Details

sample88.0ms

Algorithm

intervals

Results

45.0ms	122×	body	1280	valid
14.0ms	19×	body	2560	valid
12.0ms	54×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	27×	body	80	valid
1.0ms	6×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

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: 36.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (tan (+ x eps)) (tan x))
3.6b	(tan (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

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

series50.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(- (tan (+ x eps)) (tan x))
19.0ms	(tan (+ x eps))

simplify56.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4947	335
1	4947	335

prune66.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 14.6b

Counts

32 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

3.0ms	(- 1 (* (tan x) (tan eps)))
5.0ms	(+ (tan x) (tan eps))
6.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series190.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- 1 (* (tan x) (tan eps)))
23.0ms	(+ (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
113.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5294	964

prune148.0ms

Filtered

55 candidates to 74 candidates (-34.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	10	74
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	70	12	82

Merged error: 12.5b

Counts

82 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (+ (cos eps) (* 1 (* (sin x) (/ (neg (sin eps)) (cos x))))))
0.2b	(* (sin x) (/ (neg (sin eps)) (cos x)))
0.3b	(* (sin x) (/ (neg (sin eps)) (cos eps)))
3.8b	(- (/ (sin x) (+ (cos x) (* 1 (* (sin x) (/ (neg (sin eps)) (cos eps)))))) (/ (sin x) (cos x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
81×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
68×	`associate-r`
59×	`add-cube-cbrt`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
16×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `distribute-lft-out--`
7×	`distribute-lft-out`
6×	`neg-mul-1` `associate-l` `add-log-exp`
5×	`div-inv`
4×	`prod-exp` `associate-/r*` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`associate-r/` `distribute-frac-neg` `pow-prod-down` `associate-/r/` `-commutative` `distribute-rgt-neg-out`
1×	`sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `clear-num` `frac-sub` `flip--` `flip-+`

Counts

4 → 166

Calls

4 calls:

6.0ms	(/ (sin eps) (+ (cos eps) (* 1 (* (sin x) (/ (neg (sin eps)) (cos x))))))
16.0ms	(* (sin x) (/ (neg (sin eps)) (cos x)))
13.0ms	(* (sin x) (/ (neg (sin eps)) (cos eps)))
18.0ms	(- (/ (sin x) (+ (cos x) (* 1 (* (sin x) (/ (neg (sin eps)) (cos eps)))))) (/ (sin x) (cos x)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (sin eps) (+ (cos eps) (* 1 (* (sin x) (/ (neg (sin eps)) (cos x))))))
22.0ms	(* (sin x) (/ (neg (sin eps)) (cos x)))
20.0ms	(* (sin x) (/ (neg (sin eps)) (cos eps)))
51.0ms	(- (/ (sin x) (+ (cos x) (* 1 (* (sin x) (/ (neg (sin eps)) (cos eps)))))) (/ (sin x) (cos x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5310	2692

prune286.0ms

Filtered

132 candidates to 178 candidates (-34.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	164	14	178
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	170	20	190

Merged error: 12.4b

Counts

190 → 20

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (neg (sin eps)) (cos x)))
0.3b	(* (sin x) (/ (sin eps) (cos eps)))
0.3b	(* (sin x) (/ (sin eps) (cos eps)))
3.7b	(- (cos x) (- (cos x) (* (sin x) (/ (sin eps) (cos eps)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

60×	`associate-r`
58×	`add-sqr-sqrt`
51×	`times-frac`
43×	`*-un-lft-identity`
41×	`add-cube-cbrt`
19×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l` `add-log-exp`
6×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`cbrt-undiv` `neg-mul-1` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`
2×	`sub-neg` `associate--r+`
1×	`flip3--` `distribute-frac-neg` `distribute-rgt-neg-out` `flip--` `distribute-lft-out--` `associate--r-` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

13.0ms	(* (sin x) (/ (neg (sin eps)) (cos x)))
8.0ms	(* (sin x) (/ (sin eps) (cos eps)))
8.0ms	(* (sin x) (/ (sin eps) (cos eps)))
6.0ms	(- (cos x) (- (cos x) (* (sin x) (/ (sin eps) (cos eps)))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (sin x) (/ (neg (sin eps)) (cos x)))
22.0ms	(* (sin x) (/ (sin eps) (cos eps)))
18.0ms	(* (sin x) (/ (sin eps) (cos eps)))
19.0ms	(- (cos x) (- (cos x) (* (sin x) (/ (sin eps) (cos eps)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4920	1572
1	4920	1572

prune157.0ms

Filtered

107 candidates to 148 candidates (-38.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	9	10	19
Picked	1	0	1
Done	0	0	0
Total	154	14	168

Merged error: 0.1b

Counts

168 → 14

regimes187.0ms

Accuracy

0% (0.2b 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 (1.0ms)

Iter	Nodes	Cost
0	48	70
1	48	70

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	3322×	body	1280	valid
491.0ms	668×	body	2560	valid
384.0ms	1802×	body	640	valid
109.0ms	745×	body	320	valid
50.0ms	1108×	body	80	valid
35.0ms	355×	body	160	valid

Details

sample88.0ms

simplify2.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series50.0ms

simplify56.0ms

prune66.0ms

localize12.0ms

rewrite28.0ms

series190.0ms

simplify37.0ms

prune148.0ms

localize26.0ms

rewrite60.0ms

series127.0ms

simplify55.0ms

prune286.0ms

localize28.0ms

rewrite41.0ms

series78.0ms

simplify55.0ms

prune157.0ms

regimes187.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling