Details

Time bar (total: 16.5s)

sample110.0ms

Algorithm
intervals
Results
25.0ms29×body2560valid
19.0ms186×body80valid
11.0ms24×body1280valid
9.0ms102×body80nan
5.0ms14×body640valid
3.0ms5×body5120valid
2.0ms9×body320valid
1.0ms4×body160valid

simplify115.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01417
12517
24616
38616
411916
512816
done12816

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.6b
(- (* b b) (* (* 4.0 a) c))
1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite235.0ms

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-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 183
Calls
4 calls:
114.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
13.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series479.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
79.0ms
(- (* b b) (* (* 4.0 a) c))
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
195 → 195
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03214967
18194606
238494288
done50004286

prune900.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite310.0ms

Algorithm
rewrite-expression-head
Rules
3251×times-frac
1774×add-sqr-sqrt
1519×*-un-lft-identity
1265×add-cube-cbrt
254×difference-of-squares
142×sqrt-prod
129×div-inv
127×distribute-lft-out--
71×associate-/r*
64×add-exp-log
54×div-exp
25×add-cbrt-cube
19×prod-diff
15×cbrt-undiv 1-exp associate-/r/
13×associate-/l*
8×add-log-exp
7×fma-neg
6×rec-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip--
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 1122
Calls
4 calls:
73.0ms
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
13.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
60.0ms
(- (* b b) (* (* 4.0 a) c))
94.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify758.0ms

Counts
1134 → 1134
Iterations

Useful iterations: done (693.0ms)

IterNodesCost
0152448578
done500143122

prune3.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.7b

localize36.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite122.0ms

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×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
49.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
46.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
126.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify993.0ms

Counts
128 → 128
Iterations

Useful iterations: done (988.0ms)

IterNodesCost
01132856
12952330
212261950
done50001810

prune670.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.7b

localize37.0ms

Local error

Found 4 expressions with local error:

7.6b
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×expm1-log1p-u cbrt-div flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×prod-diff sqrt-prod
2×pow1/3 sqrt-div
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log
Counts
4 → 65
Calls
4 calls:
20.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
137.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
77 → 77
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01641691
14321596
219061378
done50011338

prune620.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.7b

regimes444.0ms

Accuracy

83.5% (4.7b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 33.9b

bsearch186.0ms

Steps
ItersRangePoint
9
7.013128997607284e-77
5.714800893424793e-72
3.3620065154544137e-75
9
-3.792961868720521e+75
-7.261872368850313e+67
-3.5695008721667037e+75

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02942
13540
done3540

end0.0ms

sample2.8s

Algorithm
intervals
Results
796.0ms1054×body2560valid
604.0ms877×body1280valid
459.0ms5961×body80valid
296.0ms2946×body80nan
94.0ms455×body640valid
38.0ms214×body320valid
36.0ms97×body5120valid
12.0ms111×body160valid