Details

analyze725.0ms (13.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.1s (19.8%)

Results

984.0ms	8256×	body	128	valid
61.0ms	521×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	18	18
2	22	18
3	22	18

prune3.0ms (0.1%)

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

23.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	23.0b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a c (*.f64 b d))
✓	22.7b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series86.0ms (1.6%)

Counts

2 → 96

Calls

2 calls:

78.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
8.0ms	(fma.f64 a c (*.f64 b d))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
0.0ms	(fma.f64 a c (*.f64 b d))

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary64`
410×	`associate-/l/_binary64`
377×	`fma-neg_binary64`
252×	`distribute-rgt-neg-in_binary64`
251×	`distribute-lft-neg-in_binary64`

Counts

135 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	2544
1	202	2411
2	604	2327
3	2154	2279
4	5032	2279

prune73.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	6	95

Error

0.9b

Counts

95 → 6

Alt Table

Status	Error	Program
	37.4b	(/.f64 a c)
	36.0b	(/.f64 b d)
	21.9b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	22.9b	(/.f64 (/.f64 (fma.f64 a c (.f64 b d)) (sqrt.f64 (fma.f64 c c (.f64 d d)))) (sqrt.f64 (fma.f64 c c (*.f64 d d))))
	23.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
▶	13.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))

Compiler

Compiled 2180 to 450 computations (79.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.2b	(fma.f64 d b (*.f64 c a))
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	13.0b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series221.0ms (4.1%)

Counts

4 → 168

Calls

4 calls:

99.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
95.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
17.0ms	(/.f64 1 (hypot.f64 d c))
10.0ms	(fma.f64 d b (*.f64 c a))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 130

Calls

4 calls:

8.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
2.0ms	(/.f64 1 (hypot.f64 d c))
2.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
0.0ms	(fma.f64 d b (*.f64 c a))

simplify159.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

845×	`times-frac_binary64`
428×	`fma-neg_binary64`
410×	`fma-def_binary64`
335×	`cancel-sign-sub-inv_binary64`
274×	`distribute-rgt-in_binary64`

Counts

298 → 286

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	233	6205
1	631	5720
2	2125	5547
3	4841	5539
4	5079	5539

prune161.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	282	4	286
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	287	5	292

Error

0.0b

Counts

292 → 5

Alt Table

Status	Error	Program
	30.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	32.5b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
▶	13.9b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))
	42.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
	23.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))

Compiler

Compiled 7235 to 2141 computations (70.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.1b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))
	0.2b	(fma.f64 d b (*.f64 c a))
✓	13.1b	(.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a)))

series192.0ms (3.5%)

Counts

2 → 96

Calls

2 calls:

98.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))
94.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a)))

rewrite100.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
14×	`times-frac_binary64`
13×	`associate-l_binary64`

Counts

2 → 67

Calls

2 calls:

89.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a)))
5.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))

simplify132.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

414×	`associate-/l/_binary64`
407×	`associate-/r*_binary64`
377×	`fma-neg_binary64`
358×	`associate-*l/_binary64`
266×	`fma-def_binary64`

Counts

163 → 163

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	4007
1	449	3558
2	1571	3392
3	4207	3392
4	4792	3380
5	4987	3380

prune189.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	248	6	254

Error

0.0b

Counts

254 → 6

Alt Table

Status	Error	Program
	30.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	32.5b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
✓	13.9b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))
	42.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
▶	23.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
	42.7b	(/.f64 (neg.f64 (fma.f64 (/.f64 c d) a b)) (hypot.f64 d c))

Compiler

Compiled 5870 to 2023 computations (65.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a c (*.f64 b d))
✓	0.9b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
✓	22.2b	(/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d)))

series147.0ms (2.7%)

Counts

2 → 96

Calls

2 calls:

80.0ms	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
67.0ms	(/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
2.0ms	(/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d)))

simplify160.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

514×	`fma-def_binary64`
444×	`cancel-sign-sub-inv_binary64`
303×	`associate-/l/_binary64`
234×	`fma-neg_binary64`
173×	`unswap-sqr_binary64`

Counts

203 → 214

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	7544
1	546	6829
2	2201	6547
3	4540	6547
4	4969	6547

prune157.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	235	7	242

Error

0.0b

Counts

242 → 7

Alt Table

Status	Error	Program
	30.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	32.5b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
✓	13.9b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))
	42.8b	(/.f64 1 (+.f64 (fma.f64 (/.f64 (.f64 c c) d) (/.f64 (.f64 a a) (pow.f64 b 3)) (/.f64 d b)) (*.f64 (/.f64 c b) (-.f64 (/.f64 c d) (/.f64 a b)))))
	42.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
✓	23.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
	42.7b	(/.f64 (neg.f64 (fma.f64 (/.f64 c d) a b)) (hypot.f64 d c))

Compiler

Compiled 6807 to 1800 computations (73.6% saved)

regimes1.5s (27.1%)

Accuracy

Total 9.9b remaining (98.4%)

Threshold costs 0b (0%)

Counts

120 → 5

Compiler

Compiled 11813 to 6379 computations (46% saved)

bsearch94.0ms (1.7%)

Steps

Iters	Range		Point
10	2.920818592712724e+59	6.487566340489778e+75	4.7943349601815015e+69
6	2.0899086163410493e-282	2.1873995017832087e-275	6.117043132162393e-276
8	-9.772376608186263e-167	-2.930970100023204e-169	-1.6578507474419048e-168
11	-2.9417404878192264e+132	-3.817259090653867e+110	-8.995298531255504e+122

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	108
1	38	108
2	42	108
3	45	108
4	46	108
5	46	108

end110.0ms (2%)

Compiler: Compiled 290 to 137 computations (52.8% saved)

Details

analyze725.0ms (13.4%)

sample1.1s (19.8%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series86.0ms (1.6%)

rewrite5.0ms (0.1%)

simplify75.0ms (1.4%)

prune73.0ms (1.3%)

localize9.0ms (0.2%)

series221.0ms (4.1%)

rewrite25.0ms (0.5%)

simplify159.0ms (2.9%)

prune161.0ms (3%)

localize9.0ms (0.2%)

series192.0ms (3.5%)

rewrite100.0ms (1.9%)

simplify132.0ms (2.4%)

prune189.0ms (3.5%)

localize9.0ms (0.2%)

series147.0ms (2.7%)

rewrite19.0ms (0.3%)

simplify160.0ms (2.9%)

prune157.0ms (2.9%)

regimes1.5s (27.1%)

bsearch94.0ms (1.7%)

simplify5.0ms (0.1%)

end110.0ms (2%)

Profiling