Details

analyze2.0ms

Algorithm

Search

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

sample105.0ms

Algorithm

intervals

Results

47.0ms	104×	body	1280	valid
24.0ms	21×	body	2560	valid
18.0ms	69×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	28×	body	80	valid
1.0ms	12×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	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: 37.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (sin (+ x eps)) (sin x))
2.6b	(sin (+ x eps))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 23

Calls

2 calls:

6.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series14.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
6.0ms	(sin (+ x eps))

simplify43.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5348	268

prune54.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	24	5	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	5	30

Merged error: 0.2b

Counts

30 → 5

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
2.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

5.0ms	(+ x (+ x eps))
8.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series20.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (+ x eps))
11.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5169	541

prune108.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	46	9	55

Merged error: 0.2b

Counts

55 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
0.6b	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
2.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

8.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
2.0ms	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
2.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series33.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
5.0ms	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
12.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify40.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4924	1255
1	4924	1255

prune154.0ms

Filtered

56 candidates to 97 candidates (-73.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	97	9	106

Merged error: 0.2b

Counts

106 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
2.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

7.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
12.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
8.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
9.0ms	(cos (/ (+ x (+ x eps)) 2))

series30.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
10.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
5.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5064	940

prune123.0ms

Filtered

53 candidates to 73 candidates (-37.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	73	9	82

Merged error: 0.2b

Counts

82 → 9

regimes258.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 14.8b

bsearch75.0ms

Steps

Iters	Range		Point
9	1.3472611376282578e-34	1.758468545048918e-25	1.7278717375445562e-25
9	-117615.3612092743	-0.00010668323082749249	-0.0001084741578760162

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	38
1	45	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3270×	body	1280	valid
617.0ms	636×	body	2560	valid
532.0ms	1889×	body	640	valid
153.0ms	807×	body	320	valid
63.0ms	1066×	body	80	valid
41.0ms	332×	body	160	valid

Details

analyze2.0ms

sample105.0ms

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series14.0ms

simplify43.0ms

prune54.0ms

localize13.0ms

rewrite21.0ms

series20.0ms

simplify57.0ms

prune108.0ms

localize16.0ms

rewrite22.0ms

series33.0ms

simplify40.0ms

prune154.0ms

localize16.0ms

rewrite37.0ms

series30.0ms

simplify45.0ms

prune123.0ms

regimes258.0ms

bsearch75.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling