Details

Time bar (total: 13.2s)

sample100.0ms

Algorithm
intervals
Results
21.0ms168×body80valid
16.0ms33×body2560valid
15.0ms35×body1280valid
8.0ms92×body80nan
6.0ms15×body640valid
3.0msbody5120valid
3.0msbody320valid
1.0msbody160valid

simplify106.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
add-exp-log add-cbrt-cube
add-log-exp
add-cube-cbrt
times-frac sqrt-prod associate-/l* difference-of-squares
pow1
flip3-- flip--
distribute-lft-out--
cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
139.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
15.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
69.0ms
(- (* b b) (* (* 4.0 a) c))
118.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.8s

Counts
84 → 84
Iterations

Useful iterations: 3 (2.2s)

IterNodesCost
01541592
13861488
212331332
346481324
done50021324

prune306.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.4b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune14.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
sqrt-prod add-log-exp
add-exp-log add-cbrt-cube associate-/l*
pow1 distribute-lft-out--
flip3-- flip--
associate-/r*
sub-neg sqrt-div diff-log associate-/l/
cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 84
Calls
4 calls:
91.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
16.0ms
(- (* b b) (* (* 4.0 a) c))
66.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
61.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
96 → 96
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01581888
13721774
210471658
333421650
done50001644

prune266.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.3b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.8b
(/ (/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b)) a)
11.8b
(/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
97×*-un-lft-identity
66×add-sqr-sqrt
65×add-cube-cbrt
21×associate-/l*
16×distribute-lft-out
11×add-exp-log add-cbrt-cube
10×associate-/r/
associate-/r*
div-inv add-log-exp
pow1 flip3-+ flip-+
cbrt-undiv div-exp
flip3-- div-sub distribute-frac-neg sqrt-prod flip-- associate-/l/
frac-2neg sub0-neg sqrt-div clear-num
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 156
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(/ (/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b)) a)
54.0ms
(/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series523.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
176.0ms
(/ (/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b)) a)
215.0ms
(/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b))
83.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts
168 → 168
Iterations

Useful iterations: 2 (400.0ms)

IterNodesCost
02765314
16884830
225384584
done50004584

prune529.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.2b

regimes234.0ms

Accuracy

90.1% (2.6b remaining)

Error of 8.2b against oracle of 5.6b and baseline of 31.8b

bsearch199.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
2.0162260334635464e+61
7
-4.381317687258745e-230
-2.0471743436955067e-231
-2.4298826071872637e-231
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify20.0ms

Iterations

Useful iterations: 5 (16.0ms)

IterNodesCost
04076
15175
25575
36575
46875
57174
done7174

end0.0ms

sample2.5s

Algorithm
intervals
Results
721.0ms5870×body80valid
395.0ms1051×body2560valid
333.0ms893×body1280valid
225.0ms2845×body80nan
193.0ms480×body640valid
109.0ms98×body5120valid
75.0ms218×body320valid
11.0ms108×body160valid