Details

Time bar (total: 16.4s)

sample82.0ms

Algorithm
intervals
Results
20.0ms189×body80valid
15.0ms36×body2560valid
9.0ms25×body1280valid
7.0ms104×body80nan
3.0ms16×body640valid
1.0ms6×body320valid
1.0ms2×body5120valid
0.0ms3×body160valid

simplify137.0ms

Counts
1 → 1
Iterations
IterNodes
done156
6156
5152
4142
3115
264
128
014

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
26.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite143.0ms

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-- 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 → 77
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
25.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series477.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
137.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms
(- (* b b) (* 4.0 (* a c)))
113.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
89 → 89
Iterations
IterNodes
done5000
21618
1411
0155

prune616.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize59.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
2.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.9b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
26.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-cbrt-cube add-exp-log
13×sqrt-prod
10×distribute-lft-out--
7×cbrt-undiv associate-/r* div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×clear-num frac-2neg sqrt-div prod-exp cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 138
Calls
4 calls:
12.0ms
(- (* b b) (* 4.0 (* a c)))
108.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
87.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series741.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* b b) (* 4.0 (* a c)))
260.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
296.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
104.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.2s

Counts
150 → 150
Iterations
IterNodes
done5000
23701
1654
0249

prune876.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
26.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×frac-times cbrt-undiv rec-exp sub-neg distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*r/ un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
128.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
27.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series372.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
84.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
61.0ms
(- (* b b) (* 4.0 (* a c)))
106.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
97 → 97
Iterations
IterNodes
done5001
22388
1485
0181

prune362.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
26.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log cbrt-unprod pow-flip inv-pow
Counts
4 → 125
Calls
4 calls:
40.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
18.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
121.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(- (* b b) (* 4.0 (* a c)))
103.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts
137 → 137
Iterations
IterNodes
done5001
22564
1589
0226

prune575.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.5b

regimes394.0ms

Accuracy

87.5% (3.4b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 32.7b

bsearch311.0ms

Steps
ItersRangePoint
6
5.84949006905106e+100
6.027833473435204e+101
4.547489674828777e+101
9
-1.0697531889019586e-297
-1.2775037923523436e-306
-2.1186335512684196e-302
11
-1.4585470499056154e+88
-9.653206849881042e+62
-7.741777288939024e+81

simplify9.0ms

Iterations
IterNodes
done46
246
145
037

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s1065×body2560valid
692.0ms5822×body80valid
372.0ms948×body1280valid
242.0ms2889×body80nan
142.0ms471×body640valid
104.0ms241×body320valid
96.0ms107×body160valid
75.0ms115×body5120valid