Details

Time bar (total: 16.4s)

sample210.0ms

Algorithm
intervals
Results
17.0ms33×body2560valid
16.0ms35×body1280valid
13.0ms168×body80valid
7.0ms92×body80nan
4.0ms15×body640valid
3.0msbody5120valid
2.0msbody320valid
1.0msbody160valid

simplify56.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
01013
11513
22312
33012
43212
53412
done3412

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.2b
(- (* b_2 b_2) (* a c))
2.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
add-log-exp
fma-neg
add-exp-log add-cbrt-cube associate-/l*
pow1 distribute-lft-out--
expm1-log1p-u flip3-- flip-- log1p-expm1-u
associate-/r*
sub-neg sqrt-div diff-log associate-/l/
cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 118
Calls
4 calls:
144.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
10.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
43.0ms
(- (* b_2 b_2) (* a c))
97.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
103.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.2s

Counts
130 → 130
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01952408
14532113
211071874
334021795
done50001785

prune521.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.4b

localize10.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune39.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2) a)
1.5b
(fma b_2 b_2 (- (* a c)))
2.0b
(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
24.4b
(sqrt (fma b_2 b_2 (- (* a c))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
add-exp-log fma-neg add-cbrt-cube associate-/l* add-log-exp
pow1 distribute-lft-out--
expm1-log1p-u log1p-expm1-u
associate-/r*
flip3-- flip-- associate-/l/
cbrt-undiv sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp clear-num fma-udef div-inv
Counts
4 → 110
Calls
4 calls:
51.0ms
(/ (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2) a)
0.0ms
(fma b_2 b_2 (- (* a c)))
11.0ms
(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
2.0ms
(sqrt (fma b_2 b_2 (- (* a c))))

series466.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(/ (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2) a)
87.0ms
(fma b_2 b_2 (- (* a c)))
114.0ms
(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
87.0ms
(sqrt (fma b_2 b_2 (- (* a c))))

simplify3.2s

Counts
122 → 122
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01732260
13861986
28821763
327481683
done50001632

prune461.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (pow b_2 2) (* a c))
3.8b
(/ (/ (fma c (- a) 0) (+ (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
11.8b
(/ (fma c (- a) 0) (+ (sqrt (- (pow b_2 2) (* a c))) b_2))
24.4b
(sqrt (- (pow b_2 2) (* a c)))

rewrite346.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
101×*-un-lft-identity
70×add-sqr-sqrt
69×add-cube-cbrt
21×associate-/l*
16×distribute-lft-out
11×add-exp-log add-cbrt-cube
10×associate-/r/
fma-neg prod-diff
associate-/r*
unpow-prod-down div-inv add-log-exp
pow1 flip3-+ flip-+
cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
sqrt-prod
flip3-- frac-2neg sqrt-div clear-num flip-- unpow2 sqr-pow
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 174
Calls
4 calls:
28.0ms
(- (pow b_2 2) (* a c))
154.0ms
(/ (/ (fma c (- a) 0) (+ (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
134.0ms
(/ (fma c (- a) 0) (+ (sqrt (- (pow b_2 2) (* a c))) b_2))
20.0ms
(sqrt (- (pow b_2 2) (* a c)))

series683.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (pow b_2 2) (* a c))
249.0ms
(/ (/ (fma c (- a) 0) (+ (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
300.0ms
(/ (fma c (- a) 0) (+ (sqrt (- (pow b_2 2) (* a c))) b_2))
86.0ms
(sqrt (- (pow b_2 2) (* a c)))

simplify1.8s

Counts
186 → 186
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02924592
16824341
218443927
done50013903

prune903.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

regimes360.0ms

Accuracy

88.1% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 32.6b

bsearch242.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
1.3572844331324948e+61
9
6.262918217783262e-188
1.0824447814377013e-180
3.8495586393832845e-181
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03861
14761
24961
done4961

end0.0ms

sample3.2s

Algorithm
intervals
Results
966.0ms1050×body2560valid
669.0ms5871×body80valid
406.0ms895×body1280valid
268.0ms2846×body80nan
167.0ms479×body640valid
51.0ms101×body5120valid
43.0ms218×body320valid
14.0ms106×body160valid