Details

Time bar (total: 16.6s)

sample144.0ms

Algorithm
intervals
Results
40.0ms26×body1280valid
28.0ms191×body80valid
25.0ms28×body2560valid
11.0ms19×body640valid
11.0ms82×body80nan
4.0ms9×body320valid
2.0ms2×body5120valid
1.0ms2×body160valid

simplify87.0ms

Counts
1 → 1
Iterations
IterNodes
done165
6165
5161
4151
3122
265
128
014

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.4b
(- (* b b) (* 4 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.8b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite121.0ms

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-- insert-posit16 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 → 81
Calls
4 calls:
59.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
17.0ms
(- (* b b) (* 4 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
79.0ms
(- (* b b) (* 4 (* a c)))
114.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
90.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.2s

Counts
93 → 93
Iterations
IterNodes
done5000
21621
1409
0154

prune502.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
0.4b
(- (* b b) (* 4 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.8b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
13×associate-*r* add-cube-cbrt
10×times-frac add-log-exp
9×add-cbrt-cube add-exp-log
7×pow1 associate-*l*
5×flip3-- sqrt-prod flip--
4×insert-posit16 distribute-lft-out-- difference-of-squares
3×diff-log
2×frac-times sub-neg distribute-rgt-neg-in sqrt-div associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down neg-log associate-*r/ *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
82.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
17.0ms
(- (* b b) (* 4 (* a c)))
26.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series368.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
49.0ms
(- (* b b) (* 4 (* a c)))
120.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
84.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts
101 → 101
Iterations
IterNodes
done5000
22245
1461
0177

prune518.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
2.8b
(* (/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b)) (/ 1/2 a))
10.0b
(/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b))
21.8b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
49×*-un-lft-identity times-frac
33×add-cube-cbrt
24×associate-*l*
18×add-cbrt-cube add-exp-log
16×difference-of-squares
13×associate-*r*
11×sqrt-prod
8×distribute-lft-out--
7×pow1
6×associate-/r* add-log-exp
5×cbrt-undiv div-exp
4×flip3-- prod-exp associate-/r/ cbrt-unprod insert-posit16 flip-- unswap-sqr
3×div-inv associate-/l*
2×sqrt-div associate-/l/
1×frac-times rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
Counts
4 → 138
Calls
4 calls:
38.0ms
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
113.0ms
(* (/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b)) (/ 1/2 a))
92.0ms
(/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series713.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
226.0ms
(* (/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b)) (/ 1/2 a))
249.0ms
(/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b))
110.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify2.6s

Counts
150 → 150
Iterations
IterNodes
done5000
24300
1724
0250

prune699.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) 1/2) a)
0.4b
(- (* b b) (* 4 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.8b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×add-cube-cbrt
5×pow1
4×flip3-- sqrt-prod insert-posit16 flip--
3×associate-/r* times-frac diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-*l/ distribute-lft-out-- difference-of-squares associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
38.0ms
(/ (* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) 1/2) a)
8.0ms
(- (* b b) (* 4 (* a c)))
19.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) 1/2) a)
56.0ms
(- (* b b) (* 4 (* a c)))
106.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
95.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.0s

Counts
84 → 84
Iterations
IterNodes
done5000
21969
1416
0154

prune401.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.7b

regimes286.0ms

Accuracy

89.1% (3.0b remaining)

Error of 8.3b against oracle of 5.4b and baseline of 32.7b

bsearch401.0ms

Steps
ItersRangePoint
10
1.0955696400612189e+91
1.0202913897586463e+104
2.026128983134594e+103
10
-3.7853197546515783e-110
-6.759455321393433e-120
-6.3209183644448e-115
9
-2.0190258033009663e+27
-4.429449841721669e+19
-3.234164035284793e+22

simplify9.0ms

Iterations
IterNodes
done41
241
140
034

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.6s5883×body80valid
1.0s1082×body2560valid
704.0ms890×body1280valid
393.0ms2919×body80nan
242.0ms438×body640valid
105.0ms112×body5120valid
86.0ms230×body320valid
30.0ms124×body160valid