a) 4)))

rewrite532.0ms

Algorithm
rewrite-expression-head
Rules
426×add-sqr-sqrt
347×times-frac
90×difference-of-squares
88×*-un-lft-identity
76×sqrt-prod
31×cbrt-prod
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×pow1/3 distribute-lft-out--
1×sub-neg diff-log frac-sub div-inv
Counts
4 → 149
Calls
4 calls:
512.0ms
(- (/ (/ 1 (/ 1 (sqrt (* (cbrt (- (* b b) (* (* c a) 4))) (cbrt (- (* b b) (* (* c a) 4))))))) (/ a (sqrt (cbrt (- (* b b) (* (* c a) 4)))))) (/ b a))
5.0ms
(cbrt (- (* b b) (* (* c a) 4)))
5.0ms
(cbrt (- (* b b) (* (* c a) 4)))
5.0ms
(cbrt (- (* b b) (* (* c a) 4)))

series530.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (/ (/ 1 (/ 1 (sqrt (* (cbrt (- (* b b) (* (* c a) 4))) (cbrt (- (* b b) (* (* c a) 4))))))) (/ a (sqrt (cbrt (- (* b b) (* (* c a) 4)))))) (/ b a))
120.0ms
(cbrt (- (* b b) (* (* c a) 4)))
141.0ms
(cbrt (- (* b b) (* (* c a) 4)))
151.0ms
(cbrt (- (* b b) (* (* c a) 4)))

simplify2.8s

Counts
161 → 161
Iterations
IterNodes
done5000
34569
21445
1706
0307

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.2b

regimes511.0ms

Accuracy

84.9% (4.2b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 33.8b

bsearch199.0ms

Steps
ItersRangePoint
9
1.542649851819534e-86
4.188981380654902e-77
1.2158870426682226e-82
6
-1.2115114540629089e+151
-9.504756559616229e+149
-7.397994825724217e+150

simplify12.0ms

Iterations
IterNodes
done35
135
029

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.6s1057×body2560valid
963.0ms5900×body80valid
628.0ms895×body1280valid
432.0ms2938×body80nan
357.0ms455×body640valid
116.0ms211×body320valid
105.0ms106×body5120valid
24.0ms97×body160valid