Details

sample198.0ms

Algorithm

intervals

Results

83.0ms	89×	body	1280	valid
64.0ms	29×	body	2560	valid
22.0ms	50×	body	640	valid
7.0ms	89×	body	80	valid
5.0ms	20×	body	320	valid
4.0ms	62×	body	80	nan
2.0ms	12×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	59	7
2	141	7
3	346	7
4	1171	7
5	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite545.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
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` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

220.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
102.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
194.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

370.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
250.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
205.0ms	(pow (+ 1.0 (/ i n)) n)
345.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify57.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune789.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
10.6b	(* (pow i 2) (log 1.0))
20.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv` `add-log-exp`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 186

Calls

4 calls:

8.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
131.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
6.0ms	(* (pow i 2) (log 1.0))
124.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series587.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
206.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
145.0ms	(* (pow i 2) (log 1.0))
191.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify136.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	929	3610
1	4719	3341
2	5001	3341

prune661.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
4.2b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
10.6b	(* (pow i 2) (log 1.0))
14.0b	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
127×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
53×	`add-exp-log`
48×	`associate-r`
32×	`add-cbrt-cube`
23×	`div-exp`
21×	`associate-l`
13×	`prod-exp` `associate-/r*`
12×	`cbrt-undiv` `unswap-sqr`
10×	`div-inv`
9×	`add-log-exp`
7×	`pow1` `cbrt-unprod`
6×	`log-prod`
4×	`unpow-prod-down`
3×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `frac-times` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 215

Calls

4 calls:

8.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
122.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
8.0ms	(* (pow i 2) (log 1.0))
142.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
142.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
333.0ms	(* (pow i 2) (log 1.0))
215.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

simplify63.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1153	4361
1	5001	3912

prune682.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 9.1b

localize29.0ms

Local error

Found 4 expressions with local error:

10.6b	(* (pow i 2) (log 1.0))
16.8b	(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
16.8b	(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
16.8b	(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
132×	`cbrt-prod`
120×	`add-sqr-sqrt`
114×	`add-cube-cbrt` `*-un-lft-identity`
12×	`div-inv`
9×	`add-exp-log`
8×	`associate-l`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `associate-r` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `cbrt-div` `distribute-lft-in` `pow1/3` `prod-exp` `associate-/r/`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 193

Calls

4 calls:

6.0ms	(* (pow i 2) (log 1.0))
32.0ms	(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
29.0ms	(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
30.0ms	(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

series2.5s

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (pow i 2) (log 1.0))
776.0ms	(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
764.0ms	(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
775.0ms	(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

simplify101.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	607	5581
1	2284	5400
2	5001	5249

prune651.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 9.1b

regimes221.0ms

Accuracy

48% (11.5b remaining)

Error of 22.4b against oracle of 10.9b and baseline of 33.1b

bsearch392.0ms

Steps

Iters	Range	Point
8	7.108389521057788e-152	9.857230472394243e-149	7.185948283350093e-152
9	-4.622874842024395e-243	-4.995401923428486e-252	-3.9974032830534776e-251
9	-5.979882189147821e+84	-8.548989080955097e+79	-2.7155205583837284e+82

Iters

Range

Point

7.108389521057788e-152

9.857230472394243e-149

7.185948283350093e-152

-4.622874842024395e-243

-4.995401923428486e-252

-3.9974032830534776e-251

-5.979882189147821e+84

-8.548989080955097e+79

-2.7155205583837284e+82

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	59
1	70	59

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.2s	2461×	body	1280	valid
2.0s	956×	body	2560	valid
707.0ms	1617×	body	640	valid
234.0ms	3076×	body	80	valid
232.0ms	835×	body	320	valid
125.0ms	2193×	body	80	nan
74.0ms	433×	body	160	valid
20.0ms	6×	body	5120	valid