Details

sample93.0ms

Algorithm

intervals

Results

40.0ms	102×	body	2560	valid
18.0ms	69×	body	1280	valid
10.0ms	275×	body	80	nan
8.0ms	42×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	15×	body	160	valid
1.0ms	10×	body	80	valid

simplify100.0ms

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	5002	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

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.7b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
27.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	336	587
1	1261	535
2	5002	531

prune127.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 0.6b

Counts

73 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b	(* 5.0 (* v v))
0.7b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
27.0ms	(* 5.0 (* v v))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	409	840
1	1459	784
2	5001	780

prune180.0ms

Filtered

91 candidates to 69 candidates (75.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	92	4	96

Merged error: 0.6b

Counts

96 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))
0.0b	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)
0.2b	(* 5.0 (pow v 2))
0.7b	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

135×	`add-sqr-sqrt`
96×	`times-frac`
81×	`*-un-lft-identity`
76×	`unpow-prod-down`
66×	`cbrt-prod`
60×	`cube-prod`
57×	`add-cube-cbrt`
48×	`difference-of-squares`
16×	`sqr-pow`
14×	`unpow2`
12×	`add-exp-log` `distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`associate-r` `associate-/r/`
5×	`pow1`
4×	`flip3--` `flip--` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `associate-l` `pow-exp` `prod-exp`
2×	`cube-div` `cube-mult` `pow-to-exp` `unpow3` `rem-cube-cbrt`
1×	`cbrt-undiv` `acos-asin` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 191

Calls

4 calls:

13.0ms	(cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))
12.0ms	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)
6.0ms	(* 5.0 (pow v 2))
1.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))
129.0ms	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)
24.0ms	(* 5.0 (pow v 2))
4.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))

simplify93.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	823	2467
1	3262	2263
2	5003	2247

prune255.0ms

Filtered

203 candidates to 86 candidates (42.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	202	5	207

Merged error: 0.6b

Counts

207 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))
0.9b	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
0.9b	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
1.0b	(* (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))) (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))))

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 (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))
1.0ms	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
1.0ms	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
6.0ms	(* (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))) (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))
21.0ms	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
17.0ms	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
5.0ms	(* (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))) (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	124	1162
1	452	989
2	2522	932
3	5002	893

prune186.0ms

Filtered

95 candidates to 54 candidates (56.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	0	3	3
Picked	1	0	1
Done	1	0	1
Total	93	7	100

Merged error: 0.6b

Counts

100 → 7

regimes143.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	21
1	21	21

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	3014×	body	2560	valid
654.0ms	2459×	body	1280	valid
294.0ms	8057×	body	80	nan
249.0ms	1277×	body	640	valid
89.0ms	639×	body	320	valid
38.0ms	395×	body	160	valid
12.0ms	216×	body	80	valid

Details

sample93.0ms

simplify100.0ms

prune2.0ms

localize8.0ms

rewrite16.0ms

series110.0ms

simplify41.0ms

prune127.0ms

localize10.0ms

rewrite23.0ms

series140.0ms

simplify46.0ms

prune180.0ms

localize11.0ms

rewrite44.0ms

series238.0ms

simplify93.0ms

prune255.0ms

localize14.0ms

rewrite12.0ms

series46.0ms

simplify123.0ms

prune186.0ms

regimes143.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

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