Details

analyze410.0ms (7.5%)

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 39 to 31 computations (20.5% saved)

sample2.2s (40.6%)

Results

2.2s	8256×	body	128	valid
4.0ms	5×	body	128	invalid

Compiler

Compiled 78 to 62 computations (20.5% saved)

preprocess38.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

104×	`fma-neg_binary32`
95×	`fma-def_binary32`
60×	`sub-neg_binary32`
45×	`cancel-sign-sub-inv_binary32`
30×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 cosTheta_i)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) cosTheta_i)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u2)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u1)))

Outputs
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 cosTheta_i)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
(.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 cosTheta_i)))))
(.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 cosTheta_i)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) cosTheta_i)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) cosTheta_i))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) cosTheta_i))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u2)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u1)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u2)))) (cos.f32 (.f32 u1 (*.f32 2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u2)))) (cos.f32 (.f32 2 (*.f32 u1 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u2)))) (cos.f32 (.f32 u1 (*.f32 2 (PI.f32)))))

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

40×	`fma-neg_binary32`
22×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
13×	`fma-def_binary32`
10×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Outputs
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (PI.f32) (*.f32 2 u2))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

prune4.0ms (0.1%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	14.1b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize38.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
✓	0.1b	(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
✓	0.4b	(*.f32 (PI.f32) u2)

series39.0ms (0.7%)

Counts

4 → 52

Calls

15 calls:

Time	Variable		Point	Expression
27.0ms	u2	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
2.0ms	u1	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
2.0ms	u1	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
2.0ms	u1	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
2.0ms	u2	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

rewrite60.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`prod-diff_binary32`
204×	`expm1-udef_binary32`
204×	`log1p-udef_binary32`
133×	`add-sqr-sqrt_binary32`
129×	`pow1_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	266	37
2	3250	37

Stop Event

1×	node limit

Counts

4 → 96

Calls

Call 1

Inputs
(*.f32 (PI.f32) u2)
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (PI.f32) u2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (PI.f32) u2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (PI.f32) u2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (PI.f32) u2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (PI.f32) u2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (PI.f32) u2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 u2) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (PI.f32) u2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (*.f32 (PI.f32) u2)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) (sqrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3) (pow.f32 (log1p.f32 u1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (sqrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (sqrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (sqrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (sqrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (sqrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (sqrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (sqrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 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1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) 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((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (sqrt.f32 (log1p.f32 u1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (log1p.f32 u1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (sqrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (sqrt.f32 (log1p.f32 u1))) (cbrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (log1p.f32 u1) 1/4) (pow.f32 (log1p.f32 u1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 u1)) 2)) (sqrt.f32 (cbrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 -1) (sqrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 1 1/2) (sqrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (pow.f32 (cbrt.f32 (log1p.f32 u1)) 2) 1/2) (pow.f32 (cbrt.f32 (log1p.f32 u1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 -1 1/2) (sqrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (log1p.f32 u1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (log1p.f32 u1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (log1p.f32 u1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (sqrt.f32 (log1p.f32 u1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f32 (sqrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (sqrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (sqrt.f32 (log1p.f32 u1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (log1p.f32 u1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (sqrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (sqrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (sqrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (log1p.f32 u1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (sqrt.f32 (log1p.f32 u1))) 1))))))

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary32`
560×	`associate-l_binary32`
399×	`times-frac_binary32`
346×	`associate-/r*_binary32`
306×	`associate-/l*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	1936
1	421	1724
2	1407	1554

Stop Event

1×	node limit

Counts

148 → 147

Calls

Call 1

Inputs
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) u1)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (-.f32 1/3 (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (pow.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) 2))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))))
(.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32))))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1)))) 1/3) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))))
(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
(+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 6)))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
1
(+.f32 1 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1))))))
(+.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (.f32 1/2 (/.f32 1 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))) (+.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))) (+.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (+.f32 (.f32 1/2 (/.f32 (-.f32 1/3 (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (pow.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) 2)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 3)))) (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))))))
(sqrt.f32 (log.f32 (/.f32 -1 u1)))
(+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 u1))))
(+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 u1))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (*.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (pow.f32 u1 2))))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (+.f32 (.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1)))) 1/3) (pow.f32 u1 3)))) (+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 u1))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (*.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (pow.f32 u1 2)))))))

Outputs
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)))
(.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
(.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))
(fma.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (.f32 1/2 (/.f32 (/.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) u1)))
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(fma.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (.f32 1/2 (+.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) 2)) (/.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (.f32 u1 u1)) (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)))) (/.f32 (/.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) u1))))
(fma.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (.f32 1/2 (fma.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (.f32 u1 u1)) (/.f32 (/.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))))))
(fma.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (+.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) u1) (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 2)) (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (*.f32 u1 u1))))))
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(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
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(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) u1)) (.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
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(+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 u1))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (*.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (pow.f32 u1 2))))))
(+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 1/2 (+.f32 (.f32 (/.f32 1 u1) (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (*.f32 u1 u1))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (+.f32 (/.f32 1 u1) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (*.f32 u1 u1)))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (+.f32 (/.f32 1 u1) (/.f32 (-.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) 1/4)) (*.f32 u1 u1)))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (+.f32 (.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1)))) 1/3) (pow.f32 u1 3)))) (+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 u1))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (*.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (pow.f32 u1 2)))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (fma.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (log.f32 (/.f32 -1 u1))) 1/3) (pow.f32 u1 3))) (+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 1/2 (+.f32 (.f32 (/.f32 1 u1) (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (*.f32 u1 u1)))))))
(fma.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (/.f32 (fma.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (log.f32 (/.f32 -1 u1))) 1/3) (pow.f32 u1 3)) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (+.f32 (/.f32 1 u1) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (*.f32 u1 u1)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(+.f32 (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (/.f32 (fma.f32 -1/2 (/.f32 (-.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) 1/4)) (log.f32 (/.f32 -1 u1))) 1/3) (pow.f32 u1 3)) (+.f32 (/.f32 1 u1) (/.f32 (-.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) 1/4)) (*.f32 u1 u1))))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))

prune225.0ms (4.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	134	13	147
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	136	13	149

Error

0.1b

Counts

149 → 13

Alt Table

Status	Error	Program
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 1))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 1 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))))
	8.5b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 3/2) 1/3) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2)))
	7.8b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 3)))
	9.0b	(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 2)))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 (-.f32 (pow.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) 3) (pow.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 3)) (+.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (+.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	2.7b	(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (.f32 u2 u2) (.f32 (pow.f32 (PI.f32) 2) -2) (.f32 2/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 (-.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (+.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))

Compiler

Compiled 5017 to 3140 computations (37.4% saved)

localize43.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))
✓	0.2b	(log1p.f32 (*.f32 (PI.f32) u2))
✓	0.2b	(expm1.f32 (log1p.f32 (*.f32 (PI.f32) u2)))
	0.4b	(*.f32 (PI.f32) u2)

series6.0ms (0.1%)

Counts

3 → 44

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	u2	@	0	(log1p.f32 (*.f32 (PI.f32) u2))
1.0ms	u2	@	-inf	(log1p.f32 (*.f32 (PI.f32) u2))
1.0ms	u2	@	inf	(log1p.f32 (*.f32 (PI.f32) u2))
0.0ms	u1	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))
0.0ms	u1	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))

rewrite51.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`prod-diff_binary32`
217×	`log1p-udef_binary32`
140×	`add-sqr-sqrt_binary32`
137×	`pow1_binary32`
135×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	285	29
2	3426	29

Stop Event

1×	node limit

Counts

3 → 63

Calls

Call 1

Inputs
(expm1.f32 (log1p.f32 (*.f32 (PI.f32) u2)))
(log1p.f32 (*.f32 (PI.f32) u2))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (.f32 (PI.f32) u2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (.f32 (PI.f32) u2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (PI.f32) u2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 u2 (PI.f32))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (PI.f32) u2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (.f32 (PI.f32) u2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (.f32 (PI.f32) u2)) (pow.f32 (cbrt.f32 (.f32 (PI.f32) u2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) u2)) 2) (cbrt.f32 (.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 u2) 2) (.f32 (cbrt.f32 u2) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (PI.f32) 2)) (.f32 (cbrt.f32 (PI.f32)) u2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 (PI.f32) u2)) (sqrt.f32 (.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 u2) (.f32 (sqrt.f32 u2) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) u2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (PI.f32) (pow.f32 (cbrt.f32 u2) 2)) (cbrt.f32 u2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (PI.f32) (sqrt.f32 u2)) (sqrt.f32 u2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 u2 (cbrt.f32 (pow.f32 (PI.f32) 2))) (cbrt.f32 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 u2 (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (+.f32 (.f32 (PI.f32) u2) 1) 3) 1) (+.f32 (.f32 (+.f32 (.f32 (PI.f32) u2) 1) (+.f32 (.f32 (PI.f32) u2) 1)) (+.f32 1 (.f32 (+.f32 (.f32 (PI.f32) u2) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (.f32 (+.f32 (.f32 (PI.f32) u2) 1) (+.f32 (.f32 (PI.f32) u2) 1)) 1) (+.f32 (+.f32 (.f32 (PI.f32) u2) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (PI.f32) u2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (PI.f32) u2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (PI.f32) u2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (PI.f32) u2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (PI.f32) u2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (PI.f32)) u2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (PI.f32) u2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (PI.f32) u2)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (log1p.f32 (.f32 (PI.f32) u2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (log1p.f32 (.f32 (PI.f32) u2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (log1p.f32 (.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (log1p.f32 (.f32 (PI.f32) u2))) (cbrt.f32 (pow.f32 (log1p.f32 (.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (log1p.f32 (.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (log1p.f32 (.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 (.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (log1p.f32 (.f32 (PI.f32) u2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (log1p.f32 (.f32 (PI.f32) u2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (log1p.f32 (.f32 (PI.f32) u2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (log1p.f32 (.f32 (PI.f32) u2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (log1p.f32 (.f32 (PI.f32) u2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 (.f32 (PI.f32) u2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (log1p.f32 (.f32 (PI.f32) u2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (log1p.f32 (.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (log1p.f32 (.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (sqrt.f32 (log1p.f32 u1))) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3) (pow.f32 (log1p.f32 u1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 1))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (*.f32 (PI.f32) u2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 (PI.f32) u2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (PI.f32) u2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 u2 (PI.f32))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (PI.f32) u2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (*.f32 (PI.f32) u2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 2) (cbrt.f32 (*.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 u2) 2) (*.f32 (cbrt.f32 u2) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (PI.f32) 2)) (*.f32 (cbrt.f32 (PI.f32)) u2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (*.f32 (PI.f32) u2)) (sqrt.f32 (*.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 u2) (*.f32 (sqrt.f32 u2) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (PI.f32)) (*.f32 (sqrt.f32 (PI.f32)) u2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (PI.f32) (pow.f32 (cbrt.f32 u2) 2)) (cbrt.f32 u2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (PI.f32) (sqrt.f32 u2)) (sqrt.f32 u2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 u2 (cbrt.f32 (pow.f32 (PI.f32) 2))) (cbrt.f32 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 u2 (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (+.f32 (*.f32 (PI.f32) u2) 1) 3) 1) (+.f32 (*.f32 (+.f32 (*.f32 (PI.f32) u2) 1) (+.f32 (*.f32 (PI.f32) u2) 1)) (+.f32 1 (*.f32 (+.f32 (*.f32 (PI.f32) u2) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (*.f32 (+.f32 (*.f32 (PI.f32) u2) 1) (+.f32 (*.f32 (PI.f32) u2) 1)) 1) (+.f32 (+.f32 (*.f32 (PI.f32) u2) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (PI.f32) u2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (PI.f32) u2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (PI.f32) u2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (PI.f32) u2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (PI.f32)) u2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (PI.f32) u2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (PI.f32) u2)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (log1p.f32 (*.f32 (PI.f32) u2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (log1p.f32 (*.f32 (PI.f32) u2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (log1p.f32 (*.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (log1p.f32 (*.f32 (PI.f32) u2))) (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 (PI.f32) u2)) 2)) (cbrt.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (log1p.f32 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (log1p.f32 (*.f32 (PI.f32) u2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (log1p.f32 (*.f32 (PI.f32) u2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (log1p.f32 (*.f32 (PI.f32) u2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 (*.f32 (PI.f32) u2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (log1p.f32 (*.f32 (PI.f32) u2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (*.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (sqrt.f32 (log1p.f32 u1))) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2))) 3) (pow.f32 (log1p.f32 u1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (*.f32 (PI.f32) (*.f32 u2 2))))) 1))))))

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary32`
593×	`associate-l_binary32`
532×	`associate-r_binary32`
318×	`associate-/r*_binary32`
267×	`times-frac_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1578
1	440	1448
2	1447	1326

Stop Event

1×	node limit

Counts

107 → 111

Calls

Call 1

Inputs
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(+.f32 (.f32 -1/2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (*.f32 u2 (PI.f32)))
(+.f32 (.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))) (+.f32 (.f32 -1/2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (*.f32 u2 (PI.f32))))
(+.f32 (.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))) (+.f32 (.f32 -1/2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (+.f32 (.f32 u2 (PI.f32)) (.f32 -1/4 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))))
(+.f32 (log.f32 (PI.f32)) (*.f32 -1 (log.f32 (/.f32 1 u2))))
(+.f32 (log.f32 (PI.f32)) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (.f32 -1 (log.f32 (/.f32 1 u2)))))
(-.f32 (+.f32 (log.f32 (PI.f32)) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (.f32 -1 (log.f32 (/.f32 1 u2))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(-.f32 (+.f32 (log.f32 (PI.f32)) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (+.f32 (.f32 -1 (log.f32 (/.f32 1 u2))) (.f32 1/3 (/.f32 1 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(+.f32 (log.f32 (.f32 -1 (PI.f32))) (.f32 -1 (log.f32 (/.f32 -1 u2))))
(+.f32 (.f32 -1 (log.f32 (/.f32 -1 u2))) (+.f32 (log.f32 (.f32 -1 (PI.f32))) (/.f32 1 (*.f32 u2 (PI.f32)))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 u2))) (+.f32 (log.f32 (.f32 -1 (PI.f32))) (/.f32 1 (.f32 u2 (PI.f32))))) (.f32 1/2 (/.f32 1 (*.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 u2))) (+.f32 (log.f32 (.f32 -1 (PI.f32))) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (.f32 1/3 (/.f32 1 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (.f32 1/2 (/.f32 1 (*.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) u1)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (-.f32 1/3 (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (pow.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) 2))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))))
(.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32))))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1)))) 1/3) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))))
(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
(+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 6)))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))

Outputs
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(*.f32 u2 (PI.f32))
(+.f32 (.f32 -1/2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (*.f32 u2 (PI.f32)))
(fma.f32 -1/2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (*.f32 u2 (PI.f32)))
(fma.f32 -1/2 (.f32 u2 (.f32 u2 (pow.f32 (PI.f32) 2))) (*.f32 u2 (PI.f32)))
(.f32 (PI.f32) (+.f32 (.f32 (.f32 u2 u2) (.f32 -1/2 (PI.f32))) u2))
(+.f32 (.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))) (+.f32 (.f32 -1/2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (*.f32 u2 (PI.f32))))
(fma.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (fma.f32 -1/2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 u2 (PI.f32))))
(fma.f32 (.f32 1/3 (pow.f32 u2 3)) (pow.f32 (PI.f32) 3) (fma.f32 -1/2 (.f32 u2 (.f32 u2 (pow.f32 (PI.f32) 2))) (.f32 u2 (PI.f32))))
(fma.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (.f32 (PI.f32) (+.f32 (.f32 (.f32 u2 u2) (*.f32 -1/2 (PI.f32))) u2)))
(+.f32 (.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))) (+.f32 (.f32 -1/2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (+.f32 (.f32 u2 (PI.f32)) (.f32 -1/4 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))))
(fma.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (fma.f32 -1/2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (fma.f32 u2 (PI.f32) (.f32 -1/4 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))))
(fma.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (fma.f32 -1/2 (.f32 u2 (.f32 u2 (pow.f32 (PI.f32) 2))) (fma.f32 -1/4 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (*.f32 u2 (PI.f32)))))
(fma.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (fma.f32 -1/4 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 (PI.f32) (+.f32 (.f32 (.f32 u2 u2) (.f32 -1/2 (PI.f32))) u2))))
(+.f32 (log.f32 (PI.f32)) (*.f32 -1 (log.f32 (/.f32 1 u2))))
(+.f32 (log.f32 (PI.f32)) (neg.f32 (neg.f32 (log.f32 u2))))
(+.f32 (log.f32 (PI.f32)) (log.f32 u2))
(+.f32 (log.f32 (PI.f32)) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (.f32 -1 (log.f32 (/.f32 1 u2)))))
(+.f32 (log.f32 (PI.f32)) (+.f32 (neg.f32 (neg.f32 (log.f32 u2))) (/.f32 1 (*.f32 u2 (PI.f32)))))
(+.f32 (log.f32 (PI.f32)) (+.f32 (log.f32 u2) (/.f32 1 (*.f32 u2 (PI.f32)))))
(-.f32 (+.f32 (log.f32 (PI.f32)) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (.f32 -1 (log.f32 (/.f32 1 u2))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(+.f32 (log.f32 (PI.f32)) (-.f32 (+.f32 (neg.f32 (neg.f32 (log.f32 u2))) (/.f32 1 (.f32 u2 (PI.f32)))) (/.f32 1/2 (.f32 (*.f32 u2 u2) (pow.f32 (PI.f32) 2)))))
(+.f32 (+.f32 (log.f32 u2) (/.f32 1 (.f32 u2 (PI.f32)))) (-.f32 (log.f32 (PI.f32)) (/.f32 1/2 (.f32 u2 (*.f32 u2 (pow.f32 (PI.f32) 2))))))
(+.f32 (log.f32 (PI.f32)) (+.f32 (log.f32 u2) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (/.f32 -1/2 (.f32 u2 (*.f32 u2 (pow.f32 (PI.f32) 2)))))))
(-.f32 (+.f32 (log.f32 (PI.f32)) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (+.f32 (.f32 -1 (log.f32 (/.f32 1 u2))) (.f32 1/3 (/.f32 1 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(+.f32 (log.f32 (PI.f32)) (-.f32 (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (fma.f32 -1 (neg.f32 (log.f32 u2)) (/.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))) (/.f32 1/2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)))))
(+.f32 (+.f32 (log.f32 u2) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (/.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))) (-.f32 (log.f32 (PI.f32)) (/.f32 1/2 (.f32 u2 (.f32 u2 (pow.f32 (PI.f32) 2))))))
(+.f32 (log.f32 (PI.f32)) (+.f32 (+.f32 (log.f32 u2) (/.f32 1 (.f32 u2 (PI.f32)))) (+.f32 (/.f32 (/.f32 1/3 (pow.f32 (PI.f32) 3)) (pow.f32 u2 3)) (/.f32 -1/2 (.f32 u2 (*.f32 u2 (pow.f32 (PI.f32) 2)))))))
(+.f32 (log.f32 (.f32 -1 (PI.f32))) (.f32 -1 (log.f32 (/.f32 -1 u2))))
(+.f32 (log.f32 (neg.f32 (PI.f32))) (neg.f32 (log.f32 (/.f32 -1 u2))))
(-.f32 (log.f32 (neg.f32 (PI.f32))) (log.f32 (/.f32 -1 u2)))
(+.f32 (.f32 -1 (log.f32 (/.f32 -1 u2))) (+.f32 (log.f32 (.f32 -1 (PI.f32))) (/.f32 1 (*.f32 u2 (PI.f32)))))
(fma.f32 -1 (log.f32 (/.f32 -1 u2)) (+.f32 (/.f32 1 (*.f32 u2 (PI.f32))) (log.f32 (neg.f32 (PI.f32)))))
(-.f32 (+.f32 (/.f32 1 (*.f32 u2 (PI.f32))) (log.f32 (neg.f32 (PI.f32)))) (log.f32 (/.f32 -1 u2)))
(+.f32 (/.f32 1 (*.f32 u2 (PI.f32))) (-.f32 (log.f32 (neg.f32 (PI.f32))) (log.f32 (/.f32 -1 u2))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 u2))) (+.f32 (log.f32 (.f32 -1 (PI.f32))) (/.f32 1 (.f32 u2 (PI.f32))))) (.f32 1/2 (/.f32 1 (*.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(-.f32 (fma.f32 -1 (log.f32 (/.f32 -1 u2)) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (log.f32 (neg.f32 (PI.f32))))) (/.f32 1/2 (.f32 (*.f32 u2 u2) (pow.f32 (PI.f32) 2))))
(+.f32 (-.f32 (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (log.f32 (neg.f32 (PI.f32)))) (log.f32 (/.f32 -1 u2))) (/.f32 -1/2 (.f32 u2 (*.f32 u2 (pow.f32 (PI.f32) 2)))))
(+.f32 (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (-.f32 (log.f32 (neg.f32 (PI.f32))) (log.f32 (/.f32 -1 u2)))) (/.f32 -1/2 (.f32 u2 (*.f32 u2 (pow.f32 (PI.f32) 2)))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 u2))) (+.f32 (log.f32 (.f32 -1 (PI.f32))) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (.f32 1/3 (/.f32 1 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (.f32 1/2 (/.f32 1 (*.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(-.f32 (fma.f32 -1 (log.f32 (/.f32 -1 u2)) (+.f32 (log.f32 (neg.f32 (PI.f32))) (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (/.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (/.f32 1/2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2))))
(+.f32 (-.f32 (log.f32 (neg.f32 (PI.f32))) (log.f32 (/.f32 -1 u2))) (-.f32 (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (/.f32 1/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))) (/.f32 1/2 (.f32 u2 (.f32 u2 (pow.f32 (PI.f32) 2))))))
(+.f32 (-.f32 (log.f32 (neg.f32 (PI.f32))) (log.f32 (/.f32 -1 u2))) (+.f32 (+.f32 (/.f32 1 (.f32 u2 (PI.f32))) (/.f32 (/.f32 1/3 (pow.f32 (PI.f32) 3)) (pow.f32 u2 3))) (/.f32 -1/2 (.f32 u2 (*.f32 u2 (pow.f32 (PI.f32) 2))))))
(.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)))
(.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))))
(.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))
(fma.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (.f32 1/2 (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (.f32 u1 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))))))
(fma.f32 1/2 (/.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2)))))
(fma.f32 1/2 (/.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 u2 (*.f32 2 (PI.f32))))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) u1)))))
(fma.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (.f32 1/2 (+.f32 (.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) 2)) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (.f32 u1 u1))) (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (.f32 u1 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))))))))
(fma.f32 1/2 (fma.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (.f32 u1 u1)) (/.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))) (.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))))
(fma.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (+.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) u1) (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 2)) (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (*.f32 u1 u1))))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (-.f32 1/3 (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (pow.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) 2))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))))
(fma.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) (/.f32 (-.f32 1/3 (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) 2)) (pow.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) 2)))) (pow.f32 u1 3))) (.f32 1/2 (+.f32 (.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) 2)) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (.f32 u1 u1))) (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (.f32 u1 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))))))))
(fma.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (.f32 1/2 (+.f32 (fma.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (.f32 u1 u1)) (/.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))) (.f32 (/.f32 (-.f32 1/3 (/.f32 1/2 (/.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 2))))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (pow.f32 u1 3))))))
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(.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) u1)) (.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) u1)) (.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) u1)) (.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (/.f32 (.f32 u1 u1) (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2))))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) u1)) (.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (log.f32 (/.f32 -1 u1))))))
(+.f32 (.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))) (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.f32 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (.f32 u1 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))) (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) u1))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (.f32 (+.f32 (/.f32 (+.f32 1/2 (.f32 -1/4 (/.f32 1 (log.f32 (/.f32 -1 u1))))) u1) 1) (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) u1))) (.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1)))) 1/3) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (fma.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1))) 1/3) (/.f32 (pow.f32 u1 3) (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2))))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (/.f32 (.f32 u1 u1) (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2))))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 (.f32 u2 (PI.f32)) 2)) u1)) (.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))))
(+.f32 (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) u1)) (.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))) (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (/.f32 (fma.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1))) 1/3) (/.f32 (pow.f32 u1 3) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))))) (.f32 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (.f32 u1 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))))))
(+.f32 (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (pow.f32 u1 3)) (fma.f32 -1/2 (/.f32 (+.f32 1/2 (.f32 -1/4 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (log.f32 (/.f32 -1 u1))) 1/3)) (.f32 (+.f32 (/.f32 (+.f32 1/2 (.f32 -1/4 (/.f32 1 (log.f32 (/.f32 -1 u1))))) u1) 1) (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) u1)))) (.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
(+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(fma.f32 -2 (.f32 (.f32 u2 u2) (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(fma.f32 -2 (.f32 (.f32 u2 u2) (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (+.f32 (.f32 (.f32 -2 u2) (.f32 u2 (pow.f32 (PI.f32) 2))) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))
(fma.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (fma.f32 -2 (.f32 (.f32 u2 u2) (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))
(fma.f32 2/3 (.f32 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (fma.f32 -2 (.f32 (.f32 u2 u2) (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (.f32 (.f32 -2 u2) (.f32 u2 (pow.f32 (PI.f32) 2))) (.f32 (pow.f32 u2 4) (.f32 2/3 (pow.f32 (PI.f32) 4))))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 6)))))))
(fma.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (+.f32 (fma.f32 -2 (.f32 (.f32 u2 u2) (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 6))))))
(fma.f32 2/3 (.f32 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (fma.f32 -2 (.f32 (.f32 u2 u2) (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (fma.f32 -4/45 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 (pow.f32 (PI.f32) 6) (pow.f32 u2 6))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
(+.f32 (.f32 (+.f32 (.f32 (.f32 -2 u2) (.f32 u2 (pow.f32 (PI.f32) 2))) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (.f32 -4/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))) (.f32 (pow.f32 u2 4) (*.f32 2/3 (pow.f32 (PI.f32) 4))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 u2 (PI.f32)) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

prune295.0ms (5.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	127	13	140

Error

0.1b

Counts

140 → 13

Alt Table

Status	Error	Program
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 1))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 1 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))))
	8.5b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 3/2) 1/3) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2)))
	7.8b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 3)))
	9.0b	(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 2)))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	2.7b	(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (.f32 u2 u2) (.f32 (pow.f32 (PI.f32) 2) -2) (.f32 2/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))))
	2.0b	(+.f32 (.f32 (+.f32 (.f32 (.f32 -2 u2) (.f32 u2 (pow.f32 (PI.f32) 2))) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (.f32 -4/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))) (.f32 (pow.f32 u2 4) (*.f32 2/3 (pow.f32 (PI.f32) 4))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 (-.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (+.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))

Compiler

Compiled 3828 to 2442 computations (36.2% saved)

localize61.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (.f32 (PI.f32) (.f32 u2 2)))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
✓	0.2b	(expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))
✓	0.4b	(.f32 (PI.f32) (.f32 u2 2))

series6.0ms (0.1%)

Counts

4 → 56

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	u2	@	0	(.f32 (PI.f32) (.f32 u2 2))
0.0ms	u1	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
0.0ms	u2	@	inf	(.f32 (PI.f32) (.f32 u2 2))
0.0ms	u1	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
0.0ms	u1	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))

rewrite57.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

500×	`prod-diff_binary32`
211×	`expm1-udef_binary32`
211×	`log1p-udef_binary32`
137×	`add-sqr-sqrt_binary32`
134×	`pow1_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	49
1	282	45
2	3356	45

Stop Event

1×	node limit

Counts

4 → 78

Calls

Call 1

Inputs
(.f32 (PI.f32) (.f32 u2 2))
(expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
(cos.f32 (.f32 (PI.f32) (.f32 u2 2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 u2 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (PI.f32) (.f32 u2 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (PI.f32) (.f32 u2 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 u2 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 u2 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (PI.f32) (.f32 u2 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (PI.f32)) (.f32 u2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (PI.f32) (.f32 u2 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 u2 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 u2 2) 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (PI.f32) (.f32 u2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 u2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (PI.f32) (.f32 u2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (PI.f32) (.f32 u2 2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2) (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 3) 1) (fma.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) (+.f32 1 (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 (cbrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)) (cbrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1))) (cbrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (hypot.f32 1 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))) (hypot.f32 1 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (sqrt.f32 (log1p.f32 u1))) (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3) (pow.f32 (log1p.f32 u1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) (sqrt.f32 (log1p.f32 u1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) (sqrt.f32 (log1p.f32 u1)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2) (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 3) 1) (fma.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) (+.f32 1 (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 (cbrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)) (cbrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1))) (cbrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (hypot.f32 1 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))) (hypot.f32 1 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 1))))))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-def_binary32`
466×	`associate-l_binary32`
396×	`associate-r_binary32`
258×	`times-frac_binary32`
205×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1590
1	334	1476
2	1079	1345
3	4908	1345

Stop Event

1×	node limit

Counts

134 → 90

Calls

Call 1

Inputs
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
1
(+.f32 1 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) u1)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (-.f32 1/3 (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (pow.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) 2))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))))
(.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32))))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1)))) 1/3) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))))
(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
(+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 6)))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
1
(+.f32 1 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))

Outputs
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
1
(+.f32 1 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (.f32 (.f32 -2 (*.f32 u2 u2)) (pow.f32 (PI.f32) 2)))
(fma.f32 -2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) 1)
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 (.f32 -2 (.f32 u2 u2)) (pow.f32 (PI.f32) 2))))
(+.f32 1 (fma.f32 -2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)))))
(fma.f32 -2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (fma.f32 2/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 1))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (fma.f32 -2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 -4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (fma.f32 (.f32 -2 (.f32 u2 u2)) (pow.f32 (PI.f32) 2) (.f32 -4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(+.f32 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 (.f32 u2 -2)) (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)))) (fma.f32 -4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)) 1))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))
(fma.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 1/2 (/.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) u1)))
(fma.f32 1/2 (/.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))))
(fma.f32 1/2 (/.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) u1)))))
(fma.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 1/2 (+.f32 (.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) 2)) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 u1 u1))) (/.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) u1))))
(fma.f32 1/2 (fma.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) 2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 u1 u1)) (/.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))))
(fma.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (+.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 2)) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (*.f32 u1 u1))))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (-.f32 1/3 (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (pow.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) 2))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))))
(fma.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) (/.f32 (+.f32 1/3 (.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) 2)) (pow.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1)))))) 2)))) (pow.f32 u1 3))) (.f32 1/2 (+.f32 (.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) 2)) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 u1 u1))) (/.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (neg.f32 (neg.f32 (log.f32 u1))))))) u1)))))
(fma.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1))) (.f32 1/2 (+.f32 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) (/.f32 (-.f32 1/3 (/.f32 1/2 (/.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)) (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) 2))))) (pow.f32 u1 3))) (fma.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) 2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 u1 u1)) (/.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1))))))))
(fma.f32 1/2 (+.f32 (/.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (+.f32 (/.f32 (-.f32 1/3 (.f32 (/.f32 -1/2 (+.f32 (log.f32 -1) (log.f32 u1))) (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 2)))) (pow.f32 u1 3)) (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 2)) (.f32 u1 u1))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))))
(.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1)) (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(fma.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))))
(fma.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1)) (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (/.f32 (.f32 u1 u1) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1)) (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))))
(+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))) (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) u1)) (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) u1))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (.f32 (+.f32 (/.f32 (+.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) -1/4)) u1) 1) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1)))) 1/3) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (fma.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (log.f32 (/.f32 -1 u1))) 1/3) (/.f32 (pow.f32 u1 3) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (/.f32 (.f32 u1 u1) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1)) (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))))
(fma.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (.f32 (/.f32 (fma.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (log.f32 (/.f32 -1 u1))) 1/3) (pow.f32 u1 3)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))) (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) u1)) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1)))))
(+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))) (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (+.f32 (/.f32 (fma.f32 -1/2 (/.f32 (+.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) -1/4)) (log.f32 (/.f32 -1 u1))) 1/3) (.f32 u1 u1)) (/.f32 (+.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) -1/4)) u1))) (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) u1))))
(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
(+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(fma.f32 -2 (.f32 (.f32 (*.f32 u2 u2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(fma.f32 -2 (.f32 (.f32 u2 u2) (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (fma.f32 -2 (.f32 (*.f32 u2 u2) (pow.f32 (PI.f32) 2)) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))
(fma.f32 2/3 (.f32 (.f32 (pow.f32 u2 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 4)) (fma.f32 -2 (.f32 (.f32 (*.f32 u2 u2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))
(fma.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (fma.f32 -2 (.f32 (.f32 u2 u2) (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 (.f32 u2 -2)) (.f32 2/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 6)))))))
(fma.f32 2/3 (.f32 (.f32 (pow.f32 u2 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 4)) (+.f32 (fma.f32 -2 (.f32 (.f32 (.f32 u2 u2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (.f32 (.f32 -4/45 (pow.f32 u2 6)) (.f32 (pow.f32 (PI.f32) 6) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))))
(fma.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (fma.f32 -2 (.f32 (.f32 u2 u2) (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (fma.f32 -4/45 (.f32 (pow.f32 u2 6) (*.f32 (pow.f32 (PI.f32) 6) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
(+.f32 (.f32 (fma.f32 -2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 -4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
1
(+.f32 1 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (.f32 (.f32 -2 (*.f32 u2 u2)) (pow.f32 (PI.f32) 2)))
(fma.f32 -2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) 1)
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 (.f32 -2 (.f32 u2 u2)) (pow.f32 (PI.f32) 2))))
(+.f32 1 (fma.f32 -2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)))))
(fma.f32 -2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (fma.f32 2/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 1))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (fma.f32 -2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 -4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (fma.f32 (.f32 -2 (.f32 u2 u2)) (pow.f32 (PI.f32) 2) (.f32 -4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(+.f32 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 (.f32 u2 -2)) (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)))) (fma.f32 -4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)) 1))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))

prune142.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	5	6	11
Picked	0	1	1
Done	0	1	1
Total	92	11	103

Error

0.1b

Counts

103 → 11

Alt Table

Status	Error	Program
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) u2))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))))
	8.5b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 3/2) 1/3) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 1) -1))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2)))
	7.8b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 3)))
	9.0b	(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 2)))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	1.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (.f32 (cbrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)) (cbrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1))) (cbrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)) -1))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 (-.f32 (pow.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 3) 1) (fma.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) (+.f32 1 (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) 1)))))

Compiler

Compiled 2788 to 1947 computations (30.2% saved)

localize61.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cos.f32 (.f32 (PI.f32) (.f32 u2 2)))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 1) -1))
✓	0.2b	(+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1)
	0.4b	(.f32 (PI.f32) (.f32 u2 2))

series3.0ms (0.1%)

Counts

2 → 32

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	u1	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 1) -1))
0.0ms	u1	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 1) -1))
0.0ms	u2	@	0	(+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1)
0.0ms	u1	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 1) -1))
0.0ms	u2	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 1) -1))

rewrite61.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

861×	`prod-diff_binary32`
176×	`add-sqr-sqrt_binary32`
171×	`pow1_binary32`
170×	`*-un-lft-identity_binary32`
163×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	356	27
2	4598	27

Stop Event

1×	node limit

Counts

2 → 69

Calls

Call 1

Inputs
(+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1)
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 1) -1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2)) (/.f32 1 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) (pow.f32 (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 2) (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 2) (*.f32 (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) (*.f32 (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 -1 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 3)) (/.f32 1 (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) (-.f32 1 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) -1) (/.f32 1 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (sqrt.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)) 1) (-.f32 (sqrt.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) (-.f32 1 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) -1))) (+.f32 -1 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2) (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 -1 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 3)) (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) (-.f32 1 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 -1 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 3)) (+.f32 1 (-.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) -1) (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 -1 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 3))) (neg.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) (-.f32 1 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) -1)) (neg.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 3) 0) (+.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2) (-.f32 0 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2) 0) (-.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2)) (-.f32 -1 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)) 2) (cbrt.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 2) (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)) (sqrt.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (sqrt.f32 (log1p.f32 u1)) (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1))) (*.f32 0 (sqrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1))) (*.f32 (sqrt.f32 (log1p.f32 u1)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1))) (sqrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1))) 1) (sqrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1))) 3) (pow.f32 (log1p.f32 u1) 3/2)) (+.f32 (*.f32 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1))) (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1)))) (-.f32 (log1p.f32 u1) (*.f32 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1))) (sqrt.f32 (log1p.f32 u1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (*.f32 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1))) (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1)))) (log1p.f32 u1)) (-.f32 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1))) (sqrt.f32 (log1p.f32 u1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 -1 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 3)) (sqrt.f32 (log1p.f32 u1))) (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) (-.f32 1 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) -1) (sqrt.f32 (log1p.f32 u1))) (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (+.f32 -1 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 3))) (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) (-.f32 1 (*.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (sqrt.f32 (log1p.f32 u1)) (+.f32 (pow.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) 2) -1)) (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (*.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (sqrt.f32 (log1p.f32 u1))) (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 3) (pow.f32 (log1p.f32 u1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1)) (sqrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (log1p.f32 u1)) (+.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1) (sqrt.f32 (log1p.f32 u1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (log1p.f32 u1)))) 1))))))

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-def_binary32`
465×	`associate-l_binary32`
396×	`associate-r_binary32`
258×	`times-frac_binary32`
205×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1320
1	334	1208
2	1079	1079
3	4909	1079

Stop Event

1×	node limit

Counts

101 → 104

Calls

Call 1

Inputs
1
(+.f32 1 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))))
(+.f32 1 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(cos.f32 (.f32 2 (.f32 u2 (PI.f32))))
(.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) u1)))))
(+.f32 (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (-.f32 1/3 (.f32 1/2 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (pow.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) 2))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1))))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 1 u1)))))) (pow.f32 u1 2)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 1 u1)))))) u1))))))
(.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32))))))
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(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))

Outputs
1
(+.f32 1 (.f32 -2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (.f32 (.f32 -2 (*.f32 u2 u2)) (pow.f32 (PI.f32) 2)))
(fma.f32 -2 (.f32 (.f32 (pow.f32 (PI.f32) 2) u2) u2) 1)
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(+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))) (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) u1)) (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) u1))))
(fma.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (.f32 (+.f32 (/.f32 (+.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) -1/4)) u1) 1) (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) u1)))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (log.f32 (/.f32 -1 u1)))) 1/3) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 3)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (.f32 (-.f32 1/2 (pow.f32 (.f32 -1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) 2)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (fma.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (log.f32 (/.f32 -1 u1))) 1/3) (/.f32 (pow.f32 u1 3) (cos.f32 (.f32 (.f32 2 u2) (PI.f32)))))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (/.f32 (.f32 u1 u1) (cos.f32 (.f32 (.f32 2 u2) (PI.f32)))))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 (.f32 2 u2) (PI.f32))) u1)) (.f32 (cos.f32 (.f32 (*.f32 2 u2) (PI.f32))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (.f32 (/.f32 (fma.f32 -1/2 (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (log.f32 (/.f32 -1 u1))) 1/3) (pow.f32 u1 3)) (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))) (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (/.f32 (-.f32 1/2 (pow.f32 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) u1)) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1)))))
(+.f32 (.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))) (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (/.f32 (fma.f32 -1/2 (/.f32 (+.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) -1/4)) (log.f32 (/.f32 -1 u1))) 1/3) (pow.f32 u1 3))) (.f32 (+.f32 (/.f32 (+.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) -1/4)) u1) 1) (/.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) u1)))))
(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
(+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(fma.f32 -2 (.f32 (.f32 (*.f32 u2 u2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(fma.f32 -2 (.f32 u2 (.f32 u2 (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (fma.f32 -2 (.f32 u2 (*.f32 u2 (pow.f32 (PI.f32) 2))) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))
(fma.f32 2/3 (.f32 (.f32 (pow.f32 u2 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 4)) (fma.f32 -2 (.f32 (.f32 (*.f32 u2 u2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))
(fma.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (fma.f32 -2 (.f32 u2 (.f32 u2 (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 -2 (.f32 u2 (.f32 u2 (pow.f32 (PI.f32) 2))) (.f32 2/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))))
(+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 2) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 2)))) (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 -4/45 (.f32 (pow.f32 u2 6) (*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (pow.f32 (PI.f32) 6)))))))
(fma.f32 2/3 (.f32 (.f32 (pow.f32 u2 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 4)) (+.f32 (fma.f32 -2 (.f32 (.f32 (.f32 u2 u2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (pow.f32 (PI.f32) 2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (.f32 (.f32 -4/45 (pow.f32 u2 6)) (.f32 (pow.f32 (PI.f32) 6) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))))
(fma.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (fma.f32 -2 (.f32 u2 (.f32 u2 (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))) (fma.f32 -4/45 (.f32 (pow.f32 u2 6) (*.f32 (pow.f32 (PI.f32) 6) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
(+.f32 (.f32 (fma.f32 (pow.f32 u2 6) (.f32 -4/45 (pow.f32 (PI.f32) 6)) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 -2 (.f32 u2 (.f32 u2 (pow.f32 (PI.f32) 2))) (.f32 2/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 2 u2) (PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 2 u2) (PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 2 u2) (PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 2 u2) (PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 2 u2) (PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 2 u2) (PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 2 u2) (PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))))
(.f32 (cos.f32 (.f32 (*.f32 2 u2) (PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

prune154.0ms (2.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	3	5	8
Picked	1	0	1
Done	1	1	2
Total	122	10	132

Error

0.1b

Counts

132 → 10

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2)))) 3))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))))
	8.5b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 3/2) 1/3) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (+.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 u2 2) 3) (pow.f32 (PI.f32) 3)))) 1) -1))
	7.8b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 3)))
	9.0b	(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 2)))
	1.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (pow.f32 (cbrt.f32 (+.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) 1)) 2) (cbrt.f32 (+.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1)) -1))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 1 (/.f32 (+.f32 (pow.f32 (+.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) 1) 2) (-.f32 1 (.f32 (+.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) 1) -1))) (+.f32 -1 (pow.f32 (+.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) 1) 3)))))

Compiler

Compiled 3396 to 2225 computations (34.5% saved)

regimes1.1s (19.6%)

Accuracy

Total 0.2b remaining (67.6%)

Threshold costs 0.2b (67.6%)

Counts

146 → 1

Compiler

Compiled 3127 to 1762 computations (43.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	24	25
2	28	25
3	30	25

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log1p.f32 (expm1.f32 (*.f32 (PI.f32) u2))))))

Outputs
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log1p.f32 (expm1.f32 (*.f32 (PI.f32) u2))))))

end184.0ms (3.4%)

Stop Event

1×

fuel

Compiler

Compiled 295 to 243 computations (17.6% saved)

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Details

analyze410.0ms (7.5%)

sample2.2s (40.6%)

preprocess38.0ms (0.7%)

simplify12.0ms (0.2%)

prune4.0ms (0.1%)

localize38.0ms (0.7%)

series39.0ms (0.7%)

rewrite60.0ms (1.1%)

simplify68.0ms (1.2%)

prune225.0ms (4.1%)

localize43.0ms (0.8%)

series6.0ms (0.1%)

rewrite51.0ms (0.9%)

simplify44.0ms (0.8%)

prune295.0ms (5.4%)

localize61.0ms (1.1%)

series6.0ms (0.1%)

rewrite57.0ms (1%)

simplify61.0ms (1.1%)

prune142.0ms (2.6%)

localize61.0ms (1.1%)

series3.0ms (0.1%)

rewrite61.0ms (1.1%)

simplify52.0ms (0.9%)

prune154.0ms (2.8%)

regimes1.1s (19.6%)

simplify2.0ms (0%)

end184.0ms (3.4%)

Profiling

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21