Details

analyze553.0ms (15.8%)

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
0%	99.9%	0.1%	7
0%	99.9%	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)

sample1.3s (38.4%)

Results

1.1s	8256×	body	128	valid
115.0ms	1000×	body	128	invalid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify127.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

724×	`div-sub_binary64`
708×	`fma-neg_binary64`
609×	`sub-neg_binary64`
598×	`times-frac_binary64`
477×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	17
2	55	15
3	125	15
4	274	15
5	564	11
6	1031	11
7	1668	11
8	2410	11
9	3506	11
10	4269	11
11	4538	11
12	4833	11
13	4950	11
14	4672	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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(fma.f64 (/.f64 4 y) (-.f64 x z) 4)
▶	0.1b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y))

Compiler

Compiled 78 to 57 computations (26.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y 3/4))
✓	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y))
✓	0.0b	(-.f64 (+.f64 x (*.f64 y 3/4)) z)
✓	0.1b	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y)

series43.0ms (1.2%)

Counts

4 → 132

Calls

4 calls:

18.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y)
16.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y))
5.0ms	(-.f64 (+.f64 x (*.f64 y 3/4)) z)
3.0ms	(+.f64 x (*.f64 y 3/4))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-log-exp_binary64`
9×	`prod-diff_binary64`

Counts

4 → 90

Calls

4 calls:

10.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y)
5.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y))
4.0ms	(-.f64 (+.f64 x (*.f64 y 3/4)) z)
2.0ms	(+.f64 x (*.f64 y 3/4))

simplify71.0ms (2%)

Algorithm

1×	egg-herbie

Rules

622×	`distribute-rgt-in_binary64`
614×	`fma-def_binary64`
601×	`distribute-lft-in_binary64`
327×	`times-frac_binary64`
139×	`cancel-sign-sub-inv_binary64`

Counts

222 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	2475
1	458	2396
2	1494	2220
3	5136	2220

prune118.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	168	3	171

Error

Counts

171 → 3

Alt Table

Status	Error	Program
	0.3b	(+.f64 1 (/.f64 4 (/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z))))
▶	0.0b	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 4) (.f64 4 (/.f64 z y)))
✓	0.1b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y))

Compiler

Compiled 3327 to 2202 computations (33.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 4 (/.f64 z y))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 4) (.f64 4 (/.f64 z y)))
✓	0.0b	(*.f64 4 (/.f64 x y))

series28.0ms (0.8%)

Counts

3 → 27

Calls

3 calls:

15.0ms	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 4) (.f64 4 (/.f64 z y)))
6.0ms	(*.f64 4 (/.f64 x y))
6.0ms	(*.f64 4 (/.f64 z y))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
26×	`associate-r_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`

Counts

3 → 92

Calls

3 calls:

6.0ms	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 4) (.f64 4 (/.f64 z y)))
6.0ms	(*.f64 4 (/.f64 z y))
4.0ms	(*.f64 4 (/.f64 x y))

simplify71.0ms (2%)

Algorithm

1×	egg-herbie

Rules

426×	`associate-l_binary64`
386×	`times-frac_binary64`
376×	`associate-*r/_binary64`
365×	`associate-r_binary64`
348×	`associate-*l/_binary64`

Counts

119 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	1549
1	448	1471
2	1300	1434
3	4641	1434
4	5185	1434

prune103.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	137	3	140

Error

Counts

140 → 3

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 1 (/.f64 4 (/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z))))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 4) (.f64 4 (/.f64 z y)))
✓	0.1b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y))

Compiler

Compiled 2795 to 1579 computations (43.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 4 (/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z))))
	0.0b	(-.f64 (+.f64 x (*.f64 y 3/4)) z)
✓	0.1b	(/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z))
✓	0.2b	(/.f64 4 (/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z)))

series69.0ms (2%)

Counts

3 → 108

Calls

3 calls:

36.0ms	(/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z))
17.0ms	(+.f64 1 (/.f64 4 (/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z))))
16.0ms	(/.f64 4 (/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z)))

rewrite47.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
106×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 160

Calls

3 calls:

18.0ms	(+.f64 1 (/.f64 4 (/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z))))
8.0ms	(/.f64 4 (/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z)))
5.0ms	(/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z))

simplify141.0ms (4%)

Algorithm

1×	egg-herbie

Rules

224×	`cancel-sign-sub-inv_binary64`
213×	`times-frac_binary64`
210×	`associate-/r/_binary64`
195×	`associate-/l*_binary64`
180×	`*-commutative_binary64`

Counts

268 → 326

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	6665
1	1147	6510
2	4304	6446
3	5037	6446

prune287.0ms (8.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	380	0	380
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	380	3	383

Error

Counts

383 → 3

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 1 (/.f64 4 (/.f64 y (-.f64 (+.f64 x (*.f64 y 3/4)) z))))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (/.f64 x y)) 4) (.f64 4 (/.f64 z y)))
✓	0.1b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 3/4)) z)) y))

Compiler

Compiled 9863 to 6415 computations (35% saved)

regimes371.0ms (10.6%)

Accuracy

Total 0.0b remaining (80.2%)

Threshold costs 0.0b (80.2%)

Counts

70 → 1

Compiler

Compiled 4617 to 3586 computations (22.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	13	17
2	13	17

end58.0ms (1.7%)

Compiler: Compiled 78 to 58 computations (25.6% saved)

Details

analyze553.0ms (15.8%)

sample1.3s (38.4%)

simplify127.0ms (3.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series43.0ms (1.2%)

rewrite24.0ms (0.7%)

simplify71.0ms (2%)

prune118.0ms (3.4%)

localize7.0ms (0.2%)

series28.0ms (0.8%)

rewrite20.0ms (0.6%)

simplify71.0ms (2%)

prune103.0ms (2.9%)

localize8.0ms (0.2%)

series69.0ms (2%)

rewrite47.0ms (1.3%)

simplify141.0ms (4%)

prune287.0ms (8.2%)

regimes371.0ms (10.6%)

simplify2.0ms (0.1%)

end58.0ms (1.7%)

Profiling