Details

sample35.0ms

Algorithm

intervals

Results

16.0ms	372×	body	80	valid
4.0ms	103×	body	80	nan

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 3.8b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.2b	(* a (pow k m))
3.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
7×	`associate-r`
6×	`fma-def` `prod-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `div-exp` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `times-frac` `associate-l` `associate-/r*` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `sqr-pow`
1×	`associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 88

Calls

4 calls:

3.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms	(* a (pow k m))
12.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ 1.0 (* 10.0 k))
19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
64.0ms	(* a (pow k m))
119.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify61.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	477	629
1	2275	544
2	5001	524

prune246.0ms

Filtered

100 candidates to 79 candidates (79.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Merged error: 0.3b

Counts

102 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 10.0 k 1.0)
0.2b	(* a (pow k m))
3.7b	(/ (* a (pow k m)) (fma k k (fma 10.0 k 1.0)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
13×	`add-sqr-sqrt`
10×	`add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`prod-exp`
4×	`unpow-prod-down` `div-exp`
3×	`pow1` `expm1-log1p-u` `times-frac` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `pow-to-exp` `pow-exp` `cbrt-unprod` `sqr-pow`
1×	`frac-2neg` `clear-num` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

3 → 62

Calls

3 calls:

1.0ms	(fma 10.0 k 1.0)
5.0ms	(* a (pow k m))
5.0ms	(/ (* a (pow k m)) (fma k k (fma 10.0 k 1.0)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma 10.0 k 1.0)
59.0ms	(* a (pow k m))
127.0ms	(/ (* a (pow k m)) (fma k k (fma 10.0 k 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	327	406
1	1538	360
2	5001	358

prune165.0ms

Filtered

71 candidates to 53 candidates (74.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	71	4	75

Merged error: 0.3b

Counts

75 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

3.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
3.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.6b	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.6b	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
18×	`sqrt-prod`
14×	`add-sqr-sqrt` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
8×	`div-exp` `associate-/r/`
6×	`pow1` `prod-exp` `associate-/r*`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `clear-num` `cbrt-unprod` `associate-/l*`

Counts

4 → 98

Calls

4 calls:

9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
7.0ms	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
7.0ms	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))

series676.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
123.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
216.0ms	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
217.0ms	(sqrt (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))

simplify60.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	459	1340
1	2040	1200
2	5001	1158

prune357.0ms

Filtered

110 candidates to 90 candidates (81.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Merged error: 0.3b

Counts

114 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt k) m)
0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
3.7b	(/ (* (* a (pow (sqrt k) m)) (pow (sqrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
21×	`prod-exp`
13×	`div-exp` `add-cbrt-cube`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`pow-to-exp` `pow-exp`
6×	`pow1` `unpow-prod-down` `fma-def`
4×	`expm1-log1p-u` `sum-log` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `pow-pow` `flip3-+` `times-frac` `associate-/r*` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`+-commutative` `associate-/r/`
1×	`associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sqrt-pow2` `div-inv` `associate-/l*` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

3.0ms	(pow (sqrt k) m)
3.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
12.0ms	(/ (* (* a (pow (sqrt k) m)) (pow (sqrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(pow (sqrt k) m)
35.0ms	(+ 1.0 (* 10.0 k))
19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
260.0ms	(/ (* (* a (pow (sqrt k) m)) (pow (sqrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	542	850
1	2474	710
2	5001	659

prune243.0ms

Filtered

108 candidates to 74 candidates (68.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	108	4	112

Merged error: 0.3b

Counts

112 → 4

regimes101.0ms

Accuracy

98.2% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 1.8b

bsearch64.0ms

Steps

Iters	Range		Point
8	4.0479147671149326e+104	1.14701201731836e+107	1.0418578754338997e+107

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	32
1	49	32
2	49	32

end0.0ms

sample1.1s

Algorithm

intervals

Results

547.0ms	11987×	body	80	valid
158.0ms	4270×	body	80	nan