Details

Time bar (total: 19.3s)

sample442.0ms

Algorithm
intervals
Results
130.0ms109×body160valid
66.0ms112×body320valid
29.0ms266×body80nan
24.0ms522×pre80true
3.0ms9×body640valid
2.0ms26×body80valid

simplify225.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
30.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite155.0ms

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:
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series431.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
57.0ms
(- (* b b) (* (* 4.0 a) c))
162.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
113.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify2.0s

Counts
102 → 102
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01671697
14521588
221181361
done50011352

prune377.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite346.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×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
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
33.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(- (* b b) (* (* 4.0 a) c))
172.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
119.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series766.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(- (* b b) (* (* 4.0 a) c))
272.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
308.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify605.0ms

Counts
243 → 243
Iterations

Useful iterations: done (595.0ms)

IterNodesCost
033910026
18617622
done50006606

prune926.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c))))))
0.5b
(/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c)))
0.6b
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

rewrite419.0ms

Algorithm
rewrite-expression-head
Rules
121×times-frac
119×add-sqr-sqrt
118×pow1
89×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
49×add-cube-cbrt
36×associate-/l*
30×difference-of-squares
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp
6×associate-/r/
5×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-- frac-2neg pow-plus clear-num flip-- associate-/l/
1×pow2 flip3-+ swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 226
Calls
4 calls:
129.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
93.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c))))))
5.0ms
(/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c)))
166.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

series1.0s

Counts
4 → 12
Calls
4 calls:
397.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
389.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c))))))
150.0ms
(/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c)))
66.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

simplify655.0ms

Counts
238 → 238
Iterations

Useful iterations: done (637.0ms)

IterNodesCost
033610248
18759541
done50018728

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c))))))) (* 2.0 a))
0.3b
(/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c))))
0.3b
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))))))
0.6b
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
331×add-sqr-sqrt
280×times-frac
132×sqrt-prod
118×pow1
111×*-un-lft-identity
80×difference-of-squares
71×add-cube-cbrt
66×pow-prod-down
56×add-exp-log add-cbrt-cube
51×associate-/l*
29×prod-exp cbrt-unprod
20×associate-/r* distribute-lft-out--
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp
6×associate-/r/
5×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-- frac-2neg pow-plus clear-num flip-- associate-/l/
1×pow2 flip3-+ swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 288
Calls
4 calls:
535.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c))))))) (* 2.0 a))
7.0ms
(/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c))))
290.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))))))
178.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

series991.0ms

Counts
4 → 12
Calls
4 calls:
380.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c))))))) (* 2.0 a))
179.0ms
(/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c))))
374.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))))))
59.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

simplify734.0ms

Counts
300 → 300
Iterations

Useful iterations: done (702.0ms)

IterNodesCost
037717492
195114591
done500013011

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes180.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02553
13251
25351
37351
47951
58051
done8051

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.3s3615×body320valid
1.2s16159×pre80true
771.0ms8159×body80nan
537.0ms3016×body160valid
180.0ms465×body640valid
108.0ms904×body80valid