Details

sample182.0ms

Algorithm

intervals

Results

77.0ms	36×	body	2560	valid
56.0ms	79×	body	1280	valid
21.0ms	58×	body	640	valid
6.0ms	35×	body	320	valid
3.0ms	69×	body	80	valid
2.0ms	59×	body	80	nan
2.0ms	19×	body	160	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 47.7b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.6b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite87.0ms

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:

34.0ms	(* 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)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

347.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
236.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
199.0ms	(pow (+ 1.0 (/ i n)) n)
341.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify71.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune711.0ms

Filtered

333 candidates to 242 candidates (72.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	327	6	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	328	6	334

Merged error: 23.7b

Counts

334 → 6

localize15.0ms

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)))
11.1b	(* (pow i 2) (log 1.0))
19.7b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite35.0ms

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))
14.0ms	(* 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))

series597.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
211.0ms	(* 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)))
131.0ms	(* (pow i 2) (log 1.0))
194.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify110.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (18.0ms)

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

prune683.0ms

Filtered

198 candidates to 152 candidates (76.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	186	12	198
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	187	17	204

Merged error: 12.1b

Counts

204 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) 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))
10.6b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.1b	(* (pow i 2) (log 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`associate-l`
22×	`add-cbrt-cube`
19×	`times-frac`
12×	`pow1`
10×	`prod-exp`
8×	`associate-r` `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-*l/` `div-inv` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `log-pow`

Counts

4 → 122

Calls

4 calls:

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)
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) 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))

series682.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
207.0ms	(* 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)
139.0ms	(* (pow i 2) (log 1.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	476	1783
1	2011	1521
2	5001	1513

prune413.0ms

Filtered

134 candidates to 92 candidates (68.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	134	17	151

Merged error: 12.1b

Counts

151 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

11.1b	(* (pow i 2) (log 1.0))
11.3b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
11.3b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
11.3b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-l`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `unpow-prod-down` `associate-r` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `prod-exp`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 75

Calls

4 calls:

6.0ms	(* (pow i 2) (log 1.0))
1.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
1.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
1.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (pow i 2) (log 1.0))
717.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
739.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
713.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	279	1170
1	893	1076
2	5002	1061

prune470.0ms

Filtered

87 candidates to 69 candidates (79.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	1	14	15
Picked	1	0	1
Done	0	1	1
Total	86	18	104

Merged error: 12.1b

Counts

104 → 18

regimes232.0ms

Accuracy

61.3% (7.1b remaining)

Error of 17.8b against oracle of 10.7b and baseline of 29.0b

bsearch231.0ms

Steps

Iters	Range		Point
11	5.359589792685655e-35	0.011261476250181132	0.011056763714875576
9	-19839.740086288697	-1.810013627382575e-05	-0.24222034813966126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	35
1	57	35

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.1s	2874×	body	1280	valid
1.8s	964×	body	2560	valid
557.0ms	1772×	body	640	valid
155.0ms	880×	body	320	valid
122.0ms	2442×	body	80	valid
75.0ms	2178×	body	80	nan
43.0ms	407×	body	160	valid
11.0ms	3×	body	5120	valid