Details

analyze581.0ms (15.2%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
40.6%	56.9%	2.5%	9
46%	49.5%	4.4%	10
50.3%	44.9%	4.8%	11
60.3%	30.5%	9.2%	12
62.9%	25.7%	11.4%	13
65.2%	23.2%	11.7%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	31×	body	128	invalid

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

639×	`associate-/l*_binary64`
549×	`associate-/r*_binary64`
448×	`distribute-neg-frac_binary64`
376×	`cancel-sign-sub-inv_binary64`
359×	`div-sub_binary64`

Counts

1 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	19
2	51	19
3	113	19
4	226	16
5	409	13
6	1281	13
7	3908	13
8	4540	13
9	4743	13

prune3.0ms (0.1%)

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

Error

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.2b	(+.f64 (*.f64 (/.f64 4 y) (-.f64 x z)) 2)
▶	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

Compiler

Compiled 68 to 51 computations (25% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (+.f64 x (*.f64 y 1/4)) z)
0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
0.0b	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)

rewrite60.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

3 → 53

Calls

3 calls:

7.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)
5.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
4.0ms	(-.f64 (+.f64 x (*.f64 y 1/4)) z)

Compiler

Compiled 1168 to 810 computations (30.7% saved)

series105.0ms (2.8%)

Error

0.0b

Counts

3 → 54

Calls

3 calls:

34.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
33.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)
20.0ms	(-.f64 (+.f64 x (*.f64 y 1/4)) z)

Compiler

Compiled 1382 to 1041 computations (24.7% saved)

simplify83.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

583×	`distribute-rgt-in_binary64`
569×	`distribute-lft-in_binary64`
351×	`associate-/l*_binary64`
327×	`times-frac_binary64`
236×	`div-sub_binary64`

Counts

107 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1564
1	357	1501
2	1038	1405
3	4726	1405
4	5473	1405

prune35.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	78	4	82

Error

Counts

82 → 4

Alt Table

Status	Error	Program
	44.0b	(+.f64 1 (/.f64 (.f64 4 (/.f64 (-.f64 (pow.f64 (+.f64 (.f64 1/4 y) x) 3) (pow.f64 z 3)) (+.f64 (.f64 z z) (.f64 (+.f64 (.f64 1/4 y) x) (+.f64 z (+.f64 (.f64 1/4 y) x)))))) y))
	0.2b	(+.f64 1 (/.f64 4 (/.f64 y (+.f64 (*.f64 1/4 y) (-.f64 x z)))))
	1.2b	(+.f64 1 (.f64 (/.f64 4 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (+.f64 (*.f64 1/4 y) (-.f64 x z)) (cbrt.f64 y))))
▶	0.0b	(+.f64 (*.f64 4 (/.f64 (-.f64 x z) y)) 2)

Compiler

Compiled 965 to 608 computations (37% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 4 (/.f64 (-.f64 x z) y))
0.0b	(/.f64 (-.f64 x z) y)

rewrite59.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

41×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

2 → 76

Calls

2 calls:

7.0ms	(*.f64 4 (/.f64 (-.f64 x z) y))
4.0ms	(/.f64 (-.f64 x z) y)

Compiler

Compiled 1152 to 483 computations (58.1% saved)

series54.0ms (1.4%)

Error

Counts

2 → 30

Calls

2 calls:

24.0ms	(*.f64 4 (/.f64 (-.f64 x z) y))
21.0ms	(/.f64 (-.f64 x z) y)

Compiler

Compiled 740 to 553 computations (25.3% saved)

simplify216.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

446×	`associate-/r*_binary64`
310×	`distribute-rgt-neg-out_binary64`
285×	`div-sub_binary64`
282×	`associate-/r/_binary64`
276×	`distribute-lft-neg-out_binary64`

Counts

106 → 64

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	131	1323
1	310	1237
2	813	1237
3	2354	1237
4	4757	1237
5	4967	1237

prune24.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Error

Counts

68 → 4

Alt Table

Status	Error	Program
	0.9b	(+.f64 (.f64 (/.f64 4 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 x z) (cbrt.f64 y))) 2)
▶	0.2b	(+.f64 (*.f64 (sqrt.f64 4) (/.f64 2 (/.f64 y (-.f64 x z)))) 2)
	44.0b	(+.f64 1 (/.f64 (.f64 4 (/.f64 (-.f64 (pow.f64 (+.f64 (.f64 1/4 y) x) 3) (pow.f64 z 3)) (+.f64 (.f64 z z) (.f64 (+.f64 (.f64 1/4 y) x) (+.f64 z (+.f64 (.f64 1/4 y) x)))))) y))
✓	0.0b	(+.f64 (*.f64 4 (/.f64 (-.f64 x z) y)) 2)

Compiler

Compiled 607 to 344 computations (43.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (sqrt.f64 4) (/.f64 2 (/.f64 y (-.f64 x z))))
0.0b	(/.f64 y (-.f64 x z))
0.4b	(/.f64 2 (/.f64 y (-.f64 x z)))

rewrite181.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

252×	`times-frac_binary64`
190×	`add-sqr-sqrt_binary64`
172×	`*-un-lft-identity_binary64`
122×	`add-cube-cbrt_binary64`
68×	`associate-r_binary64`

Counts

3 → 235

Calls

3 calls:

24.0ms	(*.f64 (sqrt.f64 4) (/.f64 2 (/.f64 y (-.f64 x z))))
7.0ms	(/.f64 2 (/.f64 y (-.f64 x z)))
6.0ms	(/.f64 y (-.f64 x z))

Compiler

Compiled 4815 to 2504 computations (48% saved)

series107.0ms (2.8%)

Error

Counts

3 → 51

Calls

3 calls:

40.0ms	(/.f64 2 (/.f64 y (-.f64 x z)))
31.0ms	(/.f64 y (-.f64 x z))
24.0ms	(*.f64 (sqrt.f64 4) (/.f64 2 (/.f64 y (-.f64 x z))))

Compiler

Compiled 1754 to 1342 computations (23.5% saved)

simplify248.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

502×	`times-frac_binary64`
449×	`distribute-rgt-in_binary64`
437×	`distribute-lft-in_binary64`
245×	`associate-/r/_binary64`
211×	`*-commutative_binary64`

Counts

286 → 227

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	5215
1	787	5022
2	2520	4945
3	4957	4945
4	4990	4945
5	5018	4945

prune133.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	227	4	231

Error

Counts

231 → 4

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4))) (.f64 (.f64 2 (/.f64 (-.f64 x z) y)) (sqrt.f64 (cbrt.f64 4)))) 2)
	0.9b	(+.f64 (.f64 (/.f64 4 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 x z) (cbrt.f64 y))) 2)
✓	0.2b	(+.f64 (*.f64 (sqrt.f64 4) (/.f64 2 (/.f64 y (-.f64 x z)))) 2)
✓	0.0b	(+.f64 (*.f64 4 (/.f64 (-.f64 x z) y)) 2)

Compiler

Compiled 3271 to 1690 computations (48.3% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x z) y)
0.3b	(.f64 (.f64 2 (/.f64 (-.f64 x z) y)) (sqrt.f64 (cbrt.f64 4)))
0.4b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4))) (.f64 (.f64 2 (/.f64 (-.f64 x z) y)) (sqrt.f64 (cbrt.f64 4))))
1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

rewrite220.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`add-exp-log_binary64`
29×	`add-cbrt-cube_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 130

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4))) (.f64 (.f64 2 (/.f64 (-.f64 x z) y)) (sqrt.f64 (cbrt.f64 4))))
10.0ms	(.f64 (.f64 2 (/.f64 (-.f64 x z) y)) (sqrt.f64 (cbrt.f64 4)))
6.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
5.0ms	(/.f64 (-.f64 x z) y)

Compiler

Compiled 3241 to 2400 computations (25.9% saved)

series174.0ms (4.6%)

Error

Counts

4 → 45

Calls

4 calls:

76.0ms	(.f64 (sqrt.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4))) (.f64 (.f64 2 (/.f64 (-.f64 x z) y)) (sqrt.f64 (cbrt.f64 4))))
56.0ms	(.f64 (.f64 2 (/.f64 (-.f64 x z) y)) (sqrt.f64 (cbrt.f64 4)))
26.0ms	(/.f64 (-.f64 x z) y)
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

Compiler

Compiled 2171 to 1875 computations (13.6% saved)

simplify94.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-*l/_binary64`
440×	`distribute-rgt-in_binary64`
431×	`distribute-lft-in_binary64`
261×	`associate-l_binary64`
258×	`associate-r_binary64`

Counts

175 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	2988
1	553	2348
2	1673	2340
3	5421	2340

prune83.0ms (2.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	122	4	126

Error

Counts

126 → 4

Alt Table

Status	Error	Program
	0.3b	(+.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4))) (.f64 (.f64 2 (/.f64 (-.f64 x z) y)) (sqrt.f64 (cbrt.f64 4)))) 2)
	0.9b	(+.f64 (.f64 (/.f64 4 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 x z) (cbrt.f64 y))) 2)
	0.2b	(+.f64 (*.f64 (sqrt.f64 4) (/.f64 2 (/.f64 y (-.f64 x z)))) 2)
	0.0b	(+.f64 (*.f64 4 (/.f64 (-.f64 x z) y)) 2)

Compiler

Compiled 1313 to 995 computations (24.2% saved)

regimes430.0ms (11.3%)

Accuracy

Total 0.0b remaining (40.7%)

Threshold costs 0.0b (40.7%)

Compiler

Compiled 7484 to 5658 computations (24.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	24	22
2	32	22
3	38	22
4	43	22
5	46	22
6	47	22
7	45	22

end1.0ms (0%)

Compiler: Compiled 18 to 14 computations (22.2% saved)

sample799.0ms (20.9%)

Algorithm

1×

intervals

Results

421.0ms	8000×	body	128	valid
45.0ms	974×	body	128	invalid

Compiler

Compiled 107 to 83 computations (22.4% saved)

Details

analyze581.0ms (15.2%)

sample26.0ms (0.7%)

simplify62.0ms (1.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite60.0ms (1.6%)

series105.0ms (2.8%)

simplify83.0ms (2.2%)

prune35.0ms (0.9%)

localize6.0ms (0.2%)

rewrite59.0ms (1.5%)

series54.0ms (1.4%)

simplify216.0ms (5.6%)

prune24.0ms (0.6%)

localize8.0ms (0.2%)

rewrite181.0ms (4.7%)

series107.0ms (2.8%)

simplify248.0ms (6.5%)

prune133.0ms (3.5%)

localize14.0ms (0.4%)

rewrite220.0ms (5.8%)

series174.0ms (4.6%)

simplify94.0ms (2.5%)

prune83.0ms (2.2%)

regimes430.0ms (11.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample799.0ms (20.9%)

Profiling