Details

Time bar (total: 6.5s)

sample278.0ms

Algorithm
intervals
Results
8.0ms33×body2560valid
6.0ms38×body1280valid
6.0ms177×body80valid
3.0ms21×body640valid
2.0ms79×body80nan
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms7×body160valid

simplify26.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01013
11913
23313
34513
44713
done4713

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
42.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify743.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
02425993
15664363
217123549
done50013549

prune381.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize4.0ms

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

prune22.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b
(- (* b_2 b_2) (* a c))
1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
170×*-un-lft-identity
165×times-frac
118×add-cube-cbrt
61×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
15×add-exp-log
11×fma-neg
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×neg-mul-1 flip3-- div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 257
Calls
4 calls:
28.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
33.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
269 → 269
Iterations

Useful iterations: 2 (287.0ms)

IterNodesCost
03518660
17966655
227305553
done50015553

prune400.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.4b
(- (* b_2 b_2) (* a c))
1.7b
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt
16×distribute-lft-neg-in distribute-rgt-neg-in
12×associate-/l*
9×distribute-lft-out
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u neg-mul-1 log1p-expm1-u
3×fma-def associate-/r* sqrt-prod
2×flip3-- flip3-+ sqrt-div flip-- flip-+ associate-/l/ distribute-neg-frac
1×cbrt-undiv +-commutative neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub distribute-frac-neg div-exp prod-diff clear-num sum-log div-inv
Counts
4 → 119
Calls
4 calls:
42.0ms
(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
3.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
32.0ms
(- (* b_2 b_2) (* a c))
73.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify521.0ms

Counts
131 → 131
Iterations

Useful iterations: done (518.0ms)

IterNodesCost
01972260
14422136
214412031
done50002020

prune317.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.0b

regimes200.0ms

Accuracy

83.6% (4.4b remaining)

Error of 10.1b against oracle of 5.7b and baseline of 32.6b

bsearch74.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.1199128263687574e+46
5
-1.2023865605984147e-79
-5.347575839305805e-80
-8.364554704106616e-80

simplify9.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02740
14036
24936
35636
45836
done5836

end0.0ms

sample1.0s

Algorithm
intervals
Results
217.0ms1075×body2560valid
203.0ms5860×body80valid
150.0ms904×body1280valid
92.0ms2862×body80nan
59.0ms457×body640valid
28.0ms114×body5120valid
20.0ms211×body320valid
8.0ms120×body160valid