Details

Time bar (total: 17.0s)

sample119.0ms

Algorithm
intervals
Results
23.0ms307×body80nan
22.0ms150×body160valid
18.0ms563×pre80true
8.0ms106×body80valid

simplify148.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
30.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite170.0ms

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:
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
33.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(- (* b b) (* (* 4.0 a) c))
159.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
109.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01671697
14331584
214811361
done50001347

prune358.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite269.0ms

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:
47.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
99.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
87.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series604.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
165.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
300.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.5s

Counts
243 → 243
Iterations

Useful iterations: done (1.5s)

IterNodesCost
034010026
18127598
232366483
done50016397

prune770.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite367.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
135×add-sqr-sqrt
133×*-un-lft-identity
125×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
15×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
7×associate-*r*
6×pow1
4×expm1-log1p-u sub-neg flip3-- associate-*r/ prod-exp flip-- cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp associate-*l* associate-/l*
2×associate-*l/ associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ pow-prod-down neg-log clear-num associate-/r* *-commutative flip-+ div-inv unswap-sqr
Counts
4 → 285
Calls
4 calls:
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
129.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
164.0ms
(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series605.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms
(- (* b b) (* (* 4.0 a) c))
181.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
243.0ms
(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify2.1s

Counts
297 → 297
Iterations

Useful iterations: done (2.1s)

IterNodesCost
037517028
178611195
232458620
done50018367

prune621.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*r*
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
8×add-log-exp
6×pow1 distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
4×expm1-log1p-u distribute-rgt-neg-out log1p-expm1-u
3×flip3-+ times-frac associate-*l* flip-+ associate-/l*
2×cbrt-undiv flip3-- sqrt-div associate-*r/ div-exp associate-*l/ prod-exp associate-/r/ flip-- cbrt-unprod associate-/l/ distribute-neg-frac
1×+-commutative distribute-lft-neg-out neg-mul-1 sub-neg distribute-neg-out fma-def frac-2neg fma-neg diff-log unsub-neg prod-diff pow-prod-down clear-num associate-/r* sum-log *-commutative div-inv unswap-sqr
Counts
4 → 96
Calls
4 calls:
11.0ms
(+ (* (- a) b) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
58.0ms
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(/ (+ 0 (* (* a c) 4.0)) (* (+ (* (- a) b) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0))

series653.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(+ (* (- a) b) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
117.0ms
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
52.0ms
(- (* b b) (* (* 4.0 a) c))
325.0ms
(/ (+ 0 (* (* a c) 4.0)) (* (+ (* (- a) b) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0))

simplify1.7s

Counts
108 → 108
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02052343
15442092
225351756
done50011755

prune875.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes253.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
03048
14246
25345
36345
46645
done6645

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.3s8589×body80nan
798.0ms4475×body160valid
594.0ms16589×pre80true
331.0ms3525×body80valid