Details

Time bar (total: 10.4s)

sample44.0ms

Algorithm
intervals
Results
9.0ms37×body2560valid
8.0ms195×body80valid
4.0ms21×body1280valid
3.0ms81×body80nan
3.0ms19×body640valid
1.0ms3×body5120valid
0.0ms4×body320valid
0.0ms4×body160valid

simplify55.0ms

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: 30.9b

localize12.0ms

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))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
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 → 183
Calls
4 calls:
37.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
24.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series494.0ms

Counts
4 → 12
Calls
4 calls:
286.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
50.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify917.0ms

Counts
195 → 195
Iterations

Useful iterations: done (904.0ms)

IterNodesCost
03194967
17514592
221594283
done50004264

prune536.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize14.0ms

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))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
452×add-sqr-sqrt
377×*-un-lft-identity
303×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
52×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
19×prod-diff
17×div-inv
15×div-exp
13×add-cbrt-cube
8×add-log-exp
7×fma-neg
6×pow1 cbrt-undiv
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u
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 → 388
Calls
4 calls:
36.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
48.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
400 → 400
Iterations

Useful iterations: done (1.3s)

IterNodesCost
061012852
1142711390
2357410561
done500010543

prune661.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (fma b b (- (* (* a c) 4.0)))) b) (/ (/ 1 a) 2.0))
0.5b
(fma b b (- (* (* a c) 4.0)))
1.1b
(- (sqrt (fma b b (- (* (* a c) 4.0)))) b)
20.6b
(sqrt (fma b b (- (* (* a c) 4.0))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
71×times-frac
60×*-un-lft-identity
55×add-cube-cbrt
43×associate-*r*
19×add-exp-log
18×prod-diff
17×sqrt-prod
13×add-cbrt-cube
7×pow1
6×fma-neg div-exp associate-*l* add-log-exp
5×prod-exp
4×expm1-log1p-u log1p-expm1-u div-inv difference-of-squares unswap-sqr
3×cbrt-undiv flip3-- flip-- cbrt-unprod
2×frac-times associate-*l/ distribute-lft-out--
1×sub-neg rem-sqrt-square rec-exp sqrt-pow1 pow1/2 diff-log 1-exp associate-*r/ pow-prod-down *-commutative fma-udef
Counts
4 → 143
Calls
4 calls:
38.0ms
(* (- (sqrt (fma b b (- (* (* a c) 4.0)))) b) (/ (/ 1 a) 2.0))
0.0ms
(fma b b (- (* (* a c) 4.0)))
6.0ms
(- (sqrt (fma b b (- (* (* a c) 4.0)))) b)
1.0ms
(sqrt (fma b b (- (* (* a c) 4.0))))

series349.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (- (sqrt (fma b b (- (* (* a c) 4.0)))) b) (/ (/ 1 a) 2.0))
52.0ms
(fma b b (- (* (* a c) 4.0)))
91.0ms
(- (sqrt (fma b b (- (* (* a c) 4.0)))) b)
84.0ms
(sqrt (fma b b (- (* (* a c) 4.0))))

simplify987.0ms

Counts
155 → 155
Iterations

Useful iterations: done (982.0ms)

IterNodesCost
02833455
17162972
219932592
done50012565

prune445.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize15.0ms

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))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
23.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
83.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
128 → 128
Iterations

Useful iterations: 3 (630.0ms)

IterNodesCost
01122856
12612310
27561948
328861774
done50001774

prune377.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes173.0ms

Accuracy

83.3% (4.8b remaining)

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

bsearch148.0ms

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

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13940
24740
done4740

end0.0ms

sample1.3s

Algorithm
intervals
Results
282.0ms1096×body2560valid
258.0ms5880×body80valid
181.0ms852×body1280valid
118.0ms2945×body80nan
76.0ms471×body640valid
34.0ms109×body5120valid
26.0ms211×body320valid
9.0ms107×body160valid