Details

Time bar (total: 15.6s)

sample83.0ms

Algorithm
intervals
Results
17.0ms45×body1280valid
15.0ms184×body80valid
14.0ms25×body2560valid
5.0ms69×body80nan
5.0ms17×body640valid
2.0ms8×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify118.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
119.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
30.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
118.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
62.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
82 → 82
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune353.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.5b
(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.2b
(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
133.0ms
(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
116.0ms
(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series767.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (* b b) (* (* 4.0 a) c))
304.0ms
(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
292.0ms
(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
160 → 160
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
02524912
16234364
226814036
done50004036

prune773.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
14.8b
(/ (* 2.0 a) (* 4.0 (* a c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
42.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: 2 (428.0ms)

IterNodesCost
01571330
14121216
22082994
done5000994

prune346.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ 1 1) (* (/ 2.0 (/ 4.0 (/ 1 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
207×add-exp-log
154×div-exp
49×add-cbrt-cube
42×1-exp prod-exp
31×times-frac
27×cbrt-undiv
24×add-sqr-sqrt
23×*-un-lft-identity
21×rec-exp
19×add-cube-cbrt
13×associate-/l*
10×add-log-exp
8×cbrt-unprod
5×pow1 flip3-- associate-/r/ flip--
4×sqrt-prod
3×diff-log div-inv
2×frac-times sub-neg sqrt-div associate-*r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log associate-*l/ clear-num associate-/r* associate-/l/
Counts
4 → 147
Calls
4 calls:
89.0ms
(/ (/ 1 1) (* (/ 2.0 (/ 4.0 (/ 1 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
269.0ms
(/ (/ 1 1) (* (/ 2.0 (/ 4.0 (/ 1 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
124.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
87.0ms
(- (* b b) (* (* 4.0 a) c))
135.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
159 → 159
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03064384
16913760
219812954
done50012816

prune325.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.2b

regimes253.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.7b

bsearch223.0ms

Steps
ItersRangePoint
2
5.341589198600723e+134
5.967668210703041e+134
5.732888581164671e+134
10
-1.2529167750641135e-296
-2.859335985249397e-307
-3.1046203401759487e-300
9
-8.712513212907472e+114
-1.0414090820182828e+108
-2.463372194426505e+111

simplify12.0ms

Iterations

Useful iterations: done (11.0ms)

IterNodesCost
03868
14966
done4964

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.1s922×body1280valid
577.0ms1056×body2560valid
534.0ms5848×body80valid
416.0ms2941×body80nan
261.0ms479×body640valid
103.0ms113×body5120valid
49.0ms208×body320valid
17.0ms109×body160valid