Details

Time bar (total: 11.6s)

sample37.0ms

Algorithm
intervals
Results
6.0ms37×body2560valid
5.0ms175×body80valid
5.0ms32×body1280valid
3.0ms103×body80nan
2.0ms17×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify21.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
65.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
23.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
74.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms
(- (* b_2 b_2) (* a c))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts
103 → 103
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01561821
13661727
210051611
327701595
done50011593

prune250.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.9b
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.2b
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt
42×*-un-lft-identity
28×add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×difference-of-squares
13×associate-/l*
10×sqrt-prod associate-/r/
9×associate-/r*
7×cbrt-undiv flip3-- div-exp flip-- distribute-lft-out--
6×div-inv add-log-exp
5×pow1
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 127
Calls
4 calls:
44.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
83.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
54.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series679.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
350.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
193.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
139 → 139
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02393118
15932899
219412569
done50002563

prune330.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (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)
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite114.0ms

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-exp-log associate-/r* add-cbrt-cube
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 83
Calls
4 calls:
47.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms
(- (* b_2 b_2) (* a c))
44.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
35.0ms
(- (* b_2 b_2) (* a c))
77.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts
95 → 95
Iterations

Useful iterations: 4 (1.6s)

IterNodesCost
01471588
13111491
27731393
318141389
445821375
done50001375

prune223.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize12.0ms

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)
23.4b
(sqrt (- (* b_2 b_2) (* a c)))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
45.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
47.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
76.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
72 → 72
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0781064
1182944
2496884
31172876
42461864
done5000862

prune210.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes238.0ms

Accuracy

93.8% (1.5b remaining)

Error of 6.7b against oracle of 5.3b and baseline of 29.1b

bsearch96.0ms

Steps
ItersRangePoint
6
2.0335150395734557e+19
1.0746392320557105e+20
8.439475397424872e+19
7
-1.9418910170184396e-283
-5.421319756117139e-285
-5.489520038969419e-285
7
-1.3907042211653736e+140
-2.4882870722039588e+138
-6.256826279459624e+138

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03255
13953
done3953

end0.0ms

sample1.0s

Algorithm
intervals
Results
196.0ms1077×body2560valid
183.0ms5759×body80valid
132.0ms915×body1280valid
78.0ms2830×body80nan
52.0ms465×body640valid
23.0ms105×body5120valid
21.0ms249×body320valid
7.0ms115×body160valid