Details

Time bar (total: 19.1s)

sample112.0ms

Algorithm
intervals
Results
28.0ms40×body2560valid
16.0ms178×body80valid
16.0ms36×body1280valid
8.0ms88×body80nan
5.0ms15×body640valid
2.0ms7×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify110.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 3.0 a) c))
0.2b
(* (* 3.0 a) c)
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square sub-neg distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative associate-+l- flip-+
Counts
4 → 60
Calls
4 calls:
9.0ms
(- (* b b) (* (* 3.0 a) c))
19.0ms
(* (* 3.0 a) c)
18.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (* b b) (* (* 3.0 a) c))
27.0ms
(* (* 3.0 a) c)
105.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
102.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify927.0ms

Counts
72 → 72
Iterations
IterNodes
done5000
21770
1329
0122

prune454.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* c (* a 3.0)))))
4.2b
(/ (/ (+ 0 (* c (* a 3.0))) (- (- b) (sqrt (- (* b b) (* c (* a 3.0)))))) (* 3.0 a))
10.1b
(/ (+ 0 (* c (* a 3.0))) (- (- b) (sqrt (- (* b b) (* c (* a 3.0))))))
24.4b
(sqrt (- (* b b) (* c (* a 3.0))))

rewrite177.0ms

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:
21.0ms
(- (- b) (sqrt (- (* b b) (* c (* a 3.0)))))
75.0ms
(/ (/ (+ 0 (* c (* a 3.0))) (- (- b) (sqrt (- (* b b) (* c (* a 3.0)))))) (* 3.0 a))
67.0ms
(/ (+ 0 (* c (* a 3.0))) (- (- b) (sqrt (- (* b b) (* c (* a 3.0))))))
7.0ms
(sqrt (- (* b b) (* c (* a 3.0))))

series808.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(- (- b) (sqrt (- (* b b) (* c (* a 3.0)))))
308.0ms
(/ (/ (+ 0 (* c (* a 3.0))) (- (- b) (sqrt (- (* b b) (* c (* a 3.0)))))) (* 3.0 a))
280.0ms
(/ (+ 0 (* c (* a 3.0))) (- (- b) (sqrt (- (* b b) (* c (* a 3.0))))))
81.0ms
(sqrt (- (* b b) (* c (* a 3.0))))

simplify1.8s

Counts
166 → 166
Iterations
IterNodes
done5000
23870
1659
0254

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ a (* a 3.0)) (/ 3.0 c))
0.4b
(/ (/ 1 1) (* (* (/ a (* a 3.0)) (/ 3.0 c)) (- (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))))
0.8b
(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
24.4b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
283×add-exp-log
144×div-exp
113×prod-exp
109×add-cbrt-cube
45×cbrt-undiv
44×times-frac
40×1-exp
38×cbrt-unprod
34×add-sqr-sqrt
30×*-un-lft-identity
28×add-cube-cbrt
16×rec-exp
13×associate-*r* associate-/l*
11×associate-/r/
10×frac-times
8×distribute-neg-frac
7×pow1 associate-*l* associate-*l/
6×associate-*r/ add-log-exp
5×flip3-+ flip-+ div-inv
3×sqrt-prod
2×sqrt-div unswap-sqr
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log frac-2neg sqrt-pow1 flip3-- pow1/2 pow-prod-down *-commutative flip-- distribute-lft-out associate-/l/
Counts
4 → 194
Calls
4 calls:
42.0ms
(* (/ a (* a 3.0)) (/ 3.0 c))
137.0ms
(/ (/ 1 1) (* (* (/ a (* a 3.0)) (/ 3.0 c)) (- (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))))
16.0ms
(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
13.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series437.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (/ a (* a 3.0)) (/ 3.0 c))
208.0ms
(/ (/ 1 1) (* (* (/ a (* a 3.0)) (/ 3.0 c)) (- (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))))
101.0ms
(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
107.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify741.0ms

Counts
206 → 206
Iterations
IterNodes
done5000
11414
0381

prune969.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* c 3.0) a))
0.3b
(/ (/ 1 (/ 1 3.0)) (/ 3.0 c))
0.8b
(+ b (sqrt (- (* b b) (* (* c 3.0) a))))
24.4b
(sqrt (- (* b b) (* (* c 3.0) a)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
1901×times-frac
812×*-un-lft-identity
811×add-sqr-sqrt
810×add-cube-cbrt
102×div-inv
83×add-exp-log
67×div-exp
44×associate-/l*
25×add-cbrt-cube
15×cbrt-undiv associate-/r/
14×rec-exp 1-exp
13×associate-/r*
8×add-log-exp
5×pow1
3×sqrt-prod
2×flip3-- sqrt-div flip--
1×+-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log flip-+ distribute-lft-out associate-/l/
Counts
4 → 712
Calls
4 calls:
6.0ms
(- (* b b) (* (* c 3.0) a))
45.0ms
(/ (/ 1 (/ 1 3.0)) (/ 3.0 c))
21.0ms
(+ b (sqrt (- (* b b) (* (* c 3.0) a))))
7.0ms
(sqrt (- (* b b) (* (* c 3.0) a)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* (* c 3.0) a))
24.0ms
(/ (/ 1 (/ 1 3.0)) (/ 3.0 c))
114.0ms
(+ b (sqrt (- (* b b) (* (* c 3.0) a))))
125.0ms
(sqrt (- (* b b) (* (* c 3.0) a)))

simplify5.0s

Counts
724 → 724
Iterations
IterNodes
done5000
14927
01246

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

regimes299.0ms

Accuracy

93.4% (1.5b remaining)

Error of 7.9b against oracle of 6.4b and baseline of 29.7b

bsearch328.0ms

Steps
ItersRangePoint
10
4.0721326822252617e+40
3.6590220876252264e+50
3.628799960716312e+50
9
-8.630995884000565e-306
7.211886341925621e-305
-1.9172930711399763e-308
8
-3.539957239594031e+126
-1.2441774927265154e+123
-1.3476084363078382e+126

simplify9.0ms

Iterations
IterNodes
done73
273
170
052

end0.0ms

sample3.2s

Algorithm
intervals
Results
614.0ms1053×body2560valid
580.0ms450×body640valid
537.0ms5900×body80valid
419.0ms898×body1280valid
268.0ms2831×body80nan
102.0ms111×body5120valid
51.0ms240×body320valid
15.0ms103×body160valid