Details

analyze804.0ms (10.6%)

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
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)

sample1.2s (16%)

Results

1.1s	8256×	body	128	valid
74.0ms	510×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify6.0ms (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

23.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	23.6b	(/.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 2 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 a c (*.f64 b d))
✓	23.2b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series98.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

85.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
12.0ms	(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))

simplify79.0ms (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

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

prune67.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	87	7	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	7	95

Error

1.8b

Counts

95 → 7

Alt Table

Status	Error	Program
▶	16.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	38.1b	(/.f64 a c)
	16.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	21.5b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	23.5b	(/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (.f64 d d))))
	32.5b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	45.4b	(.f64 (sqrt.f64 (fma.f64 d b (.f64 c a))) (/.f64 (sqrt.f64 (fma.f64 d b (.f64 c a))) (fma.f64 d d (.f64 c c))))

Compiler

Compiled 2270 to 482 computations (78.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series216.0ms (2.9%)

Counts

3 → 144

Calls

3 calls:

107.0ms	(.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))
9.0ms	(fma.f64 d b (*.f64 c a))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 97

Calls

3 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 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
0.0ms	(fma.f64 d b (*.f64 c a))

simplify144.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

708×	`times-frac_binary64`
275×	`fma-def_binary64`
269×	`associate-/l/_binary64`
266×	`distribute-rgt-in_binary64`
261×	`fma-neg_binary64`

Counts

241 → 222

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	5189
1	492	4744
2	1678	4587
3	4596	4569
4	5010	4569

prune148.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	215	7	222
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	220	9	229

Error

0.2b

Counts

229 → 9

Alt Table

Status	Error	Program
	30.9b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	44.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
▶	16.1b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
	44.4b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
✓	16.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	44.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 b))
	16.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	34.1b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	22.5b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))

Compiler

Compiled 5736 to 1549 computations (73% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
✓	0.5b	(fma.f64 a c (*.f64 d b))
✓	15.1b	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))

series210.0ms (2.8%)

Counts

3 → 144

Calls

3 calls:

106.0ms	(/.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 (0.2%)

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:

4.0ms	(/.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))

simplify148.0ms (2%)

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

prune156.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	245	4	249
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	249	9	258

Error

0.1b

Counts

258 → 9

Alt Table

Status	Error	Program
	34.1b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	44.2b	(/.f64 (fma.f64 (/.f64 d c) b a) (hypot.f64 d c))
▶	16.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.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))
	43.1b	(/.f64 (fma.f64 (/.f64 c d) a b) (hypot.f64 d c))
✓	16.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	44.9b	(/.f64 (neg.f64 b) (hypot.f64 d c))
	44.4b	(/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
	22.5b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))

Compiler

Compiled 6486 to 1229 computations (81.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a))))
✓	3.4b	(/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a)))) (hypot.f64 d c))
✓	15.8b	(cbrt.f64 (fma.f64 d b (*.f64 c a)))

series430.0ms (5.7%)

Counts

4 → 192

Calls

4 calls:

155.0ms	(/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a)))) (hypot.f64 d c))
106.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
96.0ms	(.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a))))
72.0ms	(cbrt.f64 (fma.f64 d b (*.f64 c a)))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
32×	`add-exp-log_binary64`
31×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`cbrt-prod_binary64`

Counts

4 → 139

Calls

4 calls:

10.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
4.0ms	(.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a))))
4.0ms	(/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a)))) (hypot.f64 d c))
1.0ms	(cbrt.f64 (fma.f64 d b (*.f64 c a)))

simplify399.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
378×	`*-commutative_binary64`
286×	`cancel-sign-sub-inv_binary64`
196×	`sub-neg_binary64`
134×	`fma-neg_binary64`

Counts

331 → 451

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	937	18197
1	3237	16442
2	4726	16086
3	5000	16086
4	4964	16086

prune557.0ms (7.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	639	0	639
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	639	9	648

Error

0.1b

Counts

648 → 9

Alt Table

Status	Error	Program
	34.1b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	44.2b	(/.f64 (fma.f64 (/.f64 d c) b a) (hypot.f64 d c))
✓	16.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.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))
	43.1b	(/.f64 (fma.f64 (/.f64 c d) a b) (hypot.f64 d c))
✓	16.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	44.9b	(/.f64 (neg.f64 b) (hypot.f64 d c))
	44.4b	(/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
	22.5b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))

Compiler

Compiled 37673 to 14378 computations (61.8% saved)

regimes2.4s (32.1%)

Accuracy

Total 10.6b remaining (98%)

Threshold costs 0b (0%)

Counts

155 → 5

Compiler

Compiled 15288 to 8444 computations (44.8% saved)

bsearch98.0ms (1.3%)

Steps

Iters	Range		Point
10	3.102909357052664e+86	7.491316036254363e+98	2.0670348214171683e+97
10	3.0258255729790073e-180	4.5844607242057906e-163	2.88893887034297e-173
4	-3.5504229365985006e-142	-1.9699080442950435e-142	-3.099134525215515e-142
9	-9.556000818875074e+45	-1.6382890493197275e+37	-9.393577737026942e+45

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-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	34	110
1	42	110
2	46	110
3	49	110
4	50	110
5	49	110

end239.0ms (3.2%)

Compiler: Compiled 320 to 141 computations (55.9% saved)

Details

analyze804.0ms (10.6%)

sample1.2s (16%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series98.0ms (1.3%)

rewrite5.0ms (0.1%)

simplify79.0ms (1%)

prune67.0ms (0.9%)

localize9.0ms (0.1%)

series216.0ms (2.9%)

rewrite19.0ms (0.2%)

simplify144.0ms (1.9%)

prune148.0ms (2%)

localize12.0ms (0.2%)

series210.0ms (2.8%)

rewrite19.0ms (0.2%)

simplify148.0ms (2%)

prune156.0ms (2.1%)

localize12.0ms (0.2%)

series430.0ms (5.7%)

rewrite37.0ms (0.5%)

simplify399.0ms (5.3%)

prune557.0ms (7.4%)

regimes2.4s (32.1%)

bsearch98.0ms (1.3%)

simplify5.0ms (0.1%)

end239.0ms (3.2%)

Profiling