Details

Time bar (total: 26.1s)

sample246.0ms

Algorithm
intervals
Results
72.0ms369×body80nan
14.0ms164×body80valid
14.0ms31×body1280nan
11.0ms31×body1280valid
10.0ms30×body640nan
7.0ms22×body640valid
7.0ms29×body320valid
3.0ms13×body320nan
2.0ms10×body160valid
1.0ms5×body160nan

simplify4.0s

Counts
1 → 1
Iterations
IterNodes
done5000
74703
61985
51092
4526
3232
2100
141
018

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
0.3b
(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
11.8b
(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
21.1b
(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
76×times-frac
74×add-sqr-sqrt
59×*-un-lft-identity add-cube-cbrt
42×associate-*r*
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r* sqrt-div associate-/l* add-log-exp
5×unswap-sqr
4×expm1-log1p-u flip3-- associate-/r/ log1p-expm1-u flip--
3×associate-*l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×rem-sqrt-square sqrt-undiv clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down associate-*r/ *-commutative
Counts
4 → 164
Calls
4 calls:
85.0ms
(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
37.0ms
(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
17.0ms
(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
40.0ms
(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

series2.2s

Counts
4 → 12
Calls
4 calls:
629.0ms
(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
687.0ms
(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
353.0ms
(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
493.0ms
(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

simplify1.2s

Counts
176 → 176
Iterations
IterNodes
done5000
22141
1518
0216

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 30.4b

localize53.0ms

Local error

Found 4 expressions with local error:

3.2b
(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
5.7b
(/ (* l l) x)
9.0b
(/ (* t t) x)
27.7b
(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
3×sqrt-prod
2×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 71
Calls
4 calls:
1.0ms
(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
15.0ms
(/ (* l l) x)
15.0ms
(/ (* t t) x)
3.0ms
(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

series401.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
20.0ms
(/ (* l l) x)
27.0ms
(/ (* t t) x)
244.0ms
(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

simplify1.3s

Counts
83 → 83
Iterations
IterNodes
done5000
22768
1352
0131

prune564.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* t (/ (sqrt 2.0) (* 1 (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))))))
0.4b
(/ (sqrt 2.0) (* 1 (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))))
3.2b
(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
27.7b
(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
18×add-cbrt-cube
16×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac sqrt-prod
10×associate-*r*
8×prod-exp
7×pow1
6×div-exp associate-/l*
5×cbrt-unprod
4×expm1-log1p-u cbrt-undiv log1p-expm1-u add-log-exp
3×associate-*l*
2×1-exp div-inv
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ *-commutative fma-udef unswap-sqr
Counts
4 → 88
Calls
4 calls:
47.0ms
(* t (/ (sqrt 2.0) (* 1 (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))))))
9.0ms
(/ (sqrt 2.0) (* 1 (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))))
0.0ms
(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
1.0ms
(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
347.0ms
(* t (/ (sqrt 2.0) (* 1 (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))))))
296.0ms
(/ (sqrt 2.0) (* 1 (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))))
125.0ms
(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
269.0ms
(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))

simplify1.2s

Counts
100 → 100
Iterations
IterNodes
done5000
21912
1352
0146

prune702.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma l (/ l x) (* t t))
0.1b
(* t (/ (sqrt 2.0) (sqrt (fma (/ (* t 4.0) x) t (* 2.0 (fma l (/ l x) (* t t)))))))
0.4b
(/ (sqrt 2.0) (sqrt (fma (/ (* t 4.0) x) t (* 2.0 (fma l (/ l x) (* t t))))))
27.7b
(sqrt (fma (/ (* t 4.0) x) t (* 2.0 (fma l (/ l x) (* t t)))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
76×times-frac
74×add-sqr-sqrt
59×*-un-lft-identity add-cube-cbrt
40×associate-*r*
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r* associate-/l*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ *-commutative fma-udef
Counts
4 → 152
Calls
4 calls:
0.0ms
(fma l (/ l x) (* t t))
42.0ms
(* t (/ (sqrt 2.0) (sqrt (fma (/ (* t 4.0) x) t (* 2.0 (fma l (/ l x) (* t t)))))))
12.0ms
(/ (sqrt 2.0) (sqrt (fma (/ (* t 4.0) x) t (* 2.0 (fma l (/ l x) (* t t))))))
3.0ms
(sqrt (fma (/ (* t 4.0) x) t (* 2.0 (fma l (/ l x) (* t t)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
63.0ms
(fma l (/ l x) (* t t))
376.0ms
(* t (/ (sqrt 2.0) (sqrt (fma (/ (* t 4.0) x) t (* 2.0 (fma l (/ l x) (* t t)))))))
333.0ms
(/ (sqrt 2.0) (sqrt (fma (/ (* t 4.0) x) t (* 2.0 (fma l (/ l x) (* t t))))))
250.0ms
(sqrt (fma (/ (* t 4.0) x) t (* 2.0 (fma l (/ l x) (* t t)))))

simplify883.0ms

Counts
164 → 164
Iterations
IterNodes
done5000
21676
1403
0183

prune935.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

regimes648.0ms

Accuracy

70.7% (6.8b remaining)

Error of 10.8b against oracle of 3.9b and baseline of 27.2b

bsearch1.7s

Steps
ItersRangePoint
9
9.302190505211976e+16
7.445004787773374e+23
7.30958659336468e+23
10
9.657462100703732e-164
3.031856998694715e-153
5.5815895806141096e-155
8
1.567848216510623e-295
4.048090763928206e-293
4.0088796644560363e-293
10
-3.4801109198288895e-286
-4.7771503152615563e-296
-1.6191443127207628e-287
8
-1.185302419643378e-162
-2.4464775612223304e-166
-8.68838282607017e-163
6
-8.884635004656325e+106
-1.469680632787173e+106
-8.435929301784522e+106

simplify24.0ms

Iterations
IterNodes
done80
380
277
173
057

end0.0ms

sample6.5s

Algorithm
intervals
Results
1.4s10213×body80nan
974.0ms1064×body640valid
903.0ms604×body1280nan
809.0ms5001×body80valid
512.0ms885×body1280valid
308.0ms624×body640nan
257.0ms656×body320valid
177.0ms338×body320nan
82.0ms394×body160valid
39.0ms202×body160nan