Details

sample210.0ms

Algorithm

intervals

Results

63.0ms	138×	body	1280	valid
39.0ms	66×	body	1280	nan
25.0ms	57×	body	640	nan
20.0ms	39×	body	10240	exit
16.0ms	51×	body	640	valid
8.0ms	198×	body	80	nan
5.0ms	21×	body	320	nan
5.0ms	26×	body	320	valid
4.0ms	91×	body	80	valid
3.0ms	19×	body	160	nan
2.0ms	15×	body	160	valid

simplify33.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

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: 29.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series485.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(pow x (/ 1.0 n))
147.0ms	(pow (+ x 1.0) (/ 1.0 n))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune207.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 17.8b

Counts

89 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(* (log (+ x 1.0)) (/ 1.0 n))
0.8b	(log (+ x 1.0))
1.6b	(- (exp (* (log (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`times-frac`
13×	`pow-unpow` `associate-r`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
6×	`add-log-exp`
4×	`unpow-prod-down` `log-prod` `associate-l`
3×	`difference-of-squares`
2×	`log-div` `prod-exp` `log-pow` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `associate-r/` `div-exp` `rem-log-exp` `pow-prod-down` `pow-exp` `-commutative` `flip--` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 91

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
7.0ms	(* (log (+ x 1.0)) (/ 1.0 n))
3.0ms	(log (+ x 1.0))
8.0ms	(- (exp (* (log (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow x (/ 1.0 n))
110.0ms	(* (log (+ x 1.0)) (/ 1.0 n))
41.0ms	(log (+ x 1.0))
280.0ms	(- (exp (* (log (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify65.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	618	758
1	2494	692
2	5001	690

prune244.0ms

Filtered

103 candidates to 81 candidates (78.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	101	6	107

Merged error: 17.5b

Counts

107 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* (log x) 1.0) (* x (pow n 2)))
2.8b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.2b	(/ (/ 0.5 n) (pow x 2))
8.1b	(* x (pow n 2))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
113×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
98×	`add-cube-cbrt`
46×	`add-exp-log` `unpow-prod-down`
23×	`add-cbrt-cube`
17×	`div-exp`
16×	`unpow2` `sqr-pow`
14×	`associate-/l*`
13×	`prod-exp`
11×	`div-inv`
9×	`associate-/r*` `add-log-exp`
8×	`associate-r`
7×	`cbrt-undiv`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod`
4×	`pow1` `frac-sub` `unswap-sqr`
3×	`diff-log` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--` `associate--r+`
1×	`*-commutative` `associate-/l/` `associate--r-`

Counts

4 → 220

Calls

4 calls:

6.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
65.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
8.0ms	(/ (/ 0.5 n) (pow x 2))
9.0ms	(* x (pow n 2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
65.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
30.0ms	(/ (/ 0.5 n) (pow x 2))
30.0ms	(* x (pow n 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1857

prune544.0ms

Filtered

232 candidates to 140 candidates (60.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	225	7	232
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	227	11	238

Merged error: 17.4b

Counts

238 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

1.9b	(log (exp (/ 0.5 (* (pow x 2) n))))
2.8b	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.5b	(* (pow x 2) n)
8.1b	(* x (pow n 2))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
14×	`add-exp-log` `add-cube-cbrt`
11×	`associate-r` `associate-l`
9×	`log-pow`
8×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
7×	`exp-prod`
6×	`pow1` `log-prod` `times-frac` `prod-exp`
5×	`associate--r+` `distribute-lft-out--`
4×	`unpow2` `sqr-pow`
3×	`diff-log` `associate--l+` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod`
1×	`rem-log-exp` `div-inv` `associate--r-`

Counts

4 → 100

Calls

4 calls:

4.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
32.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
5.0ms	(* (pow x 2) n)
5.0ms	(* x (pow n 2))

series141.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
70.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
18.0ms	(* (pow x 2) n)
31.0ms	(* x (pow n 2))

simplify72.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	514	973
1	2276	880
2	5001	868

prune312.0ms

Filtered

112 candidates to 77 candidates (68.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	110	13	123

Merged error: 17.4b

Counts

123 → 13

regimes261.0ms

Accuracy

82.4% (2.0b remaining)

Error of 23.8b against oracle of 21.9b and baseline of 33.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	38
1	51	38

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.8s	3890×	body	1280	valid
1.3s	2237×	body	1280	nan
737.0ms	1810×	body	640	nan
632.0ms	1871×	body	640	valid
618.0ms	1455×	body	10240	exit
262.0ms	6267×	body	80	nan
224.0ms	912×	body	320	nan
196.0ms	898×	body	320	valid
150.0ms	3123×	body	80	valid
64.0ms	436×	body	160	valid
63.0ms	444×	body	160	nan