Details

Time bar (total: 15.3s)

sample70.0ms

Algorithm
intervals
Results
36.0ms88×body1280valid
13.0ms53×body640valid
7.0ms26×body2560valid
3.0ms21×body320valid
2.0ms58×body80valid
1.0ms10×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
079
1108
done108

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.1b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(sqrt (+ (* x x) 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
7×add-cube-cbrt
6×pow1
5×add-exp-log
4×expm1-log1p-u log-prod fma-def flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow hypot-def
Counts
4 → 66
Calls
4 calls:
3.0ms
(+ (* x x) 1.0)
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series302.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x x) 1.0)
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
167.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms
(sqrt (+ (* x x) 1.0))

simplify402.0ms

Counts
78 → 78
Iterations

Useful iterations: done (400.0ms)

IterNodesCost
0149949
1358794
21194707
done5000695

prune226.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv expm1-log1p-u associate-*r/ pow-prod-down *-commutative log1p-expm1-u div-inv add-log-exp
Counts
1 → 272
Calls
1 calls:
72.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series142.0ms

Counts
1 → 3
Calls
1 calls:
142.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify2.8s

Counts
275 → 275
Iterations

Useful iterations: 2 (383.0ms)

IterNodesCost
02953852
17423044
238872556
done50002556

prune364.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.0625 (pow x 5))
0.8b
(/ 0.125 (pow x 3))
14.6b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
20.3b
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

rewrite610.0ms

Algorithm
rewrite-expression-head
Rules
1870×times-frac
1245×add-sqr-sqrt
1195×*-un-lft-identity
1178×add-cube-cbrt
1000×prod-diff
627×unpow-prod-down
250×cube-prod
215×sqr-pow
82×cube-mult unpow3
68×div-inv
40×fma-neg
22×difference-of-squares
19×associate-/r*
15×add-exp-log
8×log-prod add-cbrt-cube
7×distribute-lft-out--
6×div-exp associate-/l* add-log-exp
5×pow1 log-div frac-sub
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip--
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num
1×sub-neg diff-log rem-log-exp log-pow
Counts
4 → 1215
Calls
4 calls:
4.0ms
(/ 0.0625 (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
378.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
95.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

series373.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ 0.0625 (pow x 5))
34.0ms
(/ 0.125 (pow x 3))
169.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
123.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

simplify799.0ms

Counts
1227 → 1227
Iterations

Useful iterations: done (717.0ms)

IterNodesCost
0121665758
1260355948
done500153212

prune1.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3))))
0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.8b
(/ 0.125 (pow x 3))
11.9b
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
888×times-frac
634×add-sqr-sqrt
609×*-un-lft-identity
603×add-cube-cbrt
520×prod-diff
131×unpow-prod-down cube-prod
55×div-inv
45×sqr-pow
43×cube-mult unpow3
13×fma-neg
12×associate-/r*
10×add-exp-log difference-of-squares
6×add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×log-prod div-exp associate-/l*
2×distribute-lft-out--
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log rem-log-exp pow-exp clear-num log-pow frac-sub flip-- fma-udef
Counts
4 → 651
Calls
4 calls:
0.0ms
(fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3))))
54.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
4.0ms
(/ 0.125 (pow x 3))
1.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3))))
86.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
41.0ms
(/ 0.125 (pow x 3))
157.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify4.2s

Counts
663 → 663
Iterations

Useful iterations: 2 (556.0ms)

IterNodesCost
075031474
1165125632
2483316348
done500016348

prune555.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.8b

bsearch83.0ms

Steps
ItersRangePoint
10
5.968040026638966e-05
117627206.70733242
0.9001758350297782
10
-64880754058.88788
-2.651420353119469e-05
-0.9989549344709008

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03456
13656
done3656

end0.0ms

sample1.9s

Algorithm
intervals
Results
989.0ms2398×body1280valid
373.0ms1535×body640valid
220.0ms806×body2560valid
110.0ms761×body320valid
67.0ms2126×body80valid
30.0ms374×body160valid