Details

Time bar (total: 18.5s)

sample160.0ms

Algorithm
intervals
Results
17.0ms32×body2560valid
16.0ms184×body80valid
12.0ms30×body1280valid
7.0ms24×body640valid
6.0ms83×body80nan
2.0ms7×body320valid
1.0ms4×body160valid

simplify120.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
01013
11913
23313
34613
44913
done4913

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize27.0ms

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))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite198.0ms

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:
108.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms
(- (* b_2 b_2) (* a c))
46.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms
(- (* b_2 b_2) (* a c))
113.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
132.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
183 → 183
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02425993
15464313
214083549
done50003001

prune564.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b
(fma b_2 b_2 (- (* c a)))
2.5b
(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
9.2b
(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
19.7b
(sqrt (fma b_2 b_2 (- (* c a))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
27×associate-/l*
19×sqrt-prod
16×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
6×div-inv
5×pow1 flip3-- flip--
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×associate-/l/
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ fma-udef
Counts
4 → 186
Calls
4 calls:
1.0ms
(fma b_2 b_2 (- (* c a)))
76.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
40.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
2.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

series732.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(fma b_2 b_2 (- (* c a)))
238.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
318.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
115.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.3s

Counts
198 → 198
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02955516
16784787
221104608
done50004543

prune689.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
0.5b
(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
0.8b
(fma b_2 b_2 (- (* c a)))
19.7b
(sqrt (fma b_2 b_2 (- (* c a))))

rewrite39.0ms

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
6×add-exp-log fma-neg associate-/r* add-cbrt-cube add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×associate-/l*
2×flip3-- associate-/r/ flip--
1×cbrt-undiv sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-exp clear-num fma-udef div-inv
Counts
4 → 109
Calls
4 calls:
21.0ms
(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
11.0ms
(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
0.0ms
(fma b_2 b_2 (- (* c a)))
2.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

series576.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
140.0ms
(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
81.0ms
(fma b_2 b_2 (- (* c a)))
87.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.5s

Counts
121 → 121
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01672224
13341950
27021731
319681653
done50001598

prune429.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b
(fma b_2 b_2 (- (* c a)))
2.6b
(* (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) (/ 1 a))
9.2b
(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
19.7b
(sqrt (fma b_2 b_2 (- (* c a))))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
52×times-frac
49×*-un-lft-identity
33×add-cube-cbrt
28×add-exp-log
24×associate-*l*
18×add-cbrt-cube
14×difference-of-squares
13×associate-*r*
10×sqrt-prod
9×div-exp
8×prod-exp
7×pow1 distribute-lft-out--
6×associate-/r* unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u associate-/r/ cbrt-unprod log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+ fma-udef
Counts
4 → 140
Calls
4 calls:
1.0ms
(fma b_2 b_2 (- (* c a)))
96.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) (/ 1 a))
62.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
3.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

series730.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(fma b_2 b_2 (- (* c a)))
246.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) (/ 1 a))
291.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
134.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.6s

Counts
152 → 152
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02413394
16272889
219452585
done50002452

prune602.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.4b

regimes197.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.6b

bsearch235.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.7151811081882383e+78
9
3.6976431258031608e-267
1.8292500652683027e-260
7.061692521831336e-266
8
-6.990724105819741e+111
-2.6156774686163576e+108
-5.674469085146397e+110

simplify18.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
03553
14449
24649
done4649

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s5908×body80valid
623.0ms1082×body2560valid
361.0ms891×body1280valid
175.0ms3009×body80nan
117.0ms472×body640valid
68.0ms212×body320valid
58.0ms107×body5120valid
13.0ms104×body160valid