Details

analyze350.0ms (13.3%)

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
12.5%	87.4%	0.1%	4
18.7%	81.1%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	78%	0.1%	7
27.3%	61.6%	11.1%	8
28.5%	60.5%	11.1%	9
32.6%	53.4%	14%	10
40.2%	38.1%	21.7%	11
41.8%	35.8%	22.4%	12
44.5%	29.2%	26.3%	13
47.1%	21.3%	31.6%	14

sample30.0ms (1.1%)

Algorithm

1×

intervals

Results

8.0ms	258×	body	80	invalid
8.0ms	256×	body	80	valid

simplify68.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5057	8

prune6.0ms (0.2%)

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: 7.5b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) (/ y x))
7.1b	(/ (* (cosh x) (/ y x)) z)

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`add-exp-log` `add-cbrt-cube`
13×	`add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-r*`
5×	`pow1` `cbrt-undiv` `cosh-def` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-l` `associate-/r*` `associate-/l/` `add-log-exp`
2×	`frac-times` `associate-r/` `associate-l/` `div-inv` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

3 → 68

Calls

3 calls:

9.0ms	(/ (* (cosh x) (/ y x)) z)
6.0ms	(* (cosh x) (/ y x))
1.0ms	(cosh x)

series46.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ (* (cosh x) (/ y x)) z)
15.0ms	(* (cosh x) (/ y x))
6.0ms	(cosh x)

simplify45.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4959	631
1	4959	631

prune107.0ms (4.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	5	78

Merged error: 0.0b

Counts

78 → 5

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(* (+ (exp x) (exp (neg x))) y)
0.0b	(+ (exp x) (exp (neg x)))
6.3b	(/ (* (+ (exp x) (exp (neg x))) y) (* z (* x 2)))

rewrite25.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-exp-log` `add-cbrt-cube`
10×	`prod-exp` `cbrt-unprod`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt` `associate-l` `add-log-exp`
4×	`associate-*l/`
3×	`flip3-+` `associate-r` `flip-+`
2×	`cosh-undef` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

3 → 62

Calls

3 calls:

12.0ms	(/ (* (+ (exp x) (exp (neg x))) y) (* z (* x 2)))
7.0ms	(* (+ (exp x) (exp (neg x))) y)
4.0ms	(+ (exp x) (exp (neg x)))

series36.0ms (1.4%)

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ (* (+ (exp x) (exp (neg x))) y) (* z (* x 2)))
11.0ms	(* (+ (exp x) (exp (neg x))) y)
3.0ms	(+ (exp x) (exp (neg x)))

simplify53.0ms (2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4957	679
1	4957	679

prune99.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Merged error: 0.0b

Counts

76 → 7

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp x) (exp (neg x))))
0.4b	(* y (sqrt (+ (exp x) (exp (neg x)))))
0.4b	(* (sqrt (+ (exp x) (exp (neg x)))) (* y (sqrt (+ (exp x) (exp (neg x))))))
6.3b	(/ (* (sqrt (+ (exp x) (exp (neg x)))) (* y (sqrt (+ (exp x) (exp (neg x)))))) (* z (* x 2)))

rewrite50.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-div`
22×	`prod-exp` `cbrt-unprod`
18×	`associate-*r/`
16×	`*-un-lft-identity` `sqrt-prod`
15×	`add-sqr-sqrt`
14×	`flip3-+` `flip-+`
12×	`pow1`
11×	`associate-l`
10×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp` `associate-r`
8×	`frac-times` `associate-/l/`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
3×	`cosh-undef` `distribute-lft-out`
2×	`*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 113

Calls

4 calls:

18.0ms	(/ (* (sqrt (+ (exp x) (exp (neg x)))) (* y (sqrt (+ (exp x) (exp (neg x)))))) (* z (* x 2)))
13.0ms	(* (sqrt (+ (exp x) (exp (neg x)))) (* y (sqrt (+ (exp x) (exp (neg x))))))
10.0ms	(* y (sqrt (+ (exp x) (exp (neg x)))))
5.0ms	(sqrt (+ (exp x) (exp (neg x))))

series53.0ms (2%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* (sqrt (+ (exp x) (exp (neg x)))) (* y (sqrt (+ (exp x) (exp (neg x)))))) (* z (* x 2)))
13.0ms	(* y (sqrt (+ (exp x) (exp (neg x)))))
11.0ms	(* (sqrt (+ (exp x) (exp (neg x)))) (* y (sqrt (+ (exp x) (exp (neg x))))))
6.0ms	(sqrt (+ (exp x) (exp (neg x))))

simplify35.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4963	1620
1	4963	1620

prune178.0ms (6.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	126	6	132

Merged error: 0b

Counts

132 → 6

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) y)
0.2b	(* (* (cosh x) y) (/ 1 x))
7.1b	(/ (* (* (cosh x) y) (/ 1 x)) z)

rewrite23.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-exp-log`
36×	`add-cbrt-cube`
25×	`prod-exp`
17×	`add-sqr-sqrt` `div-exp`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`cbrt-unprod`
12×	`times-frac`
11×	`pow1`
9×	`cbrt-undiv`
7×	`associate-*l/`
6×	`cosh-def`
4×	`rec-exp` `1-exp` `associate-l` `pow-prod-down` `associate-/l/` `add-log-exp`
3×	`associate-/r*`
2×	`frac-times` `associate-r/` `un-div-inv` `-commutative` `div-inv`
1×	`frac-2neg` `clear-num` `associate-/l*` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

8.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)
7.0ms	(* (* (cosh x) y) (/ 1 x))
3.0ms	(* (cosh x) y)
1.0ms	(cosh x)

series62.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)
17.0ms	(* (* (cosh x) y) (/ 1 x))
13.0ms	(* (cosh x) y)
6.0ms	(cosh x)

simplify57.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4967	875
1	4967	875

prune119.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	114	6	120

Merged error: 0b

Counts

120 → 6

regimes309.0ms (11.7%)

Accuracy

Total 0.4b remaining (79.2%)

Threshold costs 0.4b (79.2%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	43
1	39	43

end0.0ms (0%)

sample826.0ms (31.3%)

Algorithm

1×

intervals

Results

263.0ms	8000×	body	80	valid
245.0ms	7606×	body	80	invalid

Details

analyze350.0ms (13.3%)

sample30.0ms (1.1%)

simplify68.0ms (2.6%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite18.0ms (0.7%)

series46.0ms (1.8%)

simplify45.0ms (1.7%)

prune107.0ms (4.1%)

localize11.0ms (0.4%)

rewrite25.0ms (0.9%)

series36.0ms (1.4%)

simplify53.0ms (2%)

prune99.0ms (3.8%)

localize13.0ms (0.5%)

rewrite50.0ms (1.9%)

series53.0ms (2%)

simplify35.0ms (1.3%)

prune178.0ms (6.8%)

localize7.0ms (0.3%)

rewrite23.0ms (0.9%)

series62.0ms (2.3%)

simplify57.0ms (2.2%)

prune119.0ms (4.5%)

regimes309.0ms (11.7%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample826.0ms (31.3%)

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