Details

analyze488.0ms (19.2%)

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
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample99.0ms (3.9%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	28×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	11

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

11.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	11.7b	(/.f64 (fma.f64 x (-.f64 y z) x) z)
▶	11.7b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 66 to 38 computations (42.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 (-.f64 y z) 1))
✓	10.9b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

series25.0ms (1%)

Counts

2 → 72

Calls

2 calls:

18.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
7.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 51

Calls

2 calls:

7.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
6.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))

simplify64.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

555×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
516×	`associate-/l*_binary64`
469×	`times-frac_binary64`
227×	`fma-def_binary64`

Counts

123 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1568
1	273	1257
2	1027	1253
3	4803	1253
4	4971	1253

prune62.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	99	5	104

Error

0.0b

Counts

104 → 5

Alt Table

Status	Error	Program
✓	11.7b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
▶	3.3b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))
	31.7b	(/.f64 (.f64 x (-.f64 (.f64 (-.f64 y z) (-.f64 y z)) (.f64 1 1))) (.f64 z (-.f64 (-.f64 y z) 1)))
	11.8b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	3.9b	(*.f64 x (/.f64 (-.f64 (+.f64 1 y) z) z))

Compiler

Compiled 1551 to 694 computations (55.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (+.f64 (-.f64 y z) 1))
✓	3.1b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))

series28.0ms (1.1%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(/.f64 z (+.f64 (-.f64 y z) 1))
13.0ms	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))

rewrite29.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`*-un-lft-identity_binary64`
138×	`times-frac_binary64`
70×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`
32×	`distribute-lft-out_binary64`

Counts

2 → 143

Calls

2 calls:

10.0ms	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))
5.0ms	(/.f64 z (+.f64 (-.f64 y z) 1))

simplify169.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
653×	`fma-def_binary64`
173×	`fma-neg_binary64`
164×	`associate-/r/_binary64`
142×	`distribute-neg-in_binary64`

Counts

203 → 240

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	292	4769
1	700	4591
2	2636	4422
3	4765	4413
4	4988	4413
5	4967	4413

prune141.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	241	4	245

Error

Counts

245 → 4

Alt Table

Status	Error	Program
▶	3.4b	(/.f64 x (*.f64 z (/.f64 1 (+.f64 (-.f64 y z) 1))))
	3.9b	(*.f64 x (/.f64 (-.f64 (+.f64 1 y) z) z))
✓	11.7b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
	7.2b	(*.f64 (/.f64 x z) (+.f64 (-.f64 y z) 1))

Compiler

Compiled 5167 to 2619 computations (49.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 (-.f64 y z) 1))
✓	0.2b	(*.f64 z (/.f64 1 (+.f64 (-.f64 y z) 1)))
✓	3.1b	(/.f64 x (*.f64 z (/.f64 1 (+.f64 (-.f64 y z) 1))))

series42.0ms (1.7%)

Counts

3 → 84

Calls

3 calls:

16.0ms	(*.f64 z (/.f64 1 (+.f64 (-.f64 y z) 1)))
13.0ms	(/.f64 x (*.f64 z (/.f64 1 (+.f64 (-.f64 y z) 1))))
12.0ms	(/.f64 1 (+.f64 (-.f64 y z) 1))

rewrite33.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64`
35×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
31×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 118

Calls

3 calls:

13.0ms	(*.f64 z (/.f64 1 (+.f64 (-.f64 y z) 1)))
8.0ms	(/.f64 x (*.f64 z (/.f64 1 (+.f64 (-.f64 y z) 1))))
6.0ms	(/.f64 1 (+.f64 (-.f64 y z) 1))

simplify109.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

923×	`fma-def_binary64`
266×	`distribute-neg-in_binary64`
208×	`associate-+r+_binary64`
197×	`cancel-sign-sub-inv_binary64`
188×	`times-frac_binary64`

Counts

202 → 223

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	4115
1	750	3820
2	2864	3657
3	4901	3657
4	4974	3657

prune133.0ms (5.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	223	4	227

Error

Counts

227 → 4

Alt Table

Status	Error	Program
✓	3.4b	(/.f64 x (*.f64 z (/.f64 1 (+.f64 (-.f64 y z) 1))))
	3.9b	(*.f64 x (/.f64 (-.f64 (+.f64 1 y) z) z))
✓	11.7b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
▶	1.0b	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)

Compiler

Compiled 4735 to 2852 computations (39.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)
✓	2.7b	(fma.f64 y (/.f64 x z) (/.f64 x z))

series36.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

20.0ms	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)
16.0ms	(fma.f64 y (/.f64 x z) (/.f64 x z))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

3.0ms	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)
0.0ms	(fma.f64 y (/.f64 x z) (/.f64 x z))

simplify80.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
419×	`associate-l_binary64`
343×	`associate-r_binary64`
336×	`fma-def_binary64`
307×	`distribute-rgt-out_binary64`

Counts

113 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1550
1	160	1399
2	607	1157
3	2713	1152
4	4451	1152
5	4961	1152

prune46.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	74	4	78

Error

Counts

78 → 4

Alt Table

Status	Error	Program
✓	3.4b	(/.f64 x (*.f64 z (/.f64 1 (+.f64 (-.f64 y z) 1))))
	3.9b	(*.f64 x (/.f64 (-.f64 (+.f64 1 y) z) z))
✓	11.7b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
✓	1.0b	(-.f64 (fma.f64 y (/.f64 x z) (/.f64 x z)) x)

Compiler

Compiled 1383 to 275 computations (80.1% saved)

regimes190.0ms (7.5%)

Accuracy

Total 1.7b remaining (99.4%)

Threshold costs 0b (0%)

Counts

49 → 1

Compiler

Compiled 3123 to 1922 computations (38.5% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	9	14
2	14	14
3	16	14
4	17	14
5	17	14

end0.0ms (0%)

Compiler: Compiled 13 to 6 computations (53.8% saved)

sample667.0ms (26.3%)

Algorithm

1×

intervals

Results

328.0ms	8000×	body	128	valid
37.0ms	956×	body	128	invalid

Compiler

Compiled 80 to 50 computations (37.5% saved)

Details

analyze488.0ms (19.2%)

sample99.0ms (3.9%)

simplify47.0ms (1.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series25.0ms (1%)

rewrite15.0ms (0.6%)

simplify64.0ms (2.5%)

prune62.0ms (2.5%)

localize5.0ms (0.2%)

series28.0ms (1.1%)

rewrite29.0ms (1.1%)

simplify169.0ms (6.7%)

prune141.0ms (5.6%)

localize6.0ms (0.2%)

series42.0ms (1.7%)

rewrite33.0ms (1.3%)

simplify109.0ms (4.3%)

prune133.0ms (5.3%)

localize5.0ms (0.2%)

series36.0ms (1.4%)

rewrite5.0ms (0.2%)

simplify80.0ms (3.1%)

prune46.0ms (1.8%)

regimes190.0ms (7.5%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample667.0ms (26.3%)

Profiling