Details

Time bar (total: 19.0s)

sample98.0ms

Algorithm
intervals
Results
22.0ms43×body2560valid
16.0ms176×body80valid
12.0ms31×body1280valid
8.0ms106×body80nan
6.0ms18×body640valid
3.0ms4×body5120valid
2.0ms7×body320valid
1.0ms4×body160valid

simplify122.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
92.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
20.0ms
(- (* b b) (* 4.0 (* a c)))
26.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series435.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
66.0ms
(- (* b b) (* 4.0 (* a c)))
123.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
99.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01651697
14341584
214651361
done50001347

prune458.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize50.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.1b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.7b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
63.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
114.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
115.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series714.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
218.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
284.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
111.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts
244 → 244
Iterations

Useful iterations: done (2.0s)

IterNodesCost
033710067
18097605
229436508
done50006422

prune917.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.7b
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite401.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
152×times-frac
150×*-un-lft-identity
109×add-cube-cbrt
94×add-exp-log
85×associate-*r*
61×prod-diff
58×add-cbrt-cube
43×sqrt-prod
39×div-exp
35×prod-exp
31×distribute-rgt-neg-in
21×cbrt-undiv distribute-lft-neg-in cbrt-unprod
20×distribute-lft-out-- difference-of-squares
11×fma-neg
10×add-log-exp
7×pow1 neg-mul-1 associate-*l*
6×flip3-- associate-/r/ flip--
5×div-inv
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u unswap-sqr
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative
Counts
4 → 265
Calls
4 calls:
20.0ms
(- (* b b) (* 4.0 (* a c)))
39.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
289.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
21.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* 4.0 (* a c)))
146.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
203.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
110.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.6s

Counts
277 → 277
Iterations

Useful iterations: done (2.6s)

IterNodesCost
044310420
112367945
242786391
done50006390

prune941.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.8b
(/ (* a (* c 4.0)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 152
Calls
4 calls:
10.0ms
(- (* b b) (* 4.0 (* a c)))
46.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(/ (* a (* c 4.0)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
26.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (* b b) (* 4.0 (* a c)))
119.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
228.0ms
(/ (* a (* c 4.0)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts
164 → 164
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02566823
16504764
228823590
done50023505

prune437.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.2b

regimes194.0ms

Accuracy

93.5% (1.5b remaining)

Error of 7.3b against oracle of 5.8b and baseline of 29.0b

bsearch321.0ms

Steps
ItersRangePoint
9
1.7084993271036838e+35
8.915315724770326e+40
8.75372275402518e+40
9
-4.09118134758863e-163
-1.5699591568311042e-168
-1.5885810260222291e-168
6
-2.3823986784004295e+101
-2.936095699822542e+100
-1.555632367828989e+101

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04064
15062
done5062

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.3s5876×body80valid
800.0ms885×body1280valid
706.0ms1074×body2560valid
406.0ms3010×body80nan
162.0ms492×body640valid
60.0ms107×body5120valid
50.0ms218×body320valid
15.0ms92×body160valid