Details

analyze50.0ms (0.8%)

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
74.9%	25%	0.2%	5
74.9%	25%	0.2%	6
74.9%	25%	0.2%	7
87.3%	12.5%	0.2%	8
93.6%	6.2%	0.2%	9
93.6%	6.2%	0.2%	10
93.6%	6.2%	0.2%	11
96.7%	3.1%	0.2%	12
98.2%	1.6%	0.2%	13
98.2%	1.6%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample859.0ms (13.7%)

Infinites

5.6% of outputs are infinite.

Results

812.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify15.0ms (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

prune6.0ms (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

25.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	25.9b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
▶	25.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 104 to 54 computations (48.1% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a c) (.f64 b d))
✓	25.6b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

series90.0ms (1.4%)

Counts

2 → 96

Calls

2 calls:

81.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
8.0ms	(+.f64 (.f64 a c) (.f64 b d))

rewrite15.0ms (0.2%)

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 → 47

Calls

2 calls:

7.0ms	(+.f64 (.f64 a c) (.f64 b d))
6.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

simplify103.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

472×	`associate-l_binary64`
420×	`fma-def_binary64`
391×	`associate-r_binary64`
343×	`times-frac_binary64`
331×	`fma-neg_binary64`

Counts

143 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	2682
1	341	2585
2	1159	2501
3	4461	2489
4	4888	2489
5	4980	2489

prune75.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Error

0.2b

Counts

109 → 5

Alt Table

Status	Error	Program
	25.7b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
▶	17.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	33.8b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	26.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 a c) (.f64 b d))) (cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))) (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (cbrt.f64 (+.f64 (.f64 a c) (.f64 b d))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
	28.2b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))

Compiler

Compiled 2811 to 540 computations (80.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 d b (*.f64 c a))
✓	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	17.3b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series234.0ms (3.7%)

Counts

4 → 168

Calls

4 calls:

103.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
99.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
22.0ms	(/.f64 1 (hypot.f64 d c))
9.0ms	(fma.f64 d b (*.f64 c a))

rewrite22.0ms (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))

simplify145.0ms (2.3%)

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

prune210.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	283	3	286
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	284	7	291

Error

0.2b

Counts

291 → 7

Alt Table

Status	Error	Program
✓	17.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
▶	17.8b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
	28.2b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	46.7b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
	18.0b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (sqrt.f64 (/.f64 1 (hypot.f64 d c)))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))
	25.7b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	33.8b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))

Compiler

Compiled 7319 to 2180 computations (70.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a c (*.f64 d b))
✓	0.1b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
✓	17.3b	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))

series205.0ms (3.3%)

Counts

3 → 144

Calls

3 calls:

101.0ms	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
95.0ms	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))
9.0ms	(fma.f64 a c (*.f64 d b))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

7.0ms	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
2.0ms	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))
0.0ms	(fma.f64 a c (*.f64 d b))

simplify146.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

674×	`times-frac_binary64`
512×	`associate-/l*_binary64`
382×	`associate-/l/_binary64`
345×	`fma-neg_binary64`
339×	`associate-/r*_binary64`

Counts

255 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	6272
1	538	5929
2	1440	5628
3	4524	5565
4	5033	5565

prune146.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	249	7	256

Error

0.2b

Counts

256 → 7

Alt Table

Status	Error	Program
✓	17.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	17.8b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
	28.2b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	46.7b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
▶	18.0b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (sqrt.f64 (/.f64 1 (hypot.f64 d c)))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))
	33.8b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	18.1b	(/.f64 1 (.f64 (hypot.f64 d c) (/.f64 (hypot.f64 d c) (fma.f64 d b (.f64 c a)))))

Compiler

Compiled 6410 to 1206 computations (81.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (hypot.f64 d c)))
✓	0.3b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (sqrt.f64 (/.f64 1 (hypot.f64 d c)))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))
✓	0.4b	(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (sqrt.f64 (/.f64 1 (hypot.f64 d c))))
	17.3b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series151.0ms (2.4%)

Counts

3 → 80

Calls

3 calls:

102.0ms

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

26.0ms

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

23.0ms

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

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`add-sqr-sqrt_binary64`
95×	`sqrt-prod_binary64`
89×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64`

Counts

3 → 191

Calls

3 calls:

17.0ms

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

12.0ms

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

2.0ms

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

simplify180.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

955×	`times-frac_binary64`
348×	`cancel-sign-sub-inv_binary64`
346×	`fma-def_binary64`
245×	`associate-l_binary64`
206×	`fma-neg_binary64`

Counts

271 → 298

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	5740
1	637	5237
2	2254	5055
3	4782	5055
4	4942	5055

prune344.0ms (5.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	431	0	431
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	431	7	438

Error

0.2b

Counts

438 → 7

Alt Table

Status	Error	Program
✓	17.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	17.8b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
	28.2b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	46.7b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
✓	18.0b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (sqrt.f64 (/.f64 1 (hypot.f64 d c)))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))
	33.8b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	18.1b	(/.f64 1 (.f64 (hypot.f64 d c) (/.f64 (hypot.f64 d c) (fma.f64 d b (.f64 c a)))))

Compiler

Compiled 13717 to 5491 computations (60% saved)

regimes3.0s (47.7%)

Accuracy

Total 9.8b remaining (98.1%)

Threshold costs 0b (0%)

Counts

202 → 5

Compiler

Compiled 24304 to 13057 computations (46.3% saved)

bsearch61.0ms (1%)

Steps

Iters	Range		Point
5	2.748169300587671e+77	6.230464810441544e+77	4.637490032372509e+77
9	-4.677684765432969e-302	-2.772761058196398e-307	-1.657834802134664e-306
8	-2.355875229743919e-111	-1.6012003708454764e-115	-4.171294695866961e-113
6	-7.084776950732577e+99	-6.7626492079986e+98	-1.2126922600481525e+99

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	37	116
1	43	116
2	47	116
3	50	116
4	51	116
5	51	116

end106.0ms (1.7%)

Compiler: Compiled 301 to 144 computations (52.2% saved)

Details

analyze50.0ms (0.8%)

sample859.0ms (13.7%)

simplify15.0ms (0.2%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

series90.0ms (1.4%)

rewrite15.0ms (0.2%)

simplify103.0ms (1.6%)

prune75.0ms (1.2%)

localize9.0ms (0.1%)

series234.0ms (3.7%)

rewrite22.0ms (0.3%)

simplify145.0ms (2.3%)

prune210.0ms (3.3%)

localize8.0ms (0.1%)

series205.0ms (3.3%)

rewrite19.0ms (0.3%)

simplify146.0ms (2.3%)

prune146.0ms (2.3%)

localize11.0ms (0.2%)

series151.0ms (2.4%)

rewrite51.0ms (0.8%)

simplify180.0ms (2.9%)

prune344.0ms (5.5%)

regimes3.0s (47.7%)

bsearch61.0ms (1%)

simplify5.0ms (0.1%)

end106.0ms (1.7%)

Profiling