Details

analyze721.0ms (7.9%)

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)

sample1.1s (12.2%)

Results

1.0s	8256×	body	128	valid
65.0ms	535×	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

23.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	23.7b	(/.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
✓	0.3b	(fma.f64 a c (*.f64 b d))
✓	23.3b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series93.0ms (1%)

Counts

2 → 96

Calls

2 calls:

84.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
9.0ms	(fma.f64 a c (*.f64 b d))

rewrite4.0ms (0%)

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))

simplify69.0ms (0.8%)

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

prune66.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	8	95

Error

3.1b

Counts

95 → 8

Alt Table

Status	Error	Program
	17.1b	(.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)))
	38.4b	(/.f64 b d)
	23.7b	(/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (.f64 d d))))
	24.2b	(/.f64 (/.f64 (fma.f64 a c (.f64 b d)) (.f64 (cbrt.f64 (fma.f64 c c (.f64 d d))) (cbrt.f64 (fma.f64 c c (.f64 d d))))) (cbrt.f64 (fma.f64 c c (*.f64 d d))))
▶	16.6b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	23.7b	(/.f64 (fma.f64 d b (.f64 c a)) (fma.f64 c c (.f64 d d)))
	34.3b	(fma.f64 b (/.f64 d (*.f64 c c)) (/.f64 a c))
	36.9b	(/.f64 a c)

Compiler

Compiled 2286 to 492 computations (78.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 d c)
✓	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)))
✓	15.5b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series233.0ms (2.5%)

Counts

4 → 144

Calls

4 calls:

101.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
101.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
19.0ms	(/.f64 1 (hypot.f64 d c))
11.0ms	(hypot.f64 d c)

rewrite22.0ms (0.2%)

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	(hypot.f64 d c)

simplify179.0ms (2%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-def_binary64`
415×	`cancel-sign-sub-inv_binary64`
363×	`fma-neg_binary64`
199×	`sub-neg_binary64`
192×	`distribute-rgt-in_binary64`

Counts

274 → 306

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	6223
1	741	5824
2	2442	5629
3	4679	5621
4	4982	5621
5	4960	5621

prune247.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	339	9	348
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	347	9	356

Error

0.4b

Counts

356 → 9

Alt Table

Status	Error	Program
	23.7b	(/.f64 (.f64 1 (fma.f64 d b (.f64 c a))) (*.f64 (hypot.f64 d c) (hypot.f64 d c)))
	44.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
	16.8b	(.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))))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 b))
	44.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
	41.7b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
▶	16.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))))
	33.1b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	31.3b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 9128 to 3019 computations (66.9% 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)))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))))
✓	7.7b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
✓	7.9b	(/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))

series367.0ms (4%)

Counts

4 → 136

Calls

4 calls:

138.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))
104.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))))
98.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
27.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))

rewrite69.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

169×	`add-exp-log_binary64`
113×	`add-sqr-sqrt_binary64`
103×	`times-frac_binary64`
76×	`prod-exp_binary64`
73×	`*-un-lft-identity_binary64`

Counts

4 → 252

Calls

4 calls:

13.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
11.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))))
8.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))
3.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))

simplify272.0ms (3%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-def_binary64`
544×	`cancel-sign-sub-inv_binary64`
314×	`associate-r_binary64`
300×	`fma-neg_binary64`
229×	`associate-l_binary64`

Counts

388 → 418

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	357	11460
1	913	9098
2	2964	8941
3	4860	8941
4	4974	8941
5	4948	8941

prune266.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	418	0	418
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	418	9	427

Error

0.4b

Counts

427 → 9

Alt Table

Status	Error	Program
	23.7b	(/.f64 (.f64 1 (fma.f64 d b (.f64 c a))) (*.f64 (hypot.f64 d c) (hypot.f64 d c)))
	44.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
▶	16.8b	(.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))))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 b))
	44.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
	41.7b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
✓	16.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))))
	33.1b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	31.3b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 13819 to 4206 computations (69.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 a c (*.f64 d b))
✓	0.3b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
✓	0.3b	(.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))))
✓	15.5b	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))

series421.0ms (4.6%)

Counts

4 → 176

Calls

4 calls:

206.0ms	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
105.0ms	(.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))))
101.0ms	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))
9.0ms	(fma.f64 a c (*.f64 d b))

rewrite104.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

350×	`times-frac_binary64`
261×	`add-sqr-sqrt_binary64`
181×	`*-un-lft-identity_binary64`
171×	`add-cube-cbrt_binary64`
110×	`sqrt-prod_binary64`

Counts

4 → 314

Calls

4 calls:

32.0ms	(.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))))
13.0ms	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (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))

simplify339.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-def_binary64`
427×	`cancel-sign-sub-inv_binary64`
311×	`associate-/l*_binary64`
301×	`associate-*l/_binary64`
275×	`associate-/l/_binary64`

Counts

490 → 533

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	414	16438
1	1148	14606
2	3695	14421
3	4913	14421
4	5238	14421

prune329.0ms (3.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	531	2	533
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	533	9	542

Error

0.4b

Counts

542 → 9

Alt Table

Status	Error	Program
	44.1b	(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (neg.f64 b) (sqrt.f64 (hypot.f64 d c))))
	44.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
	23.7b	(/.f64 (.f64 1 (fma.f64 d b (.f64 c a))) (*.f64 (hypot.f64 d c) (hypot.f64 d c)))
	44.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
	41.8b	(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 (/.f64 d c) b a) (sqrt.f64 (hypot.f64 d c))))
✓	16.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))))
	33.1b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	31.3b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
✓	16.8b	(.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))))

Compiler

Compiled 19321 to 3919 computations (79.7% saved)

regimes3.9s (42.2%)

Accuracy

Total 10.6b remaining (98.4%)

Threshold costs 0b (0%)

Counts

211 → 7

Compiler

Compiled 24223 to 13359 computations (44.8% saved)

bsearch132.0ms (1.4%)

Steps

Iters	Range		Point
11	6.063323146069527e+185	5.515239562154484e+208	6.164541131217644e+185
7	3.559551160767353e-66	1.2488211763571394e-64	3.7980760572038457e-66
9	-1.919474161879987e-103	-7.530027389557997e-109	-3.840391229221447e-106
9	-4.626390944981006e+29	-2.5417371811117338e+20	-4.34100723376406e+29
8	-1.0401112411771789e+42	-3.409232113202445e+37	-3.4710805651394907e+37
4	-9.235502145661662e+148	-5.0843124959565825e+148	-7.798094340522651e+148

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	160
1	49	160
2	48	160

end191.0ms (2.1%)

Compiler: Compiled 407 to 181 computations (55.5% saved)

Details

analyze721.0ms (7.9%)

sample1.1s (12.2%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series93.0ms (1%)

rewrite4.0ms (0%)

simplify69.0ms (0.8%)

prune66.0ms (0.7%)

localize9.0ms (0.1%)

series233.0ms (2.5%)

rewrite22.0ms (0.2%)

simplify179.0ms (2%)

prune247.0ms (2.7%)

localize15.0ms (0.2%)

series367.0ms (4%)

rewrite69.0ms (0.8%)

simplify272.0ms (3%)

prune266.0ms (2.9%)

localize11.0ms (0.1%)

series421.0ms (4.6%)

rewrite104.0ms (1.1%)

simplify339.0ms (3.7%)

prune329.0ms (3.6%)

regimes3.9s (42.2%)

bsearch132.0ms (1.4%)

simplify4.0ms (0%)

end191.0ms (2.1%)

Profiling