Details

Time bar (total: 15.1s)

sample89.0ms

Algorithm
intervals
Results
17.0ms36×body2560valid
14.0ms176×body80valid
13.0ms33×body1280valid
6.0ms79×body80nan
5.0ms19×body640valid
4.0ms6×body5120valid
2.0ms10×body320valid
0.0ms3×body160valid

simplify138.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize25.0ms

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)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite133.0ms

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:
91.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series427.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
65.0ms
(- (* b b) (* 4.0 (* a c)))
123.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
125.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify702.0ms

Counts
89 → 89
Iterations
IterNodes
done5000
21618
1411
0155

prune514.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize50.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
6.9b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite222.0ms

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:
34.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
98.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
72.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series811.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
242.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
318.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
130.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
153 → 153
Iterations
IterNodes
done5001
23611
1648
0250

prune871.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize29.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
2.2b
(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
5.2b
(/ (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) a)
24.4b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
54×add-cbrt-cube add-exp-log
41×add-sqr-sqrt
27×*-un-lft-identity
25×times-frac
24×associate-*r*
21×cbrt-undiv div-exp
19×add-cube-cbrt
16×prod-exp cbrt-unprod
8×difference-of-squares
7×pow1 associate-*l* sqrt-prod
6×add-log-exp
4×distribute-lft-out--
3×associate-/r* flip3-- div-inv flip-- associate-/l/
2×frac-times sqrt-div associate-*l/ associate-*r/ associate-/r/ unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down *-commutative associate-/l*
Counts
4 → 121
Calls
4 calls:
69.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
170.0ms
(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
51.0ms
(/ (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) a)
8.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series766.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
297.0ms
(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
225.0ms
(/ (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) a)
131.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify568.0ms

Counts
133 → 133
Iterations
IterNodes
done5000
1787
0260

prune840.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize33.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
2.2b
(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
5.3b
(* (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) (/ 1 a))
24.4b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite399.0ms

Algorithm
rewrite-expression-head
Rules
148×add-exp-log
90×add-cbrt-cube
68×prod-exp
49×div-exp
46×add-sqr-sqrt
38×cbrt-unprod
37×associate-*r*
32×*-un-lft-identity
31×times-frac
28×cbrt-undiv
24×add-cube-cbrt
12×pow1
8×associate-*l* difference-of-squares
7×rec-exp 1-exp sqrt-prod
6×frac-times associate-*l/ add-log-exp
4×pow-prod-down associate-*r/ distribute-lft-out--
3×flip3-- div-inv flip--
2×sqrt-div associate-/r/ *-commutative unswap-sqr
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log un-div-inv
Counts
4 → 161
Calls
4 calls:
44.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
155.0ms
(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
175.0ms
(* (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) (/ 1 a))
17.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series759.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
314.0ms
(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
245.0ms
(* (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) (/ 1 a))
93.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify645.0ms

Counts
173 → 173
Iterations
IterNodes
done5000
11036
0317

prune864.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

regimes370.0ms

Accuracy

90.2% (2.6b remaining)

Error of 8.0b against oracle of 5.4b and baseline of 32.3b

bsearch364.0ms

Steps
ItersRangePoint
9
2.1340360609407003e+79
6.102484722804822e+84
6.033691444141405e+84
10
8.852475844905406e-209
2.711563690867585e-195
8.958852798091287e-209
9
-31812840434242.992
-117892343.0362464
-9661478263987.111

simplify20.0ms

Iterations
IterNodes
done58
158
044

end0.0ms

sample3.4s

Algorithm
intervals
Results
911.0ms1065×body2560valid
747.0ms5799×body80valid
460.0ms921×body1280valid
416.0ms2883×body80nan
146.0ms455×body640valid
105.0ms239×body320valid
55.0ms86×body5120valid
17.0ms111×body160valid