Details

sample105.0ms

Algorithm

intervals

Results

45.0ms	105×	body	1280	valid
23.0ms	25×	body	2560	valid
15.0ms	61×	body	640	valid
11.0ms	28×	body	320	valid
1.0ms	28×	body	80	valid
1.0ms	9×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 37.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite13.0ms

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))
5.0ms	(sin (+ x eps))

series61.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify164.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	135	186
1	306	177
2	942	175
3	3450	175
4	5002	175

prune87.0ms

Filtered

32 candidates to 25 candidates (78.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	4	33

Merged error: 0.4b

Counts

33 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin eps) (cos x))
0.1b	(* (cos eps) (sin x))
0.2b	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
1.2b	(- (* (cos eps) (sin x)) (sin x))

rewrite49.0ms

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))
22.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
10.0ms	(- (* (cos eps) (sin x)) (sin x))

series286.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin eps) (cos x))
44.0ms	(* (cos eps) (sin x))
129.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
62.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	360	723
1	1274	687
2	5001	670

prune285.0ms

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	3	0	3
Picked	1	0	1
Done	0	0	0
Total	82	14	96

Merged error: 0.2b

Counts

96 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin eps) (cos x))
0.1b	(* (sin x) (- (cos eps) 1))
0.2b	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
1.1b	(- (cos eps) 1)

rewrite49.0ms

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))
28.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
5.0ms	(- (cos eps) 1)

series241.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin eps) (cos x))
53.0ms	(* (sin x) (- (cos eps) 1))
122.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
20.0ms	(- (cos eps) 1)

simplify65.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	385	633
1	1582	590
2	5002	587

prune296.0ms

Filtered

96 candidates to 62 candidates (64.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	96	14	110

Merged error: 0.1b

Counts

110 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (log (exp (- (cos eps) 1))))
0.2b	(+ (* (sin eps) (cos x)) (* (sin x) (log (exp (- (cos eps) 1)))))
1.1b	(log (exp (- (cos eps) 1)))
1.1b	(- (cos eps) 1)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

11.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
33.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (log (exp (- (cos eps) 1)))))
6.0ms	(log (exp (- (cos eps) 1)))
5.0ms	(- (cos eps) 1)

series220.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
132.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (log (exp (- (cos eps) 1)))))
20.0ms	(log (exp (- (cos eps) 1)))
20.0ms	(- (cos eps) 1)

simplify47.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	329	818
1	1195	707
2	5002	697

prune315.0ms

Filtered

112 candidates to 73 candidates (65.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	111	15	126

Merged error: 0.1b

Counts

126 → 15

regimes143.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3261×	body	1280	valid
618.0ms	685×	body	2560	valid
449.0ms	1820×	body	640	valid
124.0ms	776×	body	320	valid
63.0ms	1143×	body	80	valid
34.0ms	315×	body	160	valid