Details

Time bar (total: 24.7s)

sample139.0ms

Algorithm
intervals
Results
37.0ms40×body2560valid
36.0ms187×body80valid
23.0ms32×body1280valid
13.0ms96×body80nan
4.0ms8×body640valid
2.0ms5×body320valid
2.0ms2×body5120valid
1.0ms2×body160valid

simplify113.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* a -4) c)
1.1b
(- (sqrt (fma b b (* (* a -4) c))) b)
1.5b
(fma b b (* (* a -4) c))
20.1b
(sqrt (fma b b (* (* a -4) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×sqrt-prod
10×pow1
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log associate-*l* *-commutative fma-udef flip-- distribute-lft-out--
Counts
4 → 86
Calls
4 calls:
13.0ms
(* (* a -4) c)
7.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms
(fma b b (* (* a -4) c))
1.0ms
(sqrt (fma b b (* (* a -4) c)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (* a -4) c)
140.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
61.0ms
(fma b b (* (* a -4) c))
86.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify1.4s

Counts
98 → 98
Iterations
IterNodes
32736
2835
1316
0142

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
1.1b
(- (sqrt (fma b b (* -4 (* a c)))) b)
1.5b
(fma b b (* -4 (* a c)))
20.1b
(sqrt (fma b b (* -4 (* a c))))

rewrite42.0ms

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 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 → 110
Calls
4 calls:
21.0ms
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
16.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms
(fma b b (* -4 (* a c)))
2.0ms
(sqrt (fma b b (* -4 (* a c))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
129.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
68.0ms
(fma b b (* -4 (* a c)))
102.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify1.6s

Counts
122 → 122
Iterations
IterNodes
32548
2945
1399
0175

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (fma b b (* -4 (* a c)))) b) (/ 1 a))
1.1b
(- (sqrt (fma b b (* -4 (* a c)))) b)
1.5b
(fma b b (* -4 (* a c)))
20.1b
(sqrt (fma b b (* -4 (* a c))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u prod-exp log1p-expm1-u difference-of-squares
3×flip3-- flip-- unswap-sqr
2×frac-times div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sub-neg sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef div-inv
Counts
4 → 111
Calls
4 calls:
38.0ms
(* (- (sqrt (fma b b (* -4 (* a c)))) b) (/ 1 a))
7.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms
(fma b b (* -4 (* a c)))
1.0ms
(sqrt (fma b b (* -4 (* a c))))

series502.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (- (sqrt (fma b b (* -4 (* a c)))) b) (/ 1 a))
152.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
67.0ms
(fma b b (* -4 (* a c)))
116.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify3.4s

Counts
123 → 123
Iterations
IterNodes
33126
21148
1462
0195

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (fma b b (* -4 (* a c)))) a)
1.5b
(fma b b (* -4 (* a c)))
6.8b
(- (/ (sqrt (fma b b (* -4 (* a c)))) a) (/ b a))
20.1b
(sqrt (fma b b (* -4 (* a c))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
481×times-frac
378×add-sqr-sqrt
366×*-un-lft-identity
358×add-cube-cbrt
286×prod-diff
143×sqrt-prod
39×div-inv
22×fma-neg
6×add-cbrt-cube add-exp-log associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×associate-/r*
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- distribute-rgt-out-- pow1/2 diff-log div-exp frac-sub fma-udef flip-- sub-div
Counts
4 → 401
Calls
4 calls:
4.0ms
(/ (sqrt (fma b b (* -4 (* a c)))) a)
0.0ms
(fma b b (* -4 (* a c)))
15.0ms
(- (/ (sqrt (fma b b (* -4 (* a c)))) a) (/ b a))
1.0ms
(sqrt (fma b b (* -4 (* a c))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (sqrt (fma b b (* -4 (* a c)))) a)
70.0ms
(fma b b (* -4 (* a c)))
131.0ms
(- (/ (sqrt (fma b b (* -4 (* a c)))) a) (/ b a))
93.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify1.1s

Counts
413 → 413
Iterations
IterNodes
22344
11056
0474

prune5.7s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.5b

regimes459.0ms

Accuracy

85.3% (4.1b remaining)

Error of 9.7b against oracle of 5.6b and baseline of 33.3b

bsearch230.0ms

Steps
ItersRangePoint
8
1.248337945535211e-66
3.048951962881303e-62
3.0168583404714427e-66
8
-5.208994295225817e+99
-1.4013492266633723e+97
-4.170773079316174e+99

simplify5.0ms

Iterations
IterNodes
230
130
026

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.4s5910×body80valid
1.0s1086×body2560valid
812.0ms2909×body80nan
741.0ms918×body1280valid
283.0ms434×body640valid
111.0ms119×body5120valid
85.0ms216×body320valid
25.0ms109×body160valid