Details

analyze48.0ms (1%)

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)

sample953.0ms (20.7%)

Infinites

6% of outputs are infinite.

Results

809.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify68.0ms (1.5%)

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 (0.1%)

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

24.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

Compiler

Compiled 69 to 33 computations (52.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (.f64 b c) (.f64 a d))
✓	24.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series103.0ms (2.2%)

Counts

2 → 96

Calls

2 calls:

88.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
14.0ms	(-.f64 (.f64 b c) (.f64 a d))

rewrite9.0ms (0.2%)

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 → 48

Calls

2 calls:

4.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
2.0ms	(-.f64 (.f64 b c) (.f64 a d))

simplify89.0ms (1.9%)

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

144 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2762
1	323	2614
2	1084	2567
3	4430	2567
4	4952	2567

prune63.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	7	110

Error

1.6b

Counts

110 → 7

Alt Table

Status	Error	Program
	24.7b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	41.1b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	38.4b	(/.f64 b c)
	36.8b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	32.1b	(neg.f64 (/.f64 a d))
▶	17.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	25.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (cbrt.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))))) (/.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (cbrt.f64 (fma.f64 c c (.f64 d d)))))

Compiler

Compiled 2797 to 587 computations (79% saved)

localize12.0ms (0.3%)

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 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
✓	0.5b	(-.f64 (.f64 c b) (.f64 a d))
✓	17.1b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series229.0ms (5%)

Counts

4 → 132

Calls

4 calls:

106.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
96.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
17.0ms	(/.f64 1 (hypot.f64 d c))
9.0ms	(-.f64 (.f64 c b) (.f64 a d))

rewrite30.0ms (0.6%)

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 → 139

Calls

4 calls:

11.0ms	(.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))
2.0ms	(-.f64 (.f64 c b) (.f64 a d))
2.0ms	(/.f64 1 (hypot.f64 d c))

simplify123.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

874×	`times-frac_binary64`
537×	`fma-def_binary64`
368×	`cancel-sign-sub-inv_binary64`
196×	`fma-neg_binary64`
181×	`sub-neg_binary64`

Counts

271 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	6415
1	744	5877
2	2552	5818
3	5061	5818

prune184.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	265	6	271
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	268	10	278

Error

1.6b

Counts

278 → 10

Alt Table

Status	Error	Program
	38.4b	(/.f64 b c)
	42.4b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (/.f64 (.f64 c b) d) a))
	32.1b	(neg.f64 (/.f64 a d))
	18.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c))))
	46.8b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (/.f64 (.f64 a d) c) b))
	24.7b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	41.1b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	18.2b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))) (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (*.f64 a d))) (cbrt.f64 (hypot.f64 d c))))
▶	17.5b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	40.6b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 a (/.f64 (.f64 c b) d)))

Compiler

Compiled 7513 to 2240 computations (70.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.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))
	17.1b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series106.0ms (2.3%)

Counts

1 → 48

Calls

1 calls:

106.0ms

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

rewrite17.0ms (0.4%)

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 (2.5%)

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

prune146.0ms (3.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	227	4	231
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	231	10	241

Error

1.6b

Counts

241 → 10

Alt Table

Status	Error	Program
▶	18.1b	(/.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (cbrt.f64 (hypot.f64 d c)))) (hypot.f64 d c))
	40.6b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 a (/.f64 (.f64 c b) d)))
	24.7b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	41.1b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	38.4b	(/.f64 b c)
	42.4b	(/.f64 (-.f64 (/.f64 (*.f64 c b) d) a) (hypot.f64 d c))
	32.1b	(neg.f64 (/.f64 a d))
✓	17.5b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	46.7b	(/.f64 (-.f64 (/.f64 (*.f64 a d) c) b) (hypot.f64 d c))
	30.1b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) 3)) (hypot.f64 d c))

Compiler

Compiled 6312 to 1332 computations (78.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))
✓	0.5b	(cbrt.f64 (hypot.f64 d c))
✓	6.9b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (cbrt.f64 (hypot.f64 d c)))
✓	10.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (cbrt.f64 (hypot.f64 d c))))

series583.0ms (12.6%)

Counts

4 → 144

Calls

4 calls:

402.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (cbrt.f64 (hypot.f64 d c)))
98.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (cbrt.f64 (hypot.f64 d c))))
46.0ms	(*.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))
36.0ms	(cbrt.f64 (hypot.f64 d c))

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
53×	`add-exp-log_binary64`
51×	`times-frac_binary64`
46×	`*-un-lft-identity_binary64`
43×	`cbrt-prod_binary64`

Counts

4 → 171

Calls

4 calls:

12.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (cbrt.f64 (hypot.f64 d c))))
5.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (cbrt.f64 (hypot.f64 d c)))
4.0ms	(*.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))
1.0ms	(cbrt.f64 (hypot.f64 d c))

simplify252.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

435×	`associate-r_binary64`
381×	`fma-neg_binary64`
329×	`associate-l_binary64`
273×	`*-commutative_binary64`
222×	`fma-def_binary64`

Counts

315 → 379

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	447	9807
1	1302	8462
2	4534	8267
3	4996	8267
4	4994	8267
5	4954	8267

prune282.0ms (6.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	473	0	473
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	473	10	483

Error

1.6b

Counts

483 → 10

Alt Table

Status	Error	Program
✓	18.1b	(/.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (cbrt.f64 (hypot.f64 d c)))) (hypot.f64 d c))
	40.6b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 a (/.f64 (.f64 c b) d)))
	24.7b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	41.1b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	38.4b	(/.f64 b c)
	42.4b	(/.f64 (-.f64 (/.f64 (*.f64 c b) d) a) (hypot.f64 d c))
	32.1b	(neg.f64 (/.f64 a d))
✓	17.5b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	46.7b	(/.f64 (-.f64 (/.f64 (*.f64 a d) c) b) (hypot.f64 d c))
	30.1b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) 3)) (hypot.f64 d c))

Compiler

Compiled 18644 to 5606 computations (69.9% saved)

regimes944.0ms (20.5%)

Accuracy

Total 10.1b remaining (83.4%)

Threshold costs 0b (0%)

Counts

91 → 5

Compiler

Compiled 10393 to 5594 computations (46.2% saved)

bsearch62.0ms (1.3%)

Steps

Iters	Range		Point
7	4.0354548311811365e+126	5.58930270475422e+128	2.8401337548471847e+128
8	7.977234154488967e-103	4.551326919586386e-98	8.114742458283298e-103
8	-8.581413122176708e-299	-4.677684765432969e-302	-5.787984791490119e-300
9	-1.894972773015628e+86	-4.0004577221764496e+77	-4.331249049106995e+81

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
11×	`*-commutative_binary64`
9×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	109
1	46	109
2	65	109
3	84	109
4	98	109
5	105	109
6	107	109
7	107	109

end113.0ms (2.5%)

Compiler: Compiled 333 to 164 computations (50.8% saved)

Details

analyze48.0ms (1%)

sample953.0ms (20.7%)

simplify68.0ms (1.5%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series103.0ms (2.2%)

rewrite9.0ms (0.2%)

simplify89.0ms (1.9%)

prune63.0ms (1.4%)

localize12.0ms (0.3%)

series229.0ms (5%)

rewrite30.0ms (0.6%)

simplify123.0ms (2.7%)

prune184.0ms (4%)

localize8.0ms (0.2%)

series106.0ms (2.3%)

rewrite17.0ms (0.4%)

simplify113.0ms (2.5%)

prune146.0ms (3.2%)

localize13.0ms (0.3%)

series583.0ms (12.6%)

rewrite39.0ms (0.9%)

simplify252.0ms (5.5%)

prune282.0ms (6.1%)

regimes944.0ms (20.5%)

bsearch62.0ms (1.3%)

simplify6.0ms (0.1%)

end113.0ms (2.5%)

Profiling