Details

Time bar (total: 10.3s)

sample47.0ms

Algorithm
intervals
Results
8.0ms206×body80valid
8.0ms28×body1280valid
6.0ms28×body2560valid
4.0ms107×body80nan
2.0ms13×body640valid
1.0ms2×body5120valid
1.0ms6×body160valid
1.0ms4×body320valid

simplify76.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize12.0ms

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)))
1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
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 → 106
Calls
4 calls:
87.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
50.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
52.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
79.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify979.0ms

Counts
118 → 118
Iterations

Useful iterations: done (975.0ms)

IterNodesCost
01932476
14812169
214191861
done50001789

prune296.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×times-frac
50×*-un-lft-identity
40×add-cube-cbrt
25×add-exp-log
20×sqrt-prod
19×prod-diff
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×add-log-exp
7×flip3-- fma-neg flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
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 → 152
Calls
4 calls:
55.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
10.0ms
(- (* b b) (* 4.0 (* a c)))
47.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series362.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
52.0ms
(- (* b b) (* 4.0 (* a c)))
88.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify971.0ms

Counts
164 → 164
Iterations

Useful iterations: done (965.0ms)

IterNodesCost
02594025
15883484
216333082
done50002938

prune326.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) a)
1.0b
(- (pow b 2) (* 4.0 (* a c)))
1.2b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.3b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
44×*-un-lft-identity
34×add-cube-cbrt
26×prod-diff
20×sqrt-prod
18×times-frac
14×fma-neg
10×difference-of-squares
8×add-log-exp
6×add-exp-log unpow-prod-down add-cbrt-cube associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/ unpow2 sqr-pow
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 132
Calls
4 calls:
134.0ms
(/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) a)
17.0ms
(- (pow b 2) (* 4.0 (* a c)))
77.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
17.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) a)
53.0ms
(- (pow b 2) (* 4.0 (* a c)))
83.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
79.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify974.0ms

Counts
144 → 144
Iterations

Useful iterations: done (970.0ms)

IterNodesCost
02122996
15002658
212602358
done50002278

prune366.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.3b
(sqrt (- (* b b) (* 4.0 (* a c))))
21.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite123.0ms

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:
47.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
47.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
13.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
87.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts
128 → 128
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01122856
12672310
27161948
326691774
done50011674

prune340.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.4b

regimes189.0ms

Accuracy

78% (6.2b remaining)

Error of 11.6b against oracle of 5.4b and baseline of 33.4b

bsearch213.0ms

Steps
ItersRangePoint
8
0.0001820196720056695
0.3848154462067827
0.00018465375781150442
6
3.6410892437809104e-110
3.0960233903298005e-109
4.731827132847258e-110
8
1.0691773024250323e-170
5.5548132533506025e-168
2.175674080408203e-169
9
-1.4924982923623064e+60
-5.817343306680769e+54
-1.4784065354805617e+60

simplify9.0ms

Iterations

Useful iterations: done (8.0ms)

IterNodesCost
03676
14772
25055
35355
done5354

end0.0ms

sample1.5s

Algorithm
intervals
Results
450.0ms1042×body2560valid
248.0ms5926×body80valid
168.0ms905×body1280valid
110.0ms2856×body80nan
75.0ms463×body640valid
28.0ms102×body5120valid
25.0ms225×body320valid
7.0ms95×body160valid