Details

analyze3.0s (17.4%)

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)

sample6.0s (35.5%)

Results

6.0s

8256×

body

128

valid

Compiler

Compiled 338 to 238 computations (29.6% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary32`
601×	`times-frac_binary32`
347×	`distribute-rgt-in_binary32`
336×	`associate-/l/_binary32`
284×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	138
1	66	133
2	121	125
3	235	117
4	495	117
5	1791	117

Stop Event

1×	node limit

Counts

1 → 2

prune7.0ms (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 u0 (.f32 (fma.f32 (cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax)))) (/.f32 (cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax)))) (.f32 alphax alphax)) (.f32 (sin.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax)))) (/.f32 (sin.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax)))) (.f32 alphay alphay)))) (-.f32 1 u0))))))

Status

Error

Program

▶

0.2b

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

Compiler

Compiled 319 to 225 computations (29.5% saved)

localize104.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax)))) (*.f32 alphax alphax))
✓	0.4b	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
✓	12.7b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
✓	13.3b	(cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax))))

series116.0ms (0.7%)

Counts

4 → 96

Calls

4 calls:

70.0ms	(/.f32 (cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax)))) (*.f32 alphax alphax))
24.0ms	(cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax))))
20.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
2.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))

rewrite68.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`log1p-udef_binary32`
171×	`add-sqr-sqrt_binary32`
159×	`add-log-exp_binary32`
159×	`log1p-expm1-u_binary32`
159×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	68
1	337	67
2	4348	67

Stop Event

1×	node limit

Counts

4 → 95

Calls

4 calls:

66.0ms	(/.f32 (cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax)))) (*.f32 alphax alphax))
66.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
66.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
66.0ms	(cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax))))

simplify49.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

714×	`times-frac_binary32`
573×	`associate-r_binary32`
481×	`associate-l_binary32`
462×	`associate-/l*_binary32`
278×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	2477
1	213	2437
2	809	2434

Stop Event

1×	node limit

Counts

191 → 113

prune772.0ms (4.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	295	1	296
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	296	1	297

Error

0.2b

Counts

297 → 1

Alt Table

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

Status

Error

Program

▶

0.2b

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

Compiler

Compiled 24693 to 17051 computations (30.9% saved)

localize128.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
	12.7b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
	13.3b	(cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax))))
✓	13.4b	(-.f32 (exp.f32 (log1p.f32 (cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax)))))) 1)

series1.2s (6.8%)

Counts

1 → 36

Calls

1 calls:

1.2s	(-.f32 (exp.f32 (log1p.f32 (cos.f32 (atan.f32 (.f32 alphay (/.f32 (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) alphax)))))) 1)

rewrite58.0ms (0.3%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	356	21
2	4324	21

Stop Event

1×	node limit

Counts

1 → 38

Calls

1 calls:

57.0ms

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

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	756
1	20	756
2	32	756
3	49	756
4	61	756

Stop Event

1×

saturated

Counts

74 → 39

prune697.0ms (4.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	299	0	299
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	299	1	300

Error

0.2b

Counts

300 → 1

Alt Table

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

Status

Error

Program

✓

0.2b

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

Compiler

Compiled 26136 to 18352 computations (29.8% saved)

regimes4.7s (27.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

163 → 1

Compiler

Compiled 168835 to 124133 computations (26.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`
4×	`+-commutative_binary32`
3×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	124
1	44	124
2	48	124
3	50	124
4	51	124

Stop Event

1×

saturated

end139.0ms (0.8%)

Compiler: Compiled 243 to 180 computations (25.9% saved)

Details

analyze3.0s (17.4%)

sample6.0s (35.5%)

simplify22.0ms (0.1%)

prune7.0ms (0%)

localize104.0ms (0.6%)

series116.0ms (0.7%)

rewrite68.0ms (0.4%)

simplify49.0ms (0.3%)

prune772.0ms (4.5%)

localize128.0ms (0.7%)

series1.2s (6.8%)

rewrite58.0ms (0.3%)

simplify23.0ms (0.1%)

prune697.0ms (4.1%)

regimes4.7s (27.5%)

simplify4.0ms (0%)

end139.0ms (0.8%)

Profiling