Details

Time bar (total: 10.2s)

sample41.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
7.0ms195×body80valid
4.0ms21×body1280valid
3.0ms81×body80nan
3.0ms19×body640valid
1.0ms3×body5120valid
0.0ms4×body320valid
0.0ms4×body160valid

simplify59.0ms

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: 30.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.4b
(- (* b b) (* (* 4.0 a) c))
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

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:
37.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
3.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (/ (- (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)
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify970.0ms

Counts
195 → 195
Iterations

Useful iterations: done (957.0ms)

IterNodesCost
03214967
17514592
221844283
done50014264

prune517.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
0.4b
(- (* b b) (* (* 4.0 a) c))
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite98.0ms

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:
36.0ms
(/ 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)
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
46.0ms
(- (* 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)))

simplify1.4s

Counts
400 → 400
Iterations

Useful iterations: done (1.4s)

IterNodesCost
061212852
1142811390
2357510561
done500010543

prune626.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 a) 2.0))
0.4b
(- (* b b) (* (* 4.0 a) c))
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite114.0ms

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:
77.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 a) 2.0))
3.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 a) 2.0))
45.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts
163 → 163
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03063645
17863137
223562737
done50012710

prune437.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

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:
23.0ms
(- (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)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
128 → 128
Iterations

Useful iterations: 3 (630.0ms)

IterNodesCost
01132856
12622310
27561948
328771774
done50011774

prune364.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes172.0ms

Accuracy

83.3% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.3b

bsearch140.0ms

Steps
ItersRangePoint
10
3.056596725548563e-78
7.076105677608322e-63
3.446447862996811e-75
10
-1.852183237050365e+100
-1.9127319211193897e+86
-4.123103533644211e+95

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample1.2s

Algorithm
intervals
Results
256.0ms1096×body2560valid
238.0ms5880×body80valid
166.0ms852×body1280valid
110.0ms2945×body80nan
69.0ms471×body640valid
33.0ms109×body5120valid
25.0ms211×body320valid
8.0ms107×body160valid