Details

Time bar (total: 6.6s)

sample66.0ms

Algorithm
intervals
Results
20.0ms58×body1280valid
11.0ms47×body640valid
10.0ms245×body80nan
9.0ms111×body80valid
4.0ms28×body320valid
1.0ms12×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize7.0ms

Local error

Found 2 expressions with local error:

3.2b
(log (+ N 1.0))
3.4b
(- (log (+ N 1.0)) (log N))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×pow1 add-sqr-sqrt prod-diff
14×add-cube-cbrt log-pow
11×log-prod
4×log-div fma-neg associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 65
Calls
2 calls:
2.0ms
(log (+ N 1.0))
7.0ms
(- (log (+ N 1.0)) (log N))

series10.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(log (+ N 1.0))
6.0ms
(- (log (+ N 1.0)) (log N))

simplify121.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (115.0ms)

IterNodesCost
0277598
1837444
23748347
35001343

prune275.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.7b
(/ 1 (pow N 2))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
11×add-exp-log
8×associate-/r*
6×div-exp
4×add-cbrt-cube unpow2 sqr-pow
3×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv pow-flip frac-2neg clear-num fma-udef div-inv inv-pow
Counts
2 → 69
Calls
2 calls:
0.0ms
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
4.0ms
(/ 1 (pow N 2))

series6.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
2.0ms
(/ 1 (pow N 2))

simplify31.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0208384
1789315
25001269

prune245.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.7b
(/ 1 (pow N 2))
4.0b
(exp (log (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))))
17.7b
(log (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
14×add-exp-log
12×unpow-prod-down
8×associate-/r*
6×pow1 log-prod div-exp add-cbrt-cube
4×expm1-log1p-u exp-prod log1p-expm1-u unpow2 add-log-exp sqr-pow
3×pow-to-exp rec-exp 1-exp exp-sum pow-exp associate-/l*
2×log-pow
1×cbrt-undiv pow-flip frac-2neg rem-log-exp clear-num fma-udef div-inv rem-exp-log inv-pow
Counts
4 → 100
Calls
4 calls:
0.0ms
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
4.0ms
(/ 1 (pow N 2))
1.0ms
(exp (log (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))))
1.0ms
(log (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

series19.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
2.0ms
(/ 1 (pow N 2))
5.0ms
(exp (log (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))))
8.0ms
(log (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

simplify42.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0355760
11298641
25001577

prune514.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- (log 1.0) (log N)) (+ (* (/ 1 (pow N 2)) (- 0.3333333333333333 (/ 0.125 (pow 1.0 2)))) (/ (- 0.5) N)))
0.4b
(* (/ 1 (pow N 2)) (- 0.3333333333333333 (/ 0.125 (pow 1.0 2))))
0.7b
(/ 1 (pow N 2))
3.2b
(exp (+ (- (log 1.0) (log N)) (+ (* (/ 1 (pow N 2)) (- 0.3333333333333333 (/ 0.125 (pow 1.0 2)))) (/ (- 0.5) N))))

rewrite549.0ms

Algorithm
rewrite-expression-head
Rules
226×add-sqr-sqrt
224×*-un-lft-identity
204×times-frac
194×add-cube-cbrt
184×prod-diff
86×distribute-rgt-in distribute-lft-in
78×unpow-prod-down
33×add-exp-log
28×associate-*l* unpow2 sqr-pow
26×pow1
24×frac-add
21×associate-+l+ add-log-exp
20×log-pow
13×flip3-- flip-- distribute-lft-out--
12×div-exp sum-log
11×add-cbrt-cube
10×prod-exp distribute-lft-out
9×associate-*r* unswap-sqr
8×associate-+r- exp-prod fma-def associate-/r* div-inv
6×frac-times pow-to-exp rec-exp 1-exp associate-*r/ pow-exp difference-of-squares
5×rem-exp-log
4×expm1-log1p-u exp-diff diff-log distribute-frac-neg log1p-expm1-u
3×sub-neg log-prod flip3-+ associate-*l/ associate--l+ flip-+ associate-/l*
2×cbrt-undiv neg-sub0 associate-+l- div-sub unsub-neg cbrt-unprod
1×+-commutative associate-+r+ pow-flip frac-2neg exp-sum pow-prod-down clear-num *-commutative inv-pow
Counts
4 → 401
Calls
4 calls:
99.0ms
(+ (- (log 1.0) (log N)) (+ (* (/ 1 (pow N 2)) (- 0.3333333333333333 (/ 0.125 (pow 1.0 2)))) (/ (- 0.5) N)))
77.0ms
(* (/ 1 (pow N 2)) (- 0.3333333333333333 (/ 0.125 (pow 1.0 2))))
4.0ms
(/ 1 (pow N 2))
344.0ms
(exp (+ (- (log 1.0) (log N)) (+ (* (/ 1 (pow N 2)) (- 0.3333333333333333 (/ 0.125 (pow 1.0 2)))) (/ (- 0.5) N))))

series26.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (- (log 1.0) (log N)) (+ (* (/ 1 (pow N 2)) (- 0.3333333333333333 (/ 0.125 (pow 1.0 2)))) (/ (- 0.5) N)))
5.0ms
(* (/ 1 (pow N 2)) (- 0.3333333333333333 (/ 0.125 (pow 1.0 2))))
2.0ms
(/ 1 (pow N 2))
11.0ms
(exp (+ (- (log 1.0) (log N)) (+ (* (/ 1 (pow N 2)) (- 0.3333333333333333 (/ 0.125 (pow 1.0 2)))) (/ (- 0.5) N))))

simplify118.0ms

Algorithm
egg-herbie
Counts
413 → 413
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
025008466
150037106

prune2.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.9b

bsearch11.0ms

Steps
ItersRangePoint
6
7065.8830381017015
33294.97377914132
9018.887363236374

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0219
1219

end0.0ms

sample1.8s

Algorithm
intervals
Results
604.0ms1782×body1280valid
333.0ms8078×body80nan
304.0ms1317×body640valid
242.0ms3981×body80valid
99.0ms629×body320valid
29.0ms291×body160valid