Details

analyze490.0ms (10.4%)

Algorithm

1×

Search

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

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample2.2s (46.6%)

Results

2.2s	8256×	body	128	valid
4.0ms	4×	body	128	invalid

preprocess34.0ms (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 (0.3%)

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))))

prune3.0ms (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
	13.1b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize47.0ms (1%)

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)))
✓	0.1b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
✓	0.3b	(*.f32 (PI.f32) u2)

series40.0ms (0.8%)

Counts

4 → 52

Calls

15 calls:

Time	Variable		Point	Expression
26.0ms	u2	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
3.0ms	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))))
1.0ms	u2	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

rewrite54.0ms (1.2%)

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 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 log1p.f32 (expm1.f32 (*.f32 (PI.f32) u2)))))))
((#(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 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 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 +.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 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)))))))) 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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 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))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (sqrt.f32 (log1p.f32 u1))))))))

simplify46.0ms (1%)

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))))

prune257.0ms (5.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	133	14	147
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	135	14	149

Error

0.1b

Counts

149 → 14

Alt Table

Status	Error	Program
	8.9b	(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	8.2b	(.f32 (.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 u1)) 2)) (sqrt.f32 (cbrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	1.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 2))
	0.5b	(.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))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2) (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))
	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))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32))))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))
	0.5b	(.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 (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)))))))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
	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 (.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)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2)))))))

Compiler

Compiled 5213 to 3256 computations (37.5% saved)

localize48.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))
✓	0.1b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))
✓	0.3b	(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
✓	1.0b	(pow.f32 (PI.f32) 3)

series9.0ms (0.2%)

Counts

4 → 32

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	u2	@	-inf	(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
1.0ms	u2	@	0	(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
1.0ms	u2	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))
1.0ms	u2	@	inf	(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
0.0ms	u1	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))

rewrite61.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`prod-diff_binary32`
253×	`log1p-udef_binary32`
166×	`add-sqr-sqrt_binary32`
160×	`pow1_binary32`
157×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	360	40
2	4088	40

Stop Event

1×	node limit

Counts

4 → 93

Calls

Call 1

Inputs
(pow.f32 (PI.f32) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))
(cos.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (pow.f32 (PI.f32) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (PI.f32) (pow.f32 (PI.f32) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (PI.f32) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (pow.f32 (PI.f32) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (PI.f32) 2) (PI.f32))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (.f32 (cbrt.f32 (PI.f32)) (pow.f32 (PI.f32) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (PI.f32) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (PI.f32) 3/2) (pow.f32 (PI.f32) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (sqrt.f32 (PI.f32)) 3) (pow.f32 (sqrt.f32 (PI.f32)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (pow.f32 (PI.f32) 2) 1) (PI.f32))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (PI.f32) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (pow.f32 (PI.f32) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (pow.f32 (PI.f32) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 3 (log.f32 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 3 (log.f32 (PI.f32))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (pow.f32 (PI.f32) 3)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (pow.f32 (.f32 (PI.f32) u2) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (PI.f32) u2) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (PI.f32) u2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (.f32 (PI.f32) u2) 3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (PI.f32) u2) 3/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (PI.f32) u2) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (pow.f32 (.f32 (PI.f32) u2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (pow.f32 (.f32 (PI.f32) u2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (pow.f32 (.f32 (PI.f32) u2) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) 3) 3) (pow.f32 (pow.f32 u2 3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (pow.f32 u2 3) 3) (pow.f32 (pow.f32 (PI.f32) 3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (pow.f32 (.f32 (PI.f32) u2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 3 (log.f32 (.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 3 (log.f32 (.f32 (PI.f32) u2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (PI.f32) u2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (pow.f32 (.f32 (PI.f32) u2) 3)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (sqrt.f32 (log1p.f32 u1))) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) 3) (pow.f32 (log1p.f32 u1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 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 u2 (.f32 (PI.f32) 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 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1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 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 expm1.f32 (log1p.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2)))))))))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	1360
1	348	1248
2	1112	1119
3	4999	1119

Stop Event

1×	node limit

Counts

125 → 131

Calls

Call 1

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

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

prune344.0ms (7.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	123	8	131
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	132	13	145

Error

0.1b

Counts

145 → 13

Alt Table

Status	Error	Program
	8.2b	(.f32 (.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 u1)) 2)) (sqrt.f32 (cbrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	1.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 2))
	2.0b	(+.f32 (.f32 (fma.f32 -4/45 (.f32 (pow.f32 u2 6) (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 (pow.f32 u2 4) (.f32 2/3 (pow.f32 (PI.f32) 4)) (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 (*.f32 u2 -2))))))
	0.5b	(.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))))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 u2 3) (.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2)))))))
	0.5b	(.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 (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)))))))
	8.9b	(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))))))
	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))))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2) (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))
	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 (.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)))))))

Compiler

Compiled 4704 to 2836 computations (39.7% saved)

localize66.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (pow.f32 u2 3) (.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))
✓	1.0b	(*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2))
✓	1.0b	(.f32 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32)))
✓	1.0b	(pow.f32 (PI.f32) 2)

series1.0ms (0%)

Counts

4 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

u2

(*.f32 (pow.f32 u2 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))

0.0ms

u2

inf

(*.f32 (pow.f32 u2 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))

0.0ms

u2

-inf

(*.f32 (pow.f32 u2 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))

rewrite47.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

875×	`log1p-expm1-u_binary32`
875×	`expm1-log1p-u_binary32`
112×	`add-sqr-sqrt_binary32`
109×	`pow1_binary32`
106×	`associate-r_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	256	28
2	2698	28

Stop Event

1×	node limit

Counts

4 → 64

Calls

Call 1

Inputs
(pow.f32 (PI.f32) 2)
(.f32 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32)))
(*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2))
(.f32 (pow.f32 u2 3) (.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))

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

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

974×	`unswap-sqr_binary32`
626×	`sqr-pow_binary32`
403×	`*-commutative_binary32`
237×	`pow-sqr_binary32`
219×	`cube-prod_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	7	132
1	21	132
2	56	132
3	189	132
4	715	96
5	1279	96
6	2703	96
7	2792	96
8	2934	96
9	3093	96
10	3264	96
11	3494	96
12	3790	96
13	4142	96
14	4566	96

Stop Event

1×	node limit

Counts

76 → 66

Calls

Call 1

Inputs
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))

Outputs
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)
(*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))
(pow.f32 (*.f32 u2 (PI.f32)) 3)

prune173.0ms (3.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	66	13	79

Error

0.1b

Counts

79 → 13

Alt Table

Status	Error	Program
	8.2b	(.f32 (.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 u1)) 2)) (sqrt.f32 (cbrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	1.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 2))
	2.0b	(+.f32 (.f32 (fma.f32 -4/45 (.f32 (pow.f32 u2 6) (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 (pow.f32 u2 4) (.f32 2/3 (pow.f32 (PI.f32) 4)) (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 (*.f32 u2 -2))))))
	0.5b	(.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))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 u2 3) (.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2)))))))
	0.5b	(.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 (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)))))))
	8.9b	(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))))))
	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))))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2) (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))
	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 (.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)))))))

Compiler

Compiled 2543 to 1594 computations (37.3% saved)

localize52.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2)))))))
✓	0.3b	(expm1.f32 (*.f32 (PI.f32) u2))
	0.3b	(*.f32 (PI.f32) u2)
✓	13.0b	(log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2))))

series43.0ms (0.9%)

Counts

3 → 44

Calls

12 calls:

Time	Variable		Point	Expression
22.0ms	u2	@	inf	(log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2))))
13.0ms	u2	@	-inf	(log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2))))
1.0ms	u2	@	0	(log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2))))
1.0ms	u2	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2)))))))
1.0ms	u2	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2)))))))

rewrite56.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

718×	`prod-diff_binary32`
159×	`add-sqr-sqrt_binary32`
154×	`pow1_binary32`
153×	`*-un-lft-identity_binary32`
148×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	33
1	345	29
2	3956	29

Stop Event

1×	node limit

Counts

3 → 74

Calls

Call 1

Inputs

(log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2))))

(expm1.f32 (*.f32 (PI.f32) u2))

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (*.f32 2 (log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2)))))))

Outputs

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

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

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

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

331×	`distribute-rgt-in_binary32`
319×	`distribute-lft-in_binary32`
296×	`associate-+l+_binary32`
258×	`times-frac_binary32`
205×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	1531
1	488	1339
2	1839	1124

Stop Event

1×	node limit

Counts

118 → 113

Calls

Call 1

Inputs
(*.f32 u2 (PI.f32))
(+.f32 (.f32 1/2 (.f32 (pow.f32 u2 2) (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)))) (.f32 u2 (PI.f32)))
(+.f32 (.f32 1/2 (.f32 (pow.f32 u2 2) (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)))) (+.f32 (.f32 1/6 (.f32 (pow.f32 u2 3) (+.f32 (.f32 2 (pow.f32 (PI.f32) 3)) (+.f32 (pow.f32 (PI.f32) 3) (.f32 -3 (pow.f32 (PI.f32) 3)))))) (.f32 u2 (PI.f32))))
(+.f32 (.f32 1/2 (.f32 (pow.f32 u2 2) (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)))) (+.f32 (.f32 1/6 (.f32 (pow.f32 u2 3) (+.f32 (.f32 2 (pow.f32 (PI.f32) 3)) (+.f32 (pow.f32 (PI.f32) 3) (.f32 -3 (pow.f32 (PI.f32) 3)))))) (+.f32 (.f32 1/24 (.f32 (+.f32 (.f32 12 (pow.f32 (PI.f32) 4)) (+.f32 (.f32 -3 (pow.f32 (PI.f32) 4)) (+.f32 (.f32 -4 (pow.f32 (PI.f32) 4)) (+.f32 (pow.f32 (PI.f32) 4) (.f32 -6 (pow.f32 (PI.f32) 4)))))) (pow.f32 u2 4))) (.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 1/2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (+.f32 (.f32 u2 (PI.f32)) (.f32 1/6 (*.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 (.f32 1/24 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 1/6 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(.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 (.f32 (pow.f32 u2 3) (.f32 (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (PI.f32))))) (+.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 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (+.f32 (.f32 2/3 (pow.f32 (PI.f32) 4)) (+.f32 (.f32 -1/2 (pow.f32 (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)) 2)) (.f32 -2/3 (.f32 (+.f32 (pow.f32 (PI.f32) 3) (+.f32 (.f32 2 (pow.f32 (PI.f32) 3)) (.f32 -3 (pow.f32 (PI.f32) 3)))) (PI.f32))))))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 3) (.f32 (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (PI.f32))))) (+.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 (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 (.f32 1/2 (.f32 (pow.f32 u2 2) (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)))) (.f32 u2 (PI.f32)))
(fma.f32 1/2 (.f32 (.f32 u2 u2) (.f32 0 (pow.f32 (PI.f32) 2))) (.f32 u2 (PI.f32)))
(fma.f32 u2 (PI.f32) (.f32 (.f32 u2 u2) 0))
(fma.f32 u2 (PI.f32) 0)
(+.f32 (.f32 1/2 (.f32 (pow.f32 u2 2) (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)))) (+.f32 (.f32 1/6 (.f32 (pow.f32 u2 3) (+.f32 (.f32 2 (pow.f32 (PI.f32) 3)) (+.f32 (pow.f32 (PI.f32) 3) (.f32 -3 (pow.f32 (PI.f32) 3)))))) (.f32 u2 (PI.f32))))
(fma.f32 1/2 (.f32 (.f32 u2 u2) (.f32 0 (pow.f32 (PI.f32) 2))) (.f32 u2 (PI.f32)))
(fma.f32 u2 (PI.f32) (.f32 (.f32 u2 u2) 0))
(fma.f32 u2 (PI.f32) 0)
(+.f32 (.f32 1/2 (.f32 (pow.f32 u2 2) (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)))) (+.f32 (.f32 1/6 (.f32 (pow.f32 u2 3) (+.f32 (.f32 2 (pow.f32 (PI.f32) 3)) (+.f32 (pow.f32 (PI.f32) 3) (.f32 -3 (pow.f32 (PI.f32) 3)))))) (+.f32 (.f32 1/24 (.f32 (+.f32 (.f32 12 (pow.f32 (PI.f32) 4)) (+.f32 (.f32 -3 (pow.f32 (PI.f32) 4)) (+.f32 (.f32 -4 (pow.f32 (PI.f32) 4)) (+.f32 (pow.f32 (PI.f32) 4) (.f32 -6 (pow.f32 (PI.f32) 4)))))) (pow.f32 u2 4))) (.f32 u2 (PI.f32)))))
(fma.f32 1/2 (.f32 (.f32 u2 u2) (.f32 0 (pow.f32 (PI.f32) 2))) (fma.f32 1/6 (.f32 (pow.f32 u2 3) (fma.f32 2 (pow.f32 (PI.f32) 3) (.f32 -2 (pow.f32 (PI.f32) 3)))) (fma.f32 1/24 (.f32 (fma.f32 12 (pow.f32 (PI.f32) 4) (fma.f32 -3 (pow.f32 (PI.f32) 4) (fma.f32 -4 (pow.f32 (PI.f32) 4) (.f32 -5 (pow.f32 (PI.f32) 4))))) (pow.f32 u2 4)) (.f32 u2 (PI.f32)))))
(+.f32 (.f32 (.f32 u2 u2) 0) (fma.f32 1/6 (.f32 (pow.f32 u2 3) (.f32 (pow.f32 (PI.f32) 3) 0)) (fma.f32 1/24 (.f32 (+.f32 (.f32 (pow.f32 (PI.f32) 4) -9) (.f32 (pow.f32 (PI.f32) 4) 9)) (pow.f32 u2 4)) (.f32 u2 (PI.f32)))))
(+.f32 0 (fma.f32 1/24 (.f32 (.f32 (pow.f32 (PI.f32) 4) 0) (pow.f32 u2 4)) (*.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 u2 (PI.f32) (.f32 1/2 (.f32 (*.f32 u2 u2) (pow.f32 (PI.f32) 2))))
(.f32 (PI.f32) (+.f32 u2 (.f32 (.f32 1/2 (.f32 u2 u2)) (PI.f32))))
(+.f32 (.f32 1/2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (+.f32 (.f32 u2 (PI.f32)) (.f32 1/6 (*.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 1/6 (.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 (pow.f32 u2 3) (.f32 (pow.f32 (PI.f32) 3) 1/6))))
(fma.f32 1/2 (.f32 u2 (.f32 u2 (pow.f32 (PI.f32) 2))) (fma.f32 u2 (PI.f32) (.f32 (pow.f32 u2 3) (.f32 (pow.f32 (PI.f32) 3) 1/6))))
(+.f32 (.f32 1/2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (+.f32 (.f32 u2 (PI.f32)) (+.f32 (.f32 1/24 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 1/6 (*.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) (fma.f32 1/24 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 u2 4)) (.f32 1/6 (*.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) (fma.f32 1/24 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 u2 4)) (.f32 (pow.f32 u2 3) (*.f32 (pow.f32 (PI.f32) 3) 1/6)))))
(fma.f32 1/2 (.f32 u2 (.f32 u2 (pow.f32 (PI.f32) 2))) (fma.f32 u2 (PI.f32) (fma.f32 1/24 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 u2 4)) (.f32 (pow.f32 u2 3) (*.f32 (pow.f32 (PI.f32) 3) 1/6)))))
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(expm1.f32 (*.f32 u2 (PI.f32)))
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(expm1.f32 (*.f32 u2 (PI.f32)))
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(expm1.f32 (*.f32 u2 (PI.f32)))
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(expm1.f32 (*.f32 u2 (PI.f32)))
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(expm1.f32 (*.f32 u2 (PI.f32)))
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(expm1.f32 (*.f32 u2 (PI.f32)))
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(expm1.f32 (*.f32 u2 (PI.f32)))
(-.f32 (exp.f32 (*.f32 u2 (PI.f32))) 1)
(expm1.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 -1)) (log.f32 u1))) (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 (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 (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))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) u1) (.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1))) (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2)))))
(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)))))
(+.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 -1)) (log.f32 u1)))) 2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (.f32 u1 u1)) (/.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) u1)) (.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1))) (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 (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))))))
(+.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 -1)) (log.f32 u1))) (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 -1)) (log.f32 u1)))) 2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (.f32 u1 u1)) (/.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) u1)) (.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) (/.f32 (+.f32 1/3 (.f32 (/.f32 (-.f32 1/2 (pow.f32 (/.f32 1/2 (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) 2)) (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1))) -1/2)) (pow.f32 u1 3))))))
(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 (.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (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 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) u1) (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 (*.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 (.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)))))
(+.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 (.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 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (.f32 u1 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))) (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) u1))))
(+.f32 (.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (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 (PI.f32) 2))) 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 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 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 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)))))))
(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 u2 (.f32 (PI.f32) 2)))) (+.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 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) -1/2) 2)) (.f32 u1 u1)) (cos.f32 (.f32 u2 (.f32 (PI.f32) 2)))) (/.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))) u1)))))
(+.f32 (.f32 (.f32 1/2 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 (PI.f32) 2))) (pow.f32 u1 3)) (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 (+.f32 (/.f32 (+.f32 1/2 (.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))) -1/4)) u1) 1) (/.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)))))
(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 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 (+.f32 (.f32 (.f32 (.f32 u2 u2) -2) (pow.f32 (PI.f32) 2)) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(+.f32 (.f32 -2 (.f32 (pow.f32 u2 3) (.f32 (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (PI.f32))))) (+.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 (pow.f32 u2 3) (.f32 (.f32 0 (pow.f32 (PI.f32) 2)) (.f32 (PI.f32) (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 (.f32 0 (pow.f32 u2 3)) (PI.f32)) (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 0 (.f32 (+.f32 (.f32 (.f32 (.f32 u2 u2) -2) (pow.f32 (PI.f32) 2)) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
(+.f32 (.f32 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (+.f32 (.f32 2/3 (pow.f32 (PI.f32) 4)) (+.f32 (.f32 -1/2 (pow.f32 (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)) 2)) (.f32 -2/3 (.f32 (+.f32 (pow.f32 (PI.f32) 3) (+.f32 (.f32 2 (pow.f32 (PI.f32) 3)) (.f32 -3 (pow.f32 (PI.f32) 3)))) (PI.f32))))))) (+.f32 (.f32 -2 (.f32 (pow.f32 u2 3) (.f32 (+.f32 (.f32 -1 (pow.f32 (PI.f32) 2)) (pow.f32 (PI.f32) 2)) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (PI.f32))))) (+.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 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (fma.f32 2/3 (pow.f32 (PI.f32) 4) (fma.f32 -1/2 (pow.f32 (.f32 0 (pow.f32 (PI.f32) 2)) 2) (.f32 -2/3 (.f32 (PI.f32) (+.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 (PI.f32) 3) -1))))))) (fma.f32 -2 (.f32 (pow.f32 u2 3) (.f32 (.f32 0 (pow.f32 (PI.f32) 2)) (.f32 (PI.f32) (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 (pow.f32 u2 4) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (pow.f32 (PI.f32) 4) 2/3 (fma.f32 -2/3 (.f32 (PI.f32) (.f32 (pow.f32 (PI.f32) 3) 0)) 0))) (fma.f32 -2 (.f32 (.f32 (.f32 0 (pow.f32 u2 3)) (PI.f32)) (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 (.f32 (+.f32 (.f32 (.f32 (.f32 u2 u2) -2) (pow.f32 (PI.f32) 2)) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (fma.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (.f32 2/3 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) 0))
(.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 (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 (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 (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 (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 (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 (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 (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)))))

prune302.0ms (6.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	129	13	142

Error

0.1b

Counts

142 → 13

Alt Table

Status	Error	Program
	8.2b	(.f32 (.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 u1)) 2)) (sqrt.f32 (cbrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	1.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 2))
	2.0b	(+.f32 (.f32 (fma.f32 -4/45 (.f32 (pow.f32 u2 6) (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 (pow.f32 u2 4) (.f32 2/3 (pow.f32 (PI.f32) 4)) (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 (*.f32 u2 -2))))))
	0.5b	(.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))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 u2 3) (.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))))))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) u2)))))))
	0.5b	(.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 (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)))))))
	8.9b	(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 2)))
	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 (.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)))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))))))
	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))))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2) (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))

Compiler

Compiled 3700 to 2314 computations (37.5% saved)

regimes139.0ms (3%)

Accuracy

Total -18.7b remaining (-5428.2%)

Threshold costs -18.7b (-5428.2%)

Counts

25 → 1

Calls

Call 1

Inputs
(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 2)))
(+.f32 (.f32 (fma.f32 -4/45 (.f32 (pow.f32 u2 6) (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 (pow.f32 u2 4) (.f32 2/3 (pow.f32 (PI.f32) 4)) (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 (*.f32 u2 -2))))))
(.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))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 u2 3) (.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))))))
(.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 (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)))))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 u2 (*.f32 (PI.f32) 2))))))
(.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))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
(.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 (.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)))))))
(sqrt.f32 (.f32 (log1p.f32 u1) (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 2)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
(.f32 (.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (log1p.f32 u1)) 2)) (sqrt.f32 (cbrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 2))
(.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))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))) 2) (cbrt.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))))
(.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))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32))))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))
(.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 (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)))))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
(.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 (.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)))))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (*.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 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Outputs
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 u2 3) (.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))))))

Results

10.0ms	0.3b	`cosTheta_i`
11.0ms	0.3b	`u1`
11.0ms	0.3b	`u2`
9.0ms	0.3b	`(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))`
7.0ms	0.3b	`(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))`
7.0ms	0.3b	`(neg.f32 (log.f32 (-.f32 1 u1)))`
11.0ms	0.3b	`(log.f32 (-.f32 1 u1))`
10.0ms	0.3b	`(-.f32 1 u1)`
9.0ms	0.3b	`(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))`
8.0ms	0.3b	`(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))`
11.0ms	0.3b	`(.f32 (.f32 2 (PI.f32)) u2)`
12.0ms	0.3b	`(.f32 (.f32 2 (PI.f32)) u2)`

Compiler

Compiled 969 to 500 computations (48.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-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	21	44
1	32	44
2	36	44
3	38	44

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 u2 3) (.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))))))

Outputs

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (*.f32 2 (cbrt.f32 (*.f32 (pow.f32 u2 3) (*.f32 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))))))))

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (*.f32 2 (cbrt.f32 (*.f32 (pow.f32 u2 3) (*.f32 (cbrt.f32 (PI.f32)) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 (cbrt.f32 (PI.f32)) 2))))))))

end21.0ms (0.4%)

Stop Event

1×

fuel

Compiler

Compiled 56 to 46 computations (17.9% 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

analyze490.0ms (10.4%)

sample2.2s (46.6%)

preprocess34.0ms (0.7%)

simplify12.0ms (0.3%)

prune3.0ms (0.1%)

localize47.0ms (1%)

series40.0ms (0.8%)

rewrite54.0ms (1.2%)

simplify46.0ms (1%)

prune257.0ms (5.5%)

localize48.0ms (1%)

series9.0ms (0.2%)

rewrite61.0ms (1.3%)

simplify54.0ms (1.1%)

prune344.0ms (7.3%)

localize66.0ms (1.4%)

series1.0ms (0%)

rewrite47.0ms (1%)

simplify67.0ms (1.4%)

prune173.0ms (3.7%)

localize52.0ms (1.1%)

series43.0ms (0.9%)

rewrite56.0ms (1.2%)

simplify42.0ms (0.9%)

prune302.0ms (6.4%)

regimes139.0ms (3%)

simplify3.0ms (0.1%)

end21.0ms (0.4%)

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