Details

analyze5.9s (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 123 to 87 computations (29.3% saved)

sample12.0s (15.1%)

Results

11.8s

8256×

body

128

valid

Compiler

Compiled 338 to 238 computations (29.6% saved)

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary32`
676×	`div-sub_binary32`
601×	`times-frac_binary32`
366×	`associate-/l/_binary32`
346×	`distribute-rgt-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	138
1	66	133
2	117	125
3	212	117
4	404	117
5	1310	117
6	4092	117
7	5339	117

prune14.0ms (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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Status

Error

Program

▶

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Compiler

Compiled 319 to 215 computations (32.6% saved)

localize247.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
✓	0.4b	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
✓	11.6b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
✓	12.1b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

series340.0ms (0.4%)

Counts

4 → 96

Calls

4 calls:

235.0ms	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
50.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))
49.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
5.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))

rewrite108.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

267×	`expm1-udef_binary32`
267×	`log1p-udef_binary32`
236×	`log-pow_binary32`
148×	`add-sqr-sqrt_binary32`
137×	`add-log-exp_binary32`

Counts

4 → 99

Calls

4 calls:

104.0ms	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
104.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
104.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
104.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	290	58
2	3476	58
3	5011	58
0	0	0
1	0	0

simplify213.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

941×	`associate-/r*_binary32`
568×	`fma-def_binary32`
362×	`associate-*l/_binary32`
270×	`associate-/r/_binary32`
147×	`associate-r_binary32`

Counts

195 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	2981
1	398	2941
2	1744	2886
3	4980	2886
4	4991	2886
5	4983	2886

prune2.5s (3.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	442	2	444
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	443	2	445

Error

0.2b

Counts

445 → 2

Alt Table

Status	Error	Program
	1.3b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 2 (.f32 (PI.f32) u1)))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (.f32 alphay alphay)))) (-.f32 1 u0)))))
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (-.f32 (exp.f32 (log1p.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))))) 1) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Status

Error

Program

1.3b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 2 (*.f32 (PI.f32) u1)))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

▶

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (-.f32 (exp.f32 (log1p.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))))) 1) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Compiler

Compiled 38320 to 24524 computations (36% saved)

localize227.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
	11.6b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
	12.1b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))
✓	12.4b	(-.f32 (exp.f32 (log1p.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))))) 1)

series2.9s (3.6%)

Counts

1 → 36

Calls

1 calls:

2.9s	(-.f32 (exp.f32 (log1p.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))))) 1)

rewrite93.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

309×	`log1p-udef_binary32`
191×	`prod-diff_binary32`
175×	`add-sqr-sqrt_binary32`
166×	`expm1-log1p-u_binary32`
165×	`log1p-expm1-u_binary32`

Counts

1 → 38

Calls

1 calls:

90.0ms

(-.f32 (exp.f32 (log1p.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	352	21
2	4122	21
3	4946	21
0	0	0
1	0	0

simplify56.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary32`
9×	`fma-def_binary32`
2×	`associate-r_binary32`
2×	`associate-l_binary32`
2×	`associate-/l*_binary32`

Counts

74 → 39

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	756
1	20	756
2	32	756
3	46	756
4	53	756
5	53	756

prune1.7s (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	311	2	313

Error

0.2b

Counts

313 → 2

Alt Table

Status	Error	Program
	1.3b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 2 (.f32 (PI.f32) u1)))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (.f32 alphay alphay)))) (-.f32 1 u0)))))
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (/.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3) -1) (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 2) (+.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 1))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Status

Error

Program

1.3b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 2 (*.f32 (PI.f32) u1)))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

▶

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (/.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3) -1) (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 2) (+.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 1))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Compiler

Compiled 27565 to 18082 computations (34.4% saved)

localize327.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3)
✓	11.0b	(+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3) -1)
	11.6b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
	12.1b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

series482.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

341.0ms

(+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3) -1)

141.0ms

(pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3)

rewrite106.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

205×	`add-sqr-sqrt_binary32`
195×	`log1p-expm1-u_binary32`
195×	`expm1-log1p-u_binary32`
192×	`add-log-exp_binary32`
191×	`add-cbrt-cube_binary32`

Counts

2 → 63

Calls

2 calls:

102.0ms

(pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3)

102.0ms

(+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	57
1	422	57
2	4890	57
3	5131	57
0	0	0
1	0	0

simplify442.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

770×	`distribute-rgt-in_binary32`
498×	`distribute-lft-out_binary32`
446×	`sqr-pow_binary32`
445×	`distribute-rgt-out_binary32`
302×	`unswap-sqr_binary32`

Counts

135 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	3708
1	73	3636
2	141	3636
3	335	3564
4	1021	3564
5	2231	3564
6	2438	3564
7	2614	3564
8	2823	3564
9	3088	3564
10	3426	3564
11	4929	3564
12	4888	3564

prune3.7s (4.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	357	1	358
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	358	2	360

Error

0.2b

Counts

360 → 2

Alt Table

Status	Error	Program
	1.3b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 2 (.f32 (PI.f32) u1)))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (.f32 alphay alphay)))) (-.f32 1 u0)))))
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (/.f32 (/.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 9) -1) (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 6) (-.f32 1 (.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3) -1)))) (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 2) (+.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 1))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (.f32 alphay alphay)))) (-.f32 1 u0)))))

Status

Error

Program

1.3b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 2 (*.f32 (PI.f32) u1)))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

▶

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (/.f32 (/.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 9) -1) (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 6) (-.f32 1 (*.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3) -1)))) (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 2) (+.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 1))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Compiler

Compiled 47001 to 32121 computations (31.7% saved)

localize334.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 9)
✓	9.6b	(+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 9) -1)
	11.6b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
	12.1b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

series3.1s (3.9%)

Counts

2 → 72

Calls

2 calls:

2.9s

(+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 9) -1)

249.0ms

(pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 9)

rewrite103.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

207×	`add-sqr-sqrt_binary32`
198×	`log1p-expm1-u_binary32`
198×	`expm1-log1p-u_binary32`
195×	`add-log-exp_binary32`
194×	`add-cbrt-cube_binary32`

Counts

2 → 47

Calls

2 calls:

100.0ms

(pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 9)

100.0ms

(+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 9) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	57
1	425	57
2	4957	57
3	5159	57
0	0	0
1	0	0

simplify534.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

650×	`+-commutative_binary32`
599×	`distribute-lft-out_binary32`
467×	`unswap-sqr_binary32`
412×	`distribute-rgt-in_binary32`
396×	`*-commutative_binary32`

Counts

119 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	10512
1	138	9576
2	369	9468
3	1575	9468
4	2407	9468
5	3627	9468
6	5222	9468

prune4.9s (6.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	454	0	454
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	454	2	456

Error

0.2b

Counts

456 → 2

Alt Table

Status

Error

Program

1.3b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 2 (*.f32 (PI.f32) u1)))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

✓

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (/.f32 (/.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 9) -1) (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 6) (-.f32 1 (*.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 3) -1)))) (+.f32 (pow.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 2) (+.f32 (+.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) 1) 1))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Compiler

Compiled 77097 to 53920 computations (30.1% saved)

regimes38.8s (49%)

Accuracy

Total 0.0b remaining (0.1%)

Threshold costs 0.0b (0.1%)

Counts

785 → 1

Compiler

Compiled 1031853 to 736329 computations (28.6% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary32`
7×	`cancel-sign-sub-inv_binary32`
5×	`*-commutative_binary32`
5×	`sub-neg_binary32`
3×	`distribute-rgt-neg-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	251
1	66	250
2	75	248
3	79	248
4	86	248
5	82	248

end250.0ms (0.3%)

Compiler: Compiled 553 to 397 computations (28.2% saved)

Details

analyze5.9s (7.4%)

sample12.0s (15.1%)

simplify71.0ms (0.1%)

prune14.0ms (0%)

localize247.0ms (0.3%)

series340.0ms (0.4%)

rewrite108.0ms (0.1%)

simplify213.0ms (0.3%)

prune2.5s (3.1%)

localize227.0ms (0.3%)

series2.9s (3.6%)

rewrite93.0ms (0.1%)

simplify56.0ms (0.1%)

prune1.7s (2.1%)

localize327.0ms (0.4%)

series482.0ms (0.6%)

rewrite106.0ms (0.1%)

simplify442.0ms (0.6%)

prune3.7s (4.6%)

localize334.0ms (0.4%)

series3.1s (3.9%)

rewrite103.0ms (0.1%)

simplify534.0ms (0.7%)

prune4.9s (6.2%)

regimes38.8s (49%)

simplify7.0ms (0%)

end250.0ms (0.3%)

Profiling