Details

sample79.0ms

Algorithm

intervals

Results

32.0ms	94×	body	2560	valid
18.0ms	77×	body	1280	valid
8.0ms	274×	body	80	nan
7.0ms	46×	body	640	valid
2.0ms	15×	body	320	valid
2.0ms	19×	body	160	valid
0.0ms	5×	body	80	valid

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	7
7	5001	7

prune2.0ms

Filtered

1 candidates to 0 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: 0.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- 1.0 (* 5.0 (* v v)))
0.1b	(* 5.0 (* v v))
0.7b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp`
4×	`associate-/r*` `difference-of-squares`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

7.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
3.0ms	(- 1.0 (* 5.0 (* v v)))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series173.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
61.0ms	(- 1.0 (* 5.0 (* v v)))
25.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	355	664
1	1356	609
2	5001	605

prune196.0ms

Filtered

87 candidates to 65 candidates (74.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Merged error: 0.7b

Counts

88 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
22.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
17.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
4.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify118.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	125	1002
1	427	888
2	2342	844
3	5002	813

prune153.0ms

Filtered

95 candidates to 48 candidates (50.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	5	98

Merged error: 0.7b

Counts

98 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
131.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
138.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
160.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	117	1278
1	425	1112
2	2705	1044
3	5001	1031

prune194.0ms

Filtered

85 candidates to 56 candidates (65.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	84	6	90

Merged error: 0.7b

Counts

90 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(pow (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
4.0ms	(pow (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5)

series615.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
139.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
133.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
210.0ms	(pow (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 5)

simplify58.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	144	904
1	385	814
2	1212	808
3	5001	800

prune213.0ms

Filtered

69 candidates to 54 candidates (78.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	1	2
Picked	1	0	1
Done	1	2	3
Total	70	5	75

Merged error: 0.7b

Counts

75 → 5

regimes96.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2983×	body	2560	valid
585.0ms	2509×	body	1280	valid
220.0ms	8022×	body	80	nan
200.0ms	1236×	body	640	valid
75.0ms	622×	body	320	valid
38.0ms	442×	body	160	valid
14.0ms	208×	body	80	valid