Details

sample159.0ms

Algorithm

intervals

Results

60.0ms	32×	body	2560	valid
60.0ms	82×	body	1280	valid
14.0ms	46×	body	640	valid
6.0ms	31×	body	320	valid
5.0ms	107×	body	80	valid
2.0ms	62×	body	80	nan
1.0ms	9×	body	160	valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	60	7
2	145	7
3	364	7
4	1248	7
5	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite630.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
305×	`add-sqr-sqrt`
222×	`*-un-lft-identity`
156×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
48×	`unpow-prod-down`
33×	`sqr-pow`
28×	`distribute-lft-out--`
24×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
8×	`fma-neg`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative`

Counts

4 → 321

Calls

4 calls:

239.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
132.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
228.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

369.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms	(pow (+ 1.0 (/ i n)) n)
363.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify70.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune876.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite558.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
72×	`prod-diff`
66×	`add-cube-cbrt`
46×	`unpow-prod-down`
31×	`times-frac`
26×	`distribute-rgt-in` `distribute-lft-in`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r*` `sqr-pow`
11×	`distribute-lft-out`
8×	`fma-neg`
7×	`pow1` `associate-r`
6×	`cbrt-undiv` `div-exp` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod` `div-inv`
2×	`associate-/l/` `distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `associate-/l` `unswap-sqr`

Counts

4 → 198

Calls

4 calls:

239.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
146.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms	(pow (+ 1.0 (/ i n)) n)
152.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

271.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
257.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
208.0ms	(pow (+ 1.0 (/ i n)) n)
571.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify105.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	792	2367
1	3917	1720
2	5002	1708

prune370.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b	(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
6.8b	(pow (+ 1.0 (/ i n)) (* 2 n))
6.8b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (* 100.0 (/ (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
27×	`add-exp-log`
25×	`*-un-lft-identity` `add-cbrt-cube`
21×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`associate-/r*`
11×	`cbrt-undiv` `div-exp`
8×	`unpow-prod-down`
6×	`pow1`
4×	`expm1-log1p-u` `pow-unpow` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `sqr-pow`
1×	`frac-2neg` `associate-r/` `clear-num` `associate-/r/` `fma-udef` `associate-/l/` `associate-/l`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
12.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
11.0ms	(pow (+ 1.0 (/ i n)) n)
55.0ms	(/ (* 100.0 (/ (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

series2.8s

Counts

4 → 12

Calls

4 calls:

274.0ms	(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
216.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
210.0ms	(pow (+ 1.0 (/ i n)) n)
2.1s	(/ (* 100.0 (/ (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

simplify86.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	697	1446
1	3744	1215
2	5003	1205

prune362.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b	(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
6.8b	(pow (+ 1.0 (/ i n)) (* 2 n))
6.8b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (* 100.0 (/ (log (exp (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
27×	`add-exp-log`
25×	`*-un-lft-identity` `add-cbrt-cube`
21×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`associate-/r*`
11×	`cbrt-undiv` `div-exp`
8×	`unpow-prod-down`
6×	`pow1`
4×	`expm1-log1p-u` `pow-unpow` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `sqr-pow`
1×	`frac-2neg` `associate-r/` `clear-num` `associate-/r/` `fma-udef` `associate-/l/` `associate-/l`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
12.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
13.0ms	(pow (+ 1.0 (/ i n)) n)
53.0ms	(/ (* 100.0 (/ (log (exp (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

series2.7s

Counts

4 → 12

Calls

4 calls:

275.0ms	(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
221.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
217.0ms	(pow (+ 1.0 (/ i n)) n)
2.0s	(/ (* 100.0 (/ (log (exp (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

simplify85.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	702	1506
1	3788	1252
2	5001	1226

prune386.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.6b

regimes138.0ms

Accuracy

46.7% (12.9b remaining)

Error of 31.4b against oracle of 18.5b and baseline of 42.7b

bsearch565.0ms

Steps

Iters	Range		Point
8	2.6233364391768453e+215	7.559003031217257e+219	7.395559138739582e+219
7	8.449789709258891e+21	1.927335547477129e+23	8.532543483832935e+21
6	3.1399496998840866e-125	3.7800925651486635e-124	6.02622510223327e-125
7	1.4967481787327182e-161	2.5387026277821525e-160	2.515912909264607e-160
8	-1.4252965457371644e-10	-5.035330346103121e-14	-1.3992561866449662e-10
8	-1.6450582212898727e+137	-4.094290472995023e+133	-2.561401665352169e+135

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	85
1	75	85

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.8s	2560×	body	1280	valid
1.7s	942×	body	2560	valid
467.0ms	1643×	body	640	valid
137.0ms	871×	body	320	valid
125.0ms	3062×	body	80	valid
69.0ms	2190×	body	80	nan
39.0ms	396×	body	160	valid
29.0ms	8×	body	5120	valid