Details

analyze776.0ms (10%)

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)

sample1.2s (16%)

Results

1.0s	8256×	body	128	valid
61.0ms	521×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify76.0ms (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

24.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.6b	(/.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 2 expressions with local error:

New	Error	Program
✓	0.9b	(-.f64 (.f64 b c) (.f64 a d))
✓	24.2b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series101.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

88.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
13.0ms	(-.f64 (.f64 b c) (.f64 a 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 → 48

Calls

2 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))

simplify86.0ms (1.1%)

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

prune82.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	100	9	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	9	110

Error

2.3b

Counts

110 → 9

Alt Table

Status	Error	Program
	41.9b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	40.6b	(/.f64 b c)
	37.0b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	18.5b	(.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)))
	35.7b	(neg.f64 (/.f64 a d))
	25.3b	(.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)))))
	25.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (.f64 d d)))) (cbrt.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (.f64 d d))))) (cbrt.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))))
	24.9b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (-.f64 (.f64 b c) (*.f64 a d))))
▶	18.0b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))

Compiler

Compiled 2979 to 643 computations (78.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
✓	0.9b	(-.f64 (.f64 c b) (.f64 a d))
✓	16.9b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series238.0ms (3.1%)

Counts

4 → 132

Calls

4 calls:

112.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
97.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
18.0ms	(/.f64 1 (hypot.f64 d c))
11.0ms	(-.f64 (.f64 c b) (.f64 a d))

rewrite31.0ms (0.4%)

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

simplify118.0ms (1.5%)

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

prune198.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	265	6	271
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	269	11	280

Error

2.3b

Counts

280 → 11

Alt Table

Status	Error	Program
	40.6b	(/.f64 b c)
	24.6b	(.f64 1 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (.f64 (hypot.f64 d c) (hypot.f64 d c))))
	35.7b	(neg.f64 (/.f64 a d))
	42.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 a))
▶	18.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))))
	41.9b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	44.5b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	37.0b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	46.4b	(*.f64 (/.f64 1 (hypot.f64 d c)) b)
	18.5b	(.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)))
	21.4b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))))

Compiler

Compiled 7521 to 2262 computations (69.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	0.9b	(-.f64 (.f64 c b) (.f64 a d))
	16.9b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series314.0ms (4%)

Counts

2 → 80

Calls

2 calls:

211.0ms

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

102.0ms

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

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
32×	`associate-l_binary64`
32×	`sqrt-prod_binary64`
27×	`*-un-lft-identity_binary64`

Counts

2 → 97

Calls

2 calls:

13.0ms

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

11.0ms

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

simplify142.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

722×	`times-frac_binary64`
325×	`fma-neg_binary64`
302×	`fma-def_binary64`
267×	`distribute-rgt-in_binary64`
257×	`distribute-lft-in_binary64`

Counts

177 → 175

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	5705
1	551	5165
2	1906	5099
3	4972	5097
4	5111	5097

prune201.0ms (2.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	268	1	269
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	268	12	280

Error

2.3b

Counts

280 → 12

Alt Table

Status	Error	Program
	44.5b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	42.2b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (neg.f64 a)))
	40.6b	(/.f64 b c)
	24.6b	(.f64 1 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (.f64 (hypot.f64 d c) (hypot.f64 d c))))
	35.7b	(neg.f64 (/.f64 a d))
	42.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 a))
✓	18.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))))
	41.9b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	37.0b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	46.4b	(*.f64 (/.f64 1 (hypot.f64 d c)) b)
▶	18.5b	(.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)))
	21.4b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))))

Compiler

Compiled 9310 to 3634 computations (61% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (*.f64 a d))))
	0.9b	(-.f64 (.f64 c b) (.f64 a d))
✓	4.6b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (*.f64 a d)))) (hypot.f64 d c))
✓	17.4b	(cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))

series402.0ms (5.2%)

Counts

3 → 144

Calls

3 calls:

201.0ms

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

114.0ms

(*.f64 (cbrt.f64 (-.f64 (*.f64 c b) (*.f64 a d))) (cbrt.f64 (-.f64 (*.f64 c b) (*.f64 a d))))

87.0ms

(cbrt.f64 (-.f64 (*.f64 c b) (*.f64 a d)))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`cbrt-div_binary64`
22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 96

Calls

3 calls:

9.0ms

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

8.0ms

(*.f64 (cbrt.f64 (-.f64 (*.f64 c b) (*.f64 a d))) (cbrt.f64 (-.f64 (*.f64 c b) (*.f64 a d))))

2.0ms

(cbrt.f64 (-.f64 (*.f64 c b) (*.f64 a d)))

simplify254.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-def_binary64`
372×	`*-commutative_binary64`
240×	`cancel-sign-sub-inv_binary64`
234×	`sub-neg_binary64`
184×	`fma-neg_binary64`

Counts

240 → 376

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	909	15372
1	3138	14597
2	4992	14597
3	5011	14597

prune584.0ms (7.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	642	0	642
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	642	12	654

Error

2.3b

Counts

654 → 12

Alt Table

Status	Error	Program
	44.5b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	42.2b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (neg.f64 a)))
	40.6b	(/.f64 b c)
	24.6b	(.f64 1 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (.f64 (hypot.f64 d c) (hypot.f64 d c))))
	35.7b	(neg.f64 (/.f64 a d))
	42.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 a))
✓	18.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))))
	41.9b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	37.0b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	46.4b	(*.f64 (/.f64 1 (hypot.f64 d c)) b)
✓	18.5b	(.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)))
	21.4b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))))

Compiler

Compiled 41771 to 16812 computations (59.8% saved)

regimes2.7s (34.2%)

Accuracy

Total 9.0b remaining (86.6%)

Threshold costs 0b (0%)

Counts

206 → 3

Compiler

Compiled 27423 to 14664 computations (46.5% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 19 to 11 computations (42.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	86
1	38	86
2	48	86
3	55	86
4	59	86
5	60	86
6	60	86

end135.0ms (1.7%)

Compiler: Compiled 356 to 180 computations (49.4% saved)

Details

analyze776.0ms (10%)

sample1.2s (16%)

simplify76.0ms (1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series101.0ms (1.3%)

rewrite9.0ms (0.1%)

simplify86.0ms (1.1%)

prune82.0ms (1.1%)

localize10.0ms (0.1%)

series238.0ms (3.1%)

rewrite31.0ms (0.4%)

simplify118.0ms (1.5%)

prune198.0ms (2.5%)

localize11.0ms (0.1%)

series314.0ms (4%)

rewrite34.0ms (0.4%)

simplify142.0ms (1.8%)

prune201.0ms (2.6%)

localize12.0ms (0.2%)

series402.0ms (5.2%)

rewrite31.0ms (0.4%)

simplify254.0ms (3.3%)

prune584.0ms (7.5%)

regimes2.7s (34.2%)

bsearch8.0ms (0.1%)

simplify4.0ms (0.1%)

end135.0ms (1.7%)

Profiling