Details

analyze814.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample91.0ms

Algorithm

intervals

Results

47.0ms	111×	body	1280	valid
18.0ms	22×	body	2560	valid
11.0ms	54×	body	640	valid
3.0ms	23×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	30×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	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: 38.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ x eps)) (tan x))
3.4b	(tan (+ x eps))

rewrite11.0ms

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 → 24

Calls

2 calls:

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

series41.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify46.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune65.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	21	9	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	9	31

Merged error: 15.7b

Counts

31 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

9.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series201.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(+ (tan x) (tan eps))
22.0ms	(* (tan x) (tan eps))
101.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5109	1560

prune168.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	13	97
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	90	16	106

Merged error: 15.6b

Counts

106 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
8.9b	(cbrt (* (tan x) (tan eps)))
8.9b	(cbrt (* (tan x) (tan eps)))
8.9b	(cbrt (* (tan x) (tan eps)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`tan-quot`
9×	`add-sqr-sqrt` `cbrt-div`
6×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 51

Calls

4 calls:

12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
4.0ms	(cbrt (* (tan x) (tan eps)))
4.0ms	(cbrt (* (tan x) (tan eps)))
4.0ms	(cbrt (* (tan x) (tan eps)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
38.0ms	(cbrt (* (tan x) (tan eps)))
38.0ms	(cbrt (* (tan x) (tan eps)))
40.0ms	(cbrt (* (tan x) (tan eps)))

simplify43.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4946	874
1	4946	874

prune115.0ms

Filtered

50 candidates to 63 candidates (-26.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	63	16	79

Merged error: 15.6b

Counts

79 → 16

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin eps) (/ (sin x) (* (cos x) (cos eps))))
0.2b	(/ (sin x) (* (cos x) (cos eps)))
0.2b	(/ (sin x) (* (cos x) (cos eps)))
3.3b	(+ (/ (sin x) (* (cos x) (- 1 (* (sin eps) (/ (sin x) (* (cos x) (cos eps))))))) (- (/ (sin eps) (* (cos eps) (- 1 (* (sin eps) (/ (sin x) (* (cos x) (cos eps))))))) (/ (sin x) (cos x))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
16×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`times-frac` `add-log-exp`
8×	`associate-r`
6×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`associate-l` `frac-add` `associate-/r/` `cos-mult` `div-inv`
2×	`frac-2neg` `clear-num` `associate-/r*` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+r-` `sub-neg` `associate-+r+` `flip3--` `flip3-+` `diff-log` `associate-r/` `pow-prod-down` `-commutative` `frac-sub` `flip--` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

9.0ms	(* (sin eps) (/ (sin x) (* (cos x) (cos eps))))
6.0ms	(/ (sin x) (* (cos x) (cos eps)))
6.0ms	(/ (sin x) (* (cos x) (cos eps)))
27.0ms	(+ (/ (sin x) (* (cos x) (- 1 (* (sin eps) (/ (sin x) (* (cos x) (cos eps))))))) (- (/ (sin eps) (* (cos eps) (- 1 (* (sin eps) (/ (sin x) (* (cos x) (cos eps))))))) (/ (sin x) (cos x))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (sin eps) (/ (sin x) (* (cos x) (cos eps))))
15.0ms	(/ (sin x) (* (cos x) (cos eps)))
16.0ms	(/ (sin x) (* (cos x) (cos eps)))
106.0ms	(+ (/ (sin x) (* (cos x) (- 1 (* (sin eps) (/ (sin x) (* (cos x) (cos eps))))))) (- (/ (sin eps) (* (cos eps) (- 1 (* (sin eps) (/ (sin x) (* (cos x) (cos eps))))))) (/ (sin x) (cos x))))

simplify56.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4990	2269
1	4990	2269

prune109.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	103	16	119

Merged error: 15.6b

Counts

119 → 16

regimes223.0ms

Accuracy

87.7% (0.9b remaining)

Error of 15.9b against oracle of 15.0b and baseline of 22.4b

bsearch76.0ms

Steps

Iters	Range		Point
9	1.1397706199786864e-65	6.179539952642816e-57	6.370884799891205e-62
9	-6.913421128114668e-36	-7.818557983885315e-45	-1.2303582437088547e-37

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	48
1	66	48

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3343×	body	1280	valid
583.0ms	659×	body	2560	valid
383.0ms	1745×	body	640	valid
119.0ms	803×	body	320	valid
47.0ms	1075×	body	80	valid
36.0ms	375×	body	160	valid

Details

analyze814.0ms

sample91.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series41.0ms

simplify46.0ms

prune65.0ms

localize11.0ms

rewrite33.0ms

series201.0ms

simplify48.0ms

prune168.0ms

localize16.0ms

rewrite25.0ms

series220.0ms

simplify43.0ms

prune115.0ms

localize23.0ms

rewrite50.0ms

series159.0ms

simplify56.0ms

prune109.0ms

regimes223.0ms

bsearch76.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling