Details

sample97.0ms

Algorithm

intervals

Results

43.0ms	131×	body	1280	valid
28.0ms	28×	body	2560	valid
13.0ms	61×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	1×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (cos (+ x eps)) (cos x))
2.9b	(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))

series68.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

simplify112.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune92.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.5b

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))
2.6b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite36.0ms

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:

3.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
22.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series285.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
79.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
123.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify113.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583

prune250.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.4b	(pow (* (sin x) (sin eps)) 3)
2.6b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
26.1b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt`
3×	`pow-unpow` `diff-log` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `associate--l+` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `cbrt-div` `flip3--` `pow1/3` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

4.0ms	(* (sin x) (sin eps))
3.0ms	(pow (* (sin x) (sin eps)) 3)
39.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
2.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series275.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin x) (sin eps))
65.0ms	(pow (* (sin x) (sin eps)) 3)
121.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
47.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify45.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	293	634
1	1142	580
2	5001	565

prune294.0ms

Filtered

90 candidates to 58 candidates (64.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 16.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.6b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.7b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
19.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
32.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series375.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
122.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
128.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify99.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	300	826
1	970	768
2	3675	746
3	5002	745

prune234.0ms

Filtered

85 candidates to 58 candidates (68.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 16.3b

regimes200.0ms

Accuracy

84.2% (1.6b remaining)

Error of 16.2b against oracle of 14.5b and baseline of 24.9b

bsearch119.0ms

Steps

Iters	Range		Point
7	2.8376047635535897e-09	7.206039552426127e-07	1.2472085921062031e-07
9	-2.814616726593186e-18	-2.428345818160311e-23	-2.7861772398867217e-18

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	50
1	46	50
2	46	50

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4482×	body	1280	valid
533.0ms	630×	body	2560	valid
397.0ms	1867×	body	640	valid
92.0ms	659×	body	320	valid
27.0ms	280×	body	160	valid
4.0ms	82×	body	80	valid