Details

Time bar (total: 18.3s)

sample71.0ms

Algorithm
intervals
Results
14.0ms35×body2560valid
12.0ms196×body80valid
10.0ms31×body1280valid
5.0ms89×body80nan
3.0ms11×body640valid
2.0ms3×body5120valid
0.0ms3×body160valid
0.0ms2×body320valid

simplify538.0ms

Counts
1 → 1
Iterations
IterNodes
done156
6156
5152
4142
3115
264
128
014

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(- (* b b) (* 4.0 (* a c)))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×times-frac add-cube-cbrt associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in 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 → 77
Calls
4 calls:
77.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
6.0ms
(- (* b b) (* 4.0 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series402.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms
(- (* b b) (* 4.0 (* a c)))
97.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
114.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
89 → 89
Iterations
IterNodes
done5000
21618
1411
0155

prune583.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b
(- (* b b) (* 4.0 (* a c)))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
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 → 125
Calls
4 calls:
57.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms
(- (* b b) (* 4.0 (* a c)))
25.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
67.0ms
(- (* b b) (* 4.0 (* a c)))
102.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
127.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts
137 → 137
Iterations
IterNodes
done5001
22565
1588
0226

prune666.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* 4.0 (* a c)))
0.2b
(* (/ (/ 1 a) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity
43×associate-*l*
41×add-cube-cbrt
19×add-exp-log
13×add-cbrt-cube
10×add-log-exp
7×pow1 associate-*r*
6×div-exp
5×flip3-- prod-exp sqrt-prod flip--
4×sub-neg div-inv distribute-lft-out-- difference-of-squares unswap-sqr
3×cbrt-undiv diff-log cbrt-unprod
2×distribute-rgt-in frac-times distribute-rgt-neg-in distribute-lft-in sqrt-div associate-*r/
1×associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*l/ *-commutative
Counts
4 → 125
Calls
4 calls:
12.0ms
(- (* b b) (* 4.0 (* a c)))
111.0ms
(* (/ (/ 1 a) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
18.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series471.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (* b b) (* 4.0 (* a c)))
162.0ms
(* (/ (/ 1 a) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
124.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
99.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
137 → 137
Iterations
IterNodes
done5000
22721
1678
0252

prune922.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.4b

localize60.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.6b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
58×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
22×difference-of-squares
18×add-cbrt-cube add-exp-log
14×sqrt-prod
11×distribute-lft-out--
7×cbrt-undiv associate-/r* div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×clear-num frac-2neg sqrt-div prod-exp cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 141
Calls
4 calls:
32.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
80.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
63.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series736.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
250.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
274.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts
153 → 153
Iterations
IterNodes
done5001
23611
1648
0250

prune940.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 5.4b

regimes607.0ms

Accuracy

87.1% (3.7b remaining)

Error of 9.1b against oracle of 5.4b and baseline of 33.8b

bsearch374.0ms

Steps
ItersRangePoint
10
4.0721326822252617e+40
3.6590220876252264e+50
3.628799960716312e+50
9
-8.630995884000565e-306
7.211886341925621e-305
-1.3410901614909383e-308
6
-1.278587798556269e+59
-1.7736353873113924e+58
-1.9700105655521088e+58

simplify15.0ms

Iterations
IterNodes
done40
240
139
033

end0.0ms

sample3.4s

Algorithm
intervals
Results
735.0ms2819×body80nan
624.0ms1136×body2560valid
620.0ms5797×body80valid
438.0ms867×body1280valid
134.0ms448×body640valid
112.0ms109×body5120valid
95.0ms238×body320valid
17.0ms103×body160valid