Details

Time bar (total: 17.5s)

sample100.0ms

Algorithm
intervals
Results
28.0ms184×body80valid
19.0ms45×body1280valid
12.0ms25×body2560valid
6.0ms69×body80nan
5.0ms17×body640valid
2.0ms8×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify124.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite174.0ms

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:
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
32.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
112.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
55.0ms
(- (* b b) (* 4.0 (* a c)))
104.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.3s

Counts
82 → 82
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01521565
14001461
213311245
349061231
done50011231

prune425.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize34.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
3.5b
(/ (/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.2b
(/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite344.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
17.0ms
(- (* b b) (* 4.0 (* a c)))
169.0ms
(/ (/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
127.0ms
(/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series737.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (* b b) (* 4.0 (* a c)))
252.0ms
(/ (/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
288.0ms
(/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
104.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
160 → 160
Iterations

Useful iterations: 2 (546.0ms)

IterNodesCost
02474912
16104361
224384035
done50004035

prune712.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

localize27.0ms

Local error

Found 4 expressions with local error:

9.4b
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.4b
(/ (+ (* 4.0 (* a c)) 0) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×times-frac
8×add-log-exp
6×pow1 add-exp-log sqrt-prod add-cbrt-cube
5×difference-of-squares
4×flip3-- sqrt-div associate-/r* flip--
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/ associate-/l/
1×cbrt-undiv associate--l- neg-sub0 sub-neg frac-2neg flip3-+ div-exp neg-log clear-num flip-+ div-inv
Counts
4 → 80
Calls
4 calls:
13.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
86.0ms
(/ (+ (* 4.0 (* a c)) 0) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series590.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
277.0ms
(/ (+ (* 4.0 (* a c)) 0) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
112.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
84.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
92 → 92
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01593048
13831904
214101782
done50001760

prune462.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.2b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
3.2b
(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.2b
(/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
28×add-sqr-sqrt
27×*-un-lft-identity
20×associate-/r*
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
11×add-cube-cbrt
8×distribute-lft-out-- difference-of-squares
7×sqrt-prod associate-/r/
6×add-log-exp
5×pow1 flip3-- flip--
4×distribute-rgt-neg-in div-inv
2×frac-2neg sqrt-div clear-num associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 114
Calls
4 calls:
18.0ms
(- (* b b) (* 4.0 (* a c)))
85.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
93.0ms
(/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series515.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* 4.0 (* a c)))
105.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
252.0ms
(/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
87.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
126 → 126
Iterations

Useful iterations: 2 (621.0ms)

IterNodesCost
02263382
16173188
229162606
done50002606

prune418.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.2b

regimes402.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 32.7b

bsearch146.0ms

Steps
ItersRangePoint
7
1.5383510854529177e-107
7.914847206339754e-106
6.268445144099728e-106
9
-8.712513212907472e+114
-1.0414090820182828e+108
-2.463372194426505e+111

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02941
13841
done3841

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s1056×body2560valid
669.0ms5848×body80valid
433.0ms922×body1280valid
201.0ms479×body640valid
201.0ms2941×body80nan
121.0ms113×body5120valid
79.0ms208×body320valid
15.0ms109×body160valid