Details

Time bar (total: 20.7s)

sample30.0ms

Algorithm
intervals
Results
8.0ms55×body640valid
5.0ms126×body80valid
4.0ms38×body320valid
3.0ms20×body1280valid
1.0ms17×body160valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
11815
23115
34115
48815
513515
616215
721115
844115
9120815
done500015

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
2.5b
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

rewrite564.0ms

Algorithm
rewrite-expression-head
Rules
1123×*-un-lft-identity
1026×times-frac
953×add-sqr-sqrt
678×prod-diff
610×add-cube-cbrt
236×associate--r+
127×difference-of-squares
116×distribute-lft-out--
106×distribute-lft-out
78×associate-/r/
76×div-inv
34×fma-neg
27×flip3-+ flip-+
15×flip3-- flip--
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l*
5×frac-sub
4×pow1 expm1-log1p-u diff-log log1p-expm1-u
3×sub-neg
2×cbrt-undiv frac-2neg div-exp clear-num
1×associate--r-
Counts
4 → 837
Calls
4 calls:
23.0ms
(/ 1.0 (- x 1.0))
23.0ms
(/ 1.0 (+ x 1.0))
93.0ms
(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
307.0ms
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

series451.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ 1.0 (- x 1.0))
27.0ms
(/ 1.0 (+ x 1.0))
54.0ms
(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
325.0ms
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

simplify1.6s

Counts
849 → 849
Iterations

Useful iterations: done (1.5s)

IterNodesCost
087138837
1220633703
done500127984

prune2.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ 1.0 (+ x 1.0))))
0.0b
(- (/ 2.0 x) (log1p (expm1 (/ 1.0 (+ x 1.0)))))
0.5b
(expm1 (/ 1.0 (+ x 1.0)))
2.5b
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (log1p (expm1 (/ 1.0 (+ x 1.0))))))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
320×add-sqr-sqrt
254×*-un-lft-identity
204×prod-diff
191×times-frac
163×add-cube-cbrt
67×difference-of-squares
46×distribute-lft-out--
41×associate--r+
34×fma-neg
14×associate-/r/ div-inv add-log-exp
10×flip3-- flip--
7×diff-log
5×log1p-expm1-u
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube
3×sub-neg log1p-udef
2×frac-sub
1×expm1-log1p log1p-expm1 expm1-udef associate--r-
Counts
4 → 303
Calls
4 calls:
0.0ms
(log1p (expm1 (/ 1.0 (+ x 1.0))))
25.0ms
(- (/ 2.0 x) (log1p (expm1 (/ 1.0 (+ x 1.0)))))
0.0ms
(expm1 (/ 1.0 (+ x 1.0)))
175.0ms
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (log1p (expm1 (/ 1.0 (+ x 1.0))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
235.0ms
(log1p (expm1 (/ 1.0 (+ x 1.0))))
241.0ms
(- (/ 2.0 x) (log1p (expm1 (/ 1.0 (+ x 1.0)))))
100.0ms
(expm1 (/ 1.0 (+ x 1.0)))
1.2s
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (log1p (expm1 (/ 1.0 (+ x 1.0))))))

simplify2.3s

Counts
315 → 315
Iterations

Useful iterations: done (2.2s)

IterNodesCost
041316949
197611255
236749196
done50009195

prune979.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 2.220446049250313e-16 (pow x 6))
0.2b
(/ 2.0 (pow x 5))
0.4b
(/ 2.0 (pow x 3))
13.1b
(- (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 5))) (/ 2.220446049250313e-16 (pow x 6)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
470×*-un-lft-identity
408×times-frac
261×add-sqr-sqrt
251×add-cube-cbrt
200×prod-diff
132×distribute-lft-out
109×unpow-prod-down
63×div-inv
37×sqr-pow
26×associate-/r*
19×add-exp-log
12×cube-prod
10×add-cbrt-cube
9×div-exp associate-/l* add-log-exp
8×fma-neg
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u difference-of-squares
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num frac-sub distribute-lft-out--
2×diff-log
1×sub-neg flip3-- flip3-+ frac-add associate--l+ sum-log flip-- flip-+
Counts
4 → 395
Calls
4 calls:
8.0ms
(/ 2.220446049250313e-16 (pow x 6))
13.0ms
(/ 2.0 (pow x 5))
16.0ms
(/ 2.0 (pow x 3))
1.2s
(- (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 5))) (/ 2.220446049250313e-16 (pow x 6)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ 2.220446049250313e-16 (pow x 6))
77.0ms
(/ 2.0 (pow x 5))
78.0ms
(/ 2.0 (pow x 3))
71.0ms
(- (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 5))) (/ 2.220446049250313e-16 (pow x 6)))

simplify879.0ms

Counts
407 → 407
Iterations

Useful iterations: done (857.0ms)

IterNodesCost
058416140
1137014320
done500111599

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 x) (/ 2.0 (* x x)))
0.2b
(/ 2.0 (pow x 5))
0.3b
(/ 2.0 (* x x))
13.1b
(- (+ (* (/ 1 x) (/ 2.0 (* x x))) (/ 2.0 (pow x 5))) (/ 2.220446049250313e-16 (pow x 6)))

rewrite678.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt
109×times-frac
103×*-un-lft-identity
99×add-cube-cbrt
75×prod-diff
53×add-exp-log
40×unpow-prod-down
32×add-cbrt-cube
19×div-exp
17×prod-exp
14×sqr-pow
13×associate-*l*
10×cbrt-undiv
9×cbrt-unprod add-log-exp
8×associate-/r*
7×associate-*r* div-inv
6×pow1 associate-/l* unswap-sqr
5×frac-sub
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×rec-exp fma-neg 1-exp frac-add
2×frac-times frac-2neg diff-log associate-*r/ associate-*l/ clear-num
1×pow-to-exp sub-neg flip3-- flip3-+ pow-prod-down pow-exp associate--l+ sum-log *-commutative flip-- flip-+ distribute-lft-out--
Counts
4 → 232
Calls
4 calls:
46.0ms
(* (/ 1 x) (/ 2.0 (* x x)))
9.0ms
(/ 2.0 (pow x 5))
11.0ms
(/ 2.0 (* x x))
588.0ms
(- (+ (* (/ 1 x) (/ 2.0 (* x x))) (/ 2.0 (pow x 5))) (/ 2.220446049250313e-16 (pow x 6)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (/ 1 x) (/ 2.0 (* x x)))
79.0ms
(/ 2.0 (pow x 5))
29.0ms
(/ 2.0 (* x x))
96.0ms
(- (+ (* (/ 1 x) (/ 2.0 (* x x))) (/ 2.0 (pow x 5))) (/ 2.220446049250313e-16 (pow x 6)))

simplify916.0ms

Counts
244 → 244
Iterations

Useful iterations: done (896.0ms)

IterNodesCost
05088698
113687800
done50006233

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes83.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 32.0b

bsearch165.0ms

Steps
ItersRangePoint
9
0.00015484893005477947
28918.939680702064
1.0232695486014585
10
-2676750800.736259
-2.9526231381329305e-09
-0.994187787075435

simplify18.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03664
14864
25464
35864
46164
done6164

end0.0ms

sample1.6s

Algorithm
intervals
Results
564.0ms1919×body640valid
353.0ms4124×body80valid
212.0ms540×body1280valid
156.0ms956×body320valid
109.0ms463×body160valid