Details

Time bar (total: 15.1s)

sample80.0ms

Algorithm
intervals
Results
17.0ms36×body1280valid
16.0ms38×body2560valid
12.0ms190×body80valid
5.0ms79×body80nan
3.0ms11×body640valid
2.0ms4×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify126.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01217
12117
24116
37616
49616
510416
done10416

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 3.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-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 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
9.0ms
(- (* b b) (* (* 3.0 a) c))
92.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
42.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b b) (* (* 3.0 a) c))
159.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
111.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
111.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
82 → 82
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01541565
14161463
218881247
done50001241

prune385.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.9b
(/ (/ (+ 0 (* (* c a) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
7.6b
(/ (+ 0 (* (* c a) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×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 → 154
Calls
4 calls:
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
103.0ms
(/ (/ (+ 0 (* (* c a) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
100.0ms
(/ (+ 0 (* (* c a) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series680.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
243.0ms
(/ (/ (+ 0 (* (* c a) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
239.0ms
(/ (+ 0 (* (* c a) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
102.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.1s

Counts
166 → 166
Iterations

Useful iterations: 2 (866.0ms)

IterNodesCost
02565113
16664543
242634221
done50004221

prune621.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.9b
(/ (/ (* (* c a) 3.0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
7.7b
(/ (* (* c a) 3.0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log add-cbrt-cube
26×times-frac
22×add-sqr-sqrt
21×*-un-lft-identity
19×cbrt-undiv div-exp
18×prod-exp cbrt-unprod
17×add-cube-cbrt
10×associate-*r/ associate-/r/
8×associate-/l* add-log-exp
7×flip3-- flip--
6×div-inv
5×pow1
4×associate-/r* sqrt-prod
2×frac-2neg sqrt-div diff-log clear-num distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 116
Calls
4 calls:
33.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
54.0ms
(/ (/ (* (* c a) 3.0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
48.0ms
(/ (* (* c a) 3.0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
282.0ms
(/ (/ (* (* c a) 3.0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
210.0ms
(/ (* (* c a) 3.0) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
101.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify451.0ms

Counts
128 → 128
Iterations

Useful iterations: done (446.0ms)

IterNodesCost
02513910
17133629
done50002901

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.9b
(/ (/ (/ (* c a) 1) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
7.7b
(/ (/ (* c a) 1) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
518×times-frac
322×add-sqr-sqrt
321×*-un-lft-identity
173×add-cube-cbrt
74×distribute-lft-out-- difference-of-squares
62×associate-/l*
42×div-inv
40×sqrt-prod
39×add-exp-log
37×distribute-rgt-neg-in
27×add-cbrt-cube
24×div-exp
14×cbrt-undiv
10×associate-/r* associate-/r/
8×add-log-exp
7×flip3-- flip--
5×pow1
4×1-exp prod-exp
2×frac-2neg sqrt-div diff-log clear-num cbrt-unprod associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 361
Calls
4 calls:
37.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
107.0ms
(/ (/ (/ (* c a) 1) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
78.0ms
(/ (/ (* c a) 1) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
18.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series653.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
213.0ms
(/ (/ (/ (* c a) 1) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
234.0ms
(/ (/ (* c a) 1) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
87.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify723.0ms

Counts
373 → 373
Iterations

Useful iterations: done (704.0ms)

IterNodesCost
048612491
1135810891
done500110319

prune970.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

regimes309.0ms

Accuracy

93.4% (1.6b remaining)

Error of 7.5b against oracle of 5.9b and baseline of 29.5b

bsearch275.0ms

Steps
ItersRangePoint
8
3932480935863.943
2020002846347102.2
929319867835151.5
9
-7.152300718152866e-253
-1.7963911490351415e-262
-5.4265074277492375e-260
9
-7.561250615295736e+156
-1.350243324689865e+150
-4.919628179067154e+153

simplify11.0ms

Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
03764
14461
24659
34859
done4859

end0.0ms

sample2.9s

Algorithm
intervals
Results
673.0ms2893×body80nan
589.0ms1055×body2560valid
513.0ms5920×body80valid
316.0ms903×body1280valid
138.0ms459×body640valid
82.0ms220×body320valid
39.0ms85×body5120valid
14.0ms121×body160valid