Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample112.0ms

Algorithm

intervals

Results

55.0ms	127×	body	1280	valid
25.0ms	27×	body	2560	valid
16.0ms	69×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	9×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune4.0ms

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: 42.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
2.0b	(cos (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series16.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(- (cos (+ x eps)) (cos x))
6.0ms	(cos (+ x eps))

simplify110.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune75.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	21	9	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	9	31

Merged error: 18.1b

Counts

31 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
3.1b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

5.0ms	(* (cos x) (cos eps))
5.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos x) (cos eps))
11.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
24.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	574
2	5002	565

prune150.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	67	10	77
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	71	15	86

Merged error: 17.9b

Counts

86 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (log (exp (* (sin x) (sin eps)))) (cos x))
0.2b	(* (sin x) (sin eps))
3.1b	(- (* (cos x) (cos eps)) (+ (log (exp (* (sin x) (sin eps)))) (cos x)))
4.2b	(log (exp (* (sin x) (sin eps))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-log-exp`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `log-prod` `add-cbrt-cube`
4×	`log-pow`
3×	`associate-+l+` `associate-r` `associate-l`
2×	`flip3-+` `diff-log` `sum-log` `cos-mult` `frac-sub` `flip-+` `distribute-lft-out`
1×	`+-commutative` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `associate--r+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

6.0ms	(+ (log (exp (* (sin x) (sin eps)))) (cos x))
6.0ms	(* (sin x) (sin eps))
10.0ms	(- (* (cos x) (cos eps)) (+ (log (exp (* (sin x) (sin eps)))) (cos x)))
2.0ms	(log (exp (* (sin x) (sin eps))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (log (exp (* (sin x) (sin eps)))) (cos x))
11.0ms	(* (sin x) (sin eps))
28.0ms	(- (* (cos x) (cos eps)) (+ (log (exp (* (sin x) (sin eps)))) (cos x)))
12.0ms	(log (exp (* (sin x) (sin eps))))

simplify130.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	309	701
1	1065	623
2	4315	607
3	5001	607

prune145.0ms

Filtered

55 candidates to 77 candidates (-40.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	76	16	92

Merged error: 17.9b

Counts

92 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.5b	(pow (* (cos x) (cos eps)) 3)
3.0b	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt` `pow-prod-down`
10×	`*-un-lft-identity`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `difference-of-squares` `sqr-pow`
7×	`cube-div` `cos-mult`
6×	`unpow-prod-down` `pow-unpow` `cube-prod` `add-log-exp`
4×	`pow-sqr` `pow-prod-up`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `flip3-+` `pow-plus` `unpow3` `frac-sub` `flip-+`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `flip3--` `diff-log` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 109

Calls

4 calls:

8.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
10.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
5.0ms	(pow (* (cos x) (cos eps)) 3)
17.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

series169.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (+ (* (sin x) (sin eps)) (cos x)) 3)
15.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
18.0ms	(pow (* (cos x) (cos eps)) 3)
118.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

simplify102.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	538	1143
1	2688	1062
2	5001	1058

prune211.0ms

Filtered

65 candidates to 121 candidates (-86.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	108	13	121
Fresh	9	5	14
Picked	1	0	1
Done	0	1	1
Total	118	19	137

Merged error: 17.9b

Counts

137 → 19

regimes442.0ms

Accuracy

85.3% (1.5b remaining)

Error of 15.7b against oracle of 14.2b and baseline of 24.4b

bsearch66.0ms

Steps

Iters	Range		Point
6	1.2182585195686108e-07	6.082453627221136e-07	2.3306542691574525e-07
6	-1.2809543618877441e-08	-3.1319644450542828e-09	-1.2453695641553038e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	17
1	36	17

end0.0ms

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample3.3s

Algorithm

intervals

Results

1.9s	4453×	body	1280	valid
665.0ms	662×	body	2560	valid
482.0ms	1871×	body	640	valid
122.0ms	672×	body	320	valid
33.0ms	281×	body	160	valid
4.0ms	61×	body	80	valid

Details

analyze2.0ms

sample112.0ms

simplify5.0ms

prune4.0ms

localize9.0ms

rewrite12.0ms

series16.0ms

simplify110.0ms

prune75.0ms

localize14.0ms

rewrite25.0ms

series53.0ms

simplify48.0ms

prune150.0ms

localize19.0ms

rewrite26.0ms

series66.0ms

simplify130.0ms

prune145.0ms

localize28.0ms

rewrite43.0ms

series169.0ms

simplify102.0ms

prune211.0ms

regimes442.0ms

bsearch66.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample3.3s

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