Details

Time bar (total: 17.0s)

sample198.0ms

Algorithm
intervals
Results
15.0ms198×body80valid
13.0ms27×body2560valid
10.0ms26×body1280valid
8.0ms101×body80nan
5.0ms14×body320valid
5.0ms15×body640valid
1.0ms9×body160valid
1.0ms2×body5120valid

simplify33.0ms

Counts
1 → 1
Iterations
IterNodes
done49
449
346
233
119
010

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
2.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite193.0ms

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-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
4 → 171
Calls
4 calls:
116.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
6.0ms
(- (* b_2 b_2) (* a c))
41.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
44.0ms
(- (* b_2 b_2) (* a c))
127.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts
183 → 183
Iterations
IterNodes
done5000
22152
1583
0244

prune890.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize71.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
0.6b
(cbrt a)
2.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×cbrt-prod
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
2×flip3-- pow1/3 sqrt-div diff-log flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log
Counts
4 → 133
Calls
4 calls:
1.0ms
(cbrt a)
1.0ms
(cbrt a)
44.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series792.0ms

Counts
4 → 12
Calls
4 calls:
291.0ms
(cbrt a)
294.0ms
(cbrt a)
102.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
105.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
145 → 145
Iterations
IterNodes
done5001
21604
1429
0184

prune635.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize78.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
6×sqrt-div
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg neg-log
Counts
4 → 141
Calls
4 calls:
29.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))
96.0ms
(sqrt (- (* b_2 b_2) (* a c)))
99.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
153 → 153
Iterations
IterNodes
done5001
21495
1389
0161

prune964.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt b_2) (cbrt b_2))
0.6b
(- (* b_2 b_2) (* a c))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))
21.8b
(fma (- (* (cbrt b_2) (cbrt b_2))) (cbrt b_2) (- (sqrt (- (* b_2 b_2) (* a c)))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
16×cbrt-prod
13×*-un-lft-identity add-cube-cbrt
12×pow1
6×pow1/3 swap-sqr associate-*r* associate-*l* add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u unswap-sqr
3×sqrt-prod
2×flip3-- sqrt-div pow-prod-down pow-sqr pow-prod-up flip--
1×pow2 rem-sqrt-square sub-neg sqrt-pow1 pow-plus pow1/2 fma-neg diff-log prod-diff prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 85
Calls
4 calls:
9.0ms
(* (cbrt b_2) (cbrt b_2))
12.0ms
(- (* b_2 b_2) (* a c))
28.0ms
(sqrt (- (* b_2 b_2) (* a c)))
1.0ms
(fma (- (* (cbrt b_2) (cbrt b_2))) (cbrt b_2) (- (sqrt (- (* b_2 b_2) (* a c)))))

series704.0ms

Counts
4 → 12
Calls
4 calls:
344.0ms
(* (cbrt b_2) (cbrt b_2))
65.0ms
(- (* b_2 b_2) (* a c))
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))
213.0ms
(fma (- (* (cbrt b_2) (cbrt b_2))) (cbrt b_2) (- (sqrt (- (* b_2 b_2) (* a c)))))

simplify1.2s

Counts
97 → 97
Iterations
IterNodes
done5000
21284
1324
0136

prune619.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.8b

regimes522.0ms

Accuracy

86.6% (3.9b remaining)

Error of 9.4b against oracle of 5.5b and baseline of 34.3b

bsearch168.0ms

Steps
ItersRangePoint
3
5.437233749566996e+22
6.419404774371196e+22
6.358019085320933e+22
8
5.9238016895844435e-289
2.20999447876618e-286
5.992812285264993e-289
6
-0.042530208599811804
-0.005947574473424517
-0.03099989563658143

simplify14.0ms

Iterations
IterNodes
done43
243
142
036

end0.0ms

sample2.8s

Algorithm
intervals
Results
626.0ms5931×body80valid
626.0ms1024×body2560valid
545.0ms2961×body80nan
286.0ms865×body1280valid
124.0ms491×body640valid
59.0ms116×body160valid
57.0ms112×body5120valid
48.0ms237×body320valid