Details

sample51.0ms

Algorithm

intervals

Results

29.0ms	386×	body	80	valid
5.0ms	126×	body	80	nan

simplify105.0ms

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: 2.9b

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))
0.0b	(* a (pow k m))
2.9b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite23.0ms

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))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 1.0 (* 10.0 k))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
57.0ms	(* a (pow k m))
119.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify60.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (51.0ms)

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

prune244.0ms

Filtered

100 candidates to 79 candidates (79.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Merged error: 0.0b

Counts

102 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
17.1b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.1b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
66×	`sqrt-prod`
65×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
20×	`sqrt-div`
16×	`associate-/r/`
15×	`add-cbrt-cube`
12×	`associate-/l*`
10×	`flip3-+` `flip-+`
9×	`div-exp`
8×	`div-inv`
7×	`associate-r`
6×	`pow1` `prod-exp` `associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `cbrt-unprod` `hypot-def` `sqr-pow`
1×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

5.0ms	(* a (pow k m))
15.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* a (pow k m))
116.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
52.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
46.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify106.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	753	3191
1	3781	2815
2	5002	2804

prune409.0ms

Filtered

188 candidates to 121 candidates (64.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	188	7	195

Merged error: 0.0b

Counts

195 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(+ 1.0 (* 10.0 k))
0.3b	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
2.7b	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
3.0ms	(+ 1.0 (* 10.0 k))
7.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.0ms	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
32.0ms	(+ 1.0 (* 10.0 k))
67.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
116.0ms	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

simplify77.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	634	1353
1	2939	1224
2	5001	1204

prune341.0ms

Filtered

147 candidates to 118 candidates (80.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	148	6	154

Merged error: 0.0b

Counts

154 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(expm1 (log1p (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))))
0.3b	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
2.7b	(* a (expm1 (log1p (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

3.0ms	(+ 1.0 (* 10.0 k))
1.0ms	(expm1 (log1p (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))))
7.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
3.0ms	(* a (expm1 (log1p (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))))

series371.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ 1.0 (* 10.0 k))
115.0ms	(expm1 (log1p (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))))
68.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
156.0ms	(* a (expm1 (log1p (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	497	1120
1	2145	993
2	5001	971

prune294.0ms

Filtered

108 candidates to 90 candidates (83.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	108	6	114

Merged error: 0.0b

Counts

114 → 6

regimes128.0ms

Accuracy

97.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.3b

bsearch65.0ms

Steps

Iters	Range		Point
8	24519245671.126057	1442719089351295.8	171117190665.02713

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	34
1	54	34
2	54	34

end0.0ms

sample1.4s

Algorithm

intervals

Results

821.0ms	11976×	body	80	valid
193.0ms	4402×	body	80	nan