Details

Time bar (total: 19.7s)

sample50.0ms

Algorithm
intervals
Results
21.0ms281×body80valid
5.0ms83×body80nan

simplify196.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize142.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
66.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (* b b) (* (* 4.0 a) c))
100.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
119.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.0s

Counts
152 → 152
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
01816137
14044128
211473279
348422634
done50002634

prune616.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize173.0ms

Local error

Found 4 expressions with local error:

12.6b
(- (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
19.7b
(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b
(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 flip3-- sqrt-div diff-log flip--
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 84
Calls
4 calls:
33.0ms
(- (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
3.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
3.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
100.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
136.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
96 → 96
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01312491
13001521
28781464
333631428
done50001425

prune631.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize134.0ms

Local error

Found 4 expressions with local error:

7.8b
(- (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))) b)
19.7b
(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b
(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-log-exp
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2 prod-diff
2×flip3-- sqrt-div flip--
1×sub-neg fma-neg diff-log difference-of-squares
Counts
4 → 66
Calls
4 calls:
46.0ms
(- (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))) b)
3.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
3.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series529.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(- (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))) b)
132.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
140.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
78 → 78
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01201483
12721013
2750962
32728954
done5000943

prune580.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

localize133.0ms

Local error

Found 4 expressions with local error:

19.7b
(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b
(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b
(sqrt (fma b b (- (* (* 4.0 a) c))))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
2×sqrt-div
1×flip3-- flip--
Counts
4 → 62
Calls
4 calls:
2.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
2.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
2.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
114.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
139.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
74 → 74
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0701006
1157888
2466839
31745839
done5000835

prune525.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.6b

regimes252.0ms

Accuracy

88.8% (1.4b remaining)

Error of 9.1b against oracle of 7.7b and baseline of 20.0b

bsearch134.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.822077811116171e+78
7
-2.95797388004145e+163
-3.6321213431321147e+161
-3.688468976067863e+161

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
044127
153127
261127
done61127

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.4s8776×body80valid
441.0ms3009×body80nan