Details

sample215.0ms

Algorithm

intervals

Results

51.0ms	87×	body	1280	nan
49.0ms	113×	body	1280	valid
29.0ms	42×	body	10240	exit
21.0ms	62×	body	640	valid
19.0ms	49×	body	640	nan
8.0ms	29×	body	320	nan
7.0ms	30×	body	320	valid
6.0ms	146×	body	80	nan
4.0ms	92×	body	80	valid
3.0ms	20×	body	160	nan
1.0ms	12×	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: 33.9b

Counts

2 → 1

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))
2.2b	(- (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:

6.0ms	(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)))

series467.0ms

Counts

3 → 9

Calls

3 calls:

144.0ms	(pow (+ x 1.0) (/ 1.0 n))
58.0ms	(pow x (/ 1.0 n))
265.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

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

prune246.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 20.4b

Counts

89 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))
0.0b	(pow x (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
2.2b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
66×	`sqrt-prod`
49×	`*-un-lft-identity`
34×	`unpow-prod-down`
32×	`difference-of-squares`
26×	`pow-unpow`
23×	`associate-r`
22×	`add-cube-cbrt`
18×	`times-frac` `sqr-pow`
8×	`pow1` `add-exp-log` `distribute-lft-out--`
7×	`associate-l` `distribute-lft-out`
6×	`add-cbrt-cube` `add-log-exp`
4×	`frac-times` `flip3--` `flip--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `pow-to-exp` `pow-pow` `distribute-lft-in` `associate-r/` `associate-l/` `pow-exp` `div-inv`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

31.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))
4.0ms	(pow x (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
12.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

580.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))
60.0ms	(pow x (/ 1.0 n))
54.0ms	(pow x (/ 1.0 n))
358.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

simplify74.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	641	2018
1	2688	1864
2	5003	1836

prune495.0ms

Filtered

152 candidates to 108 candidates (71.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	149	9	158

Merged error: 20.3b

Counts

158 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
4.2b	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
5.3b	(* x (pow n 2))
5.6b	(* (pow x 2) n)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
18×	`associate-l`
17×	`associate-*r/`
16×	`add-exp-log` `frac-add`
15×	`associate-r`
14×	`flip3-+` `flip-+`
12×	`add-cube-cbrt` `unpow-prod-down` `distribute-neg-frac`
10×	`frac-times` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`add-log-exp`
7×	`prod-exp` `distribute-lft-out`
6×	`pow1` `sqrt-prod`
4×	`unpow2` `sqr-pow`
3×	`*-commutative` `cbrt-unprod`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `distribute-neg-in` `distribute-lft-in` `associate-*l/` `pow-exp` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `pow-prod-down` `neg-log`

Counts

4 → 115

Calls

4 calls:

18.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
36.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
6.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series596.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
458.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
34.0ms	(* x (pow n 2))
18.0ms	(* (pow x 2) n)

simplify45.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	944	2456
1	5002	2289

prune683.0ms

Filtered

127 candidates to 92 candidates (72.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	118	9	127
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	120	16	136

Merged error: 20.1b

Counts

136 → 16

localize34.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (pow n 2))))))) (/ (/ 0.5 n) x))
3.2b	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (pow n 2)))
4.2b	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (pow n 2))))))) (/ (/ 0.5 n) x)))
5.6b	(* (pow x 2) n)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
22×	`*-un-lft-identity` `prod-exp`
17×	`add-sqr-sqrt` `associate-*r/`
16×	`associate-l` `frac-add`
14×	`flip3-+` `add-cbrt-cube` `flip-+`
12×	`distribute-neg-frac`
11×	`pow1`
10×	`frac-times` `cbrt-unprod`
9×	`add-cube-cbrt`
8×	`unpow-prod-down` `associate-r` `add-log-exp`
7×	`distribute-lft-out`
6×	`sqrt-prod`
5×	`unswap-sqr`
4×	`pow-prod-down`
3×	`pow-to-exp` `pow-exp` `*-commutative`
2×	`distribute-rgt-in` `associate-+l+` `distribute-neg-in` `distribute-lft-in` `associate-*l/` `sum-log` `unpow2` `sqr-pow`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-log`

Counts

4 → 112

Calls

4 calls:

18.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (pow n 2))))))) (/ (/ 0.5 n) x))
11.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (pow n 2)))
36.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (pow n 2))))))) (/ (/ 0.5 n) x)))
6.0ms	(* (pow x 2) n)

series670.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (pow n 2))))))) (/ (/ 0.5 n) x))
48.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (pow n 2)))
485.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (pow n 2))))))) (/ (/ 0.5 n) x)))
22.0ms	(* (pow x 2) n)

simplify50.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	985	3157
1	5001	2910

prune667.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	125	15	140

Merged error: 20.1b

Counts

140 → 15

regimes438.0ms

Accuracy

86% (1.9b remaining)

Error of 24.1b against oracle of 22.2b and baseline of 35.9b

bsearch181.0ms

Steps

Iters	Range		Point
7	7528569012387.477	507061619645407.2	7633188339970.273
7	-1681.069840156335	-49.92425379146846	-1660.743692817158

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	93
1	92	93
2	98	93
3	98	93

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.8s	3828×	body	1280	valid
1.3s	2322×	body	1280	nan
729.0ms	1849×	body	640	nan
619.0ms	1870×	body	640	valid
616.0ms	1411×	body	10240	exit
246.0ms	6075×	body	80	nan
228.0ms	969×	body	320	nan
201.0ms	918×	body	320	valid
153.0ms	3080×	body	80	valid
68.0ms	475×	body	160	nan
64.0ms	473×	body	160	valid