Details

Time bar (total: 20.6s)

sample249.0ms

Algorithm
intervals
Results
55.0ms186×body80valid
23.0ms29×body2560valid
18.0ms24×body1280valid
11.0ms88×body80nan
9.0ms17×body640valid
4.0ms10×body320valid
2.0ms3×body5120valid

simplify129.0ms

Counts
1 → 1
Iterations
IterNodes
634
534
432
330
223
115
010

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 122
Calls
4 calls:
124.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
78.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(- (* b_2 b_2) (* a c))
42.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
79.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms
(- (* b_2 b_2) (* a c))
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
134 → 134
Iterations
IterNodes
33534
21172
1463
0199

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 122
Calls
4 calls:
69.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
73.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
109.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms
(- (* b_2 b_2) (* a c))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
134 → 134
Iterations
IterNodes
33534
21172
1463
0199

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize37.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* b_2 b_2) (* a c))
1.6b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 70
Calls
4 calls:
9.0ms
(- (* b_2 b_2) (* a c))
8.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b_2 b_2) (* a c))
44.0ms
(- (* b_2 b_2) (* a c))
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
82 → 82
Iterations
IterNodes
44083
31422
2459
1166
069

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

localize66.0ms

Local error

Found 4 expressions with local error:

8.1b
(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
24.4b
(sqrt (- (* b_2 b_2) (* a c)))
25.2b
(cbrt (- (* b_2 b_2) (* a c)))
25.2b
(cbrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

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 insert-posit16 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 → 69
Calls
4 calls:
25.0ms
(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
5.0ms
(cbrt (- (* b_2 b_2) (* a c)))
5.0ms
(cbrt (- (* b_2 b_2) (* a c)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
84.0ms
(sqrt (- (* b_2 b_2) (* a c)))
123.0ms
(cbrt (- (* b_2 b_2) (* a c)))
134.0ms
(cbrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts
81 → 81
Iterations
IterNodes
33231
21077
1388
0158

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

regimes337.0ms

Accuracy

84.2% (4.4b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.0b

bsearch152.0ms

Steps
ItersRangePoint
9
2.5177836961106285e-119
1.1213560046341023e-113
7.296044290893796e-114
7
-4.611849920572465e+95
-3.3021145473587595e+93
-3.177289780863109e+94

simplify4.0ms

Iterations
IterNodes
226
126
023

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.2s1092×body2560valid
926.0ms5835×body80valid
649.0ms914×body1280valid
377.0ms2905×body80nan
311.0ms458×body640valid
99.0ms126×body5120valid
76.0ms228×body320valid
22.0ms100×body160valid