Details

Time bar (total: 21.6s)

sample129.0ms

Algorithm
intervals
Results
33.0ms39×body2560valid
30.0ms180×body80valid
23.0ms29×body1280valid
11.0ms21×body640valid
10.0ms70×body80nan
3.0ms7×body320valid
0.0ms1×body160valid

simplify95.0ms

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: 33.3b

localize28.0ms

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)))

rewrite132.0ms

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:
73.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
34.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms
(- (* b b) (* (* c a) 4))
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
95.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
48.0ms
(- (* b b) (* (* c a) 4))
87.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify3.0s

Counts
100 → 100
Iterations
IterNodes
done5011
34767
21107
1400
0161

prune588.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize45.0ms

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)))

rewrite107.0ms

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:
27.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
13.0ms
(- (* b b) (* (* c a) 4))
49.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
57.0ms
(- (* b b) (* (* c a) 4))
123.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
110.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify2.5s

Counts
109 → 109
Iterations
IterNodes
done5003
34532
21177
1413
0179

prune684.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize58.0ms

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)))

rewrite146.0ms

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:
18.0ms
(/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4)))))
7.0ms
(- (* b b) (* (* c a) 4))
101.0ms
(- (/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4))))) (/ b a))
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4)))))
57.0ms
(- (* b b) (* (* c a) 4))
149.0ms
(- (/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4))))) (/ b a))
99.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.7s

Counts
193 → 193
Iterations
IterNodes
done5000
21944
1746
0295

prune883.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize82.0ms

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)))

rewrite557.0ms

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:
518.0ms
(- (/ (/ 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))
10.0ms
(cbrt (- (* b b) (* (* c a) 4)))
11.0ms
(cbrt (- (* b b) (* (* c a) 4)))
9.0ms
(cbrt (- (* b b) (* (* c a) 4)))

series554.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(- (/ (/ 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))
107.0ms
(cbrt (- (* b b) (* (* c a) 4)))
150.0ms
(cbrt (- (* b b) (* (* c a) 4)))
159.0ms
(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

regimes426.0ms

Accuracy

84.9% (4.2b remaining)

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

bsearch224.0ms

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

simplify11.0ms

Iterations
IterNodes
done35
135
029

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s1057×body2560valid
940.0ms5900×body80valid
781.0ms2938×body80nan
674.0ms895×body1280valid
255.0ms455×body640valid
117.0ms106×body5120valid
84.0ms211×body320valid
25.0ms97×body160valid