Details

analyze1.4s (11.4%)

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)

sample50.0ms (0.4%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify24.0ms (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%)

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

28.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.5b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize18.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 a c (*.f64 b d))
✓	27.9b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

rewrite9.0ms (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:

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

series228.0ms (1.8%)

Counts

2 → 96

Calls

2 calls:

163.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
64.0ms	(fma.f64 a c (*.f64 b d))

simplify186.0ms (1.5%)

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 → 248

Iterations

Useful iterations: 3 (0.0ms)

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

prune130.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	241	7	248
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	242	7	249

Error

1.9b

Counts

249 → 7

Alt Table

Status	Error	Program
	41.5b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 d b (.f64 c a)) (fma.f64 d d (.f64 c c))) 3))
	36.5b	(/.f64 a c)
	28.6b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
	35.1b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	34.4b	(fma.f64 b (/.f64 d (*.f64 c c)) (/.f64 a c))
	28.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))) (cbrt.f64 (/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d))))) (cbrt.f64 (/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))))
▶	18.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))

Compiler

Compiled 2245 to 478 computations (78.7% saved)

localize24.0ms (0.2%)

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)))
✓	0.3b	(fma.f64 d b (*.f64 c a))
✓	17.0b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

rewrite41.0ms (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:

18.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
4.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
4.0ms	(/.f64 1 (hypot.f64 d c))
1.0ms	(fma.f64 d b (*.f64 c a))

series540.0ms (4.4%)

Counts

4 → 168

Calls

4 calls:

215.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
210.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
67.0ms	(fma.f64 d b (*.f64 c a))
46.0ms	(/.f64 1 (hypot.f64 d c))

simplify369.0ms (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 → 551

Iterations

Useful iterations: 3 (0.0ms)

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

prune439.0ms (3.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	542	9	551
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	548	10	558

Error

0.1b

Counts

558 → 10

Alt Table

Status	Error	Program
	31.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	45.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
	23.3b	(.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))))
	31.7b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	28.6b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
	18.3b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	43.0b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
	31.4b	(.f64 (/.f64 1 (hypot.f64 d c)) (cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))))
	45.8b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
▶	18.1b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))

Compiler

Compiled 7455 to 2253 computations (69.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 d c)
✓	0.1b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
✓	1.0b	(fma.f64 a c (*.f64 d b))
✓	17.0b	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

9.0ms	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
4.0ms	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))
1.0ms	(fma.f64 a c (*.f64 d b))
1.0ms	(hypot.f64 d c)

series531.0ms (4.3%)

Counts

4 → 168

Calls

4 calls:

216.0ms	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))
216.0ms	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
63.0ms	(fma.f64 a c (*.f64 d b))
34.0ms	(hypot.f64 d c)

simplify397.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

809×	`times-frac_binary64`
517×	`fma-neg_binary64`
383×	`associate-/l/_binary64`
360×	`fma-def_binary64`
309×	`cancel-sign-sub-inv_binary64`

Counts

289 → 535

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	6714
1	669	6476
2	1845	6153
3	4627	6153
4	4967	6153

prune398.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	531	4	535
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	536	9	545

Error

0.1b

Counts

545 → 9

Alt Table

Status	Error	Program
	31.4b	(.f64 (/.f64 1 (hypot.f64 d c)) (cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))))
	18.5b	(/.f64 1 (.f64 (hypot.f64 d c) (/.f64 (hypot.f64 d c) (fma.f64 d b (.f64 c a)))))
	31.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	43.0b	(/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
	28.6b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
▶	18.3b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	45.3b	(/.f64 (fma.f64 (/.f64 d c) b a) (hypot.f64 d c))
	31.7b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	45.7b	(/.f64 (fma.f64 (/.f64 c d) a b) (hypot.f64 d c))

Compiler

Compiled 7557 to 1641 computations (78.3% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 d b (*.f64 c a))
✓	0.3b	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))
✓	0.3b	(/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	17.0b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
154×	`add-sqr-sqrt_binary64`
154×	`add-cube-cbrt_binary64`
144×	`sqrt-prod_binary64`

Counts

2 → 232

Calls

2 calls:

18.0ms	(/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
6.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))

series88.0ms (0.7%)

Counts

2 → 32

Calls

2 calls:

44.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))
44.0ms	(/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))

simplify464.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-neg_binary64`
310×	`associate-r_binary64`
283×	`times-frac_binary64`
282×	`associate-l_binary64`
249×	`fma-def_binary64`

Counts

264 → 493

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	7085
1	506	6725
2	1219	6105
3	4031	5992
4	5025	5992

prune560.0ms (4.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	746	1	747
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	747	9	756

Error

0.1b

Counts

756 → 9

Alt Table

Status	Error	Program
	31.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	43.0b	(/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
	28.6b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
✓	18.3b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	45.3b	(/.f64 (fma.f64 (/.f64 d c) b a) (hypot.f64 d c))
	18.5b	(/.f64 1 (.f64 (hypot.f64 d c) (/.f64 (hypot.f64 d c) (fma.f64 d b (.f64 c a)))))
	31.7b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	18.4b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (/.f64 1 (/.f64 (hypot.f64 d c) (fma.f64 a c (.f64 d b)))))
	45.7b	(/.f64 (fma.f64 (/.f64 c d) a b) (hypot.f64 d c))

Compiler

Compiled 12419 to 3773 computations (69.6% saved)

regimes5.3s (43.1%)

Accuracy

Total 12.6b remaining (98.4%)

Threshold costs 0b (0%)

Compiler

Compiled 31338 to 16569 computations (47.1% saved)

bsearch71.0ms (0.6%)

Steps

Iters	Range		Point
10	1.8856163779316626e+33	1.0101823790300729e+52	4.291969600457141e+42
8	4.301883056855349e-210	2.314217786263026e-205	2.2529092715176455e-205
9	-2.8141482284191073e-24	-1.829637826184586e-32	-6.842778186148658e-25

Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	31	82
1	39	82
2	43	82
3	46	82
4	47	82
5	46	82

end1.0ms (0%)

Compiler: Compiled 61 to 27 computations (55.7% saved)

sample915.0ms (7.4%)

Algorithm

1×

intervals

Results

441.0ms	8000×	body	128	valid
25.0ms	492×	body	128	invalid

Compiler

Compiled 249 to 134 computations (46.2% saved)

Details

analyze1.4s (11.4%)

sample50.0ms (0.4%)

simplify24.0ms (0.2%)

prune6.0ms (0%)

localize18.0ms (0.1%)

rewrite9.0ms (0.1%)

series228.0ms (1.8%)

simplify186.0ms (1.5%)

prune130.0ms (1.1%)

localize24.0ms (0.2%)

rewrite41.0ms (0.3%)

series540.0ms (4.4%)

simplify369.0ms (3%)

prune439.0ms (3.6%)

localize17.0ms (0.1%)

rewrite34.0ms (0.3%)

series531.0ms (4.3%)

simplify397.0ms (3.2%)

prune398.0ms (3.2%)

localize27.0ms (0.2%)

rewrite62.0ms (0.5%)

series88.0ms (0.7%)

simplify464.0ms (3.7%)

prune560.0ms (4.5%)

regimes5.3s (43.1%)

bsearch71.0ms (0.6%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample915.0ms (7.4%)

Profiling