Details

Time bar (total: 16.4s)

sample101.0ms

Algorithm
intervals
Results
22.0ms45×body1280valid
19.0ms184×body80valid
16.0ms25×body2560valid
7.0ms17×body640valid
7.0ms69×body80nan
2.0ms8×body320valid
2.0ms2×body5120valid
0.0ms2×body160valid

simplify145.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize29.0ms

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)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite258.0ms

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:
152.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
69.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms
(- (* b b) (* (* 4.0 a) c))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.7s

Counts
84 → 84
Iterations

Useful iterations: 3 (2.1s)

IterNodesCost
01541592
13861488
212341332
346391324
done50021324

prune426.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize21.0ms

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)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite259.0ms

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:
181.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
52.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
106.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
93 → 93
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01801851
14421643
214811437
done50001431

prune322.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize18.0ms

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)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite185.0ms

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:
101.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
63.0ms
(- (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)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
120.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
83.0ms
(- (* b b) (* (* 4.0 a) c))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01541592
13861488
212341332
346391324
done50021324

prune286.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite167.0ms

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:
83.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
52.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
126.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
69.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
130 → 130
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02203137
14972801
214632561
done50002481

prune340.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

regimes263.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 34.1b

bsearch200.0ms

Steps
ItersRangePoint
7
1.5383510854529177e-107
7.914847206339754e-106
4.718890261991469e-106
10
-2.386196042261592e+160
-1.0923850232644114e+143
-1.119811545308531e+143

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03044
13738
done3738

end0.0ms

sample2.9s

Algorithm
intervals
Results
811.0ms5848×body80valid
662.0ms1056×body2560valid
472.0ms922×body1280valid
230.0ms2941×body80nan
203.0ms479×body640valid
57.0ms113×body5120valid
40.0ms208×body320valid
20.0ms109×body160valid