Details

Time bar (total: 15.7s)

sample54.0ms

Algorithm
intervals
Results
11.0ms38×body2560valid
10.0ms178×body80valid
7.0ms28×body1280valid
4.0ms79×body80nan
2.0ms11×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify135.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
145.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
60.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
119.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
63.0ms
(- (* b b) (* (* 4.0 a) c))
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01541592
13861488
212341332
346391324
done50021324

prune341.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite381.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
13×add-cbrt-cube
12×*-un-lft-identity
10×prod-exp
8×add-cube-cbrt add-log-exp
7×pow1 associate-*r*
6×associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod difference-of-squares
3×times-frac
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div diff-log 1-exp associate-*l/ distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 81
Calls
4 calls:
250.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
85.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
26.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
104.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
55.0ms
(- (* b b) (* (* 4.0 a) c))
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
93 → 93
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01801851
14421643
214811437
done50001431

prune288.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
47×add-sqr-sqrt
36×*-un-lft-identity
26×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×sqrt-prod add-log-exp
7×flip3-- flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 118
Calls
4 calls:
110.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
60.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
104.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify902.0ms

Counts
130 → 130
Iterations

Useful iterations: done (898.0ms)

IterNodesCost
02203137
14972801
214632561
done50002481

prune272.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (/ 1 2.0) a) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
3474×times-frac
1853×add-sqr-sqrt
1586×*-un-lft-identity
1320×add-cube-cbrt
266×difference-of-squares
145×div-inv
136×sqrt-prod
133×distribute-lft-out--
89×associate-/r/
69×add-exp-log
54×div-exp
47×flip3-- flip--
43×associate-/l*
25×add-cbrt-cube
24×associate-/r*
15×cbrt-undiv
9×rec-exp 1-exp
8×add-log-exp
5×pow1
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 1179
Calls
4 calls:
102.0ms
(/ (/ (/ 1 2.0) a) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
53.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (/ (/ 1 2.0) a) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
87.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
51.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
1191 → 1191
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0158054089
1434545253
done500143676

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.1b

regimes202.0ms

Accuracy

84% (4.6b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 34.4b

bsearch128.0ms

Steps
ItersRangePoint
8
4.924640387312937e-45
5.473977791176249e-42
5.2024432226242543e-45
8
-6.990724105819741e+111
-2.6156774686163576e+108
-1.569310777886352e+111

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample2.8s

Algorithm
intervals
Results
697.0ms5806×body80valid
507.0ms1087×body2560valid
457.0ms446×body640valid
313.0ms930×body1280valid
222.0ms2994×body80nan
79.0ms117×body5120valid
31.0ms210×body320valid
12.0ms116×body160valid