Details

analyze56.0ms (0.5%)

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)

sample1.5s (12.4%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify13.0ms (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

prune14.0ms (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

28.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.8b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 a c (*.f64 b d))
✓	28.6b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series135.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

120.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
15.0ms	(fma.f64 a c (*.f64 b d))

rewrite8.0ms (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)))
0.0ms	(fma.f64 a c (*.f64 b d))

simplify167.0ms (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

prune127.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Error

2.0b

Counts

95 → 9

Alt Table

Status	Error	Program
▶	17.4b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	34.4b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	28.8b	(.f64 (fma.f64 a c (.f64 b d)) (/.f64 1 (fma.f64 c c (*.f64 d d))))
	32.1b	(fma.f64 b (/.f64 d (*.f64 c c)) (/.f64 a c))
	42.2b	(.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)))
	17.9b	(.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)))
	29.2b	(.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)))))
	28.7b	(/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (.f64 d d))))
	36.0b	(/.f64 a c)

Compiler

Compiled 2386 to 522 computations (78.1% saved)

localize15.0ms (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)))
✓	0.2b	(fma.f64 d b (*.f64 c a))
✓	16.7b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series477.0ms (4.1%)

Counts

4 → 168

Calls

4 calls:

225.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
167.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
72.0ms	(/.f64 1 (hypot.f64 d c))
12.0ms	(fma.f64 d b (*.f64 c a))

rewrite39.0ms (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:

16.0ms	(.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))
3.0ms	(/.f64 1 (hypot.f64 d c))
1.0ms	(fma.f64 d b (*.f64 c a))

simplify314.0ms (2.7%)

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

prune429.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	279	7	286
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	287	8	295

Error

0.2b

Counts

295 → 8

Alt Table

Status	Error	Program
	17.6b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 a c (.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	44.8b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
▶	17.3b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
	46.5b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	25.0b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (cbrt.f64 (hypot.f64 d c))))
	28.8b	(.f64 (fma.f64 a c (.f64 b d)) (/.f64 1 (fma.f64 c c (*.f64 d d))))
	31.8b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	29.5b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 7381 to 2215 computations (70% saved)

localize22.0ms (0.2%)

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))
✓	16.7b	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))

series469.0ms (4%)

Counts

4 → 168

Calls

4 calls:

225.0ms	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
184.0ms	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))
33.0ms	(hypot.f64 d c)
26.0ms	(fma.f64 a c (*.f64 d b))

rewrite89.0ms (0.8%)

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)

simplify333.0ms (2.9%)

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 → 291

Iterations

Useful iterations: 2 (0.0ms)

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

prune509.0ms (4.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	329	4	333
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	334	7	341

Error

0.2b

Counts

341 → 7

Alt Table

Status	Error	Program
	46.5b	(/.f64 (neg.f64 (fma.f64 (/.f64 c d) a b)) (hypot.f64 d c))
	27.9b	(.f64 (/.f64 (fma.f64 a c (.f64 d b)) 1) (/.f64 (/.f64 1 (hypot.f64 d c)) (hypot.f64 d c)))
	44.7b	(/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
✓	17.3b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
▶	17.5b	(/.f64 (/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))
	31.8b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	29.5b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 8453 to 1923 computations (77.3% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))
	1.0b	(fma.f64 a c (*.f64 d b))
✓	7.9b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
✓	9.0b	(/.f64 (fma.f64 a c (*.f64 d b)) (sqrt.f64 (hypot.f64 d c)))

series659.0ms (5.6%)

Counts

3 → 128

Calls

3 calls:

241.0ms

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

239.0ms

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

178.0ms

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

rewrite588.0ms (5%)

Algorithm

1×	rewrite-expression-head

Rules

1644×	`times-frac_binary64`
784×	`*-un-lft-identity_binary64`
784×	`add-sqr-sqrt_binary64`
784×	`add-cube-cbrt_binary64`
624×	`sqrt-prod_binary64`

Counts

3 → 784

Calls

3 calls:

49.0ms

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

30.0ms

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

6.0ms

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

simplify2.1s (18.4%)

Algorithm

1×	egg-herbie

Rules

506×	`associate-/r*_binary64`
443×	`fma-def_binary64`
441×	`associate-/l/_binary64`
419×	`cancel-sign-sub-inv_binary64`
243×	`associate-/l*_binary64`

Counts

912 → 1004

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	774	44671
1	1769	42279
2	3445	39665
3	4825	39014
4	4974	39014
5	4956	39014

prune1.1s (9.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1024	1	1025
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	1025	7	1032

Error

0.2b

Counts

1032 → 7

Alt Table

Status	Error	Program
	29.5b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	27.9b	(.f64 (fma.f64 d b (.f64 c a)) (/.f64 (/.f64 1 (hypot.f64 d c)) (hypot.f64 d c)))
	44.7b	(/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
✓	17.3b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (hypot.f64 d c))
✓	17.5b	(/.f64 (/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))
	46.5b	(/.f64 (neg.f64 (fma.f64 (/.f64 c d) a b)) (hypot.f64 d c))
	31.8b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))

Compiler

Compiled 40980 to 5425 computations (86.8% saved)

regimes2.1s (18.1%)

Accuracy

Total 9.5b remaining (97.7%)

Threshold costs 0b (0%)

Counts

117 → 5

Compiler

Compiled 11893 to 6314 computations (46.9% saved)

bsearch131.0ms (1.1%)

Steps

Iters	Range		Point
9	2.3747717619077724e+92	7.865607200093191e+99	1.7908903707439708e+98
7	9.514026573838576e-131	2.6717172040399705e-129	8.272481472784187e-130
10	-6.075455576341602e-127	-8.581049049977316e-142	-3.6283479029046922e-140
9	-2.4807475401011038e+103	-7.293119437331218e+94	-2.1840157650846506e+101

Compiler

Compiled 5 to 4 computations (20% saved)

simplify24.0ms (0.2%)

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	38	116
1	45	116
2	49	116
3	52	116
4	53	116
5	53	116

end238.0ms (2%)

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

Details

analyze56.0ms (0.5%)

sample1.5s (12.4%)

simplify13.0ms (0.1%)

prune14.0ms (0.1%)

localize12.0ms (0.1%)

series135.0ms (1.2%)

rewrite8.0ms (0.1%)

simplify167.0ms (1.4%)

prune127.0ms (1.1%)

localize15.0ms (0.1%)

series477.0ms (4.1%)

rewrite39.0ms (0.3%)

simplify314.0ms (2.7%)

prune429.0ms (3.7%)

localize22.0ms (0.2%)

series469.0ms (4%)

rewrite89.0ms (0.8%)

simplify333.0ms (2.9%)

prune509.0ms (4.4%)

localize28.0ms (0.2%)

series659.0ms (5.6%)

rewrite588.0ms (5%)

simplify2.1s (18.4%)

prune1.1s (9.2%)

regimes2.1s (18.1%)

bsearch131.0ms (1.1%)

simplify24.0ms (0.2%)

end238.0ms (2%)

Profiling