Details

analyze823.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

sample87.0ms

Algorithm

intervals

Results

46.0ms	114×	body	2560	valid
21.0ms	75×	body	1280	valid
7.0ms	36×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	5×	body	80	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4932	14
1	4932	14

prune3.0ms

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: 0.4b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 5.0 (* v v)))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite21.0ms

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 → 74

Calls

4 calls:

3.0ms	(- 1.0 (* 5.0 (* v v)))
7.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
8.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- 1.0 (* 5.0 (* v v)))
6.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
3.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5724	1197

prune138.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Merged error: 0.4b

Counts

87 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1/2 PI) (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))
0.4b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite20.0ms

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×	`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` `associate--r-` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

4.0ms	(- (* 1/2 PI) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
8.0ms	(/ (- 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)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* 1/2 PI) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
3.0ms	(* 5.0 (* v v))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5770	1413

prune146.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	87	3	90

Merged error: 0.4b

Counts

90 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* v v) (pow v 4))
0.0b	(- (* 1/2 PI) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
0.0b	(* 4.0 (+ (* v v) (pow v 4)))
0.4b	(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

6.0ms	(+ (* v v) (pow v 4))
4.0ms	(- (* 1/2 PI) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
8.0ms	(* 4.0 (+ (* v v) (pow v 4)))
1.0ms	(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series28.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* v v) (pow v 4))
9.0ms	(- (* 1/2 PI) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
9.0ms	(* 4.0 (+ (* v v) (pow v 4)))
4.0ms	(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4910	861
1	4910	861

prune119.0ms

Filtered

46 candidates to 65 candidates (-41.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	65	3	68

Merged error: 0.4b

Counts

68 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (- (* PI 1/2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))))
0.0b	(exp (log (- (* PI 1/2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))))
0.0b	(* 4.0 (+ (* v v) (pow v 4)))
0.4b	(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

4.0ms	(log (- (* PI 1/2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))))
5.0ms	(exp (log (- (* PI 1/2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))))
8.0ms	(* 4.0 (+ (* v v) (pow v 4)))
1.0ms	(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series59.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(log (- (* PI 1/2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))))
6.0ms	(exp (log (- (* PI 1/2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))))
9.0ms	(* 4.0 (+ (* v v) (pow v 4)))
4.0ms	(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4972	1244
1	4972	1244

prune141.0ms

Filtered

48 candidates to 73 candidates (-52.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	72	4	76

Merged error: 0.4b

Counts

76 → 4

regimes110.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	112	18
1	112	18

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	3047×	body	2560	valid
703.0ms	2443×	body	1280	valid
264.0ms	1268×	body	640	valid
96.0ms	622×	body	320	valid
43.0ms	406×	body	160	valid
13.0ms	214×	body	80	valid
0.0ms	6×	body	80	nan

Details

analyze823.0ms

sample87.0ms

simplify61.0ms

prune3.0ms

localize7.0ms

rewrite21.0ms

series17.0ms

simplify45.0ms

prune138.0ms

localize10.0ms

rewrite20.0ms

series17.0ms

simplify51.0ms

prune146.0ms

localize10.0ms

rewrite20.0ms

series28.0ms

simplify66.0ms

prune119.0ms

localize14.0ms

rewrite19.0ms

series59.0ms

simplify54.0ms

prune141.0ms

regimes110.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling