Details

Time bar (total: 10.3s)

sample42.0ms

Algorithm
intervals
Results
9.0ms39×body2560valid
7.0ms36×body1280valid
6.0ms165×body80valid
3.0ms87×body80nan
2.0ms13×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms4×body160valid

simplify56.0ms

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: 33.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

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:
36.0ms
(/ (/ (- (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)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ (- (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)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify955.0ms

Counts
195 → 195
Iterations

Useful iterations: done (949.0ms)

IterNodesCost
03214967
17514592
221844283
done50014264

prune553.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) (/ 1 a))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
46×*-un-lft-identity
36×add-cube-cbrt
34×times-frac
26×add-exp-log
22×associate-*l*
19×prod-diff sqrt-prod
16×add-cbrt-cube
13×associate-*r*
8×div-exp prod-exp add-log-exp difference-of-squares
7×pow1 fma-neg
6×unswap-sqr
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u distribute-lft-out--
3×flip3-- flip--
2×sub-neg rec-exp sqrt-div diff-log 1-exp div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ un-div-inv *-commutative
Counts
4 → 142
Calls
4 calls:
54.0ms
(* (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) (/ 1 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)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) (/ 1 a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts
154 → 154
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02633349
17092930
219282497
done50002478

prune376.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

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:
37.0ms
(/ 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)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
50.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
400 → 400
Iterations

Useful iterations: done (1.4s)

IterNodesCost
061212852
1142811390
2357510561
done500010543

prune636.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

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:
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.0ms
(- (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)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
84.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
128 → 128
Iterations

Useful iterations: 3 (793.0ms)

IterNodesCost
01132856
12622310
27561948
328771774
done50011774

prune338.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.4b

regimes201.0ms

Accuracy

81.5% (5.2b remaining)

Error of 10.9b against oracle of 5.8b and baseline of 33.8b

bsearch109.0ms

Steps
ItersRangePoint
9
2.365685850767504e-168
1.2053288471691685e-161
1.1860189201379418e-161
8
-1.4395777107888637e+138
-2.299948591329529e+133
-1.9827654008890006e+134

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample1.1s

Algorithm
intervals
Results
240.0ms1025×body2560valid
238.0ms5914×body80valid
171.0ms891×body1280valid
111.0ms2997×body80nan
65.0ms450×body640valid
29.0ms107×body5120valid
23.0ms209×body320valid
8.0ms104×body160valid