Details

Time bar (total: 8.7s)

sample40.0ms

Algorithm
intervals
Results
9.0ms39×body2560valid
6.0ms36×body1280valid
6.0ms165×body80valid
3.0ms87×body80nan
2.0ms13×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms4×body160valid

simplify47.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12517
24516
38716
410616
511416
done11416

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite75.0ms

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--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 183
Calls
4 calls:
36.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
3.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
46.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
195 → 195
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03214967
17804592
230134265
done50014264

prune479.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 2.0) a))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
71×times-frac
60×*-un-lft-identity
55×add-cube-cbrt
43×associate-*r*
19×add-exp-log prod-diff
17×sqrt-prod
13×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×div-exp associate-*l*
5×flip3-- prod-exp flip--
4×expm1-log1p-u log1p-expm1-u div-inv difference-of-squares unswap-sqr
3×cbrt-undiv cbrt-unprod
2×frac-times sub-neg sqrt-div diff-log associate-*l/ distribute-lft-out--
1×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down *-commutative
Counts
4 → 151
Calls
4 calls:
71.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 2.0) a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 2.0) a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
163 → 163
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03063645
18183167
232692719
done50002718

prune426.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
452×add-sqr-sqrt
377×*-un-lft-identity
303×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
52×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
19×prod-diff
17×div-inv
15×div-exp
13×add-cbrt-cube
8×add-log-exp
7×fma-neg
6×pow1 cbrt-undiv
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u
3×rec-exp flip3-- 1-exp flip-- associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 388
Calls
4 calls:
34.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
43.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify577.0ms

Counts
400 → 400
Iterations

Useful iterations: done (561.0ms)

IterNodesCost
061212852
1146511602
done500010898

prune659.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
25.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify490.0ms

Counts
128 → 128
Iterations

Useful iterations: done (486.0ms)

IterNodesCost
01132856
12782310
210211912
done50001834

prune373.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

regimes193.0ms

Accuracy

81.5% (5.2b remaining)

Error of 10.9b against oracle of 5.8b and baseline of 33.8b

bsearch113.0ms

Steps
ItersRangePoint
9
2.365685850767504e-168
1.2053288471691685e-161
1.1860189201379418e-161
8
-1.4395777107888637e+138
-2.299948591329529e+133
-1.9827654008890006e+134

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample1.1s

Algorithm
intervals
Results
241.0ms1025×body2560valid
234.0ms5914×body80valid
167.0ms891×body1280valid
116.0ms2997×body80nan
68.0ms450×body640valid
30.0ms107×body5120valid
23.0ms209×body320valid
8.0ms104×body160valid