Details

sample97.0ms

Algorithm

intervals

Results

38.0ms	93×	body	2560	valid
23.0ms	82×	body	1280	valid
11.0ms	294×	body	80	nan
7.0ms	37×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	11×	body	80	valid

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 1.0b

Counts

2 → 1

localize12.0ms

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

rewrite17.0ms

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

series113.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

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

prune141.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.9b

Counts

73 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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:

7.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
4.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (36.0ms)

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

prune190.0ms

Filtered

91 candidates to 69 candidates (75.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	89	6	95

Merged error: 0.9b

Counts

95 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.0b	(+ (pow v 2) (pow v 4))
1.0b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
4×	`associate-r`
3×	`associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `acos-asin` `distribute-lft-in` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

10.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
7.0ms	(+ (pow v 2) (pow v 4))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series165.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
72.0ms	(+ (pow v 2) (pow v 4))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify158.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	177	315
1	834	276
2	4136	273
3	5002	273

prune105.0ms

Filtered

52 candidates to 33 candidates (63.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	52	6	58

Merged error: 0.9b

Counts

58 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.0b	(+ (pow v 2) (pow v 4))
0.0b	(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b	(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`associate-r`
3×	`associate-l`
2×	`asin-acos` `flip3-+` `associate-*r/` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `times-frac` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

10.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
7.0ms	(+ (pow v 2) (pow v 4))
7.0ms	(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0ms	(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series198.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
67.0ms	(+ (pow v 2) (pow v 4))
36.0ms	(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
4.0ms	(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify211.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	250	546
1	1032	503
2	4958	497
3	5001	497

prune139.0ms

Filtered

71 candidates to 47 candidates (66.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 0.9b

Counts

77 → 6

regimes99.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	30
1	27	30

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	3016×	body	2560	valid
662.0ms	2485×	body	1280	valid
305.0ms	7948×	body	80	nan
232.0ms	1190×	body	640	valid
95.0ms	649×	body	320	valid
45.0ms	451×	body	160	valid
12.0ms	209×	body	80	valid

Details

sample97.0ms

simplify104.0ms

prune2.0ms

localize12.0ms

rewrite17.0ms

series113.0ms

simplify42.0ms

prune141.0ms

localize13.0ms

rewrite24.0ms

series148.0ms

simplify47.0ms

prune190.0ms

localize9.0ms

rewrite19.0ms

series165.0ms

simplify158.0ms

prune105.0ms

localize12.0ms

rewrite27.0ms

series198.0ms

simplify211.0ms

prune139.0ms

regimes99.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

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