Details

analyze799.0ms (14.7%)

Algorithm

1×

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

sample99.0ms (1.8%)

Algorithm

1×

intervals

Results

45.0ms	112×	body	1280	valid
25.0ms	29×	body	2560	valid
15.0ms	55×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	36×	body	80	valid
0.0ms	4×	body	160	valid

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune6.0ms (0.1%)

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: 38.2b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(- (tan (+ x eps)) (tan x))
5.9b	(tan (+ x eps))

rewrite11.0ms (0.2%)

Algorithm

1×	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:

6.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series42.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune65.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 17.3b

Counts

31 → 8

localize11.0ms (0.2%)

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))
1.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite31.0ms (0.6%)

Algorithm

1×	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:

12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
4.0ms	(+ (tan x) (tan eps))

series192.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
53.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(* (tan x) (tan eps))
20.0ms	(+ (tan x) (tan eps))

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5109	1560

prune189.0ms (3.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	85	12	97
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	90	15	105

Merged error: 17.2b

Counts

105 → 15

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(* (sin eps) (/ (sin x) (* (cos x) (cos eps))))
0.3b	(/ (sin x) (* (cos x) (cos eps)))
0.3b	(/ (sin x) (* (cos x) (cos eps)))
1.6b	(+ (/ (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))))

rewrite47.0ms (0.9%)

Algorithm

1×	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:

25.0ms	(+ (/ (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))))
9.0ms	(* (sin eps) (/ (sin x) (* (cos x) (cos eps))))
5.0ms	(/ (sin x) (* (cos x) (cos eps)))
5.0ms	(/ (sin x) (* (cos x) (cos eps)))

series151.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (/ (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))))
22.0ms	(* (sin eps) (/ (sin x) (* (cos x) (cos eps))))
16.0ms	(/ (sin x) (* (cos x) (cos eps)))
14.0ms	(/ (sin x) (* (cos x) (cos eps)))

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4990	2269
1	4990	2269

prune207.0ms (3.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	101	17	118

Merged error: 17.1b

Counts

118 → 17

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan eps))
0.6b	(cbrt (tan eps))
0.6b	(cbrt (tan eps))
1.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (* (cbrt (tan eps)) (cbrt (tan eps)))) (cbrt (tan eps))))) (tan x))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

13.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (* (cbrt (tan eps)) (cbrt (tan eps)))) (cbrt (tan eps))))) (tan x))
2.0ms	(cbrt (tan eps))
2.0ms	(cbrt (tan eps))
2.0ms	(cbrt (tan eps))

series175.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (* (cbrt (tan eps)) (cbrt (tan eps)))) (cbrt (tan eps))))) (tan x))
25.0ms	(cbrt (tan eps))
24.0ms	(cbrt (tan eps))
24.0ms	(cbrt (tan eps))

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4868	730
1	4868	730

prune74.0ms (1.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	63	17	80

Merged error: 17.1b

Counts

80 → 17

regimes253.0ms (4.7%)

Accuracy

Total 1.1b remaining (7.1%)

Threshold costs 0b (0%)

bsearch74.0ms (1.4%)

Steps

Iters	Range		Point
8	5.2770683470140184e-73	3.334381069793267e-68	3.2766669081460135e-68
6	-5.131411321846519e-113	-4.639803412087382e-114	-5.059410338124564e-113

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	48
1	66	48

end0.0ms (0%)

sample2.7s (50.4%)

Algorithm

1×

intervals

Results

1.3s	3328×	body	1280	valid
563.0ms	640×	body	2560	valid
432.0ms	1848×	body	640	valid
115.0ms	749×	body	320	valid
54.0ms	1114×	body	80	valid
32.0ms	321×	body	160	valid

Details

analyze799.0ms (14.7%)

sample99.0ms (1.8%)

simplify4.0ms (0.1%)

prune6.0ms (0.1%)

localize9.0ms (0.2%)

rewrite11.0ms (0.2%)

series42.0ms (0.8%)

simplify46.0ms (0.9%)

prune65.0ms (1.2%)

localize11.0ms (0.2%)

rewrite31.0ms (0.6%)

series192.0ms (3.5%)

simplify50.0ms (0.9%)

prune189.0ms (3.5%)

localize24.0ms (0.4%)

rewrite47.0ms (0.9%)

series151.0ms (2.8%)

simplify54.0ms (1%)

prune207.0ms (3.8%)

localize15.0ms (0.3%)

rewrite19.0ms (0.3%)

series175.0ms (3.2%)

simplify44.0ms (0.8%)

prune74.0ms (1.4%)

regimes253.0ms (4.7%)

bsearch74.0ms (1.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (50.4%)

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