Details

sample2.2s

Algorithm

intervals

sampling

Space saved by range analysis: 50.079319%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

43.0ms	104×	body	2560	valid
20.0ms	70×	body	1280	valid
10.0ms	37×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	18×	body	160	valid
0.0ms	6×	body	80	valid

simplify101.0ms

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

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: 0.2b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b	(* 5.0 (* v v))
0.2b	(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:

7.0ms	(/ (- 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)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ (- 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)))

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

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

prune119.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

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: 0.2b

Counts

73 → 4

localize10.0ms

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))
0.1b	(* 5.0 (* v v))
0.2b	(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:

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

simplify43.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (33.0ms)

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

prune153.0ms

Filtered

69 candidates to 91 candidates (-31.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	91	4	95

Merged error: 0.2b

Counts

95 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow v 2) (pow v 4))
0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.2b	(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:

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

series21.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify154.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (23.0ms)

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

prune105.0ms

Filtered

34 candidates to 52 candidates (-52.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	51	5	56

Merged error: 0.2b

Counts

56 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
0.0b	(exp (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))
0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.2b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

1.0ms	(log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
2.0ms	(exp (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))
10.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series47.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
4.0ms	(exp (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))
9.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify148.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	193	551
1	815	484
2	3988	468
3	5002	462

prune130.0ms

Filtered

44 candidates to 70 candidates (-59.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	69	6	75

Merged error: 0.2b

Counts

75 → 6

regimes243.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	18
1	17	18

end0.0ms

sample4.6s

Algorithm

intervals

sampling

Space saved by range analysis: 50.079319%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

1.2s	2948×	body	2560	valid
717.0ms	2534×	body	1280	valid
269.0ms	1260×	body	640	valid
95.0ms	628×	body	320	valid
48.0ms	437×	body	160	valid
12.0ms	193×	body	80	valid
0.0ms	4×	body	80	nan

Details

sample2.2s

simplify101.0ms

prune3.0ms

localize7.0ms

rewrite16.0ms

series12.0ms

simplify39.0ms

prune119.0ms

localize10.0ms

rewrite23.0ms

series17.0ms

simplify43.0ms

prune153.0ms

localize9.0ms

rewrite19.0ms

series21.0ms

simplify154.0ms

prune105.0ms

localize13.0ms

rewrite15.0ms

series47.0ms

simplify148.0ms

prune130.0ms

regimes243.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.6s

Profiling