Details

sample93.0ms

Algorithm

intervals

Results

49.0ms	144×	body	1280	valid
14.0ms	17×	body	2560	valid
14.0ms	64×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	3×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 39.1b

Counts

2 → 1

localize15.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (cos (+ x eps)) (cos x))
2.8b	(cos (+ x eps))

rewrite11.0ms

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))

series15.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify115.0ms

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

prune74.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	18	12	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	12	31

Merged error: 12.5b

Counts

31 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.2b	(- (- (* (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:

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
16.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
26.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify114.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4487	582
3	5002	582

prune126.0ms

Filtered

56 candidates to 82 candidates (-46.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	78	16	94

Merged error: 12.3b

Counts

94 → 16

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))
2.2b	(- (* (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:

4.0ms	(* (cos x) (cos eps))
5.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (sin x) (sin eps))
10.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
11.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

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

prune137.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	74	19	93

Merged error: 12.3b

Counts

93 → 19

localize25.0ms

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))
0.5b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
2.0b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite35.0ms

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))

series204.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (cos x) 3)
21.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
27.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
151.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify102.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (89.0ms)

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

prune140.0ms

Filtered

63 candidates to 112 candidates (-77.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	103	9	112
Fresh	6	12	18
Picked	1	0	1
Done	0	0	0
Total	110	21	131

Merged error: 12.3b

Counts

131 → 21

regimes307.0ms

Accuracy

80.3% (2.0b remaining)

Error of 16.1b against oracle of 14.1b and baseline of 24.3b

bsearch75.0ms

Steps

Iters	Range		Point
5	2.0218584867695933e-30	5.723464640087445e-30	5.6479147762213146e-30
11	-12261081.339984152	-5.550846520329113e-21	-1.821880325799914e-06

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	28
1	36	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	4553×	body	1280	valid
515.0ms	573×	body	2560	valid
409.0ms	1829×	body	640	valid
100.0ms	666×	body	320	valid
31.0ms	296×	body	160	valid
4.0ms	83×	body	80	valid

Details

sample93.0ms

simplify4.0ms

prune3.0ms

localize15.0ms

rewrite11.0ms

series15.0ms

simplify115.0ms

prune74.0ms

localize14.0ms

rewrite24.0ms

series60.0ms

simplify114.0ms

prune126.0ms

localize14.0ms

rewrite25.0ms

series51.0ms

simplify41.0ms

prune137.0ms

localize25.0ms

rewrite35.0ms

series204.0ms

simplify102.0ms

prune140.0ms

regimes307.0ms

bsearch75.0ms

simplify1.0ms

end0.0ms

sample3.0s

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