Details

sample100.0ms

Algorithm

intervals

Results

52.0ms	142×	body	1280	valid
24.0ms	28×	body	2560	valid
10.0ms	51×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	4×	body	80	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

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: 37.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
2.3b	(cos (+ 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` `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:

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

series69.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify111.0ms

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

prune84.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	19	11	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	11	31

Merged error: 15.8b

Counts

31 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
2.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (cos x) (cos eps))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series296.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms	(* (cos x) (cos eps))
43.0ms	(* (sin x) (sin eps))
128.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify115.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4488	582
3	5001	582

prune227.0ms

Filtered

82 candidates to 57 candidates (69.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	79	14	93

Merged error: 15.7b

Counts

93 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.6b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.9b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
16×	`difference-of-squares`
11×	`add-log-exp`
10×	`add-cube-cbrt` `sqr-pow`
6×	`pow1` `add-exp-log` `pow-unpow` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`cube-div`
2×	`cube-mult` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-exp` `sum-log` `cos-mult` `flip--` `sin-mult` `rem-cube-cbrt`
1×	`difference-cubes` `+-commutative` `associate-+l-` `flip3-+` `frac-sub` `flip-+` `distribute-lft-out` `sub-div`

Counts

4 → 100

Calls

4 calls:

2.0ms	(pow (cos x) 3)
8.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
16.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series813.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (cos x) 3)
95.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
105.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
586.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify101.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	599	1433
1	2889	1321
2	5002	1280

prune387.0ms

Filtered

112 candidates to 63 candidates (56.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	103	9	112
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	111	15	126

Merged error: 15.6b

Counts

126 → 15

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)) 3))
0.6b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
0.6b	(pow (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)) 3)
1.9b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
23×	`unpow-prod-down` `cube-prod`
16×	`difference-of-squares`
14×	`cbrt-prod`
13×	`add-cube-cbrt`
11×	`sqr-pow`
8×	`cube-div`
6×	`pow1` `add-exp-log` `pow-unpow` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out--`
4×	`distribute-lft-out`
3×	`cube-mult` `unpow3`
2×	`pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `flip3-+` `pow-exp` `cos-mult` `flip--` `flip-+` `sin-mult` `rem-cube-cbrt`
1×	`difference-cubes` `sub-neg` `pow1/3` `diff-log` `frac-sub` `rem-cbrt-cube` `sub-div`

Counts

4 → 113

Calls

4 calls:

9.0ms	(cbrt (pow (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)) 3))
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
9.0ms	(pow (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)) 3)
20.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series927.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (pow (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)) 3))
106.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
138.0ms	(pow (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)) 3)
587.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify90.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	635	2021
1	2746	1871
2	5001	1844

prune373.0ms

Filtered

125 candidates to 68 candidates (54.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	125	15	140

Merged error: 15.6b

Counts

140 → 15

regimes208.0ms

Accuracy

58.1% (4.2b remaining)

Error of 18.4b against oracle of 14.2b and baseline of 24.2b

bsearch200.0ms

Steps

Iters	Range		Point
9	3.912289318874603e-28	1.4618569291717553e-22	1.4427868870974903e-22
11	-5.318320565888805e-07	-6.2203271450298025e-31	-8.567744108473295e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	112
1	72	112
2	72	112

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	4463×	body	1280	valid
624.0ms	1859×	body	640	valid
554.0ms	645×	body	2560	valid
106.0ms	674×	body	320	valid
28.0ms	277×	body	160	valid
4.0ms	82×	body	80	valid

Details

sample100.0ms

simplify5.0ms

prune2.0ms

localize8.0ms

rewrite10.0ms

series69.0ms

simplify111.0ms

prune84.0ms

localize13.0ms

rewrite24.0ms

series296.0ms

simplify115.0ms

prune227.0ms

localize29.0ms

rewrite36.0ms

series813.0ms

simplify101.0ms

prune387.0ms

localize29.0ms

rewrite48.0ms

series927.0ms

simplify90.0ms

prune373.0ms

regimes208.0ms

bsearch200.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling