Details

analyze1.7s (23.6%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.3s (18.1%)

Results

1.1s	8256×	body	128	valid
150.0ms	223×	body	8192	exit
31.0ms	247×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify10.0ms (0.1%)

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%)

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

25.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.2b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 c c (*.f64 d d))
✓	0.5b	(fma.f64 a c (*.f64 b d))
✓	24.9b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series109.0ms (1.5%)

Counts

3 → 120

Calls

3 calls:

90.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
9.0ms	(fma.f64 a c (*.f64 b d))
9.0ms	(fma.f64 c c (*.f64 d d))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 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))
0.0ms	(fma.f64 c c (*.f64 d d))

simplify84.0ms (1.1%)

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

169 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	2836
1	205	2674
2	611	2590
3	2163	2542
4	5054	2542

prune84.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	111	6	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	6	118

Error

1.8b

Counts

118 → 6

Alt Table

Status	Error	Program
	38.6b	(.f64 (/.f64 (sqrt.f64 (fma.f64 d b (.f64 c a))) (hypot.f64 d c)) (/.f64 (sqrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	37.2b	(/.f64 a c)
▶	15.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	33.8b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	35.7b	(/.f64 b d)
	25.2b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))

Compiler

Compiled 2543 to 502 computations (80.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	0.5b	(fma.f64 d b (*.f64 c a))
✓	14.9b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series242.0ms (3.3%)

Counts

4 → 168

Calls

4 calls:

112.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
100.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
19.0ms	(/.f64 1 (hypot.f64 d c))
11.0ms	(fma.f64 d b (*.f64 c a))

rewrite25.0ms (0.3%)

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))

simplify156.0ms (2.1%)

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

prune175.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	282	4	286
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	285	7	292

Error

0.2b

Counts

292 → 7

Alt Table

Status	Error	Program
	38.6b	(.f64 (/.f64 (sqrt.f64 (fma.f64 d b (.f64 c a))) (hypot.f64 d c)) (/.f64 (sqrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	33.0b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
✓	15.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	30.9b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
▶	18.6b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	25.2b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))

Compiler

Compiled 7333 to 2176 computations (70.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))
	0.5b	(fma.f64 d b (*.f64 c a))
✓	7.7b	(/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))
✓	15.1b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))

series281.0ms (3.8%)

Counts

3 → 88

Calls

3 calls:

150.0ms

(/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))

107.0ms

(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c))))

24.0ms

(/.f64 1 (sqrt.f64 (hypot.f64 d c)))

rewrite72.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

213×	`times-frac_binary64`
177×	`add-sqr-sqrt_binary64`
114×	`*-un-lft-identity_binary64`
108×	`add-cube-cbrt_binary64`
72×	`sqrt-prod_binary64`

Counts

3 → 228

Calls

3 calls:

29.0ms

(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c))))

3.0ms

(/.f64 1 (sqrt.f64 (hypot.f64 d c)))

3.0ms

(/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))

simplify231.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

455×	`fma-def_binary64`
436×	`cancel-sign-sub-inv_binary64`
294×	`fma-neg_binary64`
253×	`associate-*l/_binary64`
245×	`distribute-rgt-in_binary64`

Counts

316 → 370

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	10306
1	827	8743
2	2834	8535
3	4542	8535
4	4987	8535

prune217.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	391	1	392
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	393	6	399

Error

0.2b

Counts

399 → 6

Alt Table

Status	Error	Program
✓	15.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	30.9b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	33.0b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
▶	24.4b	(fma.f64 (/.f64 c (fma.f64 c c (.f64 d d))) a (/.f64 (.f64 d b) (fma.f64 c c (*.f64 d d))))
✓	18.6b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))

Compiler

Compiled 13327 to 3490 computations (73.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 c c (*.f64 d d))
✓	2.1b	(fma.f64 (/.f64 c (fma.f64 c c (.f64 d d))) a (/.f64 (.f64 d b) (fma.f64 c c (*.f64 d d))))
✓	16.2b	(/.f64 c (fma.f64 c c (*.f64 d d)))
✓	17.4b	(/.f64 (.f64 d b) (fma.f64 c c (.f64 d d)))

series248.0ms (3.3%)

Counts

3 → 108

Calls

3 calls:

145.0ms	(fma.f64 (/.f64 c (fma.f64 c c (.f64 d d))) a (/.f64 (.f64 d b) (fma.f64 c c (*.f64 d d))))
86.0ms	(/.f64 (.f64 d b) (fma.f64 c c (.f64 d d)))
16.0ms	(/.f64 c (fma.f64 c c (*.f64 d d)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

3.0ms	(/.f64 (.f64 d b) (fma.f64 c c (.f64 d d)))
2.0ms	(/.f64 c (fma.f64 c c (*.f64 d d)))
0.0ms	(fma.f64 (/.f64 c (fma.f64 c c (.f64 d d))) a (/.f64 (.f64 d b) (fma.f64 c c (*.f64 d d))))

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

781×	`associate-/l*_binary64`
775×	`times-frac_binary64`
354×	`fma-neg_binary64`
284×	`associate-/l/_binary64`
240×	`cancel-sign-sub-inv_binary64`

Counts

170 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	4060
1	417	3810
2	1346	3696
3	4656	3696
4	4964	3696

prune121.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	204	7	211

Error

0.0b

Counts

211 → 7

Alt Table

Status	Error	Program
✓	15.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	30.9b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	33.0b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
✓	24.4b	(fma.f64 (/.f64 c (fma.f64 c c (.f64 d d))) a (/.f64 (.f64 d b) (fma.f64 c c (*.f64 d d))))
✓	18.6b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	12.6b	(fma.f64 (/.f64 c (fma.f64 c c (.f64 d d))) a (.f64 (/.f64 d (hypot.f64 d c)) (/.f64 b (hypot.f64 d c))))

Compiler

Compiled 5561 to 1098 computations (80.3% saved)

regimes1.9s (25.4%)

Accuracy

Total 6.1b remaining (98.6%)

Threshold costs 0b (0%)

Counts

156 → 5

Compiler

Compiled 16798 to 8904 computations (47% saved)

bsearch88.0ms (1.2%)

Steps

Iters	Range		Point
8	1.3911201530396798e+119	2.188913424522284e+122	2.1546967477784777e+122
4	5.128383406173875e-177	7.541457833649871e-174	4.87134912457176e-174
7	-5.850809904216814e-141	-3.0449618591271845e-142	-3.072242908321757e-142
5	-7.0070866402637814e+159	-2.081921925101563e+159	-2.1315939500394346e+159

Compiler

Compiled 5 to 4 computations (20% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	134
1	46	134
2	53	132
3	60	132
4	63	132
5	64	132
6	62	132

end110.0ms (1.5%)

Compiler: Compiled 332 to 145 computations (56.3% saved)

Details

analyze1.7s (23.6%)

sample1.3s (18.1%)

simplify10.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series109.0ms (1.5%)

rewrite5.0ms (0.1%)

simplify84.0ms (1.1%)

prune84.0ms (1.1%)

localize10.0ms (0.1%)

series242.0ms (3.3%)

rewrite25.0ms (0.3%)

simplify156.0ms (2.1%)

prune175.0ms (2.4%)

localize15.0ms (0.2%)

series281.0ms (3.8%)

rewrite72.0ms (1%)

simplify231.0ms (3.1%)

prune217.0ms (2.9%)

localize10.0ms (0.1%)

series248.0ms (3.3%)

rewrite9.0ms (0.1%)

simplify115.0ms (1.5%)

prune121.0ms (1.6%)

regimes1.9s (25.4%)

bsearch88.0ms (1.2%)

simplify8.0ms (0.1%)

end110.0ms (1.5%)

Profiling