Details

Time bar (total: 17.1s)

sample96.0ms

Algorithm
intervals
Results
21.0ms38×body2560valid
17.0ms178×body80valid
12.0ms28×body1280valid
7.0ms79×body80nan
4.0ms11×body640valid
2.0ms3×body5120valid
2.0ms6×body320valid
0.0ms2×body160valid

simplify105.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune13.0ms

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)))

rewrite202.0ms

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:
102.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
66.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
145.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
69.0ms
(- (* b b) (* (* 4.0 a) c))
127.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.4s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01541592
13861488
212341332
346391324
done50021324

prune439.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize37.0ms

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)))

rewrite269.0ms

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:
165.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
71.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
116.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
83.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
93 → 93
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01801851
14421643
214811437
done50001431

prune386.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize26.0ms

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)))

rewrite176.0ms

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:
76.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
60.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
8.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
115.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
83.0ms
(- (* b b) (* (* 4.0 a) c))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
130 → 130
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02203137
14972801
214632561
done50002481

prune412.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize17.0ms

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)))

rewrite387.0ms

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:
109.0ms
(/ (/ (/ 1 2.0) a) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
63.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms
(- (* b b) (* (* 4.0 a) c))
30.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(/ (/ (/ 1 2.0) a) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
104.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
61.0ms
(- (* b b) (* (* 4.0 a) c))
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
1191 → 1191
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0158054089
1434545253
done500143676

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.1b

regimes200.0ms

Accuracy

84% (4.6b remaining)

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

bsearch141.0ms

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

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample2.7s

Algorithm
intervals
Results
843.0ms1087×body2560valid
588.0ms5806×body80valid
368.0ms930×body1280valid
170.0ms2994×body80nan
131.0ms446×body640valid
49.0ms117×body5120valid
34.0ms210×body320valid
13.0ms116×body160valid