Details

sample93.0ms

Algorithm

intervals

Results

45.0ms	108×	body	1280	valid
16.0ms	18×	body	2560	valid
12.0ms	51×	body	640	valid
5.0ms	43×	body	80	valid
4.0ms	27×	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

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: 35.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
4.4b	(sin (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

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

series68.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify143.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	133	186
1	298	177
2	920	175
3	3386	175
4	5001	175

prune66.0ms

Filtered

32 candidates to 25 candidates (78.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0.3b

Counts

33 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (sin eps) (cos x))
5.0ms	(* (cos eps) (sin x))
26.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
10.0ms	(- (* (cos eps) (sin x)) (sin x))

series295.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin eps) (cos x))
51.0ms	(* (cos eps) (sin x))
126.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
70.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	353	723
1	1239	687
2	5001	670

prune226.0ms

Filtered

92 candidates to 62 candidates (67.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	78	14	92
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	81	14	95

Merged error: 0.1b

Counts

95 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin eps) (cos x))
0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
3.0b	(- (cos eps) 1)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

5.0ms	(* (sin eps) (cos x))
9.0ms	(* (sin x) (- (cos eps) 1))
26.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
4.0ms	(- (cos eps) 1)

series247.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin eps) (cos x))
48.0ms	(* (sin x) (- (cos eps) 1))
129.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
21.0ms	(- (cos eps) 1)

simplify52.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	376	633
1	1544	590
2	5001	587

prune240.0ms

Filtered

96 candidates to 62 candidates (64.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	86	10	96
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	95	15	110

Merged error: 0.1b

Counts

110 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(+ (* (sin eps) (cos x)) (log (exp (* (sin x) (- (cos eps) 1)))))
3.0b	(- (cos eps) 1)
3.0b	(log (exp (* (sin x) (- (cos eps) 1))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
20×	`log-pow`
16×	`exp-prod`
14×	`log-prod` `associate-r`
11×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`pow1`
8×	`associate-l` `exp-sum`
7×	`add-exp-log` `sub-neg` `associate-+r+`
6×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `difference-of-squares`
4×	`distribute-lft-out`
3×	`difference-of-sqr-1` `distribute-lft-out--`
2×	`flip3--` `associate-r/` `rem-log-exp` `sum-log` `-commutative` `flip--` `unswap-sqr`
1×	`+-commutative` `exp-to-pow` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 101

Calls

4 calls:

8.0ms	(* (sin x) (- (cos eps) 1))
31.0ms	(+ (* (sin eps) (cos x)) (log (exp (* (sin x) (- (cos eps) 1)))))
5.0ms	(- (cos eps) 1)
10.0ms	(log (exp (* (sin x) (- (cos eps) 1))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin x) (- (cos eps) 1))
125.0ms	(+ (* (sin eps) (cos x)) (log (exp (* (sin x) (- (cos eps) 1)))))
25.0ms	(- (cos eps) 1)
50.0ms	(log (exp (* (sin x) (- (cos eps) 1))))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	337	739
1	1183	679
2	5002	671

prune239.0ms

Filtered

113 candidates to 70 candidates (61.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	112	16	128

Merged error: 0.1b

Counts

128 → 16

regimes141.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	17
1	20	17

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3298×	body	1280	valid
753.0ms	603×	body	2560	valid
498.0ms	1868×	body	640	valid
130.0ms	768×	body	320	valid
76.0ms	1119×	body	80	valid
47.0ms	344×	body	160	valid