Details

Time bar (total: 18.7s)

sample81.0ms

Algorithm
intervals
Results
36.0ms280×body80valid
9.0ms78×body80nan

simplify210.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02038
13938
27937
314337
417937
518937
619337
done19337

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize156.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
140.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
177 → 177
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02086992
15084619
226703571
done50013570

prune733.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize105.0ms

Local error

Found 4 expressions with local error:

17.1b
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
1×fma-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
122.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
73 → 73
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0711269
11741005
2677906
33809906
done5000903

prune589.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.0b

localize162.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u cbrt-div flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 64
Calls
4 calls:
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series564.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
134.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
157.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
152.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
76 → 76
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0941248
12241156
27501052
339761040
done50001038

prune787.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.0b

localize195.0ms

Local error

Found 4 expressions with local error:

17.1b
(fma (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (- b))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- sqrt-prod flip--
2×pow1/3 sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 57
Calls
4 calls:
0.0ms
(fma (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (- b))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(fma (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (- b))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
143.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
145.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
69 → 69
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01351376
13211309
211731176
done50001136

prune717.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.0b

regimes248.0ms

Accuracy

89.1% (1.4b remaining)

Error of 8.4b against oracle of 7.0b and baseline of 19.7b

bsearch272.0ms

Steps
ItersRangePoint
8
3932480935863.943
2020002846347102.2
2000198799923726.5
7
-7.561250615295736e+156
-6.888726652681395e+154
-7.031540569065605e+154

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
045135
153135
done53135

end0.0ms

sample2.0s

Algorithm
intervals
Results
984.0ms8666×body80valid
522.0ms2861×body80nan