Details

Time bar (total: 12.7s)

sample63.0ms

Algorithm
intervals
Results
13.0ms257×body80nan
12.0ms111×body320valid
10.0ms513×pre80true
7.0ms103×body160valid
2.0ms13×body640valid
1.0ms29×body80valid

simplify56.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.9b

localize11.0ms

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))
29.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite63.0ms

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:
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
50.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify899.0ms

Counts
102 → 102
Iterations

Useful iterations: done (896.0ms)

IterNodesCost
01671697
14371584
214831361
done50001351

prune251.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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

rewrite134.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
58.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
42.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
192.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.2s

Counts
243 → 243
Iterations

Useful iterations: done (1.2s)

IterNodesCost
034110754
18448227
228876648
done50016646

prune579.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* c (* 4.0 a)) (fma b b (* (* 4.0 a) c)) (pow b 4)))))) (* 2.0 a))
0.3b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* c (* 4.0 a)) (fma b b (* (* 4.0 a) c)) (pow b 4))))))
0.4b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* c (* 4.0 a)) (fma b b (* (* 4.0 a) c)) (pow b 4)))
0.8b
(pow (* (* 4.0 a) c) 3)

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
155×add-sqr-sqrt
142×times-frac
105×*-un-lft-identity
57×add-cube-cbrt
54×difference-of-squares
43×associate-/l*
26×add-exp-log add-cbrt-cube
24×distribute-lft-out--
21×sqr-pow
20×sqrt-prod
12×associate-/r*
10×pow1 distribute-rgt-neg-in
9×unpow-prod-down
8×cbrt-undiv div-exp
6×associate-/r/
5×prod-exp cbrt-unprod div-inv associate-/l/
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u add-log-exp
3×pow-unpow pow-pow frac-2neg pow-prod-down pow-exp clear-num rem-cube-cbrt
1×cube-mult pow-to-exp flip3-+ unpow3 div-sub cube-prod flip-+
Counts
4 → 222
Calls
4 calls:
157.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* c (* 4.0 a)) (fma b b (* (* 4.0 a) c)) (pow b 4)))))) (* 2.0 a))
112.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* c (* 4.0 a)) (fma b b (* (* 4.0 a) c)) (pow b 4))))))
34.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* c (* 4.0 a)) (fma b b (* (* 4.0 a) c)) (pow b 4)))
7.0ms
(pow (* (* 4.0 a) c) 3)

series677.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* c (* 4.0 a)) (fma b b (* (* 4.0 a) c)) (pow b 4)))))) (* 2.0 a))
271.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* c (* 4.0 a)) (fma b b (* (* 4.0 a) c)) (pow b 4))))))
130.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* c (* 4.0 a)) (fma b b (* (* 4.0 a) c)) (pow b 4)))
54.0ms
(pow (* (* 4.0 a) c) 3)

simplify1.2s

Counts
234 → 234
Iterations

Useful iterations: done (1.2s)

IterNodesCost
039212887
195111960
2331110811
done500110809

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize16.0ms

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))))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b
(* (/ (fma (* 4.0 a) c 0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
332×times-frac
301×add-sqr-sqrt
275×*-un-lft-identity
185×add-cube-cbrt
85×associate-*r*
61×prod-diff
52×sqrt-prod
48×add-exp-log
44×distribute-lft-out-- difference-of-squares
43×distribute-rgt-neg-in
30×add-cbrt-cube
27×associate-/l*
23×div-exp
21×distribute-lft-neg-in
14×associate-/r/
13×associate-*l*
12×cbrt-undiv
11×fma-neg
10×prod-exp div-inv add-log-exp
9×flip3-- flip--
8×unswap-sqr
7×neg-mul-1
6×pow1 cbrt-unprod
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp associate-/r*
2×sub-neg
1×associate--l- neg-sub0 frac-times frac-2neg associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 372
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
40.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
92.0ms
(* (/ (fma (* 4.0 a) c 0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series466.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
122.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
223.0ms
(* (/ (fma (* 4.0 a) c 0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify2.1s

Counts
384 → 384
Iterations

Useful iterations: done (2.1s)

IterNodesCost
050714091
1140811546
244209765
done50009764

prune815.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes126.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02029
12729
done2729

end0.0ms

sample1.6s

Algorithm
intervals
Results
380.0ms3587×body320valid
284.0ms16016×pre80true
274.0ms8016×body80nan
213.0ms2960×body160valid
73.0ms518×body640valid
34.0ms935×body80valid