Details

analyze330.0ms (13.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

sample30.0ms (1.2%)

Algorithm

1×

intervals

Results

10.0ms	55×	body	1280	valid
8.0ms	65×	body	640	valid
2.0ms	95×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	19×	body	160	valid

simplify74.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4999	7
1	4999	7

prune5.0ms (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: 40.7b

Counts

2 → 1

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1.0))
5.1b	(- (exp x) 1.0)

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

6.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series8.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ (exp x) (- (exp x) 1.0))
2.0ms	(- (exp x) 1.0)

simplify60.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5019	574

prune97.0ms (4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Merged error: 0.0b

Counts

57 → 5

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (+ x (* x (* x (+ 1/2 (* x 1/6))))))
0.0b	(* x (* x (+ 1/2 (* x 1/6))))
0.0b	(* x (+ 1/2 (* x 1/6)))
0.3b	(* x 1/6)

rewrite22.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-cbrt-cube`
14×	`add-exp-log`
13×	`pow1`
9×	`times-frac` `associate-l`
7×	`associate-r`
6×	`associate-*r/`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `-commutative` `flip-+` `associate-/l*`
2×	`associate-/r/` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 93

Calls

4 calls:

6.0ms	(* x (* x (+ 1/2 (* x 1/6))))
5.0ms	(* x (+ 1/2 (* x 1/6)))
5.0ms	(/ (exp x) (+ x (* x (* x (+ 1/2 (* x 1/6))))))
4.0ms	(* x 1/6)

series19.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

6.0ms	(* x (* x (+ 1/2 (* x 1/6))))
5.0ms	(* x (+ 1/2 (* x 1/6)))
5.0ms	(/ (exp x) (+ x (* x (* x (+ 1/2 (* x 1/6))))))
2.0ms	(* x 1/6)

simplify53.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4920	1226
1	4920	1226

prune163.0ms (6.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Merged error: 0.0b

Counts

110 → 5

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (+ (* x 1/12) (/ 1 x)))
0.0b	(+ (* x 1/12) (/ 1 x))
0.3b	(* x 1/12)

rewrite18.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`sum-log`
3×	`associate-r` `associate-l`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

9.0ms	(+ 1/2 (+ (* x 1/12) (/ 1 x)))
5.0ms	(+ (* x 1/12) (/ 1 x))
3.0ms	(* x 1/12)

series8.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (* x 1/12) (/ 1 x))
2.0ms	(+ 1/2 (+ (* x 1/12) (/ 1 x)))
2.0ms	(* x 1/12)

simplify45.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4846	420
1	4846	420

prune88.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	50	7	57

Merged error: 0.0b

Counts

57 → 7

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (* x 1/6) 1/2))
0.1b	(pow (/ (exp x) (+ x (* x (* x (+ (* x 1/6) 1/2))))) 3)
0.3b	(* x 1/6)
24.7b	(cbrt (pow (/ (exp x) (+ x (* x (* x (+ (* x 1/6) 1/2))))) 3))

rewrite29.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `*-un-lft-identity`
36×	`cbrt-prod` `times-frac`
30×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube`
10×	`add-exp-log`
9×	`pow1`
8×	`associate-/r/`
6×	`associate-r` `associate-l`
5×	`flip3-+` `flip-+`
4×	`div-inv` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `unpow3` `associate-r/` `pow-prod-down` `pow-exp` `prod-exp` `-commutative` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `cbrt-div` `pow-pow` `distribute-lft-in` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 136

Calls

4 calls:

7.0ms	(pow (/ (exp x) (+ x (* x (* x (+ (* x 1/6) 1/2))))) 3)
7.0ms	(cbrt (pow (/ (exp x) (+ x (* x (* x (+ (* x 1/6) 1/2))))) 3))
6.0ms	(* x (+ (* x 1/6) 1/2))
5.0ms	(* x 1/6)

series22.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow (/ (exp x) (+ x (* x (* x (+ (* x 1/6) 1/2))))) 3)
6.0ms	(cbrt (pow (/ (exp x) (+ x (* x (* x (+ (* x 1/6) 1/2))))) 3))
5.0ms	(* x (+ (* x 1/6) 1/2))
2.0ms	(* x 1/6)

simplify44.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5843	2756

prune296.0ms (12.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	148	7	155

Merged error: 0.0b

Counts

155 → 7

regimes118.0ms (4.8%)

Accuracy

Total 0.6b remaining (97.5%)

Threshold costs 0.6b (97.5%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	39
1	38	39

end0.0ms (0%)

sample878.0ms (35.8%)

Algorithm

1×

intervals

Results

405.0ms	2300×	body	1280	valid
190.0ms	1640×	body	640	valid
68.0ms	2814×	body	80	valid
64.0ms	819×	body	320	valid
24.0ms	427×	body	160	valid
0.0ms	2×	body	1280	invalid

Details

analyze330.0ms (13.5%)

sample30.0ms (1.2%)

simplify74.0ms (3%)

prune5.0ms (0.2%)

localize7.0ms (0.3%)

rewrite11.0ms (0.5%)

series8.0ms (0.3%)

simplify60.0ms (2.4%)

prune97.0ms (4%)

localize9.0ms (0.4%)

rewrite22.0ms (0.9%)

series19.0ms (0.8%)

simplify53.0ms (2.2%)

prune163.0ms (6.6%)

localize5.0ms (0.2%)

rewrite18.0ms (0.8%)

series8.0ms (0.3%)

simplify45.0ms (1.8%)

prune88.0ms (3.6%)

localize12.0ms (0.5%)

rewrite29.0ms (1.2%)

series22.0ms (0.9%)

simplify44.0ms (1.8%)

prune296.0ms (12.1%)

regimes118.0ms (4.8%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample878.0ms (35.8%)

Profiling