Details

Time bar (total: 26.0s)

sample155.0ms

Algorithm
intervals
Results
38.0ms28×body1280valid
33.0ms35×body2560valid
30.0ms184×body80valid
14.0ms86×body80nan
9.0ms15×body640valid
4.0ms4×body5120valid
3.0ms8×body320valid
1.0ms5×body160valid

simplify118.0ms

Counts
1 → 1
Iterations
IterNodes
8105
7105
6104
5102
494
377
244
125
014

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.8b
(fma b b (* (* a -4) c))
1.7b
(- (sqrt (fma b b (* (* a -4) c))) b)
24.6b
(sqrt (fma b b (* (* a -4) c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
39.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.0ms
(fma b b (* (* a -4) c))
8.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
2.0ms
(sqrt (fma b b (* (* a -4) c)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
65.0ms
(fma b b (* (* a -4) c))
104.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
133.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify1.3s

Counts
126 → 126
Iterations
IterNodes
32689
2950
1405
0180

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma c (* -4 a) (* b b))
0.1b
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
1.7b
(- (sqrt (fma c (* -4 a) (* b b))) b)
24.6b
(sqrt (fma c (* -4 a) (* b b)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
0.0ms
(fma c (* -4 a) (* b b))
35.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
17.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(fma c (* -4 a) (* b b))
77.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
114.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
118.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify4.6s

Counts
126 → 126
Iterations
IterNodes
46613
31992
2726
1321
0157

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize53.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (sqrt (fma b b (* (* a -4) c))) b)
1.7b
(- (sqrt (fma b b (* (* a -4) c))) b)
24.6b
(sqrt (fma b b (* (* a -4) c)))
24.6b
(sqrt (fma b b (* (* a -4) c)))

rewrite21.0ms

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 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
8.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
9.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(sqrt (fma b b (* (* a -4) c)))
1.0ms
(sqrt (fma b b (* (* a -4) c)))

series473.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
115.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
118.0ms
(sqrt (fma b b (* (* a -4) c)))
127.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify2.9s

Counts
128 → 128
Iterations
IterNodes
43225
31220
2439
1209
0100

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize34.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (sqrt (fma b b (* (* a -4) c))) b)
1.7b
(- (sqrt (fma b b (* (* a -4) c))) b)
24.6b
(sqrt (fma b b (* (* a -4) c)))
24.6b
(sqrt (fma b b (* (* a -4) c)))

rewrite20.0ms

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 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
8.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
8.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(sqrt (fma b b (* (* a -4) c)))
1.0ms
(sqrt (fma b b (* (* a -4) c)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
130.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
142.0ms
(sqrt (fma b b (* (* a -4) c)))
106.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify2.4s

Counts
128 → 128
Iterations
IterNodes
43225
31220
2439
1209
0100

prune2.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

regimes506.0ms

Accuracy

84.4% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.4b

bsearch233.0ms

Steps
ItersRangePoint
10
8.296670056881522e-85
2.5972983117194536e-74
2.326372645943808e-74
7
-1.8217288728729631e+111
-6.606823090402082e+109
-1.0027271082217074e+110

simplify5.0ms

Iterations
IterNodes
229
129
026

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.3s915×body1280valid
1.1s1126×body2560valid
996.0ms5836×body80valid
426.0ms2976×body80nan
325.0ms417×body640valid
147.0ms119×body5120valid
120.0ms236×body320valid
32.0ms115×body160valid