Details

sample274.0ms

Algorithm

intervals

Results

79.0ms	128×	body	1280	valid
51.0ms	42×	body	1280	nan
26.0ms	53×	body	640	valid
24.0ms	151×	body	80	overflowed
22.0ms	31×	body	640	nan
12.0ms	231×	body	80	nan
12.0ms	110×	body	80	valid
8.0ms	23×	body	320	valid
5.0ms	13×	body	320	nan
3.0ms	14×	body	160	valid
2.0ms	10×	body	160	nan

simplify31.0ms

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

prune3.0ms

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: 33.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite19.0ms

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)))

series70.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	552	688
1	1885	669
2	5002	641

prune183.0ms

Filtered

71 candidates to 88 candidates (-23.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 23.7b

Counts

89 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt x) (/ 1.0 n))
0.0b	(pow (sqrt x) (/ 1.0 n))
0.0b	(* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
5.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
57×	`unpow-prod-down`
34×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqrt-prod`
26×	`pow-unpow`
18×	`add-exp-log` `times-frac`
16×	`unswap-sqr`
15×	`sqr-pow`
12×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`prod-exp`
8×	`pow1` `pow-to-exp` `pow-exp`
6×	`pow-pow` `add-cbrt-cube` `add-log-exp`
3×	`difference-of-squares`
2×	`sqrt-pow1` `pow1/2` `sqrt-pow2` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod`

Counts

4 → 151

Calls

4 calls:

4.0ms	(pow (sqrt x) (/ 1.0 n))
4.0ms	(pow (sqrt x) (/ 1.0 n))
9.0ms	(* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
6.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (sqrt x) (/ 1.0 n))
26.0ms	(pow (sqrt x) (/ 1.0 n))
40.0ms	(* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
76.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))

simplify70.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	574	1380
1	2413	1293
2	5001	1283

prune264.0ms

Filtered

103 candidates to 163 candidates (-58.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	163	5	168

Merged error: 23.7b

Counts

168 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (log (sqrt x)) (/ 1.0 n)))
0.0b	(* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n))))
0.3b	(* (log (sqrt x)) (/ 1.0 n))
5.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`times-frac`
8×	`pow1` `unpow-prod-down`
7×	`add-log-exp`
6×	`unswap-sqr`
5×	`prod-exp`
4×	`exp-to-pow` `sqrt-prod`
3×	`pow-prod-down` `log-pow` `cbrt-unprod`
2×	`exp-prod` `*-commutative` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `div-exp` `pow-exp` `pow-sqr` `pow-prod-up` `flip--` `div-inv` `rem-exp-log`

Counts

4 → 90

Calls

4 calls:

2.0ms	(exp (* (log (sqrt x)) (/ 1.0 n)))
7.0ms	(* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n))))
8.0ms	(* (log (sqrt x)) (/ 1.0 n))
6.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(exp (* (log (sqrt x)) (/ 1.0 n)))
55.0ms	(* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n))))
15.0ms	(* (log (sqrt x)) (/ 1.0 n))
93.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	649	990
1	2656	814
2	5001	795

prune198.0ms

Filtered

78 candidates to 102 candidates (-30.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	102	5	107

Merged error: 23.7b

Counts

107 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (log (sqrt x)) (/ 1.0 n)))
0.0b	(pow (sqrt (pow (sqrt x) (/ 1.0 n))) 3)
0.3b	(* (log (sqrt x)) (/ 1.0 n))
5.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt (pow (sqrt x) (/ 1.0 n))) 3) (sqrt (exp (* (log (sqrt x)) (/ 1.0 n))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `sqrt-prod`
25×	`unpow-prod-down`
21×	`add-cube-cbrt` `*-un-lft-identity`
13×	`cube-prod` `associate-r`
10×	`add-exp-log` `times-frac` `add-cbrt-cube`
9×	`pow1`
7×	`add-log-exp`
6×	`associate-l`
3×	`pow-unpow` `pow-pow` `log-pow` `sqr-pow`
2×	`sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `unpow3` `associate-r/` `div-exp` `pow-prod-down` `pow-exp` `-commutative` `sqrt-pow2` `flip--` `div-inv` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 103

Calls

4 calls:

2.0ms	(exp (* (log (sqrt x)) (/ 1.0 n)))
7.0ms	(pow (sqrt (pow (sqrt x) (/ 1.0 n))) 3)
7.0ms	(* (log (sqrt x)) (/ 1.0 n))
6.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt (pow (sqrt x) (/ 1.0 n))) 3) (sqrt (exp (* (log (sqrt x)) (/ 1.0 n))))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(exp (* (log (sqrt x)) (/ 1.0 n)))
67.0ms	(pow (sqrt (pow (sqrt x) (/ 1.0 n))) 3)
15.0ms	(* (log (sqrt x)) (/ 1.0 n))
139.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt (pow (sqrt x) (/ 1.0 n))) 3) (sqrt (exp (* (log (sqrt x)) (/ 1.0 n))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	775	1148
1	3310	1007
2	5002	980

prune230.0ms

Filtered

74 candidates to 115 candidates (-55.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	115	5	120

Merged error: 23.7b

Counts

120 → 5

regimes272.0ms

Accuracy

81% (2.0b remaining)

Error of 24.5b against oracle of 22.5b and baseline of 33.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	57
1	70	57
2	70	57

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.2s	3825×	body	1280	valid
1.2s	1083×	body	1280	nan
871.0ms	1813×	body	640	valid
670.0ms	943×	body	640	nan
625.0ms	4056×	body	80	overflowed
332.0ms	6180×	body	80	nan
320.0ms	3080×	body	80	valid
305.0ms	929×	body	320	valid
197.0ms	461×	body	320	nan
101.0ms	472×	body	160	valid
48.0ms	212×	body	160	nan

Details

sample274.0ms

simplify31.0ms

prune3.0ms

localize9.0ms

rewrite19.0ms

series70.0ms

simplify46.0ms

prune183.0ms

localize11.0ms

rewrite29.0ms

series165.0ms

simplify70.0ms

prune264.0ms

localize16.0ms

rewrite26.0ms

series187.0ms

simplify64.0ms

prune198.0ms

localize19.0ms

rewrite26.0ms

series246.0ms

simplify92.0ms

prune230.0ms

regimes272.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample7.6s

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