Details

Time bar (total: 20.6s)

sample117.0ms

Algorithm
intervals
Results
27.0ms282×body80nan
21.0ms147×body160valid
17.0ms538×pre80true
9.0ms45×body320valid
5.0ms64×body80valid

simplify161.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
01417
12817
27016
312716
414016
done14016

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(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))
39.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite153.0ms

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:
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
42.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(- (* b b) (* (* 4.0 a) c))
132.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
115.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.6s

Counts
102 → 102
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01671697
110781560
done50011408

prune423.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

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))
0.2b
(/ (/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite259.0ms

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
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 neg-log associate-/l/
Counts
4 → 229
Calls
4 calls:
47.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(- (* b b) (* (* 4.0 a) c))
101.0ms
(/ (/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
84.0ms
(/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series839.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(- (* b b) (* (* 4.0 a) c))
337.0ms
(/ (/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
318.0ms
(/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.1s

Counts
241 → 241
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03319790
done50007049

prune908.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize45.0ms

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

rewrite321.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
133×add-sqr-sqrt
131×*-un-lft-identity
123×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
27×add-exp-log add-cbrt-cube
19×neg-mul-1
11×fma-neg
10×prod-exp cbrt-unprod add-log-exp
7×associate-*r*
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u sub-neg flip3-- associate-*r/ flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log associate-*l*
2×associate-/r/
1×associate--l- neg-sub0 frac-2neg times-frac pow-prod-down neg-log clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 285
Calls
4 calls:
41.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(- (* b b) (* (* 4.0 a) c))
163.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series619.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(- (* b b) (* (* 4.0 a) c))
169.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
259.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify3.3s

Counts
297 → 297
Iterations

Useful iterations: done (3.3s)

IterNodesCost
036516961
148099395
done50009394

prune948.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize40.0ms

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))
0.1b
(/ (* 4.0 (* a c)) a)
0.1b
(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt *-un-lft-identity
76×times-frac
71×add-cube-cbrt
61×prod-diff
39×sqrt-prod
30×distribute-rgt-neg-in
27×add-exp-log add-cbrt-cube
21×distribute-lft-neg-in
18×distribute-lft-out-- difference-of-squares
11×fma-neg
10×cbrt-undiv div-exp associate-/r* div-inv add-log-exp
8×associate-/l*
7×neg-mul-1
6×prod-exp cbrt-unprod
4×pow1 expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg frac-2neg clear-num associate-/r/
1×associate--l- neg-sub0 neg-log associate-/l/
Counts
4 → 217
Calls
4 calls:
54.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(/ (* 4.0 (* a c)) a)
90.0ms
(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(/ (* 4.0 (* a c)) a)
284.0ms
(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify3.5s

Counts
229 → 229
Iterations

Useful iterations: 1 (1.6s)

IterNodesCost
03238786
149986127
done50006127

prune804.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes151.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01721
12321
done2321

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.1s8502×body80nan
982.0ms4786×body160valid
673.0ms16502×pre80true
417.0ms1349×body320valid
151.0ms1865×body80valid