Details

Time bar (total: 14.2s)

sample220.0ms

Algorithm
intervals
Results
28.0ms36×body2560valid
27.0ms187×body80valid
17.0ms26×body1280valid
10.0ms84×body80nan
6.0ms12×body640valid
3.0ms8×body320valid
3.0ms3×body5120valid
1.0ms5×body160valid

simplify89.0ms

Counts
1 → 1
Iterations
IterNodes
done29
529
427
325
222
114
010

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize21.0ms

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))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
66.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms
(- (* b_2 b_2) (* a c))
42.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
39.0ms
(- (* b_2 b_2) (* a c))
93.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
113.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify659.0ms

Counts
100 → 100
Iterations
IterNodes
done2001
21029
1378
0158

prune569.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize41.0ms

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))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
26×difference-of-squares
24×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
4×insert-posit16
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 166
Calls
4 calls:
80.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
15.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
37.0ms
(- (* b_2 b_2) (* a c))
129.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
96.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify932.0ms

Counts
178 → 178
Iterations
IterNodes
done2002
21691
1626
0262

prune588.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b
(- (* b_2 b_2) (* a c))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
789×times-frac
493×add-sqr-sqrt
406×*-un-lft-identity
320×add-cube-cbrt
86×difference-of-squares
46×sqrt-prod
44×add-exp-log
43×distribute-lft-out--
40×div-inv
32×div-exp
29×associate-/r/
24×associate-/r*
17×flip3-- flip--
16×add-cbrt-cube
13×associate-/l*
8×cbrt-undiv rec-exp 1-exp add-log-exp
5×pow1
4×insert-posit16
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 427
Calls
4 calls:
58.0ms
(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
16.0ms
(- (* b_2 b_2) (* a c))
42.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
58.0ms
(- (* b_2 b_2) (* a c))
108.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
439 → 439
Iterations
IterNodes
done2000
11784
0591

prune896.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

localize65.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.7b
(sqrt (- (* b_2 b_2) (* a c)))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×sqrt-prod
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
62.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))
23.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))
101.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify932.0ms

Counts
76 → 76
Iterations
IterNodes
done2013
31579
2536
1185
080

prune800.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

regimes417.0ms

Accuracy

84.5% (4.4b remaining)

Error of 9.7b against oracle of 5.2b and baseline of 33.9b

bsearch424.0ms

Steps
ItersRangePoint
8
2.469533614662255e-16
6.384179586440732e-13
5.297236684235463e-16
9
2.201345904528094e-30
9.673336284784144e-25
1.8656332031849816e-25
10
5.0092461758030895e-88
5.0325836698121444e-76
1.739098950628615e-79
9
-7.806260788625035e+148
-1.2289413495061505e+143
-1.4758305599808076e+144

simplify8.0ms

Iterations
IterNodes
done46
146
036

end0.0ms

sample4.2s

Algorithm
intervals
Results
921.0ms1104×body2560valid
780.0ms5760×body80valid
686.0ms957×body1280valid
679.0ms482×body640valid
552.0ms2976×body80nan
119.0ms116×body5120valid
77.0ms226×body320valid
27.0ms121×body160valid