Details

Time bar (total: 12.0s)

sample159.0ms

Algorithm
intervals
Results
55.0ms118×body1280valid
26.0ms50×body10240exit
17.0ms50×body640valid
11.0ms25×body640nan
8.0ms149×body80valid
6.0ms157×body80nan
5.0ms28×body320valid
5.0ms12×body1280nan
2.0ms12×body320nan
2.0ms13×body160valid
1.0ms6×body160nan

simplify34.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1356
2856
32496
49116
550016
done50016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b
(pow (+ x 1.0) (/ 1.0 n))
1.4b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
70×unpow-prod-down
67×*-un-lft-identity
56×prod-diff
54×add-sqr-sqrt
42×add-cube-cbrt
23×sqr-pow
13×pow-unpow
10×distribute-lft-out
9×times-frac difference-of-squares
8×fma-neg
4×add-log-exp
3×pow1 add-exp-log distribute-lft-out--
2×expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×pow-to-exp sub-neg flip3-- pow-pow diff-log pow-exp flip-- div-inv
Counts
2 → 120
Calls
2 calls:
10.0ms
(pow (+ x 1.0) (/ 1.0 n))
88.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series430.0ms

Counts
2 → 6
Calls
2 calls:
153.0ms
(pow (+ x 1.0) (/ 1.0 n))
276.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify56.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05422011
116941489
250011488
done50011488

prune250.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.7b
(pow (pow (+ x 1.0) 1.0) (/ 1 n))
1.4b
(- (pow (pow (+ x 1.0) 1.0) (/ 1 n)) (pow x (/ 1.0 n)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
161×unpow-prod-down
84×prod-diff
79×*-un-lft-identity
78×add-sqr-sqrt
59×add-cube-cbrt
41×sqr-pow
15×difference-of-squares
13×pow-unpow
12×fma-neg
9×times-frac distribute-lft-out
4×add-exp-log pow-exp add-log-exp
2×pow1 expm1-log1p-u pow-to-exp add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- pow-pow diff-log flip-- div-inv distribute-lft-out--
Counts
2 → 162
Calls
2 calls:
18.0ms
(pow (pow (+ x 1.0) 1.0) (/ 1 n))
178.0ms
(- (pow (pow (+ x 1.0) 1.0) (/ 1 n)) (pow x (/ 1.0 n)))

series749.0ms

Counts
2 → 6
Calls
2 calls:
303.0ms
(pow (pow (+ x 1.0) 1.0) (/ 1 n))
445.0ms
(- (pow (pow (+ x 1.0) 1.0) (/ 1 n)) (pow x (/ 1.0 n)))

simplify73.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
07033160
122412331
250012319
done50012319

prune354.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))) (* 0.5 (/ (pow (log (/ 1 x)) 2) (pow n 2))))
1.2b
(/ (pow (log (/ 1 x)) 2) (pow n 2))
1.2b
(/ (pow (log (pow (/ 1 x) -1.0)) 2) (pow n 2))
4.5b
(fma 1/2 (/ (pow (log (pow (/ 1 x) -1.0)) 2) (pow n 2)) (- (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))) (* 0.5 (/ (pow (log (/ 1 x)) 2) (pow n 2)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
160×times-frac
156×unpow-prod-down
86×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
40×unpow2 sqr-pow
36×log-pow
28×add-exp-log
22×pow1
20×associate-/l*
18×div-exp
16×associate-/r*
12×pow-to-exp pow-exp
9×pow-flip inv-pow
8×add-cbrt-cube
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg prod-diff
2×cbrt-undiv frac-2neg clear-num fma-udef div-inv
1×sub-neg flip3-- diff-log associate--l+ flip--
Counts
4 → 271
Calls
4 calls:
6.0ms
(- (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))) (* 0.5 (/ (pow (log (/ 1 x)) 2) (pow n 2))))
17.0ms
(/ (pow (log (/ 1 x)) 2) (pow n 2))
12.0ms
(/ (pow (log (pow (/ 1 x) -1.0)) 2) (pow n 2))
0.0ms
(fma 1/2 (/ (pow (log (pow (/ 1 x) -1.0)) 2) (pow n 2)) (- (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))) (* 0.5 (/ (pow (log (/ 1 x)) 2) (pow n 2)))))

series756.0ms

Counts
4 → 12
Calls
4 calls:
230.0ms
(- (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))) (* 0.5 (/ (pow (log (/ 1 x)) 2) (pow n 2))))
87.0ms
(/ (pow (log (/ 1 x)) 2) (pow n 2))
132.0ms
(/ (pow (log (pow (/ 1 x) -1.0)) 2) (pow n 2))
306.0ms
(fma 1/2 (/ (pow (log (pow (/ 1 x) -1.0)) 2) (pow n 2)) (- (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))) (* 0.5 (/ (pow (log (/ 1 x)) 2) (pow n 2)))))

simplify100.0ms

Counts
283 → 283
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07663396
134812874
250032848
done50032848

prune964.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.8b

localize45.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (/ (pow (log (/ 1 x)) 2) (pow n 2)) (+ (- 0.5) 0.5))
11.5b
(cbrt (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))))
11.5b
(cbrt (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))))
11.5b
(cbrt (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
104×times-frac
92×associate-*l*
89×unpow-prod-down
85×add-sqr-sqrt
55×*-un-lft-identity
51×add-cube-cbrt
27×add-exp-log unpow2 sqr-pow
24×log-pow
22×pow1
17×unswap-sqr
13×associate-*r*
10×prod-exp
9×cbrt-prod div-exp add-cbrt-cube
8×pow-flip inv-pow
6×pow-to-exp pow-exp
4×distribute-lft-neg-in expm1-log1p-u distribute-rgt-out log1p-expm1-u distribute-lft-out add-log-exp
3×distribute-rgt-neg-in pow1/3
2×frac-times neg-mul-1 distribute-lft1-in flip3-+ associate-*r/ cbrt-unprod flip-+
1×cbrt-undiv distribute-rgt-in distribute-lft-in pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 191
Calls
4 calls:
89.0ms
(* (/ (pow (log (/ 1 x)) 2) (pow n 2)) (+ (- 0.5) 0.5))
1.0ms
(cbrt (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))))
1.0ms
(cbrt (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))))
1.0ms
(cbrt (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))))

series1.2s

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (/ (pow (log (/ 1 x)) 2) (pow n 2)) (+ (- 0.5) 0.5))
386.0ms
(cbrt (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))))
390.0ms
(cbrt (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))))
387.0ms
(cbrt (fma 1.0 (/ 1 (* x n)) (fma 1.0 (/ (log (/ 1 x)) n) (/ (log (pow (/ 1 x) -1.0)) n))))

simplify98.0ms

Counts
203 → 203
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
012022599
141572274
250012271
done50012271

prune1.5s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 21.8b

regimes536.0ms

Accuracy

87.3% (1.1b remaining)

Error of 21.8b against oracle of 20.7b and baseline of 29.4b

bsearch3.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02411
12411
done2411

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.4s3183×body1280valid
520.0ms1514×body640valid
515.0ms1188×body10240exit
276.0ms620×body1280nan
237.0ms4681×body80valid
204.0ms655×body640nan
200.0ms914×body320valid
171.0ms4913×body80nan
68.0ms360×body320nan
58.0ms435×body160valid
21.0ms194×body160nan