Details

sample210.0ms

Algorithm

intervals

Results

57.0ms	122×	body	1280	valid
40.0ms	69×	body	1280	nan
22.0ms	55×	body	640	nan
22.0ms	30×	body	10240	exit
21.0ms	66×	body	640	valid
9.0ms	35×	body	320	nan
8.0ms	190×	body	80	nan
7.0ms	30×	body	320	valid
4.0ms	92×	body	80	valid
1.0ms	10×	body	160	nan
1.0ms	8×	body	160	valid

simplify40.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite21.0ms

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:

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

series475.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(pow (+ x 1.0) (/ 1.0 n))
60.0ms	(pow x (/ 1.0 n))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

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

prune238.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
0.0b	(pow (pow x (/ 1.0 n)) 3)
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
44×	`unpow-prod-down`
29×	`pow-unpow` `*-un-lft-identity`
27×	`difference-of-squares`
25×	`add-cube-cbrt`
24×	`cbrt-prod`
23×	`sqr-pow`
18×	`times-frac`
16×	`cube-prod`
8×	`add-exp-log`
6×	`pow1` `pow-exp` `add-log-exp`
5×	`add-cbrt-cube`
4×	`pow-to-exp`
3×	`pow-pow`
2×	`div-inv`
1×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `distribute-lft-out` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 128

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
4.0ms	(pow (pow x (/ 1.0 n)) 3)
16.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow (+ x 1.0) (/ 1.0 n))
60.0ms	(pow x (/ 1.0 n))
84.0ms	(pow (pow x (/ 1.0 n)) 3)
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

simplify65.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	680	1196
1	2497	1152
2	5002	1138

prune352.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow x (/ 1.0 n)) 3)
0.0b	(exp (log (pow (pow x (/ 1.0 n)) 3)))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (exp (log (pow (pow x (/ 1.0 n)) 3)))))
5.0b	(log (pow (pow x (/ 1.0 n)) 3))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

64×	`unpow-prod-down` `log-prod`
61×	`add-sqr-sqrt`
44×	`exp-sum`
30×	`cube-prod` `difference-of-squares`
28×	`sqr-pow`
27×	`cbrt-prod`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
9×	`add-exp-log`
8×	`pow-exp`
6×	`add-log-exp`
5×	`rem-log-exp` `add-cbrt-cube`
4×	`pow1` `pow-to-exp` `exp-prod`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`log-pow`
1×	`sub-neg` `flip3--` `pow-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 141

Calls

4 calls:

4.0ms	(pow (pow x (/ 1.0 n)) 3)
6.0ms	(exp (log (pow (pow x (/ 1.0 n)) 3)))
23.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (exp (log (pow (pow x (/ 1.0 n)) 3)))))
5.0ms	(log (pow (pow x (/ 1.0 n)) 3))

series577.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(pow (pow x (/ 1.0 n)) 3)
90.0ms	(exp (log (pow (pow x (/ 1.0 n)) 3)))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (exp (log (pow (pow x (/ 1.0 n)) 3)))))
123.0ms	(log (pow (pow x (/ 1.0 n)) 3))

simplify66.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	577	1626
1	1912	1488
2	5001	1422

prune444.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* (log x) 1.0) (* x (pow n 2)))
3.8b	(- (/ (/ 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))
7.2b	(* 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:

7.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
66.0ms	(- (/ (/ 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))
5.0ms	(* x (pow n 2))

series200.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
63.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
29.0ms	(/ (/ 0.5 n) (pow x 2))
29.0ms	(* x (pow n 2))

simplify49.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1857

prune573.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.8b

regimes211.0ms

Accuracy

82% (1.9b remaining)

Error of 24.0b against oracle of 22.0b and baseline of 32.6b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	41
1	46	41

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.8s	3892×	body	1280	valid
1.2s	2167×	body	1280	nan
718.0ms	1801×	body	640	nan
611.0ms	1803×	body	640	valid
577.0ms	1437×	body	10240	exit
259.0ms	6260×	body	80	nan
212.0ms	871×	body	320	nan
190.0ms	881×	body	320	valid
154.0ms	3147×	body	80	valid
66.0ms	468×	body	160	valid
62.0ms	434×	body	160	nan