Details

Time bar (total: 9.1s)

sample42.0ms

Algorithm
intervals
Results
10.0ms195×body80valid
8.0ms37×body2560valid
4.0ms21×body1280valid
3.0ms81×body80nan
3.0ms19×body640valid
1.0ms3×body5120valid
0.0ms4×body320valid
0.0ms4×body160valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.4b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
20.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
40.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
43.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify822.0ms

Counts
161 → 161
Iterations

Useful iterations: done (812.0ms)

IterNodesCost
02784083
16633911
219403753
done50003752

prune431.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
20.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
438×add-sqr-sqrt
363×*-un-lft-identity
289×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
40×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
17×div-inv
15×div-exp
13×add-cbrt-cube
8×add-log-exp
6×pow1 cbrt-undiv
5×associate-/r/
3×rec-exp flip3-- 1-exp flip-- associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 354
Calls
4 calls:
40.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
18.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series342.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
48.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts
366 → 366
Iterations

Useful iterations: 2 (720.0ms)

IterNodesCost
056911964
1134210707
2335610033
done500010033

prune542.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
20.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite98.0ms

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:
67.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
50.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts
93 → 93
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01781851
14541643
215131437
done50001433

prune214.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.1b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
20.6b
(sqrt (- (* b b) (* 4.0 (* a c))))
20.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
21.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
19.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
80.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts
72 → 72
Iterations

Useful iterations: 3 (322.0ms)

IterNodesCost
0801248
11891104
25991036
320251028
done50001028

prune236.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes179.0ms

Accuracy

83.3% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.3b

bsearch130.0ms

Steps
ItersRangePoint
10
3.056596725548563e-78
7.076105677608322e-63
3.446447862996811e-75
10
-1.852183237050365e+100
-1.9127319211193897e+86
-4.123103533644211e+95

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13640
done3640

end0.0ms

sample1.1s

Algorithm
intervals
Results
252.0ms1096×body2560valid
225.0ms5880×body80valid
158.0ms852×body1280valid
107.0ms2945×body80nan
66.0ms471×body640valid
31.0ms109×body5120valid
22.0ms211×body320valid
8.0ms107×body160valid