Details

Time bar (total: 19.7s)

sample114.0ms

Algorithm
intervals
Results
22.0ms30×body1280valid
21.0ms35×body2560valid
18.0ms179×body80valid
8.0ms76×body80nan
6.0ms8×body5120valid
4.0ms10×body320valid
3.0ms9×body640valid
0.0ms2×body160valid

simplify156.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
11×add-cube-cbrt
10×pow1 fma-def
8×add-log-exp
6×distribute-rgt-neg-in distribute-lft-out
5×times-frac associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×distribute-lft-neg-in associate-*l* pow-prod-down sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ sqrt-div div-exp sum-log flip-+ associate-/l/
1×+-commutative neg-mul-1 rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 94
Calls
4 calls:
32.0ms
(* 4.0 (* a c))
74.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
32.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series431.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 4.0 (* a c))
159.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
129.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
117.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
106 → 106
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01771597
14691482
215521269
done50001255

prune448.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.5b
(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.9b
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite344.0ms

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:
64.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
157.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
92.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series774.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
239.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
284.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
116.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts
244 → 244
Iterations

Useful iterations: done (1.9s)

IterNodesCost
033710067
18127635
227406508
done50006422

prune871.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 1 (* a (* 4.0 c)))))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* 1 (* a (* 4.0 c))))))
25.7b
(sqrt (- (* b b) (* 1 (* a (* 4.0 c)))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
10×add-sqr-sqrt fma-def
9×add-cube-cbrt
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×distribute-rgt-neg-in distribute-lft-out
5×times-frac associate-/l*
4×pow1
3×distribute-lft-neg-in expm1-log1p-u sqrt-prod log1p-expm1-u
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ sqrt-div div-exp sum-log flip-+ associate-/l/
1×+-commutative neg-mul-1 rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* flip-- cbrt-unprod div-inv
Counts
3 → 74
Calls
3 calls:
84.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 1 (* a (* 4.0 c)))))) (* 2.0 a))
32.0ms
(+ (- b) (sqrt (- (* b b) (* 1 (* a (* 4.0 c))))))
13.0ms
(sqrt (- (* b b) (* 1 (* a (* 4.0 c)))))

series409.0ms

Counts
3 → 9
Calls
3 calls:
156.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 1 (* a (* 4.0 c)))))) (* 2.0 a))
134.0ms
(+ (- b) (sqrt (- (* b b) (* 1 (* a (* 4.0 c))))))
119.0ms
(sqrt (- (* b b) (* 1 (* a (* 4.0 c)))))

simplify4.1s

Counts
83 → 83
Iterations

Useful iterations: 3 (2.2s)

IterNodesCost
01511611
14091329
213291136
349831122
done50001122

prune333.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
25.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite302.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
66×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
30×add-exp-log
22×sqrt-prod
18×prod-diff associate-/r* add-cbrt-cube
14×div-exp difference-of-squares
11×associate-/r/
7×cbrt-undiv flip3-- flip-- distribute-lft-out--
6×pow1 fma-neg div-inv add-log-exp
4×expm1-log1p-u prod-exp log1p-expm1-u associate-/l*
3×rec-exp 1-exp
2×frac-2neg sqrt-div clear-num cbrt-unprod
1×sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 diff-log inv-pow
Counts
4 → 167
Calls
4 calls:
60.0ms
(/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
98.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
107.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series772.0ms

Counts
4 → 12
Calls
4 calls:
304.0ms
(/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
202.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
130.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
136.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
179 → 179
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02644500
16163949
216973478
done50013333

prune518.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

regimes423.0ms

Accuracy

83.3% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 33.9b

bsearch197.0ms

Steps
ItersRangePoint
9
2.3136842542622443e-90
1.8034474160827886e-84
3.091361180800597e-86
6
-3.779251410483496e+105
-5.080294099506613e+104
-1.361733299857302e+105

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02941
13839
done3839

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.1s1023×body2560valid
841.0ms906×body1280valid
555.0ms5866×body80valid
347.0ms2914×body80nan
182.0ms442×body640valid
146.0ms127×body5120valid
56.0ms244×body320valid
17.0ms109×body160valid