Details

Time bar (total: 12.8s)

sample48.0ms

Algorithm
intervals
Results
11.0ms43×body2560valid
7.0ms165×body80valid
7.0ms32×body1280valid
3.0ms80×body80nan
3.0ms16×body640valid
2.0ms8×body5120valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify93.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
012324
121324
241284
376284
496284
5104284
done104284

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* 3.0 a) c)
0.7b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
1.5b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
14×*-un-lft-identity add-cbrt-cube add-exp-log
10×pow1
8×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* add-log-exp difference-of-squares
4×prod-exp cbrt-unprod
3×flip3-- associate-*r* pow-prod-down flip-- distribute-lft-out--
2×cbrt-undiv sqrt-div div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub associate-*l* *-commutative div-inv
Counts
4 → 78
Calls
4 calls:
15.0ms
(* (* 3.0 a) c)
75.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
61.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 3.0 a) c)
169.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
86.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
118.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.5s

Counts
90 → 90
Iterations

Useful iterations: 2 (554.0ms)

IterNodesCost
016428262
143225925
2239425285
done500025285

prune488.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize11.0ms

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

prune72.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
0.5b
(* (* 3.0 a) c)
1.5b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
27×*-un-lft-identity
18×times-frac
17×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow1 difference-of-squares
8×sqrt-prod
6×associate-/l* add-log-exp
5×distribute-lft-out--
3×associate-/r* flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sqrt-div associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp associate-*l* *-commutative div-inv
Counts
4 → 90
Calls
4 calls:
96.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
26.0ms
(* (* 3.0 a) c)
53.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
36.0ms
(* (* 3.0 a) c)
101.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
135.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts
102 → 102
Iterations

Useful iterations: 2 (551.0ms)

IterNodesCost
017236212
142733980
2193833540
done500133540

prune516.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 3.0 (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
0.5b
(* (* 3.0 a) c)
1.5b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
27×*-un-lft-identity
18×times-frac
17×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow1 difference-of-squares
8×sqrt-prod
6×associate-/r* add-log-exp
5×distribute-lft-out--
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip-- associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-exp associate-*l* *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
34.0ms
(/ 3.0 (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
26.0ms
(* (* 3.0 a) c)
65.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ 3.0 (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
25.0ms
(* (* 3.0 a) c)
97.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
90.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts
101 → 101
Iterations

Useful iterations: 2 (455.0ms)

IterNodesCost
017536184
142233450
2195932968
done500132968

prune490.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.4b

regimes711.0ms

Accuracy

87.3% (4.3b remaining)

Error of 9.6b against oracle of 5.3b and baseline of 39.5b

bsearch51.0ms

Steps
ItersRangePoint
2
3.964947473899983e-62
4.720485511979589e-62
4.626043257219638e-62
7
-5.856362438573669e+138
-1.280729871585891e+137
-5.791348048249166e+138

simplify15.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
026789
131789
done31789

end0.0ms

sample2.8s

Algorithm
intervals
Results
895.0ms1095×body2560valid
531.0ms2874×body80nan
480.0ms5793×body80valid
331.0ms887×body1280valid
112.0ms468×body640valid
45.0ms107×body5120valid
42.0ms243×body320valid
12.0ms115×body160valid