Details

sample50.0ms

Algorithm

intervals

Results

26.0ms	380×	body	80	valid
7.0ms	156×	body	80	nan

simplify103.0ms

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

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 1.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
1.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite24.0ms

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	(* a (pow k m))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ 1.0 (* 10.0 k))
63.0ms	(* a (pow k m))
19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
117.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify64.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (51.0ms)

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

prune190.0ms

Filtered

86 candidates to 63 candidates (73.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 1.7b

Counts

87 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
15.0b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.0b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
92×	`times-frac`
52×	`sqrt-prod`
48×	`associate-r`
46×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log`
24×	`unpow-prod-down` `associate-l`
21×	`unswap-sqr`
16×	`add-cbrt-cube`
12×	`sqr-pow`
10×	`div-exp`
9×	`add-log-exp`
8×	`pow1` `sqrt-div` `prod-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`sum-log`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `div-inv`
1×	`+-commutative` `frac-times` `associate-+l+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 160

Calls

4 calls:

5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
34.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (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)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
119.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
56.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
48.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify100.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	859	2730
1	3871	2549
2	5001	2435

prune390.0ms

Filtered

172 candidates to 112 candidates (65.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	172	4	176

Merged error: 1.7b

Counts

176 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
0.6b	(cbrt k)
1.7b	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
30×	`prod-exp`
16×	`div-exp`
13×	`add-cbrt-cube`
11×	`pow-exp`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow-to-exp`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `pow1/3` `associate-/r*` `cbrt-unprod`
2×	`associate-/r/`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 71

Calls

4 calls:

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

series933.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt k)
183.0ms	(cbrt k)
178.0ms	(cbrt k)
387.0ms	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify60.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	506	882
1	2389	755
2	5001	731

prune209.0ms

Filtered

83 candidates to 57 candidates (68.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	2	2
Picked	0	1	1
Done	1	0	1
Total	83	4	87

Merged error: 0.0b

Counts

87 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.1b	(pow (+ 1.0 (* k (+ 10.0 k))) 3)
1.7b	(/ (* a (pow k m)) (cbrt (pow (+ 1.0 (* k (+ 10.0 k))) 3)))
10.0b	(cbrt (pow (+ 1.0 (* k (+ 10.0 k))) 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
17×	`add-exp-log`
15×	`times-frac` `associate-/r*`
12×	`unpow-prod-down` `cube-prod`
10×	`add-cbrt-cube`
7×	`pow1`
6×	`cube-div`
4×	`cube-mult` `cbrt-div` `flip3-+` `unpow3` `div-exp` `associate-r` `prod-exp` `flip-+` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `associate-l`
2×	`cbrt-undiv` `pow-to-exp` `associate-*r/` `pow-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `pow-pow` `frac-2neg` `distribute-lft-in` `pow1/3` `pow-prod-down` `clear-num` `-commutative` `rem-cbrt-cube` `div-inv` `distribute-lft-out` `associate-/l` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

10.0ms	(* k (+ 10.0 k))
4.0ms	(pow (+ 1.0 (* k (+ 10.0 k))) 3)
9.0ms	(/ (* a (pow k m)) (cbrt (pow (+ 1.0 (* k (+ 10.0 k))) 3)))
3.0ms	(cbrt (pow (+ 1.0 (* k (+ 10.0 k))) 3))

series237.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* k (+ 10.0 k))
44.0ms	(pow (+ 1.0 (* k (+ 10.0 k))) 3)
123.0ms	(/ (* a (pow k m)) (cbrt (pow (+ 1.0 (* k (+ 10.0 k))) 3)))
29.0ms	(cbrt (pow (+ 1.0 (* k (+ 10.0 k))) 3))

simplify77.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	573	996
1	2821	918
2	5002	904

prune218.0ms

Filtered

132 candidates to 74 candidates (56.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

regimes79.0ms

Accuracy

97.1% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.1b

bsearch79.0ms

Steps

Iters	Range		Point
9	15146.518640101762	1580762020.1433036	3884199.03848918

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	47
1	56	47

end0.0ms

sample1.4s

Algorithm

intervals

Results

816.0ms	11927×	body	80	valid
188.0ms	4128×	body	80	nan