Details

analyze752.0ms (11.2%)

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)

sample1.3s (19.1%)

Results

1.1s	8256×	body	128	valid
66.0ms	523×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1070×	`fma-neg_binary64`
881×	`fma-def_binary64`
768×	`times-frac_binary64`
551×	`cancel-sign-sub-inv_binary64`
514×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	25	20
2	47	20
3	78	20
4	149	20
5	228	20
6	324	20
7	500	20
8	694	20
9	867	20
10	999	20
11	2422	20
12	3920	20
13	4950	20

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

24.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.5b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

Compiler

Compiled 69 to 33 computations (52.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 c c (*.f64 d d))
✓	0.5b	(-.f64 (.f64 b c) (.f64 a d))
✓	24.0b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series113.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

95.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
9.0ms	(-.f64 (.f64 b c) (.f64 a d))
8.0ms	(fma.f64 c c (*.f64 d d))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 58

Calls

3 calls:

4.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
3.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(fma.f64 c c (*.f64 d d))

simplify116.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

491×	`fma-neg_binary64`
380×	`associate-l_binary64`
348×	`fma-def_binary64`
315×	`associate-r_binary64`
247×	`associate-/l*_binary64`

Counts

178 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	3054
1	326	2877
2	1091	2830
3	4396	2830
4	4994	2830
5	4942	2830

prune95.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	9	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	9	133

Error

1.6b

Counts

133 → 9

Alt Table

Status	Error	Program
▶	16.0b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	35.8b	(/.f64 b c)
	16.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (hypot.f64 d c)))
	38.8b	(neg.f64 (/.f64 a d))
	24.4b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (*.f64 d d))))
	24.9b	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a 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))))
	35.9b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	39.3b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	40.7b	(.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (hypot.f64 d c)) (/.f64 (sqrt.f64 (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c)))

Compiler

Compiled 3297 to 695 computations (78.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
✓	0.5b	(-.f64 (.f64 c b) (.f64 a d))
✓	14.9b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series258.0ms (3.8%)

Counts

3 → 108

Calls

3 calls:

136.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
112.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
10.0ms	(-.f64 (.f64 c b) (.f64 a d))

rewrite30.0ms (0.4%)

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 → 106

Calls

3 calls:

10.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
4.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
3.0ms	(-.f64 (.f64 c b) (.f64 a d))

simplify142.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

741×	`times-frac_binary64`
476×	`fma-neg_binary64`
402×	`fma-def_binary64`
256×	`cancel-sign-sub-inv_binary64`
230×	`distribute-rgt-in_binary64`

Counts

214 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	216	5451
1	603	4941
2	2097	4885
3	4752	4884
4	5041	4884

prune161.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	201	6	207
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	205	11	216

Error

1.6b

Counts

216 → 11

Alt Table

Status	Error	Program
	16.1b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	44.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	42.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 b))
	35.9b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
▶	15.8b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
✓	16.0b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	35.8b	(/.f64 b c)
	44.4b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 b (/.f64 (.f64 a d) c)))
	16.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (.f64 (/.f64 1 (cbrt.f64 (hypot.f64 d c))) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c))))
	39.3b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	38.8b	(neg.f64 (/.f64 a d))

Compiler

Compiled 5779 to 1605 computations (72.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
	14.9b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series119.0ms (1.8%)

Counts

1 → 48

Calls

1 calls:

119.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 73

Calls

1 calls:

6.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))

simplify113.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

562×	`times-frac_binary64`
475×	`associate-/l/_binary64`
466×	`associate-/l*_binary64`
465×	`fma-neg_binary64`
359×	`div-sub_binary64`

Counts

121 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	4368
1	439	4066
2	1089	3872
3	4050	3805
4	5223	3805

prune164.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	227	4	231
Fresh	3	6	9
Picked	0	1	1
Done	1	0	1
Total	231	11	242

Error

1.6b

Counts

242 → 11

Alt Table

Status	Error	Program
▶	16.1b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	42.1b	(/.f64 (neg.f64 b) (hypot.f64 d c))
	44.4b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 b (/.f64 (.f64 a d) c)))
	16.5b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (*.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (cbrt.f64 (hypot.f64 d c)))
✓	15.8b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	35.8b	(/.f64 b c)
	16.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))) (cbrt.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)))) (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (/.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c))) (cbrt.f64 (hypot.f64 d c))))
	44.2b	(/.f64 a (hypot.f64 d c))
	35.9b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	39.3b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	38.8b	(neg.f64 (/.f64 a d))

Compiler

Compiled 6420 to 1359 computations (78.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
	14.9b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series146.0ms (2.2%)

Counts

2 → 56

Calls

2 calls:

121.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
24.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))

rewrite85.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
189×	`add-sqr-sqrt_binary64`
109×	`*-un-lft-identity_binary64`
99×	`add-cube-cbrt_binary64`
82×	`associate-r_binary64`

Counts

2 → 208

Calls

2 calls:

39.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
3.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))

simplify213.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-def_binary64`
327×	`fma-neg_binary64`
284×	`associate-/l*_binary64`
271×	`associate-*l/_binary64`
246×	`associate-*r/_binary64`

Counts

264 → 295

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	9672
1	892	8271
2	2871	8187
3	4636	8187
4	5292	8187

prune277.0ms (4.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	385	4	389
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	390	10	400

Error

1.6b

Counts

400 → 10

Alt Table

Status	Error	Program
	16.0b	(.f64 (pow.f64 (hypot.f64 d c) -1/2) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	44.2b	(/.f64 a (hypot.f64 d c))
✓	15.8b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	35.8b	(/.f64 b c)
	45.2b	(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 b (sqrt.f64 (hypot.f64 d c))))
	35.9b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	17.0b	(.f64 (/.f64 (/.f64 (-.f64 (.f64 b c) (*.f64 a d)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))) (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 1 (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))))
	39.3b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	42.2b	(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (neg.f64 b) (sqrt.f64 (hypot.f64 d c))))
	38.8b	(neg.f64 (/.f64 a d))

Compiler

Compiled 14056 to 3072 computations (78.1% saved)

regimes2.2s (32.9%)

Accuracy

Total 10.7b remaining (88.4%)

Threshold costs 0b (0%)

Counts

210 → 5

Compiler

Compiled 26918 to 14304 computations (46.9% saved)

bsearch110.0ms (1.6%)

Steps

Iters	Range		Point
8	6.514562348469273e+59	1.8662296246662805e+62	7.649344911276026e+60
7	3.4850776681094617e-252	6.725181137230773e-250	7.568560534795e-251
10	-6.29252219210595e-146	-2.740249779362431e-164	-1.8647556737340625e-161
9	-6.891626218393113e+170	-1.5517169619955328e+162	-2.9316931711396905e+167

Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
9×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	109
1	50	109
2	70	109
3	83	109
4	90	109
5	91	109
6	91	109

end185.0ms (2.7%)

Compiler: Compiled 342 to 168 computations (50.9% saved)

Details

analyze752.0ms (11.2%)

sample1.3s (19.1%)

simplify71.0ms (1.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series113.0ms (1.7%)

rewrite10.0ms (0.2%)

simplify116.0ms (1.7%)

prune95.0ms (1.4%)

localize9.0ms (0.1%)

series258.0ms (3.8%)

rewrite30.0ms (0.4%)

simplify142.0ms (2.1%)

prune161.0ms (2.4%)

localize9.0ms (0.1%)

series119.0ms (1.8%)

rewrite16.0ms (0.2%)

simplify113.0ms (1.7%)

prune164.0ms (2.4%)

localize12.0ms (0.2%)

series146.0ms (2.2%)

rewrite85.0ms (1.3%)

simplify213.0ms (3.2%)

prune277.0ms (4.1%)

regimes2.2s (32.9%)

bsearch110.0ms (1.6%)

simplify7.0ms (0.1%)

end185.0ms (2.7%)

Profiling