Details

Time bar (total: 12.8s)

sample343.0ms

Algorithm
intervals
Results
7.0ms206×body80valid
5.0ms28×body2560valid
5.0ms105×body80nan
4.0ms28×body1280valid
2.0ms13×body640valid
0.0ms2×body5120valid
0.0ms6×body160valid
0.0ms4×body320valid

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
01013
11513
22312
33012
43212
53412
done3412

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b
(- (* b_2 b_2) (* a c))
1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-exp-log add-cbrt-cube associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 118
Calls
4 calls:
87.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms
(- (* b_2 b_2) (* a c))
53.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
37.0ms
(- (* b_2 b_2) (* a c))
79.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts
130 → 130
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01952408
14532113
211071874
334021795
done50001785

prune314.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b
(- (* b_2 b_2) (* a c))
1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×associate-/r/ add-cbrt-cube
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/l*
2×sub-neg rec-exp sqrt-div diff-log 1-exp
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 196
Calls
4 calls:
55.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms
(- (* b_2 b_2) (* a c))
49.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
38.0ms
(- (* b_2 b_2) (* a c))
74.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
208 → 208
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
02994764
16414074
214333649
342083500
done50003500

prune322.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b
(- (* b_2 b_2) (* a c))
1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-exp-log add-cbrt-cube associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 118
Calls
4 calls:
86.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms
(- (* b_2 b_2) (* a c))
50.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
37.0ms
(- (* b_2 b_2) (* a c))
78.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts
130 → 130
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01952408
14532113
211071874
334021795
done50001785

prune292.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b
(sqrt (- (* b_2 b_2) (* a c)))
21.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
48.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
49.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
128 → 128
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01102512
12602002
26411672
319321520
done50011420

prune321.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.2b

regimes196.0ms

Accuracy

79.3% (5.8b remaining)

Error of 11.2b against oracle of 5.4b and baseline of 33.4b

bsearch147.0ms

Steps
ItersRangePoint
8
0.0001820196720056695
0.3848154462067827
0.00018465375781150442
6
3.6410892437809104e-110
3.0960233903298005e-109
3.7052502960789305e-110
8
1.0691773024250323e-170
5.5548132533506025e-168
5.330769455174493e-168
7
-1.3907042211653736e+140
-2.4882870722039588e+138
-4.4167841993114605e+139

simplify9.0ms

Iterations

Useful iterations: done (9.0ms)

IterNodesCost
03370
14456
24745
35045
done5044

end0.0ms

sample1.1s

Algorithm
intervals
Results
204.0ms5929×body80valid
199.0ms1044×body2560valid
138.0ms905×body1280valid
91.0ms2855×body80nan
58.0ms466×body640valid
26.0ms102×body5120valid
20.0ms223×body320valid
6.0ms92×body160valid