Details

Time bar (total: 13.7s)

sample99.0ms

Algorithm
intervals
Results
17.0ms186×body80valid
16.0ms29×body2560valid
11.0ms24×body1280valid
9.0ms102×body80nan
5.0ms14×body640valid
3.0ms5×body5120valid
3.0ms9×body320valid
1.0ms4×body160valid

simplify119.0ms

Counts
1 → 1
Iterations
IterNodes
done104
5104
496
376
241
121
012

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.6b
(- (* b b) (* (* 3.0 a) c))
1.3b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
13.0ms
(* (* 3.0 a) c)
6.0ms
(- (* b b) (* (* 3.0 a) c))
60.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (* 3.0 a) c)
72.0ms
(- (* b b) (* (* 3.0 a) c))
99.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
101.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify990.0ms

Counts
72 → 72
Iterations
IterNodes
done5001
21593
1302
0120

prune386.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* c (* a 3.0))
0.6b
(- (* b b) (* c (* a 3.0)))
1.3b
(- (sqrt (- (* b b) (* c (* a 3.0)))) b)
22.9b
(sqrt (- (* b b) (* c (* a 3.0))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*l* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
24.0ms
(* c (* a 3.0))
12.0ms
(- (* b b) (* c (* a 3.0)))
45.0ms
(- (sqrt (- (* b b) (* c (* a 3.0)))) b)
7.0ms
(sqrt (- (* b b) (* c (* a 3.0))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* c (* a 3.0))
76.0ms
(- (* b b) (* c (* a 3.0)))
93.0ms
(- (sqrt (- (* b b) (* c (* a 3.0)))) b)
100.0ms
(sqrt (- (* b b) (* c (* a 3.0))))

simplify676.0ms

Counts
72 → 72
Iterations
IterNodes
done5001
21225
1288
0119

prune338.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
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×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
66.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms
(- (* b b) (* (* 3.0 a) c))
31.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
64.0ms
(- (* b b) (* (* 3.0 a) c))
118.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
125.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify932.0ms

Counts
82 → 82
Iterations
IterNodes
done5000
21881
1414
0154

prune615.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize35.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))
3.5b
(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))) (* 3.0 a))
10.9b
(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0)))))
22.9b
(sqrt (- (* b b) (* (* a c) 3.0)))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-cbrt-cube add-exp-log
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×clear-num frac-2neg sqrt-div diff-log prod-exp cbrt-unprod
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
32.0ms
(- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))
134.0ms
(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))) (* 3.0 a))
66.0ms
(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0)))))
7.0ms
(sqrt (- (* b b) (* (* a c) 3.0)))

series686.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))
247.0ms
(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0))))) (* 3.0 a))
240.0ms
(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* a c) 3.0)))))
104.0ms
(sqrt (- (* b b) (* (* a c) 3.0)))

simplify2.1s

Counts
166 → 166
Iterations
IterNodes
done5000
23835
1657
0253

prune818.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

regimes738.0ms

Accuracy

93.8% (1.5b remaining)

Error of 7.0b against oracle of 5.5b and baseline of 30.0b

bsearch283.0ms

Steps
ItersRangePoint
7
1.9371672431899034e+133
5.16149553175908e+134
1.384078670752048e+134
8
-1.830196375340447e-262
-1.1220404669500562e-265
-1.1606799443953944e-265
7
-2.967245708633018e+62
-1.745417689399421e+60
-2.908139161981603e+62

simplify5.0ms

Iterations
IterNodes
done50
150
041

end0.0ms

sample3.1s

Algorithm
intervals
Results
717.0ms5958×body80valid
579.0ms451×body640valid
573.0ms1053×body2560valid
313.0ms880×body1280valid
306.0ms2946×body80nan
57.0ms97×body5120valid
49.0ms216×body320valid
15.0ms113×body160valid