Details

sample181.0ms

Algorithm

intervals

Results

78.0ms	105×	body	1280	valid
58.0ms	30×	body	2560	valid
18.0ms	55×	body	640	valid
4.0ms	72×	body	80	valid
3.0ms	1×	body	5120	valid
3.0ms	19×	body	320	valid
2.0ms	61×	body	80	nan
2.0ms	14×	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: 48.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b	(pow (+ 1.0 (/ i n)) n)
11.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite94.0ms

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:

31.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
22.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

365.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
247.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms	(pow (+ 1.0 (/ i n)) n)
349.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune894.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.5 (pow i 2) (* (log 1.0) n))
0.1b	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
12.1b	(* (pow i 2) (log 1.0))
19.3b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite37.0ms

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`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `fma-udef`

Counts

4 → 186

Calls

4 calls:

1.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
17.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 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))
6.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series616.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
215.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
138.0ms	(* (pow i 2) (log 1.0))
199.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify120.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	731	3120
1	3626	2891
2	5002	2891

prune736.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i))
0.1b	(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
11.5b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
12.1b	(* (pow i 2) (log 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
22×	`add-cbrt-cube`
20×	`associate-r`
19×	`times-frac`
12×	`pow1` `associate-l`
10×	`prod-exp`
8×	`cbrt-unprod`
6×	`log-prod` `unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`associate-*r/` `div-inv` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-*l/` `pow-exp` `clear-num` `log-pow`

Counts

4 → 122

Calls

4 calls:

6.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i))
9.0ms	(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
3.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
6.0ms	(* (pow i 2) (log 1.0))

series674.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i))
231.0ms	(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
141.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
148.0ms	(* (pow i 2) (log 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	488	1787
1	2372	1525
2	5002	1522

prune463.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize13.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (fma i 50.0 (- (fma 100.0 (/ (* (log 1.0) n) i) 100.0) (* 50.0 (* i (log 1.0))))) n)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
1×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

1 → 20

Calls

1 calls:

3.0ms

(* (fma i 50.0 (- (fma 100.0 (/ (* (log 1.0) n) i) 100.0) (* 50.0 (* i (log 1.0))))) n)

series167.0ms

Counts

1 → 3

Calls

1 calls:

167.0ms

(* (fma i 50.0 (- (fma 100.0 (/ (* (log 1.0) n) i) 100.0) (* 50.0 (* i (log 1.0))))) n)

simplify75.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	128	316
1	436	271
2	2727	268
3	5001	265

prune65.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.9b

regimes200.0ms

Accuracy

67.3% (6.0b remaining)

Error of 16.9b against oracle of 10.9b and baseline of 29.3b

bsearch203.0ms

Steps

Iters	Range		Point
8	21.660028671588154	1194293.182570832	22.15331663854136
8	-8.718619127186496	-0.007325616698975617	-0.039044500998989144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	33
1	54	33

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	2900×	body	1280	valid
1.9s	983×	body	2560	valid
530.0ms	1730×	body	640	valid
155.0ms	884×	body	320	valid
117.0ms	2442×	body	80	valid
85.0ms	2247×	body	80	nan
48.0ms	14×	body	5120	valid
47.0ms	437×	body	160	valid