Details

Time bar (total: 16.9s)

sample92.0ms

Algorithm
intervals
Results
21.0ms43×body2560valid
14.0ms165×body80valid
13.0ms32×body1280valid
6.0ms80×body80nan
5.0ms16×body640valid
5.0ms8×body5120valid
2.0ms7×body320valid
1.0ms5×body160valid

simplify151.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
012324
122324
242284
383284
4112284
5120284
done120284

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize34.0ms

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)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
28×*-un-lft-identity
22×add-cube-cbrt
18×prod-diff sqrt-prod
14×add-cbrt-cube add-exp-log
10×pow1
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
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 → 110
Calls
4 calls:
17.0ms
(* (* 3.0 a) c)
117.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
58.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (* 3.0 a) c)
196.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
139.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
110.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.1s

Counts
122 → 122
Iterations

Useful iterations: done (3.1s)

IterNodesCost
020042464
154038188
2299534054
done500034004

prune674.0ms

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

prune62.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize29.0ms

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)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
41×*-un-lft-identity
31×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
11×add-cbrt-cube add-exp-log
10×pow1 difference-of-squares
6×fma-neg associate-/l* add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
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 → 122
Calls
4 calls:
104.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
23.0ms
(* (* 3.0 a) c)
55.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
22.0ms
(* (* 3.0 a) c)
146.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
97.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.0s

Counts
134 → 134
Iterations

Useful iterations: done (3.0s)

IterNodesCost
020850414
153346218
2242842309
done500142259

prune633.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (/ 1 (* 3.0 a)))
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)))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
28×add-exp-log
27×*-un-lft-identity
23×add-cube-cbrt
18×add-cbrt-cube prod-diff
17×sqrt-prod
13×prod-exp
12×pow1
10×associate-*r*
7×associate-*l* cbrt-unprod
6×fma-neg add-log-exp
4×expm1-log1p-u flip3-- div-exp pow-prod-down log1p-expm1-u flip-- difference-of-squares
3×times-frac
2×frac-times cbrt-undiv rec-exp sqrt-div 1-exp associate-*l/ *-commutative distribute-lft-out--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-*r/ un-div-inv div-inv unswap-sqr
Counts
4 → 119
Calls
4 calls:
157.0ms
(* (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (/ 1 (* 3.0 a)))
13.0ms
(* (* 3.0 a) c)
73.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (/ 1 (* 3.0 a)))
34.0ms
(* (* 3.0 a) c)
129.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
98.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.4s

Counts
131 → 131
Iterations

Useful iterations: done (2.4s)

IterNodesCost
022647780
161241388
2365936225
done500036125

prune623.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

regimes908.0ms

Accuracy

87.6% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 39.5b

bsearch73.0ms

Steps
ItersRangePoint
2
3.964947473899983e-62
4.720485511979589e-62
4.626043257219638e-62
7
-5.856362438573669e+138
-1.280729871585891e+137
-2.3037792410978802e+138

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
028830
136830
done36830

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.0s1095×body2560valid
527.0ms5793×body80valid
386.0ms887×body1280valid
286.0ms2874×body80nan
163.0ms468×body640valid
103.0ms107×body5120valid
79.0ms243×body320valid
16.0ms115×body160valid