Details

Time bar (total: 18.0s)

sample52.0ms

Algorithm
intervals
Results
22.0ms273×body80valid
5.0ms69×body80nan

simplify212.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize151.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

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:
18.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(- (* b b) (* (* 4.0 a) c))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
78 → 78
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0711146
11681050
2574952
32407952
done5000936

prune553.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize121.0ms

Local error

Found 4 expressions with local error:

7.4b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log flip-+
Counts
4 → 76
Calls
4 calls:
18.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
89.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.9s

Counts
88 → 88
Iterations

Useful iterations: done (3.9s)

IterNodesCost
0901548
12471095
28411019
330481007
done50001005

prune779.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize142.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.2b
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* b -2)))
8.3b
(/ (* a c) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 79
Calls
4 calls:
25.0ms
(- (* b b) (* (* 4.0 a) c))
20.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* b -2)))
13.0ms
(/ (* a c) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* b b) (* (* 4.0 a) c))
120.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* b -2)))
38.0ms
(/ (* a c) b)
125.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
91 → 91
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01611254
13671192
213231043
done50001029

prune579.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

localize150.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.2b
(/ (* 2.0 c) (fma 2.0 (* a (/ c b)) (* b -2)))
5.2b
(* a (/ c b))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
14×add-exp-log add-cbrt-cube
13×times-frac associate-*r*
7×pow1
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv div-exp associate-*l* prod-exp associate-/r* sqrt-prod cbrt-unprod
2×flip3-- sqrt-div flip-- div-inv unswap-sqr
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 90
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(/ (* 2.0 c) (fma 2.0 (* a (/ c b)) (* b -2)))
21.0ms
(* a (/ c b))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series724.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* (* 4.0 a) c))
521.0ms
(/ (* 2.0 c) (fma 2.0 (* a (/ c b)) (* b -2)))
38.0ms
(* a (/ c b))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: 2 (280.0ms)

IterNodesCost
01821345
14241273
214001110
done50011110

prune579.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

regimes319.0ms

Accuracy

92.3% (1.1b remaining)

Error of 7.8b against oracle of 6.7b and baseline of 21.3b

bsearch489.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
11
-2.859335985249397e-307
9.448397398655464e-278
-5.0660426096144e-310
9
-1.4642911230069481e+159
-8.435593739772907e+149
-1.4341281730542053e+153

simplify28.0ms

Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
049176
163140
done63140

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.1s8737×body80valid
286.0ms2941×body80nan