Details

Time bar (total: 21.6s)

sample276.0ms

Algorithm
intervals
Results
64.0ms22×body640valid
35.0ms118×body320valid
25.0ms280×body80nan
22.0ms536×pre80true
18.0ms87×body160valid
3.0ms29×body80valid

simplify131.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
25.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite226.0ms

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:
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
118.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms
(- (* b b) (* (* 4.0 a) c))
63.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series513.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
136.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms
(- (* b b) (* (* 4.0 a) c))
168.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01671697
14331584
214841361
done50001347

prune406.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite373.0ms

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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
162.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
125.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series730.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (* b b) (* (* 4.0 a) c))
126.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
247.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
289.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.3s

Counts
243 → 243
Iterations

Useful iterations: done (2.2s)

IterNodesCost
033810026
18027598
230376483
done50006397

prune845.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* 4.0 a) c))))))
0.4b
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* 4.0 a) c)))
0.5b
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

rewrite646.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
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 associate-/l/
4×expm1-log1p-u unpow-prod-down flip3-- flip-- log1p-expm1-u add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
1×pow2 flip3-+ div-sub swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 241
Calls
4 calls:
235.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
172.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* 4.0 a) c))))))
67.0ms
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* 4.0 a) c)))
158.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

series928.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
385.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* 4.0 a) c))))))
189.0ms
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* 4.0 a) c)))
48.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

simplify2.5s

Counts
253 → 253
Iterations

Useful iterations: done (2.5s)

IterNodesCost
037510313
19149573
238568717
done50018713

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(/ (/ (+ 0 (* (* 4.0 a) c)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
16×associate-/l*
7×cbrt-undiv div-exp
6×add-log-exp
4×pow1 expm1-log1p-u associate-/r* log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×sub-neg flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ fma-udef
Counts
4 → 105
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
1.0ms
(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
41.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
45.0ms
(/ (+ 0 (* (* 4.0 a) c)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (* b b) (* (* 4.0 a) c))
233.0ms
(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
388.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
442.0ms
(/ (+ 0 (* (* 4.0 a) c)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.6s

Counts
117 → 117
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02243857
15663551
222882698
done50022695

prune725.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes199.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02140
12538
done2538

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.1s3636×body320valid
994.0ms2933×body160valid
697.0ms8078×body80nan
652.0ms507×body640valid
645.0ms16078×pre80true
68.0ms924×body80valid