Details

Time bar (total: 17.1s)

sample99.0ms

Algorithm
intervals
Results
20.0ms36×body2560valid
17.0ms179×body80valid
13.0ms28×body1280valid
7.0ms79×body80nan
5.0ms15×body640valid
2.0ms3×body5120valid
2.0ms8×body320valid
0.0ms2×body160valid

simplify135.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b
(- (* b b) (* (* 4.0 a) c))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
156.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
64.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
30.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series556.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
125.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
82.0ms
(- (* b b) (* (* 4.0 a) c))
141.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
118 → 118
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01952476
14802169
214411861
done50001789

prune513.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b
(- (* b b) (* (* 4.0 a) c))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×times-frac
50×*-un-lft-identity
40×add-cube-cbrt
25×add-exp-log
20×sqrt-prod
19×prod-diff
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×add-log-exp
7×flip3-- fma-neg flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 152
Calls
4 calls:
93.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
103.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms
(- (* b b) (* (* 4.0 a) c))
33.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series768.0ms

Counts
4 → 12
Calls
4 calls:
314.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
185.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
103.0ms
(- (* b b) (* (* 4.0 a) c))
167.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
164 → 164
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02614025
15873484
216523082
done50012938

prune606.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
0.6b
(- (* b b) (* (* 4.0 a) c))
6.7b
(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
86×times-frac
71×prod-diff
57×*-un-lft-identity
56×add-sqr-sqrt
53×add-cube-cbrt
33×sqrt-prod
21×div-inv
11×fma-neg
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/ distribute-lft-out--
1×rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 164
Calls
4 calls:
27.0ms
(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
15.0ms
(- (* b b) (* (* 4.0 a) c))
155.0ms
(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
37.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series723.0ms

Counts
4 → 12
Calls
4 calls:
284.0ms
(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
70.0ms
(- (* b b) (* (* 4.0 a) c))
211.0ms
(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
158.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
176 → 176
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02756226
16705339
218974532
done50013671

prune679.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b
(- (* b b) (* (* 4.0 a) c))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
160.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
108.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
163.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
61.0ms
(- (* b b) (* (* 4.0 a) c))
139.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
118 → 118
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01952476
14802169
214411861
done50001789

prune359.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

regimes357.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.3b

bsearch135.0ms

Steps
ItersRangePoint
5
1.8656011488683937e-53
5.89324344694736e-53
1.8920981354719558e-53
8
-3.0008378519073826e+120
-1.7813274366303991e+117
-1.0062396840173395e+118

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02638
13138
done3138

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s1022×body2560valid
690.0ms5914×body80valid
405.0ms872×body1280valid
359.0ms2922×body80nan
138.0ms467×body640valid
133.0ms236×body320valid
114.0ms125×body5120valid
16.0ms109×body160valid