Details

analyze100.0ms (1.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample101.0ms (1.9%)

Algorithm

1×

intervals

Results

70.0ms	131×	body	2048	valid
16.0ms	59×	body	1024	valid
5.0ms	37×	body	512	valid
1.0ms	17×	body	256	valid
1.0ms	12×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify85.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

801×	`associate-/l*_binary64`
548×	`unswap-sqr_binary64`
536×	`div-sub_binary64`
451×	`associate-/r*_binary64`
284×	`cancel-sign-sub-inv_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	102	13
5	198	13
6	389	13
7	738	13
8	1255	13
9	3975	13
10	4882	13
11	4992	13
12	4809	13

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

28.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	28.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
3.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

28.7b

Rules

11×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64`
6×	`cancel-sign-sub-inv_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`associate-+l+_binary64`

Counts

2 → 39

Calls

2 calls:

6.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(-.f64 (exp.f64 x) 2)

Compiler

Compiled 634 to 334 computations (47.3% saved)

series21.0ms (0.4%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

7.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

Compiler

Compiled 292 to 218 computations (25.3% saved)

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

554×	`unswap-sqr_binary64`
439×	`cancel-sign-sub-inv_binary64`
350×	`*-commutative_binary64`
274×	`+-commutative_binary64`
267×	`distribute-rgt-in_binary64`

Counts

51 → 36

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	810
1	255	764
2	642	744
3	1892	732
4	2975	732
5	4876	732

prune23.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	3	37

Error

0.0b

Counts

37 → 3

Alt Table

Status	Error	Program
	28.8b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
	28.9b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))))
▶	0.4b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 x x) (.f64 1/20160 (pow.f64 x 8)))))

Compiler

Compiled 517 to 292 computations (43.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 x x) (.f64 1/20160 (pow.f64 x 8)))))
0.0b	(*.f64 1/20160 (pow.f64 x 8))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite121.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
19×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 89

Calls

4 calls:

12.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 x x) (.f64 1/20160 (pow.f64 x 8)))))
4.0ms	(*.f64 1/20160 (pow.f64 x 8))
4.0ms	(*.f64 1/12 (pow.f64 x 4))
4.0ms	(*.f64 1/360 (pow.f64 x 6))

Compiler

Compiled 2450 to 1819 computations (25.8% saved)

series40.0ms (0.8%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

16.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 x x) (.f64 1/20160 (pow.f64 x 8)))))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
6.0ms	(*.f64 1/20160 (pow.f64 x 8))
6.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 667 to 526 computations (21.1% saved)

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

633×	`distribute-rgt-in_binary64`
605×	`distribute-lft-in_binary64`
455×	`unswap-sqr_binary64`
392×	`*-commutative_binary64`
177×	`associate-+r+_binary64`

Counts

110 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	1730
1	366	1634
2	1122	1560
3	3732	1558
4	4842	1558

prune49.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	63	5	68

Error

0.0b

Counts

68 → 5

Alt Table

Status	Error	Program
	28.8b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
	52.0b	(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 12)) (pow.f64 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))) 3)) (+.f64 (.f64 (pow.f64 x 8) 1/144) (.f64 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))) (-.f64 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))) (*.f64 1/12 (pow.f64 x 4))))))
	28.9b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))))
▶	0.4b	(.f64 (sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))))) (sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (*.f64 x x))))))
	19.9b	(cbrt.f64 (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))) 3))

Compiler

Compiled 1488 to 1080 computations (27.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/12 (pow.f64 x 4))
0.1b	(*.f64 1/12 (pow.f64 x 4))
28.9b	(sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))))
28.9b	(sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))))

rewrite167.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64`
14×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

4 → 80

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))))
7.0ms	(sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))))
5.0ms	(*.f64 1/12 (pow.f64 x 4))
4.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 4237 to 3158 computations (25.5% saved)

series90.0ms (1.7%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

26.0ms	(sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))))
26.0ms	(sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))))
10.0ms	(*.f64 1/12 (pow.f64 x 4))
10.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 2156 to 1739 computations (19.3% saved)

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

455×	`distribute-rgt-neg-in_binary64`
444×	`distribute-lft-neg-in_binary64`
426×	`associate-l_binary64`
397×	`associate-r_binary64`
275×	`distribute-rgt-in_binary64`

Counts

104 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	2290
1	256	2218
2	739	2164
3	3182	2164
4	4972	2164

prune102.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	80	5	85

Error

0.0b

Counts

85 → 5

Alt Table

Status	Error	Program
	28.8b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
	52.0b	(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 12)) (pow.f64 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))) 3)) (+.f64 (.f64 (pow.f64 x 8) 1/144) (.f64 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))) (-.f64 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))) (*.f64 1/12 (pow.f64 x 4))))))
	28.9b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))))
✓	0.4b	(.f64 (sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))))) (sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (*.f64 x x))))))
▶	19.9b	(cbrt.f64 (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))) 3))

Compiler

Compiled 3272 to 2415 computations (26.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))) 3)
0.1b	(*.f64 1/12 (pow.f64 x 4))
19.4b	(cbrt.f64 (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))) 3))

rewrite157.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

26×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`
14×	`associate-r_binary64`

Counts

4 → 98

Calls

4 calls:

13.0ms	(pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))) 3)
8.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))) 3))
4.0ms	(*.f64 1/360 (pow.f64 x 6))
4.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 3290 to 2511 computations (23.7% saved)

series60.0ms (1.1%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

17.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))) 3))
14.0ms	(pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))) 3)
12.0ms	(*.f64 1/360 (pow.f64 x 6))
6.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 870 to 709 computations (18.5% saved)

simplify90.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

767×	`distribute-rgt-in_binary64`
733×	`distribute-lft-in_binary64`
244×	`unswap-sqr_binary64`
123×	`associate-l_binary64`
110×	`associate-r_binary64`

Counts

128 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	3642
1	434	3255
2	1346	3196
3	4987	3196

prune74.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	85	5	90

Error

0.0b

Counts

90 → 5

Alt Table

Status	Error	Program
	28.8b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
	52.0b	(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 12)) (pow.f64 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))) 3)) (+.f64 (.f64 (pow.f64 x 8) 1/144) (.f64 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))) (-.f64 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))) (*.f64 1/12 (pow.f64 x 4))))))
	28.9b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))))
	0.4b	(.f64 (sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x))))) (sqrt.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (*.f64 x x))))))
	19.9b	(cbrt.f64 (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 x x)))) 3))

Compiler

Compiled 1675 to 1251 computations (25.3% saved)

regimes221.0ms (4.1%)

Accuracy

Total 0.5b remaining (92.8%)

Threshold costs 0.5b (92.8%)

Compiler

Compiled 5599 to 4218 computations (24.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	31
1	29	31
2	28	31

end1.0ms (0%)

Compiler: Compiled 22 to 17 computations (22.7% saved)

sample3.5s (65.6%)

Algorithm

1×

intervals

Results

2.4s	4172×	body	2048	valid
520.0ms	1963×	body	1024	valid
155.0ms	1004×	body	512	valid
44.0ms	497×	body	256	valid
16.0ms	364×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 222 to 164 computations (26.1% saved)

Details

analyze100.0ms (1.9%)

sample101.0ms (1.9%)

simplify85.0ms (1.6%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite56.0ms (1%)

series21.0ms (0.4%)

simplify68.0ms (1.3%)

prune23.0ms (0.4%)

localize12.0ms (0.2%)

rewrite121.0ms (2.2%)

series40.0ms (0.8%)

simplify78.0ms (1.5%)

prune49.0ms (0.9%)

localize16.0ms (0.3%)

rewrite167.0ms (3.1%)

series90.0ms (1.7%)

simplify93.0ms (1.7%)

prune102.0ms (1.9%)

localize14.0ms (0.3%)

rewrite157.0ms (2.9%)

series60.0ms (1.1%)

simplify90.0ms (1.7%)

prune74.0ms (1.4%)

regimes221.0ms (4.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample3.5s (65.6%)

Profiling