Details

analyze316.0ms (5.6%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample964.0ms (17%)

Symmetry

(sort x y)

Results

879.0ms	8256×	body	128	valid
45.0ms	463×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

44×	`fma-def_binary64`
37×	`associate-l_binary64`
36×	`associate-r_binary64`
20×	`*-commutative_binary64`
19×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	14
2	41	14
3	94	14
4	122	14
5	149	14
6	153	14
7	146	14

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

5.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.2b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.3b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	5.1b	(*.f64 y (fma.f64 z z 1))

series82.0ms (1.4%)

Counts

2 → 60

Calls

2 calls:

70.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
11.0ms	(*.f64 y (fma.f64 z z 1))

rewrite53.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

895×	`log1p-expm1-u_binary64`
895×	`expm1-log1p-u_binary64`
93×	`add-sqr-sqrt_binary64`
85×	`add-cbrt-cube_binary64`
85×	`add-log-exp_binary64`

Counts

2 → 59

Calls

2 calls:

51.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
51.0ms	(*.f64 y (fma.f64 z z 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	186	22
2	2326	22
3	5603	22
0	0	0
1	0	0

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
427×	`distribute-neg-frac_binary64`
351×	`distribute-rgt-neg-in_binary64`
335×	`associate-/l*_binary64`
326×	`distribute-lft-neg-in_binary64`

Counts

119 → 84

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	55	993
1	140	903
2	338	901
3	1133	897
4	3155	873
5	4509	873
6	5031	873

prune77.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Error

3.6b

Counts

85 → 7

Alt Table

Status	Error	Program
	5.9b	(/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 z z 1))) 3))
	25.9b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) 2)
	5.7b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
	48.3b	(*.f64 (/.f64 (pow.f64 x -1/2) y) (/.f64 (pow.f64 x -1/2) (fma.f64 z z 1)))
	18.8b	(.f64 (/.f64 1 (sqrt.f64 (.f64 y (fma.f64 z z 1)))) (/.f64 (/.f64 1 x) (sqrt.f64 (*.f64 y (fma.f64 z z 1)))))
	5.7b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
▶	5.4b	(*.f64 (/.f64 (/.f64 1 x) y) (/.f64 1 (fma.f64 z z 1)))

Compiler

Compiled 1508 to 982 computations (34.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 x) y)
✓	0.4b	(/.f64 1 (fma.f64 z z 1))
✓	5.1b	(*.f64 (/.f64 (/.f64 1 x) y) (/.f64 1 (fma.f64 z z 1)))

series78.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

69.0ms	(*.f64 (/.f64 (/.f64 1 x) y) (/.f64 1 (fma.f64 z z 1)))
7.0ms	(/.f64 (/.f64 1 x) y)
2.0ms	(/.f64 1 (fma.f64 z z 1))

rewrite69.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
175×	`pow3_binary64`
175×	`log-div_binary64`

Counts

3 → 127

Calls

3 calls:

67.0ms	(/.f64 (/.f64 1 x) y)
67.0ms	(/.f64 1 (fma.f64 z z 1))
67.0ms	(*.f64 (/.f64 (/.f64 1 x) y) (/.f64 1 (fma.f64 z z 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	216	29
2	2719	29
3	5006	29
0	0	0
1	0	0

simplify106.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

697×	`times-frac_binary64`
422×	`sub-neg_binary64`
397×	`fma-def_binary64`
364×	`div-sub_binary64`
342×	`associate-/l*_binary64`

Counts

199 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	1140
1	174	1090
2	454	1088
3	1411	1078
4	4237	1078
5	4454	1078
6	4981	1078
7	4934	1078

prune148.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	161	8	169

Error

1.2b

Counts

169 → 8

Alt Table

Status	Error	Program
	30.7b	(/.f64 (sqrt.f64 (/.f64 (/.f64 1 x) y)) (/.f64 (fma.f64 z z 1) (sqrt.f64 (/.f64 (/.f64 1 x) y))))
	5.7b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
▶	3.0b	(/.f64 (/.f64 (/.f64 (/.f64 1 x) y) (hypot.f64 1 z)) (hypot.f64 1 z))
	5.9b	(/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 z z 1))) 3))
	5.2b	(/.f64 (/.f64 -1 x) (neg.f64 (*.f64 y (fma.f64 z z 1))))
	48.3b	(*.f64 (/.f64 (pow.f64 x -1/2) y) (/.f64 (pow.f64 x -1/2) (fma.f64 z z 1)))
	18.8b	(.f64 (/.f64 1 (sqrt.f64 (.f64 y (fma.f64 z z 1)))) (/.f64 (/.f64 1 x) (sqrt.f64 (*.f64 y (fma.f64 z z 1)))))
✓	5.4b	(*.f64 (/.f64 (/.f64 1 x) y) (/.f64 1 (fma.f64 z z 1)))

Compiler

Compiled 2820 to 1895 computations (32.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 z)
	0.2b	(/.f64 (/.f64 1 x) y)
✓	0.5b	(/.f64 (/.f64 (/.f64 (/.f64 1 x) y) (hypot.f64 1 z)) (hypot.f64 1 z))
✓	2.2b	(/.f64 (/.f64 (/.f64 1 x) y) (hypot.f64 1 z))

series395.0ms (7%)

Counts

3 → 84

Calls

3 calls:

298.0ms	(/.f64 (/.f64 (/.f64 1 x) y) (hypot.f64 1 z))
95.0ms	(/.f64 (/.f64 (/.f64 (/.f64 1 x) y) (hypot.f64 1 z)) (hypot.f64 1 z))
2.0ms	(hypot.f64 1 z)

rewrite74.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

597×	`log-prod_binary64`
233×	`log-div_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
177×	`log-pow_binary64`

Counts

3 → 111

Calls

3 calls:

71.0ms	(hypot.f64 1 z)
71.0ms	(/.f64 (/.f64 (/.f64 (/.f64 1 x) y) (hypot.f64 1 z)) (hypot.f64 1 z))
71.0ms	(/.f64 (/.f64 (/.f64 1 x) y) (hypot.f64 1 z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	218	33
2	2957	31
3	5399	31
0	0	0
1	0	0

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-neg_binary64`
436×	`associate-/r*_binary64`
403×	`distribute-neg-frac_binary64`
275×	`sub-neg_binary64`
262×	`fma-def_binary64`

Counts

195 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1806
1	364	1628
2	1037	1616
3	3526	1614
4	4608	1614
5	5016	1614

prune283.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	260	3	263
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	263	8	271

Error

0.0b

Counts

271 → 8

Alt Table

Status	Error	Program
✓	3.0b	(/.f64 (/.f64 (/.f64 (/.f64 1 x) y) (hypot.f64 1 z)) (hypot.f64 1 z))
	5.9b	(/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 z z 1))) 3))
	30.7b	(/.f64 (sqrt.f64 (/.f64 (/.f64 1 x) y)) (/.f64 (fma.f64 z z 1) (sqrt.f64 (/.f64 (/.f64 1 x) y))))
	48.3b	(*.f64 (/.f64 (pow.f64 x -1/2) y) (/.f64 (pow.f64 x -1/2) (fma.f64 z z 1)))
	35.5b	(/.f64 (/.f64 1 (.f64 y (.f64 z x))) (hypot.f64 1 z))
▶	1.3b	(/.f64 (.f64 (/.f64 1 x) (/.f64 1 (.f64 y (hypot.f64 1 z)))) (hypot.f64 1 z))
	18.8b	(.f64 (/.f64 1 (sqrt.f64 (.f64 y (fma.f64 z z 1)))) (/.f64 (/.f64 1 x) (sqrt.f64 (*.f64 y (fma.f64 z z 1)))))
	5.3b	(+.f64 0 (/.f64 1 (.f64 (fma.f64 z z 1) (.f64 x y))))

Compiler

Compiled 5409 to 3769 computations (30.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (hypot.f64 1 z))
✓	0.3b	(/.f64 1 (*.f64 y (hypot.f64 1 z)))
✓	0.5b	(/.f64 (.f64 (/.f64 1 x) (/.f64 1 (.f64 y (hypot.f64 1 z)))) (hypot.f64 1 z))
✓	2.9b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (hypot.f64 1 z))))

series254.0ms (4.5%)

Counts

4 → 120

Calls

4 calls:

95.0ms	(/.f64 (.f64 (/.f64 1 x) (/.f64 1 (.f64 y (hypot.f64 1 z)))) (hypot.f64 1 z))
85.0ms	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (hypot.f64 1 z))))
61.0ms	(/.f64 1 (*.f64 y (hypot.f64 1 z)))
12.0ms	(*.f64 y (hypot.f64 1 z))

rewrite120.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

648×	`log-prod_binary64`
219×	`log-div_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
194×	`log-pow_binary64`

Counts

4 → 160

Calls

4 calls:

117.0ms	(*.f64 y (hypot.f64 1 z))
117.0ms	(/.f64 1 (*.f64 y (hypot.f64 1 z)))
117.0ms	(/.f64 (.f64 (/.f64 1 x) (/.f64 1 (.f64 y (hypot.f64 1 z)))) (hypot.f64 1 z))
117.0ms	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (hypot.f64 1 z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	237	49
2	3092	49
3	5607	49
0	0	0
1	0	0

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

943×	`fma-neg_binary64`
476×	`associate-/r*_binary64`
378×	`fma-def_binary64`
284×	`associate-l_binary64`
280×	`associate-r_binary64`

Counts

280 → 250

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2514
1	471	2210
2	1321	2191
3	4466	2191
4	5263	2191

prune279.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	246	4	250
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	251	7	258

Error

Counts

258 → 7

Alt Table

Status	Error	Program
✓	3.0b	(/.f64 (/.f64 (/.f64 (/.f64 1 x) y) (hypot.f64 1 z)) (hypot.f64 1 z))
	2.4b	(pow.f64 (.f64 x (.f64 (hypot.f64 1 z) (*.f64 y (hypot.f64 1 z)))) -1)
	1.9b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 (/.f64 1 x) (*.f64 y (hypot.f64 1 z))) (hypot.f64 1 z))) 3)
	30.7b	(/.f64 (sqrt.f64 (/.f64 (/.f64 1 x) y)) (/.f64 (fma.f64 z z 1) (sqrt.f64 (/.f64 (/.f64 1 x) y))))
	1.9b	(/.f64 (.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (cbrt.f64 (.f64 y (hypot.f64 1 z)))) 3)) (hypot.f64 1 z))
	18.8b	(.f64 (/.f64 1 (sqrt.f64 (.f64 y (fma.f64 z z 1)))) (/.f64 (/.f64 1 x) (sqrt.f64 (*.f64 y (fma.f64 z z 1)))))
	1.7b	(/.f64 (/.f64 (/.f64 1 y) (*.f64 x (hypot.f64 1 z))) (hypot.f64 1 z))

Compiler

Compiled 5306 to 3718 computations (29.9% saved)

regimes1.8s (32.4%)

Accuracy

Total 1.6b remaining (97.8%)

Threshold costs 0b (0%)

Counts

178 → 1

Compiler

Compiled 24329 to 18326 computations (24.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	16	25
2	15	25

end251.0ms (4.4%)

Compiler: Compiled 213 to 164 computations (23% saved)

Details

analyze316.0ms (5.6%)

sample964.0ms (17%)

simplify9.0ms (0.2%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series82.0ms (1.4%)

rewrite53.0ms (0.9%)

simplify77.0ms (1.3%)

prune77.0ms (1.4%)

localize11.0ms (0.2%)

series78.0ms (1.4%)

rewrite69.0ms (1.2%)

simplify106.0ms (1.9%)

prune148.0ms (2.6%)

localize7.0ms (0.1%)

series395.0ms (7%)

rewrite74.0ms (1.3%)

simplify85.0ms (1.5%)

prune283.0ms (5%)

localize8.0ms (0.1%)

series254.0ms (4.5%)

rewrite120.0ms (2.1%)

simplify84.0ms (1.5%)

prune279.0ms (4.9%)

regimes1.8s (32.4%)

simplify2.0ms (0%)

end251.0ms (4.4%)

Profiling