Details

sample51.0ms

Algorithm

intervals

Results

26.0ms	386×	body	80	valid
8.0ms	126×	body	80	nan

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	24	7
1	48	7
2	96	6
3	256	6
4	891	6
5	3963	6
6	5002	6

prune6.0ms

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`
14×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`prod-exp`
4×	`pow1` `unpow-prod-down` `div-exp` `sum-log`
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 → 74

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)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ 1.0 (* 10.0 k))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
59.0ms	(* a (pow k m))
115.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify62.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	457	599
1	2146	533
2	5001	526

prune189.0ms

Filtered

86 candidates to 63 candidates (73.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	82	6	88

Merged error: 2.8b

Counts

88 → 6

localize13.0ms

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`
63×	`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×	`unpow-prod-down` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `cbrt-unprod` `sqr-pow`
1×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 166

Calls

4 calls:

5.0ms	(* a (pow k m))
16.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
5.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* a (pow k m))
114.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
50.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
47.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify102.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	739	3133
1	3702	2808
2	5002	2808

prune366.0ms

Filtered

178 candidates to 113 candidates (63.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	178	6	184

Merged error: 2.8b

Counts

184 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`times-frac`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`associate-l`
22×	`unpow-prod-down`
20×	`add-exp-log`
12×	`add-cbrt-cube`
8×	`sqr-pow`
7×	`pow1` `associate-r` `associate-/l*`
6×	`div-exp`
5×	`prod-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`flip3-+` `associate-/r*` `cbrt-unprod` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `associate-r/` `pow-prod-down` `pow-exp` `-commutative` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-*l/` `clear-num` `distribute-lft-out`

Counts

3 → 120

Calls

3 calls:

6.0ms	(* k (+ 10.0 k))
10.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
14.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

series212.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* k (+ 10.0 k))
65.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
103.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

simplify72.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	608	1105
1	2523	1041
2	5001	1035

prune264.0ms

Filtered

129 candidates to 98 candidates (76.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	130	5	135

Merged error: 2.8b

Counts

135 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
0.6b	(cbrt k)
2.7b	(* (* (pow (* (cbrt k) (cbrt k)) m) (/ (pow (cbrt k) m) (+ (* k (+ 10.0 k)) 1.0))) a)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
37×	`prod-exp`
13×	`add-cbrt-cube`
12×	`div-exp` `pow-exp`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `pow-to-exp` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`cbrt-unprod`
4×	`add-log-exp`
3×	`pow1/3` `associate-r`
1×	`cbrt-undiv` `associate-r/` `associate-l` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 67

Calls

4 calls:

1.0ms	(cbrt k)
1.0ms	(cbrt k)
1.0ms	(cbrt k)
16.0ms	(* (* (pow (* (cbrt k) (cbrt k)) m) (/ (pow (cbrt k) m) (+ (* k (+ 10.0 k)) 1.0))) a)

series865.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt k)
177.0ms	(cbrt k)
166.0ms	(cbrt k)
349.0ms	(* (* (pow (* (cbrt k) (cbrt k)) m) (/ (pow (cbrt k) m) (+ (* k (+ 10.0 k)) 1.0))) a)

simplify56.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	454	754
1	1908	619
2	5001	571

prune179.0ms

Filtered

79 candidates to 51 candidates (64.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	78	6	84

Merged error: 0.0b

Counts

84 → 6

regimes130.0ms

Accuracy

96.3% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.3b

bsearch64.0ms

Steps

Iters	Range		Point
8	24519245671.126057	1442719089351295.8	1407855369986978.5

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	41
1	51	41

end0.0ms

sample1.4s

Algorithm

intervals

Results

812.0ms	11976×	body	80	valid
199.0ms	4402×	body	80	nan