Details

Time bar (total: 16.6s)

sample104.0ms

Algorithm
intervals
Results
21.0ms198×body80valid
19.0ms31×body2560valid
19.0ms17×body640valid
14.0ms28×body1280valid
10.0ms87×body80nan
3.0ms4×body5120valid
2.0ms6×body320valid
1.0ms4×body160valid

simplify133.0ms

Counts
1 → 1
Iterations
IterNodes
done144
6144
5140
4133
3111
265
128
014

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize49.0ms

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)))))
24.3b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite123.0ms

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))
16.0ms
(- (* b b) (* 4 (* a c)))
31.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
15.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series402.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
58.0ms
(- (* b b) (* 4 (* a c)))
104.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
106.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.7s

Counts
93 → 93
Iterations
IterNodes
done5000
21333
1400
0154

prune541.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ b (sqrt (- (* b b) (* c (* a 4))))) (* a -2))
0.4b
(- (* b b) (* c (* a 4)))
1.0b
(+ b (sqrt (- (* b b) (* c (* a 4)))))
24.3b
(sqrt (- (* b b) (* c (* a 4))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
5×pow1
4×times-frac insert-posit16 associate-/l*
3×sqrt-prod distribute-lft-out
2×cbrt-undiv flip3-+ flip3-- sqrt-div div-exp flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log prod-exp cbrt-unprod div-inv
Counts
4 → 68
Calls
4 calls:
43.0ms
(/ (+ b (sqrt (- (* b b) (* c (* a 4))))) (* a -2))
8.0ms
(- (* b b) (* c (* a 4)))
11.0ms
(+ b (sqrt (- (* b b) (* c (* a 4)))))
7.0ms
(sqrt (- (* b b) (* c (* a 4))))

series390.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (+ b (sqrt (- (* b b) (* c (* a 4))))) (* a -2))
61.0ms
(- (* b b) (* c (* a 4)))
98.0ms
(+ b (sqrt (- (* b b) (* c (* a 4)))))
102.0ms
(sqrt (- (* b b) (* c (* a 4))))

simplify1.4s

Counts
80 → 80
Iterations
IterNodes
done5001
21232
1359
0139

prune522.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (* a -2) (+ b (sqrt (- (* b b) (* c (* a 4)))))))
0.4b
(- (* b b) (* c (* a 4)))
1.0b
(+ b (sqrt (- (* b b) (* c (* a 4)))))
24.3b
(sqrt (- (* b b) (* c (* a 4))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
46×times-frac
34×*-un-lft-identity
25×add-sqr-sqrt add-exp-log
24×add-cube-cbrt
13×add-cbrt-cube
12×div-exp
10×associate-/r*
9×associate-/r/
8×add-log-exp
6×pow1
5×cbrt-undiv flip3-+ flip-+ div-inv distribute-lft-out
4×insert-posit16
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div flip--
1×+-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log cbrt-unprod pow-flip inv-pow
Counts
4 → 111
Calls
4 calls:
41.0ms
(/ 1 (/ (* a -2) (+ b (sqrt (- (* b b) (* c (* a 4)))))))
8.0ms
(- (* b b) (* c (* a 4)))
13.0ms
(+ b (sqrt (- (* b b) (* c (* a 4)))))
15.0ms
(sqrt (- (* b b) (* c (* a 4))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ 1 (/ (* a -2) (+ b (sqrt (- (* b b) (* c (* a 4)))))))
52.0ms
(- (* b b) (* c (* a 4)))
116.0ms
(+ b (sqrt (- (* b b) (* c (* a 4)))))
92.0ms
(sqrt (- (* b b) (* c (* a 4))))

simplify1.4s

Counts
123 → 123
Iterations
IterNodes
done5002
21960
1540
0210

prune705.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a))
0.4b
(- (* b b) (* 4 (* a c)))
7.5b
(- (/ (- b) (* 2 a)) (/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a)))
24.3b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×add-sqr-sqrt
10×times-frac
9×add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod
8×add-log-exp
6×associate-/l*
5×pow1
4×flip3-- sqrt-div insert-posit16 flip--
3×div-inv distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* distribute-rgt-neg-in frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-sub prod-exp frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 80
Calls
4 calls:
15.0ms
(/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a))
10.0ms
(- (* b b) (* 4 (* a c)))
33.0ms
(- (/ (- b) (* 2 a)) (/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a)))
8.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a))
57.0ms
(- (* b b) (* 4 (* a c)))
130.0ms
(- (/ (- b) (* 2 a)) (/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a)))
120.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.4s

Counts
92 → 92
Iterations
IterNodes
done5001
21514
1413
0161

prune453.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.6b

regimes424.0ms

Accuracy

82.9% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 33.8b

bsearch417.0ms

Steps
ItersRangePoint
9
6.2301214455520334e+75
1.9082112581546424e+85
1.6691257204922504e+85
4
-2.3602019652593256e-123
-1.5355849018748885e-123
-2.3344326820285623e-123
9
-2.9300981025422624e-27
-1.2024011261401705e-33
-6.936587154412951e-28
8
-1.0943378505721803e-12
-1.4409381956716427e-15
-7.363255598823911e-15

simplify13.0ms

Iterations
IterNodes
done38
138
031

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.0s1057×body2560valid
1.1s5842×body80valid
838.0ms891×body1280valid
452.0ms2845×body80nan
260.0ms456×body640valid
121.0ms114×body5120valid
93.0ms228×body320valid
37.0ms117×body160valid