Details

Time bar (total: 17.2s)

sample124.0ms

Algorithm
intervals
Results
38.0ms191×body80valid
23.0ms28×body2560valid
16.0ms26×body1280valid
12.0ms19×body640valid
10.0ms82×body80nan
4.0ms9×body320valid
2.0ms2×body5120valid
1.0ms2×body160valid

simplify129.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize37.0ms

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))))

rewrite96.0ms

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:
48.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
9.0ms
(- (* b b) (* 4 (* a c)))
22.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
15.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
79.0ms
(- (* b b) (* 4 (* a c)))
135.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
115.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.3s

Counts
93 → 93
Iterations
IterNodes
done5000
21621
1409
0154

prune503.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize52.0ms

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))))

rewrite132.0ms

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:
76.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
9.0ms
(- (* b b) (* 4 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
16.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series405.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
76.0ms
(- (* b b) (* 4 (* a c)))
115.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
100.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.6s

Counts
101 → 101
Iterations
IterNodes
done5000
22245
1461
0177

prune525.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize62.0ms

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))))

rewrite252.0ms

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:
67.0ms
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
108.0ms
(* (/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b)) (/ 1/2 a))
56.0ms
(/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b))
17.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series695.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (sqrt (- (* b b) (* 4 (* a c)))) b)
220.0ms
(* (/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b)) (/ 1/2 a))
263.0ms
(/ (+ 0 (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b))
98.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify2.5s

Counts
150 → 150
Iterations
IterNodes
done5000
24300
1724
0250

prune726.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

localize27.0ms

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))))

rewrite110.0ms

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:
44.0ms
(/ (* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) 1/2) a)
17.0ms
(- (* b b) (* 4 (* a c)))
37.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
10.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series424.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) 1/2) a)
80.0ms
(- (* b b) (* 4 (* a c)))
123.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
123.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.4s

Counts
84 → 84
Iterations
IterNodes
done5000
21969
1416
0154

prune434.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.7b

regimes342.0ms

Accuracy

89.1% (3.0b remaining)

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

bsearch438.0ms

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

simplify7.0ms

Iterations
IterNodes
done41
241
140
034

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s1082×body2560valid
1.3s5883×body80valid
721.0ms890×body1280valid
366.0ms2919×body80nan
244.0ms438×body640valid
148.0ms112×body5120valid
87.0ms230×body320valid
30.0ms124×body160valid