Details

Time bar (total: 20.0s)

sample91.0ms

Algorithm
intervals
Results
15.0ms549×pre80true
15.0ms293×body80nan
15.0ms145×body160valid
8.0ms47×body320valid
3.0ms64×body80valid

simplify165.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
35.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite199.0ms

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:
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series461.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
169.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
61.0ms
(- (* b b) (* (* 4.0 a) c))
119.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01671697
14331584
214841361
done50001347

prune390.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

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 (* (* 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)))))

rewrite290.0ms

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:
53.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
93.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series658.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms
(- (* b b) (* (* 4.0 a) c))
215.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
263.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.0s

Counts
243 → 243
Iterations

Useful iterations: done (2.0s)

IterNodesCost
033810026
18027598
230396483
done50016397

prune826.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite641.0ms

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:
210.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))))) (* 2.0 a))
182.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0))))))
63.0ms
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))
173.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

series876.0ms

Counts
4 → 12
Calls
4 calls:
319.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))))) (* 2.0 a))
349.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0))))))
154.0ms
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))
54.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

simplify2.8s

Counts
253 → 253
Iterations

Useful iterations: done (2.8s)

IterNodesCost
037610313
19169573
240728717
done50008713

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite437.0ms

Algorithm
rewrite-expression-head
Rules
278×add-sqr-sqrt
250×prod-diff
222×sqrt-prod
207×*-un-lft-identity
203×add-cube-cbrt
200×times-frac
118×pow1
105×difference-of-squares
79×distribute-rgt-neg-in
78×distribute-lft-neg-in
66×pow-prod-down
63×add-exp-log add-cbrt-cube
36×prod-exp cbrt-unprod
34×unpow-prod-down sqr-pow
26×neg-mul-1
12×div-inv
10×fma-neg
9×pow-sqr pow-prod-up
8×add-log-exp
7×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×flip3-- pow-plus flip--
2×frac-2neg diff-log associate-*r/ clear-num associate-/r/ associate-/l/ distribute-lft-out--
1×associate--l- pow2 neg-sub0 sub-neg div-sub swap-sqr associate-*r* associate-*l* neg-log *-commutative
Counts
4 → 416
Calls
4 calls:
89.0ms
(- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))))
99.0ms
(/ (* (* 4.0 a) c) (* a (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))))))
72.0ms
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))
123.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

series666.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))))
278.0ms
(/ (* (* 4.0 a) c) (* a (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))))))
139.0ms
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (fma b b (* (* a c) 4.0)))
51.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

simplify2.7s

Counts
428 → 428
Iterations

Useful iterations: done (2.7s)

IterNodesCost
062644758
1139238586
2451829584
done500029583

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02340
13040
done3040

end0.0ms

sample2.4s

Algorithm
intervals
Results
495.0ms4779×body160valid
436.0ms16549×pre80true
413.0ms8549×body80nan
214.0ms1363×body320valid
98.0ms1858×body80valid