Details

analyze17.2s (73.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0%	0.2%	99.8%	3
0%	0.2%	99.8%	4
0%	0.2%	99.8%	5
0%	0.2%	99.8%	6
0%	0.2%	99.8%	7
0%	0.2%	99.8%	8
0%	0.2%	99.8%	9
0%	0.2%	99.8%	10
0%	0.2%	99.8%	11
0%	0.2%	99.8%	12
0%	0.2%	99.8%	13
0%	0.2%	99.8%	14

sample124.0ms (0.5%)

Algorithm

1×

intervals

Results

54.0ms	130×	body	1280	valid
19.0ms	256×	pre	80	true
14.0ms	57×	body	640	valid
5.0ms	30×	body	320	valid
1.0ms	28×	body	80	valid
1.0ms	11×	body	160	valid

simplify428.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	185	9
1	185	9

prune10.0ms (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: 13.9b

Counts

2 → 1

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
4.1b	(tan (+ y z))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

7.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))
5.0ms	(+ x (- (tan (+ y z)) (tan a)))

series110.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ x (- (tan (+ y z)) (tan a)))
32.0ms	(- (tan (+ y z)) (tan a))
25.0ms	(tan (+ y z))

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4916	561
1	4916	561

prune101.0ms (0.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 0.1b

Counts

50 → 7

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

14.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
13.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))
4.0ms	(+ (tan y) (tan z))

series281.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
115.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
21.0ms	(* (tan y) (tan z))
20.0ms	(+ (tan y) (tan z))

simplify30.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4951	1271
1	4951	1271

prune159.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	75	9	84

Merged error: 0.1b

Counts

84 → 9

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (log (pow (exp (tan y)) (tan z))))) (tan a))
0.2b	(pow (exp (tan y)) (tan z))
0.4b	(exp (tan y))
4.8b	(log (pow (exp (tan y)) (tan z)))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
7×	`log-prod` `add-log-exp`
6×	`unpow-prod-down` `exp-prod`
5×	`pow1` `add-exp-log`
4×	`pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `rem-log-exp`
2×	`pow-to-exp` `pow-exp` `difference-of-squares` `sqr-pow`
1×	`tan-quot` `sub-neg` `flip3--` `times-frac` `diff-log` `log-pow` `frac-sub` `flip--` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

18.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (log (pow (exp (tan y)) (tan z))))) (tan a))
4.0ms	(pow (exp (tan y)) (tan z))
3.0ms	(log (pow (exp (tan y)) (tan z)))
2.0ms	(exp (tan y))

series219.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (log (pow (exp (tan y)) (tan z))))) (tan a))
40.0ms	(log (pow (exp (tan y)) (tan z)))
31.0ms	(pow (exp (tan y)) (tan z))
10.0ms	(exp (tan y))

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4913	915
1	4913	915

prune149.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Merged error: 0.1b

Counts

85 → 8

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(* (sin z) (/ (sin y) (* (cos y) (cos z))))
0.2b	(* (sin z) (/ (sin y) (* (cos y) (cos z))))
0.3b	(/ (sin y) (* (cos y) (cos z)))
0.3b	(/ (sin y) (* (cos y) (cos z)))

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`associate-r`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`prod-exp` `cbrt-unprod`
8×	`pow1` `cbrt-undiv` `div-exp`
6×	`associate-l` `associate-/l*`
4×	`associate-/r/` `cos-mult` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `*-commutative` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

9.0ms	(* (sin z) (/ (sin y) (* (cos y) (cos z))))
9.0ms	(* (sin z) (/ (sin y) (* (cos y) (cos z))))
6.0ms	(/ (sin y) (* (cos y) (cos z)))
6.0ms	(/ (sin y) (* (cos y) (cos z)))

series74.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (sin z) (/ (sin y) (* (cos y) (cos z))))
21.0ms	(* (sin z) (/ (sin y) (* (cos y) (cos z))))
17.0ms	(/ (sin y) (* (cos y) (cos z)))
15.0ms	(/ (sin y) (* (cos y) (cos z)))

simplify56.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5087	1234

prune160.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Merged error: 0.1b

Counts

120 → 8

regimes781.0ms (3.3%)

Accuracy

Total 0.1b remaining (61.9%)

Threshold costs 0.1b (61.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	47
1	108	47

end0.0ms (0%)

sample3.2s (13.6%)

Algorithm

1×

intervals

Results

1.6s	3868×	body	1280	valid
548.0ms	8000×	pre	80	true
480.0ms	2008×	body	640	valid
109.0ms	676×	body	320	valid
60.0ms	1165×	body	80	valid
32.0ms	283×	body	160	valid

Details

analyze17.2s (73.6%)

sample124.0ms (0.5%)

simplify428.0ms (1.8%)

prune10.0ms (0%)

localize13.0ms (0.1%)

rewrite20.0ms (0.1%)

series110.0ms (0.5%)

simplify68.0ms (0.3%)

prune101.0ms (0.4%)

localize16.0ms (0.1%)

rewrite39.0ms (0.2%)

series281.0ms (1.2%)

simplify30.0ms (0.1%)

prune159.0ms (0.7%)

localize21.0ms (0.1%)

rewrite29.0ms (0.1%)

series219.0ms (0.9%)

simplify54.0ms (0.2%)

prune149.0ms (0.6%)

localize29.0ms (0.1%)

rewrite33.0ms (0.1%)

series74.0ms (0.3%)

simplify56.0ms (0.2%)

prune160.0ms (0.7%)

regimes781.0ms (3.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.2s (13.6%)

Profiling