Details

Time bar (total: 8.2s)

sample40.0ms

Algorithm
intervals
Results
9.0ms40×body2560valid
8.0ms194×body80valid
5.0ms28×body1280valid
3.0ms76×body80nan
2.0ms10×body640valid
1.0ms2×body5120valid
0.0ms3×body320valid
0.0ms1×body160valid

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410616
511416
done11416

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.4b
(- (* b b) (* 4.0 (* a c)))
24.7b
(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)
25.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
75.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
48.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify983.0ms

Counts
195 → 195
Iterations

Useful iterations: done (977.0ms)

IterNodesCost
03194967
17794592
229824265
done50004264

prune513.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* a c)))
0.4b
(- (* b b) (* 4.0 (* a c)))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series232.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* 4.0 (* a c)))
43.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
78 → 78
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0691146
11701050
2613952
32661952
done5000948

prune279.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* a c)))
0.4b
(- (* b b) (* 4.0 (* a c)))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series231.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* 4.0 (* a c)))
44.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts
78 → 78
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0691146
11701050
2613952
32661952
done5000948

prune308.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

localize24.0ms

Local error

Found 4 expressions with local error:

5.6b
(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))
25.5b
(cbrt (- (* b b) (* 4.0 (* a c))))
25.5b
(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-prod add-log-exp
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×prod-diff sqrt-prod
2×pow1/3 sqrt-div
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log
Counts
4 → 65
Calls
4 calls:
9.0ms
(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
2.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
2.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
96.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
97.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

simplify554.0ms

Counts
77 → 77
Iterations

Useful iterations: 2 (127.0ms)

IterNodesCost
01621691
14011578
214571356
done50001356

prune372.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.8b

regimes218.0ms

Accuracy

85.8% (4.1b remaining)

Error of 10.0b against oracle of 5.9b and baseline of 34.5b

bsearch124.0ms

Steps
ItersRangePoint
8
1.225968609186083e-71
5.862533224041234e-67
5.083748087944341e-70
11
-1.829086240692416e+154
-2.187052964502477e+134
-8.555281377770497e+140

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02855
13355
done3355

end0.0ms

sample1.2s

Algorithm
intervals
Results
265.0ms1104×body2560valid
253.0ms5868×body80valid
181.0ms910×body1280valid
120.0ms2861×body80nan
65.0ms422×body640valid
28.0ms96×body5120valid
24.0ms212×body320valid
10.0ms120×body160valid