Details

analyze3.1s (30.8%)

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 109 to 77 computations (29.4% saved)

sample194.0ms (1.9%)

Algorithm

1×

intervals

Results

150.0ms	256×	body	128	valid
10.0ms	256×	pre	128	true

Compiler

Compiled 205 to 145 computations (29.3% saved)

simplify51.0ms (0.5%)

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

prune7.0ms (0.1%)

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)

localize127.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	12.1b	(tan.f32 (*.f32 PI.f32 (fma.f32 2 u1 1/2)))
✓	12.1b	(tan.f32 (*.f32 PI.f32 (fma.f32 2 u1 1/2)))
	12.8b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 PI.f32 (fma.f32 2 u1 1/2))))))
✓	12.8b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 PI.f32 (fma.f32 2 u1 1/2))))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cube-cbrt_binary32`
8×	`pow1_binary32`
8×	`add-sqr-sqrt_binary32`
6×	`add-cbrt-cube_binary32`
6×	`log1p-expm1-u_binary32`

Counts

2 → 67

Calls

2 calls:

11.0ms	(tan.f32 (*.f32 PI.f32 (fma.f32 2 u1 1/2)))
10.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 PI.f32 (fma.f32 2 u1 1/2))))))

series83.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

55.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 PI.f32 (fma.f32 2 u1 1/2))))))
28.0ms	(tan.f32 (*.f32 PI.f32 (fma.f32 2 u1 1/2)))

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

705×	`times-frac_binary32`
696×	`associate-r_binary32`
622×	`associate-l_binary32`
466×	`associate-/l*_binary32`
282×	`associate-/r*_binary32`

Counts

115 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	2454
1	295	2384
2	974	2382
3	5637	2382

prune322.0ms (3.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	282	0	282
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	282	1	283

Error

0.2b

Counts

283 → 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 13254 to 8564 computations (35.4% saved)

regimes194.0ms (1.9%)

Accuracy

Total 0.0b remaining (0.2%)

Threshold costs 0.0b (0.2%)

Compiler

Compiled 3345 to 2323 computations (30.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
5×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	146
1	45	146
2	49	146
3	51	146
4	52	146
5	51	146

end2.0ms (0%)

Compiler: Compiled 92 to 64 computations (30.4% saved)

sample6.0s (58.5%)

Algorithm

1×

intervals

Results

4.7s	8000×	body	128	valid
333.0ms	8000×	pre	128	true

Compiler

Compiled 282 to 198 computations (29.8% saved)

Details

analyze3.1s (30.8%)

sample194.0ms (1.9%)

simplify51.0ms (0.5%)

prune7.0ms (0.1%)

localize127.0ms (1.2%)

rewrite24.0ms (0.2%)

series83.0ms (0.8%)

simplify75.0ms (0.7%)

prune322.0ms (3.2%)

regimes194.0ms (1.9%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample6.0s (58.5%)

Profiling