Details

analyze308.0ms (3.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample3.5s (38.4%)

Results

1.1s	934×	body	4096	valid
1.0s	5577×	body	128	valid
793.0ms	867×	body	2048	valid
360.0ms	518×	body	1024	valid
128.0ms	239×	body	512	valid
44.0ms	121×	body	256	valid

Compiler

Compiled 54 to 42 computations (22.2% saved)

preprocess69.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

685×	`fma-neg_binary64`
476×	`fma-def_binary64`
312×	`associate-l_binary64`
295×	`associate-r_binary64`
162×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	144
1	129	100
2	363	100
3	1152	100
4	4674	100
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

554×	`fma-neg_binary64`
423×	`fma-def_binary64`
380×	`cancel-sign-sub-inv_binary64`
305×	`div-sub_binary64`
227×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	36
1	44	25
2	109	25
3	296	25
4	960	25
5	3457	25

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

11.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.7b	(*.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)) (/.f64 180 (PI.f64)))
	30.1b	(.f64 180 (/.f64 (atan.f64 (.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) (PI.f64)))

Status

Error

Program

▶

11.7b

(*.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)) (/.f64 180 (PI.f64)))

30.1b

(*.f64 180 (/.f64 (atan.f64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) (PI.f64)))

Compiler

Compiled 132 to 93 computations (29.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 B (-.f64 A C))
✓	0.0b	(*.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)) (/.f64 180 (PI.f64)))
✓	0.0b	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)
✓	0.6b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C)))

series219.0ms (2.4%)

Counts

4 → 144

Calls

36 calls:

41.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)	A	0
22.0ms	(*.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)) (/.f64 180 (PI.f64)))	C	inf
9.0ms	(hypot.f64 B (-.f64 A C))	B	-inf
9.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C))) B)	B	0
8.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C)))	C	0

rewrite74.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

312×	`log1p-udef_binary64`
174×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`
166×	`expm1-log1p-u_binary64`
165×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	61
1	329	61
2	4913	61

Stop Event

1×	node limit

Counts

4 → 124

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-def_binary64`
263×	`associate-/l*_binary64`
229×	`sub-neg_binary64`
221×	`times-frac_binary64`
184×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	549	6531
1	1981	5907

Stop Event

1×	node limit

Counts

268 → 318

prune335.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	311	7	318
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	313	7	320

Error

0.3b

Counts

320 → 7

Alt Table

Status	Error	Program
	49.3b	(.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 B B) A) (.f64 (/.f64 (*.f64 B B) A) (/.f64 C A)))) B)) (/.f64 180 (PI.f64)))
	47.8b	(.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (/.f64 180 (PI.f64)))
	43.1b	(.f64 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (*.f64 (/.f64 B C) (/.f64 A C))))) (/.f64 180 (PI.f64)))
	51.9b	(*.f64 (atan.f64 (/.f64 (/.f64 (-.f64 (pow.f64 (-.f64 C A) 2) (pow.f64 (hypot.f64 B (-.f64 A C)) 2)) (+.f64 (-.f64 C A) (hypot.f64 B (-.f64 A C)))) B)) (/.f64 180 (PI.f64)))
▶	14.8b	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)) (*.f64 (PI.f64) 1/180))
	17.5b	(*.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 A C)) B))) (/.f64 180 (PI.f64)))
	17.6b	(*.f64 (atan.f64 (/.f64 (+.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (hypot.f64 B (-.f64 A C)))) B)) (/.f64 180 (PI.f64)))

Compiler

Compiled 12017 to 6522 computations (45.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)
✓	0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)) (*.f64 (PI.f64) 1/180))
✓	0.3b	(-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))
✓	0.6b	(+.f64 A (hypot.f64 B (-.f64 A C)))

series163.0ms (1.8%)

Counts

4 → 144

Calls

36 calls:

10.0ms	(/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)	A	0
8.0ms	(/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)	C	0
8.0ms	(/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)	B	-inf
7.0ms	(/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)	B	0
7.0ms	(-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))	A	0

rewrite53.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

173×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`
164×	`add-cbrt-cube_binary64`
161×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	64
1	327	64

Stop Event

1×	node limit

Counts

4 → 154

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary64`
314×	`associate--l+_binary64`
231×	`associate-/l*_binary64`
230×	`sub-neg_binary64`
196×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	488	6259
1	1763	5621

Stop Event

1×	node limit

Counts

298 → 348

prune353.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	345	3	348
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	347	8	355

Error

0.3b

Counts

355 → 8

Alt Table

Status	Error	Program
	49.3b	(.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 B B) A) (.f64 (/.f64 (*.f64 B B) A) (/.f64 C A)))) B)) (/.f64 180 (PI.f64)))
	47.8b	(.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (/.f64 180 (PI.f64)))
	43.1b	(.f64 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (*.f64 (/.f64 B C) (/.f64 A C))))) (/.f64 180 (PI.f64)))
	42.5b	(/.f64 (atan.f64 (/.f64 (-.f64 C (/.f64 (-.f64 (.f64 A A) (pow.f64 (hypot.f64 B (-.f64 A C)) 2)) (-.f64 A (hypot.f64 B (-.f64 A C))))) B)) (.f64 (PI.f64) 1/180))
✓	14.8b	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)) (*.f64 (PI.f64) 1/180))
	17.5b	(*.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 A C)) B))) (/.f64 180 (PI.f64)))
▶	16.6b	(/.f64 (atan.f64 (/.f64 (-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)) B)) (*.f64 (PI.f64) 1/180))
	46.3b	(/.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 C (.f64 (/.f64 A B) (/.f64 A B))) (/.f64 B (/.f64 A B)))) B)) (*.f64 (PI.f64) 1/180))

Compiler

Compiled 12490 to 6492 computations (48% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)) B)) (*.f64 (PI.f64) 1/180))
✓	0.0b	(/.f64 (-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)) B)
✓	5.9b	(-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A))
✓	8.5b	(fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)

series455.0ms (5%)

Counts

4 → 82

Calls

36 calls:

34.0ms	(/.f64 (-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)) B)	A	0
32.0ms	(/.f64 (-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)) B)	B	-inf
30.0ms	(/.f64 (-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)) B)	B	inf
28.0ms	(-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A))	A	0
24.0ms	(fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)	A	0

rewrite79.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

314×	`log1p-udef_binary64`
174×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`
164×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	337	64
2	4840	64

Stop Event

1×	node limit

Counts

4 → 134

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Rules

575×	`times-frac_binary64`
376×	`fma-neg_binary64`
349×	`fma-def_binary64`
215×	`+-commutative_binary64`
202×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	317	5283
1	1135	4180
2	4196	4180

Stop Event

1×	node limit

Counts

216 → 216

prune217.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	216	8	224

Error

0.3b

Counts

224 → 8

Alt Table

Status	Error	Program
	49.3b	(.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 B B) A) (.f64 (/.f64 (*.f64 B B) A) (/.f64 C A)))) B)) (/.f64 180 (PI.f64)))
	47.8b	(.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (/.f64 180 (PI.f64)))
	43.1b	(.f64 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (*.f64 (/.f64 B C) (/.f64 A C))))) (/.f64 180 (PI.f64)))
	42.5b	(/.f64 (atan.f64 (/.f64 (-.f64 C (/.f64 (-.f64 (.f64 A A) (pow.f64 (hypot.f64 B (-.f64 A C)) 2)) (-.f64 A (hypot.f64 B (-.f64 A C))))) B)) (.f64 (PI.f64) 1/180))
✓	14.8b	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)) (*.f64 (PI.f64) 1/180))
▶	17.5b	(*.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 A C)) B))) (/.f64 180 (PI.f64)))
✓	16.6b	(/.f64 (atan.f64 (/.f64 (-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)) B)) (*.f64 (PI.f64) 1/180))
	46.3b	(/.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 C (.f64 (/.f64 A B) (/.f64 A B))) (/.f64 B (/.f64 A B)))) B)) (*.f64 (PI.f64) 1/180))

Compiler

Compiled 9122 to 4684 computations (48.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 B (-.f64 A C))
✓	0.0b	(*.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 A C)) B))) (/.f64 180 (PI.f64)))
✓	0.0b	(/.f64 (hypot.f64 B (-.f64 A C)) B)
✓	6.7b	(-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 A C)) B))

series150.0ms (1.7%)

Counts

3 → 108

Calls

27 calls:

14.0ms	(/.f64 (hypot.f64 B (-.f64 A C)) B)	B	-inf
11.0ms	(-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 A C)) B))	A	0
11.0ms	(/.f64 (hypot.f64 B (-.f64 A C)) B)	B	inf
9.0ms	(-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 A C)) B))	C	0
9.0ms	(-.f64 (/.f64 (-.f64 C A) B) (/.f64 (hypot.f64 B (-.f64 A C)) B))	B	0

rewrite44.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

189×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
179×	`add-cbrt-cube_binary64`
176×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	51
1	357	51

Stop Event

1×	node limit

Counts

3 → 114

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

413×	`fma-def_binary64`
281×	`associate-+r+_binary64`
247×	`associate-+l+_binary64`
210×	`associate--r+_binary64`
195×	`associate--l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	379	5164
1	1389	4697

Stop Event

1×	node limit

Counts

222 → 242

prune353.0ms (3.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	321	8	329

Error

0.3b

Counts

329 → 8

Alt Table

Status	Error	Program
	49.3b	(.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 B B) A) (.f64 (/.f64 (*.f64 B B) A) (/.f64 C A)))) B)) (/.f64 180 (PI.f64)))
	47.8b	(.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (/.f64 180 (PI.f64)))
	43.1b	(.f64 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (*.f64 (/.f64 B C) (/.f64 A C))))) (/.f64 180 (PI.f64)))
✓	14.8b	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))) B)) (*.f64 (PI.f64) 1/180))
	17.6b	(*.f64 (atan.f64 (-.f64 (/.f64 (-.f64 C A) B) (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 B (-.f64 A C)) B) 3)))) (/.f64 180 (PI.f64)))
	25.6b	(.f64 (atan.f64 (/.f64 (-.f64 (/.f64 B (hypot.f64 B (-.f64 A C))) (.f64 (/.f64 B (-.f64 C A)) 1)) (*.f64 (/.f64 B (-.f64 C A)) (/.f64 B (hypot.f64 B (-.f64 A C)))))) (/.f64 180 (PI.f64)))
✓	16.6b	(/.f64 (atan.f64 (/.f64 (-.f64 C (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) A)) B)) (*.f64 (PI.f64) 1/180))
	46.3b	(/.f64 (atan.f64 (/.f64 (.f64 1/2 (+.f64 (/.f64 C (.f64 (/.f64 A B) (/.f64 A B))) (/.f64 B (/.f64 A B)))) B)) (*.f64 (PI.f64) 1/180))

Compiler

Compiled 13172 to 6701 computations (49.1% saved)

regimes2.1s (23.1%)

Accuracy

Total 11.3b remaining (97.2%)

Threshold costs 0b (0%)

Counts

261 → 2

Compiler

Compiled 41195 to 28609 computations (30.6% saved)

bsearch74.0ms (0.8%)

Algorithm

1×	binary-search

Calls

1 calls:

62.0ms

Steps

Iters	Point		Range
4.283004787062823e+31	∈ [	1.936685331243197e+29	,	4.916011673615074e+31	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	62
1	41	62
2	51	62
3	57	62
4	60	62

Stop Event

1×

saturated

end130.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 280 to 175 computations (37.5% saved)

Details

analyze308.0ms (3.4%)

sample3.5s (38.4%)

preprocess69.0ms (0.8%)

simplify26.0ms (0.3%)

prune5.0ms (0%)

localize10.0ms (0.1%)

series219.0ms (2.4%)

rewrite74.0ms (0.8%)

simplify88.0ms (1%)

prune335.0ms (3.7%)

localize11.0ms (0.1%)

series163.0ms (1.8%)

rewrite53.0ms (0.6%)

simplify88.0ms (1%)

prune353.0ms (3.9%)

localize12.0ms (0.1%)

series455.0ms (5%)

rewrite79.0ms (0.9%)

simplify88.0ms (1%)

prune217.0ms (2.4%)

localize12.0ms (0.1%)

series150.0ms (1.7%)

rewrite44.0ms (0.5%)

simplify70.0ms (0.8%)

prune353.0ms (3.9%)

regimes2.1s (23.1%)

bsearch74.0ms (0.8%)

simplify4.0ms (0%)

end130.0ms (1.4%)

Profiling