Details

Time bar (total: 14.5s)

sample42.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
7.0ms177×body80valid
6.0ms31×body1280valid
3.0ms92×body80nan
2.0ms16×body640valid
1.0ms5×body5120valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 183
Calls
4 calls:
39.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
24.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
47.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
195 → 195
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03214967
17594592
221934283
done50004264

prune505.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
3251×times-frac
1774×add-sqr-sqrt
1519×*-un-lft-identity
1265×add-cube-cbrt
254×difference-of-squares
142×sqrt-prod
129×div-inv
127×distribute-lft-out--
71×associate-/r*
64×add-exp-log
54×div-exp
25×add-cbrt-cube
19×prod-diff
15×cbrt-undiv 1-exp associate-/r/
13×associate-/l*
8×add-log-exp
7×fma-neg
6×rec-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip--
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 1122
Calls
4 calls:
54.0ms
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
23.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
79.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
46.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify5.1s

Counts
1134 → 1134
Iterations

Useful iterations: done (5.0s)

IterNodesCost
0152448578
1452440803
done500038703

prune707.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ a (/ 1 2.0)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
726×times-frac
494×add-sqr-sqrt
401×*-un-lft-identity
309×add-cube-cbrt
92×difference-of-squares
61×sqrt-prod
46×distribute-lft-out--
44×associate-/r*
29×div-inv
19×add-exp-log prod-diff
13×add-cbrt-cube
11×div-exp
8×associate-/r/ add-log-exp
7×fma-neg
6×cbrt-undiv associate-/l*
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×sub-neg sqrt-div diff-log associate-/l/
1×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp div-sub clear-num
Counts
4 → 412
Calls
4 calls:
61.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ a (/ 1 2.0)))
24.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ a (/ 1 2.0)))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
45.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts
424 → 424
Iterations

Useful iterations: done (1.0s)

IterNodesCost
064314498
1180513016
done500012417

prune701.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
44.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
78 → 78
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0711146
11691050
2603952
32524952
done5000948

prune438.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.9b

regimes255.0ms

Accuracy

85.2% (4.2b remaining)

Error of 9.8b against oracle of 5.6b and baseline of 33.8b

bsearch125.0ms

Steps
ItersRangePoint
11
4.489865195692553e-133
5.932607888300091e-106
2.0569776426586135e-106
8
-6.10058349091927e+155
-9.408528429616011e+151
-7.93152454634662e+153

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13440
done3440

end0.0ms

sample1.1s

Algorithm
intervals
Results
246.0ms1046×body2560valid
235.0ms5918×body80valid
162.0ms861×body1280valid
110.0ms2864×body80nan
70.0ms452×body640valid
34.0ms113×body5120valid
28.0ms230×body320valid
7.0ms100×body160valid