Details

Time bar (total: 16.0s)

sample81.0ms

Algorithm
intervals
Results
25.0ms178×body80valid
15.0ms38×body2560valid
9.0ms28×body1280valid
5.0ms79×body80nan
3.0ms11×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify120.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
98.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
102 → 102
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01671697
14331584
214861361
done50001347

prune452.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
122.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
56.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
112.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
58.0ms
(- (* b b) (* (* 4.0 a) c))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01671697
14331584
214861361
done50001347

prune447.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×*-un-lft-identity
14×add-sqr-sqrt
13×add-cbrt-cube
11×add-cube-cbrt
10×fma-def prod-exp add-log-exp
7×pow1 associate-*r*
5×distribute-rgt-neg-in associate-*l*
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out
3×distribute-lft-neg-in flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 100
Calls
4 calls:
154.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
40.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
133.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
89.0ms
(- (* b b) (* (* 4.0 a) c))
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
112 → 112
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01942017
14971794
217891516
done50001490

prune426.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
11.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* b b) (* (* 4.0 a) c))
50.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.4s

Counts
78 → 78
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0711146
11681050
2574952
32407952
done5000936

prune385.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.2b

regimes225.0ms

Accuracy

89.2% (3.1b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 34.4b

bsearch275.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.4479393508684064e+78
11
-1.0472779812871276e-269
-2.473343252086336e-295
-2.0759438211365155e-290
8
-6.990724105819741e+111
-2.6156774686163576e+108
-1.569310777886352e+111

simplify9.0ms

Iterations

Useful iterations: done (8.0ms)

IterNodesCost
03870
14770
done4768

end0.0ms

sample3.4s

Algorithm
intervals
Results
743.0ms2994×body80nan
708.0ms5806×body80valid
616.0ms1087×body2560valid
425.0ms930×body1280valid
193.0ms446×body640valid
94.0ms117×body5120valid
44.0ms210×body320valid
17.0ms116×body160valid