Details

analyze676.0ms (10.2%)

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)

sample137.0ms (2.1%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify68.0ms (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

27.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.9b	(/.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))
✓	27.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series111.0ms (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))
7.0ms	(fma.f64 c c (*.f64 d d))

rewrite11.0ms (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:

5.0ms	(/.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))

simplify121.0ms (1.8%)

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

prune87.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	8	132
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	124	9	133

Error

2.0b

Counts

133 → 9

Alt Table

Status	Error	Program
	18.4b	(.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)))
	39.6b	(/.f64 b c)
	28.4b	(/.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))))
	42.9b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (.f64 d d))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (.f64 d d)))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))))
	34.7b	(neg.f64 (/.f64 a d))
▶	17.8b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	40.7b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
✓	27.9b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	37.0b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))

Compiler

Compiled 3309 to 683 computations (79.4% saved)

localize11.0ms (0.2%)

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)))
✓	0.5b	(-.f64 (.f64 c b) (.f64 a d))
✓	16.6b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series249.0ms (3.8%)

Counts

4 → 132

Calls

4 calls:

116.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
104.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
18.0ms	(/.f64 1 (hypot.f64 d c))
10.0ms	(-.f64 (.f64 c b) (.f64 a d))

rewrite31.0ms (0.5%)

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:

10.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
5.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
3.0ms	(-.f64 (.f64 c b) (.f64 a d))
2.0ms	(/.f64 1 (hypot.f64 d c))

simplify131.0ms (2%)

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

prune195.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	265	6	271
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	269	11	280

Error

2.0b

Counts

280 → 11

Alt Table

Status	Error	Program
	17.9b	(.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))))
	46.0b	(*.f64 (/.f64 1 (hypot.f64 d c)) b)
▶	17.7b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
	43.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 a))
	17.9b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	40.7b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	47.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 b))
✓	27.9b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	39.6b	(/.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))
	34.7b	(neg.f64 (/.f64 a d))

Compiler

Compiled 7465 to 2248 computations (69.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.1b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
✓	16.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d)))

series217.0ms (3.3%)

Counts

2 → 96

Calls

2 calls:

113.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
104.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
14×	`times-frac_binary64`
13×	`associate-l_binary64`

Counts

2 → 79

Calls

2 calls:

9.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
8.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d)))

simplify127.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary64`
441×	`associate-/l/_binary64`
315×	`fma-neg_binary64`
248×	`cancel-sign-sub-inv_binary64`
228×	`distribute-rgt-in_binary64`

Counts

175 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	4543
1	569	4060
2	2124	3990
3	4767	3988
4	4988	3988

prune196.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	267	4	271
Fresh	5	4	9
Picked	0	1	1
Done	1	0	1
Total	273	9	282

Error

2.0b

Counts

282 → 9

Alt Table

Status	Error	Program
▶	17.8b	(/.f64 (/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	43.1b	(/.f64 (neg.f64 a) (hypot.f64 d c))
	17.9b	(.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))))
	46.0b	(/.f64 b (hypot.f64 d c))
✓	17.7b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
	40.7b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	47.2b	(/.f64 (neg.f64 b) (hypot.f64 d 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))
	34.7b	(neg.f64 (/.f64 a d))

Compiler

Compiled 7057 to 2321 computations (67.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (sqrt.f64 (hypot.f64 d c)))
✓	0.2b	(/.f64 (/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
	16.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d)))

series336.0ms (5.1%)

Counts

2 → 80

Calls

2 calls:

225.0ms

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

110.0ms

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

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
60×	`sqrt-prod_binary64`
49×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
49×	`add-cube-cbrt_binary64`

Counts

2 → 137

Calls

2 calls:

11.0ms

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

8.0ms

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

simplify228.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
289×	`fma-neg_binary64`
258×	`cancel-sign-sub-inv_binary64`
238×	`distribute-rgt-in_binary64`
227×	`distribute-lft-in_binary64`

Counts

217 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	8475
1	748	7200
2	2426	6998
3	4754	6956
4	4977	6956
5	4952	6956

prune233.0ms (3.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	362	2	364
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	362	11	373

Error

2.0b

Counts

373 → 11

Alt Table

Status	Error	Program
	46.5b	(/.f64 (/.f64 (-.f64 (/.f64 (*.f64 a d) c) b) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	34.7b	(neg.f64 (/.f64 a d))
✓	17.8b	(/.f64 (/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	43.1b	(/.f64 (neg.f64 a) (hypot.f64 d c))
	17.9b	(.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))))
	46.0b	(/.f64 b (hypot.f64 d c))
✓	17.7b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
	46.0b	(/.f64 (/.f64 b (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	40.7b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	47.2b	(/.f64 (neg.f64 b) (hypot.f64 d 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))

Compiler

Compiled 11888 to 3259 computations (72.6% saved)

regimes2.4s (37%)

Accuracy

Total 9.2b remaining (85.6%)

Threshold costs 0b (0%)

Counts

195 → 3

Compiler

Compiled 21068 to 12159 computations (42.3% saved)

bsearch7.0ms (0.1%)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	94
1	42	94
2	54	92
3	63	92
4	69	92
5	71	92
6	71	92

end1.0ms (0%)

Compiler: Compiled 66 to 25 computations (62.1% saved)

sample889.0ms (13.4%)

Algorithm

1×

intervals

Results

451.0ms	8000×	body	128	valid
23.0ms	462×	body	128	invalid

Compiler

Compiled 288 to 157 computations (45.5% saved)

Details

analyze676.0ms (10.2%)

sample137.0ms (2.1%)

simplify68.0ms (1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series111.0ms (1.7%)

rewrite11.0ms (0.2%)

simplify121.0ms (1.8%)

prune87.0ms (1.3%)

localize11.0ms (0.2%)

series249.0ms (3.8%)

rewrite31.0ms (0.5%)

simplify131.0ms (2%)

prune195.0ms (3%)

localize10.0ms (0.1%)

series217.0ms (3.3%)

rewrite24.0ms (0.4%)

simplify127.0ms (1.9%)

prune196.0ms (3%)

localize13.0ms (0.2%)

series336.0ms (5.1%)

rewrite39.0ms (0.6%)

simplify228.0ms (3.4%)

prune233.0ms (3.5%)

regimes2.4s (37%)

bsearch7.0ms (0.1%)

simplify9.0ms (0.1%)

end1.0ms (0%)

sample889.0ms (13.4%)

Profiling