Details

sample1.6min

Algorithm

intervals

Results

25.0ms	375×	body	80	valid
5.0ms	129×	body	80	nan

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (3.0ms)

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

prune9.0ms

Filtered

1 candidates to 1 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: 1.7b

Counts

2 → 2

localize9.0ms

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))
1.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite21.0ms

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:

2.0ms	(+ 1.0 (* 10.0 k))
4.0ms	(+ (+ 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)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ 1.0 (* 10.0 k))
2.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
13.0ms	(* a (pow k m))
32.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify53.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	471	611
1	2227	545
2	5002	538

prune105.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Merged error: 1.7b

Counts

88 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* k (+ 10.0 k)))
0.0b	(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
0.1b	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
3.8b	(/ (+ 1.0 (* k (+ 10.0 k))) a)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

1073×	`times-frac`
496×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
198×	`unpow-prod-down`
105×	`associate-/r*`
68×	`add-exp-log`
66×	`sqr-pow`
51×	`div-exp`
43×	`div-inv`
20×	`add-cbrt-cube`
19×	`associate-/l*`
10×	`cbrt-undiv`
8×	`pow-to-exp` `pow-exp`
7×	`rec-exp` `1-exp`
6×	`add-log-exp`
5×	`pow1`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`associate-+r+` `flip3-+` `flip-+`
1×	`+-commutative` `distribute-rgt-in` `pow-flip` `distribute-lft-in` `sum-log` `associate-/r/` `inv-pow`

Counts

4 → 592

Calls

4 calls:

3.0ms	(+ 1.0 (* k (+ 10.0 k)))
9.0ms	(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
21.0ms	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
5.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) a)

series66.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (* k (+ 10.0 k)))
31.0ms	(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
27.0ms	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
6.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) a)

simplify117.0ms

Algorithm

egg-herbie

Counts

604 → 604

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2149	9179
1	5001	8748

prune948.0ms

Filtered

374 candidates to 604 candidates (-61.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	602	2	604
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	602	6	608

Merged error: 1.7b

Counts

608 → 6

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))))
13.8b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
13.8b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite35.0ms

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))
14.0ms	(/ (/ (* 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)))
6.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* a (pow k m))
30.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
3.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
3.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify96.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	753	3143
1	3787	2820
2	5001	2820

prune277.0ms

Filtered

113 candidates to 178 candidates (-57.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	178	6	184

Merged error: 1.7b

Counts

184 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ 1.0 (* k (+ 10.0 k)))) (/ (sqrt (+ 1.0 (* k (+ 10.0 k)))) a))
0.1b	(/ 1 (/ (* (sqrt (+ 1.0 (* k (+ 10.0 k)))) (/ (sqrt (+ 1.0 (* k (+ 10.0 k)))) a)) (pow k m)))
13.8b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
13.8b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-exp-log`
83×	`times-frac`
63×	`add-sqr-sqrt`
57×	`div-exp`
45×	`add-cube-cbrt` `*-un-lft-identity`
23×	`sqrt-prod` `add-cbrt-cube`
22×	`associate-r`
20×	`prod-exp`
12×	`unpow-prod-down`
11×	`associate-/r*`
10×	`rec-exp` `1-exp`
9×	`pow1` `cbrt-undiv` `pow-to-exp` `pow-exp`
8×	`sqrt-div`
6×	`associate-l` `div-inv` `unswap-sqr`
4×	`flip3-+` `cbrt-unprod` `flip-+` `add-log-exp` `sqr-pow`
3×	`associate-/l*`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r/` `-commutative` `inv-pow`

Counts

4 → 176

Calls

4 calls:

14.0ms	(* (sqrt (+ 1.0 (* k (+ 10.0 k)))) (/ (sqrt (+ 1.0 (* k (+ 10.0 k)))) a))
12.0ms	(/ 1 (/ (* (sqrt (+ 1.0 (* k (+ 10.0 k)))) (/ (sqrt (+ 1.0 (* k (+ 10.0 k)))) a)) (pow k m)))
2.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
2.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (+ 1.0 (* k (+ 10.0 k)))) (/ (sqrt (+ 1.0 (* k (+ 10.0 k)))) a))
27.0ms	(/ 1 (/ (* (sqrt (+ 1.0 (* k (+ 10.0 k)))) (/ (sqrt (+ 1.0 (* k (+ 10.0 k)))) a)) (pow k m)))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify99.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	842	2574
1	4169	2085
2	5002	2006

prune212.0ms

Filtered

98 candidates to 188 candidates (-91.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	188	6	194

Merged error: 1.7b

Counts

194 → 6

regimes212.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample53.0s

Algorithm

intervals

Results

Details

sample1.6min

simplify98.0ms

prune9.0ms

localize9.0ms

rewrite21.0ms

series51.0ms

simplify53.0ms

prune105.0ms

localize12.0ms

rewrite77.0ms

series66.0ms

simplify117.0ms

prune948.0ms

localize12.0ms

rewrite35.0ms

series50.0ms

simplify96.0ms

prune277.0ms

localize13.0ms

rewrite37.0ms

series40.0ms

simplify99.0ms

prune212.0ms

regimes212.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample53.0s

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