Details

analyze1.4s (13.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample235.0ms (2.3%)

Algorithm

1×

intervals

Results

133.0ms	46×	body	2560	valid
62.0ms	96×	body	1280	valid
17.0ms	61×	body	640	valid
6.0ms	15×	body	160	valid
4.0ms	22×	body	320	valid
1.0ms	16×	body	80	valid

simplify463.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

prune7.0ms (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: 33.7b

Counts

2 → 1

localize24.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.2b	(- x (sin x))
2.2b	(- x (tan x))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 78

Calls

3 calls:

7.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
3.0ms	(- x (sin x))

series38.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

20.0ms	(- x (tan x))
13.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune120.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 0.1b

Counts

88 → 5

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
0.1b	(* x (* x 9/40))
0.2b	(* x 9/40)
15.1b	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

8.0ms	(* (pow x 4) -27/2800)
7.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))
4.0ms	(* x (* x 9/40))
3.0ms	(* x 9/40)

series14.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))
4.0ms	(* (pow x 4) -27/2800)
3.0ms	(* x (* x 9/40))
2.0ms	(* x 9/40)

simplify56.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4903	646
1	4903	646

prune164.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	86	5	91

Merged error: 0.1b

Counts

91 → 5

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (- x (sin x)) (- x (tan x))))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
2.2b	(- x (sin x))
2.2b	(- x (tan x))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt` `*-un-lft-identity`
62×	`exp-prod`
50×	`times-frac`
32×	`log-pow`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
9×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
3×	`log-prod`
2×	`sub-neg` `exp-diff` `diff-log` `div-sub` `div-inv`
1×	`log-div` `rem-log-exp` `rem-exp-log`

Counts

4 → 110

Calls

4 calls:

11.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
9.0ms	(exp (/ (- x (sin x)) (- x (tan x))))
3.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series45.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(exp (/ (- x (sin x)) (- x (tan x))))
13.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
10.0ms	(- x (tan x))
5.0ms	(- x (sin x))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4919	1379
1	4919	1379

prune171.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	122	5	127

Merged error: 0.0b

Counts

127 → 5

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
2.2b	(- x (tan x))
2.2b	(- x (tan x))
2.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 91

Calls

4 calls:

28.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(/ (sin x) (- x (tan x)))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series63.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
12.0ms	(- x (tan x))
11.0ms	(/ (sin x) (- x (tan x)))
10.0ms	(- x (tan x))

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5028	1430

prune110.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	104	4	108

Merged error: 0.0b

Counts

108 → 4

regimes49.0ms (0.5%)

Accuracy

Total 0.0b remaining (23.2%)

Threshold costs 0.0b (23.2%)

bsearch46.0ms (0.4%)

Steps

Iters	Range		Point
10	4.6803344332587176e-14	0.1717659009207132	0.02727798752832581
9	-0.03849650220869293	-9.559634869391715e-10	-0.029873394671195968

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	65
1	64	65

end0.0ms (0%)

sample6.8s (67.2%)

Algorithm

1×

intervals

Results

4.2s	1586×	body	2560	valid
1.6s	2669×	body	1280	valid
565.0ms	1991×	body	640	valid
171.0ms	936×	body	320	valid
64.0ms	481×	body	160	valid
32.0ms	337×	body	80	valid

Details

analyze1.4s (13.8%)

sample235.0ms (2.3%)

simplify463.0ms (4.5%)

prune7.0ms (0.1%)

localize24.0ms (0.2%)

rewrite20.0ms (0.2%)

series38.0ms (0.4%)

simplify64.0ms (0.6%)

prune120.0ms (1.2%)

localize9.0ms (0.1%)

rewrite24.0ms (0.2%)

series14.0ms (0.1%)

simplify56.0ms (0.5%)

prune164.0ms (1.6%)

localize14.0ms (0.1%)

rewrite32.0ms (0.3%)

series45.0ms (0.4%)

simplify68.0ms (0.7%)

prune171.0ms (1.7%)

localize10.0ms (0.1%)

rewrite43.0ms (0.4%)

series63.0ms (0.6%)

simplify49.0ms (0.5%)

prune110.0ms (1.1%)

regimes49.0ms (0.5%)

bsearch46.0ms (0.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.8s (67.2%)

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