Details

Time bar (total: 6.5s)

sample56.0ms

Algorithm
intervals
Results
14.0ms145×body160valid
10.0ms524×pre80true
9.0ms268×body80nan
4.0ms111×body80valid

simplify57.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.3b
(- (* b b) (* (* 4.0 a) c))
27.9b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
add-exp-log add-cbrt-cube
add-log-exp
fma-neg
pow1 div-inv
expm1-log1p-u log1p-expm1-u
cbrt-undiv flip3-- div-exp associate-/r* flip--
sub-neg sqrt-div diff-log div-sub
rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 183
Calls
4 calls:
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
39.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
3.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series305.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
47.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.0s

Counts
195 → 195
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03214967
17594592
221944283
done50004264

prune518.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.9b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune77.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 8.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b
(/ (* a c) b)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-exp-log add-cbrt-cube
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×cbrt-undiv div-exp
associate-/l*
associate-/r* div-inv
prod-exp cbrt-unprod
pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
associate-/l/
Counts
2 → 77
Calls
2 calls:
10.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
3.0ms
(/ (* a c) b)

series40.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
20.0ms
(/ (* a c) b)

simplify874.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (203.0ms)

IterNodesCost
01711200
14441154
21838992
done5000992

prune253.0ms

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 8.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
0.3b
(/ (* a c) b)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u div-inv associate-/l* add-log-exp
associate-*r/ associate-/l/
Counts
2 → 55
Calls
2 calls:
9.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
4.0ms
(/ (* a c) b)

series43.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
23.0ms
(/ (* a c) b)

simplify1.0s

Counts
61 → 61
Iterations

Useful iterations: 2 (171.0ms)

IterNodesCost
0111818
1343787
21853559
done5001559

prune86.0ms

Pruning

38 alts after pruning (36 fresh and 2 done)

Merged error: 8.7b

regimes530.0ms

Accuracy

42.9% (7.6b remaining)

Error of 16.8b against oracle of 9.1b and baseline of 22.5b

bsearch4.0ms

Steps
ItersRangePoint
0
4947.217786474198
5174.453079191142
5060.8354328326695

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02238
12638
done2638

end0.0ms

sample1.4s

Algorithm
intervals
Results
330.0ms4520×body160valid
310.0ms16557×pre80true
294.0ms8557×body80nan
127.0ms3480×body80valid