Details

sample158.0ms

Algorithm

intervals

Results

61.0ms	78×	body	1280	valid
58.0ms	30×	body	2560	valid
15.0ms	53×	body	640	valid
4.0ms	25×	body	320	valid
4.0ms	98×	body	80	valid
2.0ms	56×	body	80	nan
1.0ms	12×	body	160	valid

simplify41.0ms

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

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.9b	(pow (+ 1.0 (/ i n)) n)
10.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite589.0ms

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:

239.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
110.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
208.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

364.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
246.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
211.0ms	(pow (+ 1.0 (/ i n)) n)
347.0ms	(/ (- (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

prune777.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
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)))
10.9b	(* (pow i 2) (log 1.0))
16.6b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
111×	`add-sqr-sqrt`
90×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-r`
28×	`add-exp-log`
22×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-/r*`
11×	`unswap-sqr`
9×	`prod-exp` `div-inv`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`cbrt-unprod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-prod-down` `clear-num` `log-pow` `flip--`

Counts

4 → 200

Calls

4 calls:

6.0ms	(* 0.5 (pow i 2))
138.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
7.0ms	(* (pow i 2) (log 1.0))
130.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series572.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 0.5 (pow i 2))
216.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
141.0ms	(* (pow i 2) (log 1.0))
189.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify143.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	907	3537
1	4856	3275
2	5001	3275

prune734.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
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)
10.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.9b	(* (pow i 2) (log 1.0))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`add-exp-log`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-cbrt-cube`
15×	`associate-r`
12×	`associate-l`
11×	`prod-exp`
10×	`pow1`
9×	`times-frac`
8×	`unpow-prod-down` `unswap-sqr`
7×	`cbrt-unprod`
6×	`log-prod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `pow-to-exp` `div-exp` `pow-exp` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r/` `associate-l/` `clear-num` `log-pow` `flip--` `div-inv`

Counts

4 → 112

Calls

4 calls:

6.0ms	(* 0.5 (pow i 2))
144.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
128.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms	(* (pow i 2) (log 1.0))

series513.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.5 (pow i 2))
212.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
135.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
142.0ms	(* (pow i 2) (log 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	525	1462
1	2535	1228
2	5002	1224

prune382.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
1.6b	(* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
10.9b	(* (pow i 2) (log 1.0))
12.0b	(/ (* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)

rewrite450.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
22×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1` `associate-l`
10×	`associate-r` `prod-exp`
8×	`cbrt-unprod`
6×	`distribute-rgt-in` `log-prod` `distribute-lft-in` `associate-*r/`
5×	`unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `associate-*l/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `times-frac` `div-exp` `associate-/r` `-commutative` `flip--`
2×	`sub-neg` `associate--l+` `associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `log-pow` `div-inv` `associate-/l*`

Counts

4 → 105

Calls

4 calls:

132.0ms	(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
157.0ms	(* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
7.0ms	(* (pow i 2) (log 1.0))
152.0ms	(/ (* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)

series626.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
160.0ms	(* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
145.0ms	(* (pow i 2) (log 1.0))
206.0ms	(/ (* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)

simplify97.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	539	1687
1	3113	1361
2	5001	1336

prune316.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.3b

regimes339.0ms

Accuracy

55.6% (9.8b remaining)

Error of 21.0b against oracle of 11.1b and baseline of 33.3b

bsearch628.0ms

Steps

Iters	Range		Point
8	2.2112458842293344e-05	0.01694346711308432	0.0006093521534695529
8	7.60401498810488e-233	2.248873935831e-229	8.587016406998776e-230
9	7.333478328566493e-293	2.09185199160616e-287	2.6939372834177335e-290
9	-30.29444851407267	-2.830682320409962e-08	-0.14141811154607586

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	63
1	78	63

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.8s	949×	body	2560	valid
1.8s	2495×	body	1280	valid
472.0ms	1592×	body	640	valid
147.0ms	876×	body	320	valid
132.0ms	3055×	body	80	valid
78.0ms	2313×	body	80	nan
45.0ms	447×	body	160	valid
23.0ms	7×	body	5120	valid