Details

analyze32.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample34.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	150×	body	128	valid
8.0ms	39×	body	1024	valid
7.0ms	46×	body	512	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

44×	`sub-neg_binary64`
41×	`cancel-sign-sub-inv_binary64`
28×	`distribute-rgt-in_binary64`
28×	`unsub-neg_binary64`
25×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	59	22
4	101	22
5	165	22
6	198	22
7	217	22
8	216	22
9	192	22

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

10.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 48 to 39 computations (18.8% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
1.8b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite175.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

10.0b

Rules

94×	`*-un-lft-identity_binary64`
62×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
26×	`cancel-sign-sub-inv_binary64`

Counts

3 → 124

Calls

3 calls:

36.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
16.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
5.0ms	(/.f64 1 (-.f64 x 1))

Compiler

Compiled 2589 to 2082 computations (19.6% saved)

series56.0ms (1.3%)

Error

0.1b

Counts

3 → 35

Calls

3 calls:

15.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
11.0ms	(/.f64 1 (-.f64 x 1))
9.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))

Compiler

Compiled 1064 to 872 computations (18% saved)

simplify118.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

418×	`associate-l_binary64`
325×	`distribute-rgt-in_binary64`
282×	`associate-*l/_binary64`
280×	`associate-/l*_binary64`
273×	`distribute-lft-in_binary64`

Counts

159 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	2761
1	602	2675
2	1688	2638
3	4547	2636
4	5057	2636

prune54.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	2	143

Error

0.1b

Counts

143 → 2

Alt Table

Status	Error	Program
	35.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
▶	28.7b	(+.f64 (/.f64 -2 x) (*.f64 -2 (+.f64 x (pow.f64 x 3))))

Compiler

Compiled 1602 to 1255 computations (21.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (/.f64 -2 x) (*.f64 -2 (+.f64 x (pow.f64 x 3))))
0.0b	(+.f64 x (pow.f64 x 3))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

6×	`add-log-exp_binary64`
5×	`*-un-lft-identity_binary64`
3×	`flip-+_binary64`
3×	`flip3-+_binary64`
2×	`associate-+r+_binary64`

Counts

2 → 30

Calls

2 calls:

5.0ms	(+.f64 (/.f64 -2 x) (*.f64 -2 (+.f64 x (pow.f64 x 3))))
4.0ms	(+.f64 x (pow.f64 x 3))

Compiler

Compiled 612 to 447 computations (27% saved)

series31.0ms (0.8%)

Error

0.1b

Counts

2 → 15

Calls

2 calls:

19.0ms	(+.f64 (/.f64 -2 x) (*.f64 -2 (+.f64 x (pow.f64 x 3))))
8.0ms	(+.f64 x (pow.f64 x 3))

Compiler

Compiled 334 to 264 computations (21% saved)

simplify88.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

789×	`associate-l_binary64`
658×	`associate-r_binary64`
459×	`distribute-rgt-in_binary64`
431×	`distribute-lft-in_binary64`
358×	`unsub-neg_binary64`

Counts

45 → 27

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	754
1	248	672
2	796	663
3	4020	660
4	4954	660
5	4963	660

prune14.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	27	2	29

Error

0.1b

Counts

29 → 2

Alt Table

Status	Error	Program
▶	35.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
✓	28.7b	(+.f64 (/.f64 -2 x) (*.f64 -2 (+.f64 x (pow.f64 x 3))))

Compiler

Compiled 458 to 339 computations (26% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 2 (pow.f64 x 5))
0.1b	(/.f64 2 (pow.f64 x 9))
0.1b	(/.f64 2 (pow.f64 x 3))
0.2b	(/.f64 2 (pow.f64 x 7))

rewrite239.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

99×	`times-frac_binary64`
77×	`*-un-lft-identity_binary64`
77×	`add-sqr-sqrt_binary64`
77×	`add-cube-cbrt_binary64`
48×	`unpow-prod-down_binary64`

Counts

4 → 200

Calls

4 calls:

4.0ms	(/.f64 2 (pow.f64 x 3))
3.0ms	(/.f64 2 (pow.f64 x 9))
3.0ms	(/.f64 2 (pow.f64 x 7))
3.0ms	(/.f64 2 (pow.f64 x 5))

Compiler

Compiled 5603 to 4624 computations (17.5% saved)

series38.0ms (0.9%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 2 (pow.f64 x 9))
10.0ms	(/.f64 2 (pow.f64 x 7))
8.0ms	(/.f64 2 (pow.f64 x 5))
7.0ms	(/.f64 2 (pow.f64 x 3))

Compiler

Compiled 600 to 500 computations (16.7% saved)

simplify182.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

564×	`times-frac_binary64`
540×	`associate-l_binary64`
482×	`log-prod_binary64`
390×	`associate-/l/_binary64`
380×	`associate-/l*_binary64`

Counts

212 → 121

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	285	3034
1	473	2914
2	1357	2858
3	4169	2802
4	4460	2726
5	4977	2726
6	4904	2726

prune67.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	117	6	123

Error

0.0b

Counts

123 → 6

Alt Table

Status	Error	Program
▶	35.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3))) (/.f64 2 (pow.f64 x 9)))))
✓	28.7b	(+.f64 (/.f64 -2 x) (*.f64 -2 (+.f64 x (pow.f64 x 3))))
✓	35.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
	51.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 (pow.f64 x 3/2)) (sqrt.f64 (pow.f64 x 3))) (/.f64 2 (pow.f64 x 9)))))
	35.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) (pow.f64 (cbrt.f64 x) 3)) (/.f64 2 (pow.f64 x 9)))))
	35.5b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (.f64 (.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 2) x)) (/.f64 (cbrt.f64 2) (*.f64 x x))) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 1884 to 1558 computations (17.3% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3)))
0.2b	(/.f64 2 (pow.f64 x 7))
0.5b	(/.f64 2 (*.f64 x x))
39.3b	(cbrt.f64 (pow.f64 x 3))

rewrite319.0ms (7.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

177×	`times-frac_binary64`
108×	`cbrt-prod_binary64`
89×	`*-un-lft-identity_binary64`
89×	`add-sqr-sqrt_binary64`
89×	`add-cube-cbrt_binary64`

Counts

4 → 231

Calls

4 calls:

17.0ms	(/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3)))
5.0ms	(/.f64 2 (pow.f64 x 7))
3.0ms	(/.f64 2 (*.f64 x x))
2.0ms	(cbrt.f64 (pow.f64 x 3))

Compiler

Compiled 7448 to 5611 computations (24.7% saved)

series44.0ms (1.1%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3)))
9.0ms	(/.f64 2 (*.f64 x x))
9.0ms	(/.f64 2 (pow.f64 x 7))
8.0ms	(cbrt.f64 (pow.f64 x 3))

Compiler

Compiled 825 to 666 computations (19.3% saved)

simplify233.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

565×	`associate-/l*_binary64`
524×	`associate-/r/_binary64`
487×	`associate-*l/_binary64`
366×	`associate-*r/_binary64`
291×	`unswap-sqr_binary64`

Counts

243 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	296	4007
1	447	3866
2	1491	3793
3	4486	3604
4	4633	3604
5	4981	3604
6	4941	3604

prune102.0ms (2.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	193	7	200

Error

0.0b

Counts

200 → 7

Alt Table

Status	Error	Program
	35.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3))) (/.f64 2 (pow.f64 x 9)))))
	28.7b	(+.f64 (/.f64 -2 x) (*.f64 -2 (+.f64 x (pow.f64 x 3))))
	35.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
	51.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 (pow.f64 x 3/2)) (sqrt.f64 (pow.f64 x 3))) (/.f64 2 (pow.f64 x 9)))))
	35.2b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (.f64 (/.f64 1 x) (/.f64 2 (.f64 x x))) (/.f64 2 (pow.f64 x 9)))))
	35.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) (pow.f64 (cbrt.f64 x) 3)) (/.f64 2 (pow.f64 x 9)))))
	35.5b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (.f64 (.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 2) x)) (/.f64 (cbrt.f64 2) (*.f64 x x))) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 2631 to 1990 computations (24.4% saved)

regimes922.0ms (22.2%)

Accuracy

Total 0.0b remaining (17.6%)

Threshold costs 0.0b (17.6%)

Compiler

Compiled 11994 to 9720 computations (19% saved)

bsearch51.0ms (1.2%)

Steps

Iters	Range		Point
11	1.8304986078710816e-20	2167.5366474301054	0.9952177512660615
9	-81.46946986698865	-0.0009693369695234871	-0.9950424650401456

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	104
1	51	104
2	53	104
3	54	104
4	54	104

end2.0ms (0%)

Compiler: Compiled 71 to 53 computations (25.4% saved)

sample1.2s (29.7%)

Algorithm

1×

intervals

Results

279.0ms	4406×	body	128	valid
259.0ms	1361×	body	1024	valid
225.0ms	1490×	body	512	valid
72.0ms	743×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 273 to 216 computations (20.9% saved)

Details

analyze32.0ms (0.8%)

sample34.0ms (0.8%)

simplify16.0ms (0.4%)

prune2.0ms (0%)

localize12.0ms (0.3%)

rewrite175.0ms (4.2%)

series56.0ms (1.3%)

simplify118.0ms (2.9%)

prune54.0ms (1.3%)

localize6.0ms (0.1%)

rewrite29.0ms (0.7%)

series31.0ms (0.8%)

simplify88.0ms (2.1%)

prune14.0ms (0.3%)

localize21.0ms (0.5%)

rewrite239.0ms (5.8%)

series38.0ms (0.9%)

simplify182.0ms (4.4%)

prune67.0ms (1.6%)

localize21.0ms (0.5%)

rewrite319.0ms (7.7%)

series44.0ms (1.1%)

simplify233.0ms (5.6%)

prune102.0ms (2.5%)

regimes922.0ms (22.2%)

bsearch51.0ms (1.2%)

simplify8.0ms (0.2%)

end2.0ms (0%)

sample1.2s (29.7%)

Profiling