Details

Time bar (total: 17.6s)

sample124.0ms

Algorithm
intervals
Results
33.0ms25×body2560valid
22.0ms45×body1280valid
20.0ms184×body80valid
7.0ms69×body80nan
6.0ms17×body640valid
2.0ms8×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify146.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite190.0ms

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:
115.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
148.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(- (* b b) (* (* 4.0 a) c))
130.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01671697
14331584
214861361
done50001347

prune498.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite316.0ms

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×expm1-log1p-u log1p-expm1-u 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 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
19.0ms
(- (* b b) (* (* 4.0 a) c))
160.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
110.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series644.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (* b b) (* (* 4.0 a) c))
211.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
274.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
170 → 170
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02625076
16444511
227154181
done50024179

prune774.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

localize21.0ms

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
(/ (+ 0 (* (* 4.0 a) c)) (- (- 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)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
12×times-frac
10×fma-neg prod-diff
8×add-log-exp
6×pow1 add-exp-log distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod add-cbrt-cube
5×difference-of-squares
4×expm1-log1p-u flip3-- sqrt-div associate-/r* flip-- log1p-expm1-u
3×associate-/l*
2×neg-mul-1 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 → 108
Calls
4 calls:
31.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
82.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series628.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
259.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
120 → 120
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01874229
14462511
215112378
done50012338

prune710.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.2b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite201.0ms

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×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u div-inv
2×frac-2neg sqrt-div clear-num associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 124
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(/ (* 2.0 a) (/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
79.0ms
(/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series614.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (* b b) (* (* 4.0 a) c))
120.0ms
(/ (* 2.0 a) (/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
310.0ms
(/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
136 → 136
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02393526
16453322
229882738
done50002737

prune512.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.2b

regimes267.0ms

Accuracy

93.9% (1.6b remaining)

Error of 6.9b against oracle of 5.4b and baseline of 31.0b

bsearch338.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
3.2014259215130234e+53
10
-1.2529167750641135e-296
-2.859335985249397e-307
-3.1046203401759487e-300
9
-8.712513212907472e+114
-1.0414090820182828e+108
-2.463372194426505e+111

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
03870
14870
done4870

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.0s1056×body2560valid
651.0ms479×body640valid
559.0ms5848×body80valid
375.0ms922×body1280valid
342.0ms2941×body80nan
150.0ms113×body5120valid
44.0ms208×body320valid
15.0ms109×body160valid