Details

Time bar (total: 13.5s)

sample55.0ms

Algorithm
intervals
Results
10.0ms35×body2560valid
9.0ms185×body80valid
6.0ms23×body1280valid
5.0ms103×body80nan
4.0ms19×body640valid
1.0ms7×body160valid
1.0ms4×body320valid

simplify151.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312117
415317
516017
616417
done16417

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize366.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
89.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms
(- (* b b) (* 4.0 (* a c)))
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
85.0ms
(- (* b b) (* 4.0 (* a c)))
126.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
169 → 169
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02416688
16104728
224673765
done50013677

prune754.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log cbrt-unprod pow-flip inv-pow
Counts
4 → 205
Calls
4 calls:
53.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
7.0ms
(- (* b b) (* 4.0 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
76.0ms
(- (* b b) (* 4.0 (* a c)))
94.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
217 → 217
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03118365
17816147
233035140
done50005052

prune897.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×distribute-rgt-neg-in add-exp-log
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×frac-times cbrt-undiv rec-exp sub-neg sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*r/ un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
103.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
7.0ms
(- (* b b) (* 4.0 (* a c)))
39.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
60.0ms
(- (* b b) (* 4.0 (* a c)))
100.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
94.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
177 → 177
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02676945
16834917
230423860
done50023772

prune796.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

localize10.0ms

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

prune1.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.5b

regimes425.0ms

Accuracy

82.5% (5.1b remaining)

Error of 10.6b against oracle of 5.5b and baseline of 34.5b

bsearch187.0ms

Steps
ItersRangePoint
9
6.258218916731328e+93
1.8883840965187804e+99
2.9380396584045826e+94
5
-1.0485618335166142e-22
-4.7809817903638944e-23
-7.668263498157484e-23

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02941
13741
done3741

end0.0ms

sample3.4s

Algorithm
intervals
Results
841.0ms884×body1280valid
676.0ms1114×body2560valid
664.0ms5781×body80valid
261.0ms2931×body80nan
235.0ms464×body640valid
105.0ms250×body320valid
64.0ms110×body5120valid
20.0ms127×body160valid