Details

analyze426.0ms (5.9%)

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)

sample2.1s (28.3%)

Results

2.0s	8256×	body	128	valid
2.0ms	8×	body	128	invalid

Compiler

Compiled 78 to 62 computations (20.5% saved)

preprocess37.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

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

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

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune8.0ms (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
	14.0b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
▶	0.3b	(.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)

localize50.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series156.0ms (2.2%)

Counts

4 → 32

Calls

15 calls:

Time	Variable		Point	Expression
67.0ms	u2	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
57.0ms	u2	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
6.0ms	u1	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
5.0ms	u1	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
4.0ms	u1	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

rewrite54.0ms (0.7%)

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

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

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

538×	`cancel-sign-sub-inv_binary32`
348×	`times-frac_binary32`
276×	`associate-*l/_binary32`
247×	`associate-/r*_binary32`
214×	`associate-/l*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	1948
1	571	1783
2	2097	1637

Stop Event

1×	node limit

Counts

128 → 144

Calls

Call 1

Inputs
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))))
(+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (.f32 1/4 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))))) (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))))))
(-.f32 (+.f32 (.f32 1/16 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 5))))) (+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 1/6 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (.f32 1/4 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))))))) (+.f32 (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))))) (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3)))))))
(.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 (.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 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)))))
(-.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 (.f32 1/16 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 5))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)))) (+.f32 (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)))) (+.f32 (.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))))) (+.f32 (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2))))))
(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
(-.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 2 (.f32 (pow.f32 u2 2) (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))))
(-.f32 (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))) (.f32 2 (.f32 (pow.f32 u2 2) (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))))
(-.f32 (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))) (+.f32 (.f32 2 (.f32 (pow.f32 u2 2) (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))) (.f32 4/45 (.f32 (pow.f32 u2 6) (*.f32 (pow.f32 (PI.f32) 6) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (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 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (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 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (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 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 1 u1))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 1 u1))) (+.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 1 (pow.f32 u1 2)))))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))) (/.f32 1 (pow.f32 u1 2)))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 1 u1))) (+.f32 (.f32 1/16 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 5))) (/.f32 1 (pow.f32 u1 3)))) (+.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (+.f32 (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 1 (pow.f32 u1 2)))) (.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 1 (pow.f32 u1 3)))))))) (+.f32 (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))) (/.f32 1 (pow.f32 u1 2)))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))) (/.f32 1 (pow.f32 u1 3))))))
(sqrt.f32 (log.f32 (/.f32 -1 u1)))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 u1))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
(-.f32 (+.f32 (.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 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 (pow.f32 u1 2)))))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 1 (pow.f32 u1 2)))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 u1))) (+.f32 (.f32 1/16 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 5))) (/.f32 1 (pow.f32 u1 3)))) (+.f32 (.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 (pow.f32 u1 3)))) (+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 (pow.f32 u1 2)))))))) (+.f32 (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 1 (pow.f32 u1 3)))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 1 (pow.f32 u1 2))))))
1
(-.f32 1 (.f32 2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(-.f32 (+.f32 1 (.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 (+.f32 1 (.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)))))

Outputs
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))
(.f32 (cos.f32 (.f32 (PI.f32) (*.f32 2 u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (log.f32 u1)))))
(+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))
(fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))))
(fma.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) u1) (.f32 1/2 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))))))
(fma.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (log.f32 u1)))) (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (.f32 1/2 (sqrt.f32 (/.f32 1 (neg.f32 (+.f32 (log.f32 -1) (log.f32 u1))))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (.f32 1/4 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))))) (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))))))
(+.f32 (fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))) (fma.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 u1 u1)))))) (.f32 -1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (*.f32 u1 u1)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 3))))))
(+.f32 (fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) u1) (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))) (fma.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (.f32 u1 u1)) (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 1/4)))) (.f32 (.f32 -1/8 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (*.f32 u1 u1))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 3)))))
(+.f32 (fma.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 -1) (log.f32 u1)))) (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (.f32 1/2 (sqrt.f32 (/.f32 1 (neg.f32 (+.f32 (log.f32 -1) (log.f32 u1)))))))) (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 u1 u1)) (-.f32 (.f32 (sqrt.f32 (/.f32 1 (neg.f32 (+.f32 (log.f32 -1) (log.f32 u1))))) 1/4) (.f32 1/8 (sqrt.f32 (/.f32 1 (pow.f32 (neg.f32 (+.f32 (log.f32 -1) (log.f32 u1))) 3)))))))
(-.f32 (+.f32 (.f32 1/16 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 5))))) (+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 1/6 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (.f32 1/4 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))))))) (+.f32 (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))))) (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3)))))))
(-.f32 (fma.f32 1/16 (/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 5)))) (pow.f32 u1 3)) (fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))) (fma.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3))) (fma.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 u1 u1)))))))) (.f32 1/8 (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 3))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3))) (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (.f32 u1 u1)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 3)))))))
(+.f32 (fma.f32 1/16 (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 5)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (.f32 u1 u1)) (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) 1/4))) (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (+.f32 (.f32 1/2 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) u1)) (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (pow.f32 u1 3)) 1/6))))) (.f32 -1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 3))) (+.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (pow.f32 u1 3)) (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (.f32 u1 u1))))))
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(.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 (cos.f32 (.f32 (PI.f32) (*.f32 2 u2))) (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 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))))
(fma.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (.f32 1/2 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) u1))))
(fma.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))))))
(-.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 (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)))))
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(fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (+.f32 (.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)))) (.f32 u1 u1)) (-.f32 (.f32 1/4 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (.f32 1/8 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))))))))
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(fma.f32 1/2 (*.f32 (/.f32 1 u1) (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
(fma.f32 1/2 (/.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) u1) (sqrt.f32 (log.f32 (/.f32 -1 u1))))
(-.f32 (+.f32 (.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 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 (pow.f32 u1 2)))))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 1 (pow.f32 u1 2)))))
(+.f32 (+.f32 (fma.f32 1/2 (.f32 (/.f32 1 u1) (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (sqrt.f32 (log.f32 (/.f32 -1 u1)))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 (.f32 u1 u1))))) (.f32 -1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 1 (*.f32 u1 u1)))))
(+.f32 (fma.f32 1/2 (/.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) u1) (fma.f32 1/4 (/.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (.f32 u1 u1)) (sqrt.f32 (log.f32 (/.f32 -1 u1))))) (.f32 (/.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (*.f32 u1 u1)) -1/8))
(+.f32 (+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (+.f32 (/.f32 1/2 u1) (/.f32 1/4 (.f32 u1 u1))))) (.f32 (/.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (.f32 u1 u1)) -1/8))
(-.f32 (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 u1))) (+.f32 (.f32 1/16 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 5))) (/.f32 1 (pow.f32 u1 3)))) (+.f32 (.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 (pow.f32 u1 3)))) (+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 (pow.f32 u1 2)))))))) (+.f32 (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 1 (pow.f32 u1 3)))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 1 (pow.f32 u1 2))))))
(-.f32 (fma.f32 1/2 (.f32 (/.f32 1 u1) (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1))))) (fma.f32 1/16 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 5))) (/.f32 1 (pow.f32 u1 3))) (fma.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 (pow.f32 u1 3))) (+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 1 (.f32 u1 u1)))))))) (.f32 1/8 (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 1 (pow.f32 u1 3))) (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 1 (.f32 u1 u1))))))
(+.f32 (fma.f32 1/2 (/.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) u1) (fma.f32 1/16 (/.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 5))) (pow.f32 u1 3)) (fma.f32 1/6 (/.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (pow.f32 u1 3)) (fma.f32 1/4 (/.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (.f32 u1 u1)) (sqrt.f32 (log.f32 (/.f32 -1 u1))))))) (.f32 -1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (+.f32 (/.f32 1 (pow.f32 u1 3)) (/.f32 1 (.f32 u1 u1))))))
(-.f32 (fma.f32 1/2 (/.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) u1) (fma.f32 1/16 (/.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 5))) (pow.f32 u1 3)) (+.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (+.f32 (/.f32 1/4 (.f32 u1 u1)) (/.f32 1/6 (pow.f32 u1 3))))))) (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (+.f32 (/.f32 1/8 (.f32 u1 u1)) (/.f32 1/8 (pow.f32 u1 3)))))
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))))
(+.f32 1 (.f32 (.f32 (*.f32 u2 u2) (pow.f32 (PI.f32) 2)) -2))
(-.f32 (+.f32 1 (.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 2 (.f32 (*.f32 u2 u2) (pow.f32 (PI.f32) 2)))))
(+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) -2)))
(-.f32 (+.f32 1 (.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 (-.f32 (.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 (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 1) (fma.f32 2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 (pow.f32 u2 6) (*.f32 (pow.f32 (PI.f32) 6) 4/45))))
(-.f32 (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (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)))))

prune180.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	133	11	144
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	134	12	146

Error

0.1b

Counts

146 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	9.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 3/2) 1/3) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	14.0b	(.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)))) (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 1))
	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)))))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (*.f32 (PI.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 (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))))
	1.9b	(-.f32 (.f32 (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (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))))))
	9.0b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	8.6b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (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))))

Compiler

Compiled 4994 to 3126 computations (37.4% saved)

localize46.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
✓	0.2b	(log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2)))))
✓	0.3b	(.f32 (PI.f32) (.f32 u2 2))
✓	0.6b	(expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))

series137.0ms (1.9%)

Counts

4 → 56

Calls

15 calls:

Time	Variable		Point	Expression
56.0ms	u2	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
52.0ms	u2	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
5.0ms	u1	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
5.0ms	u1	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
4.0ms	u1	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	51
1	283	47
2	3352	47

Stop Event

1×	node limit

Counts

4 → 70

Calls

Call 1

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

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

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary32`
665×	`associate-l_binary32`
428×	`cancel-sign-sub-inv_binary32`
172×	`associate-/r*_binary32`
162×	`times-frac_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	1748
1	464	1670
2	1585	1558

Stop Event

1×	node limit

Counts

126 → 115

Calls

Call 1

Inputs
(-.f32 (E.f32) 1)
(-.f32 (E.f32) (+.f32 (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (*.f32 (pow.f32 u2 2) (E.f32)))) 1))
(-.f32 (+.f32 (.f32 8/3 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 u2 4) (E.f32)))) (E.f32)) (+.f32 (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (pow.f32 u2 2) (E.f32)))) 1))
(-.f32 (+.f32 (.f32 8/3 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 u2 4) (E.f32)))) (E.f32)) (+.f32 (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (pow.f32 u2 2) (E.f32)))) (+.f32 (.f32 124/45 (.f32 (pow.f32 (PI.f32) 6) (*.f32 (pow.f32 u2 6) (E.f32)))) 1)))
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 u2 (PI.f32)))
1
(-.f32 1 (.f32 2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(-.f32 (+.f32 1 (.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 (+.f32 1 (.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 (PI.f32) u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(+.f32 (.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) u1))))
(-.f32 (+.f32 (.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 2)))))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (pow.f32 u1 2)))))
(-.f32 (+.f32 (.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1))) (+.f32 (.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 3)))) (+.f32 (.f32 1/16 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 5))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 3)))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 2)))))))) (+.f32 (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 3)))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (pow.f32 u1 2))))))
(.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2)))))
(-.f32 (+.f32 (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (pow.f32 u1 2)))))
(-.f32 (+.f32 (.f32 1/16 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 5))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 3)))) (+.f32 (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1))) (+.f32 (.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 3)))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))))))) (+.f32 (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 2)))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (pow.f32 u1 3))))))
(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
(-.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 2 (.f32 (pow.f32 u2 2) (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))))
(-.f32 (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))) (.f32 2 (.f32 (pow.f32 u2 2) (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))))
(-.f32 (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))) (+.f32 (.f32 2 (.f32 (pow.f32 u2 2) (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))) (.f32 4/45 (.f32 (pow.f32 u2 6) (*.f32 (pow.f32 (PI.f32) 6) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (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 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (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 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (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 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

Outputs
(-.f32 (E.f32) 1)
(+.f32 (E.f32) -1)
(expm1.f32 1)
(-.f32 (E.f32) (+.f32 (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (*.f32 (pow.f32 u2 2) (E.f32)))) 1))
(-.f32 (E.f32) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (E.f32) (*.f32 u2 u2))) 1))
(-.f32 (E.f32) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (*.f32 (E.f32) u2) u2)) 1))
(+.f32 (expm1.f32 1) (.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (E.f32) (.f32 u2 u2))) -2))
(-.f32 (+.f32 (.f32 8/3 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 u2 4) (E.f32)))) (E.f32)) (+.f32 (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (pow.f32 u2 2) (E.f32)))) 1))
(-.f32 (fma.f32 8/3 (.f32 (pow.f32 (PI.f32) 4) (.f32 (E.f32) (pow.f32 u2 4))) (E.f32)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (E.f32) (*.f32 u2 u2))) 1))
(-.f32 (fma.f32 8/3 (.f32 (E.f32) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 u2 4))) (E.f32)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (*.f32 (E.f32) u2) u2)) 1))
(-.f32 (fma.f32 (pow.f32 (PI.f32) 4) (.f32 (E.f32) (.f32 (pow.f32 u2 4) 8/3)) (E.f32)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (E.f32) (*.f32 u2 u2))) 1))
(-.f32 (+.f32 (.f32 8/3 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 u2 4) (E.f32)))) (E.f32)) (+.f32 (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (pow.f32 u2 2) (E.f32)))) (+.f32 (.f32 124/45 (.f32 (pow.f32 (PI.f32) 6) (*.f32 (pow.f32 u2 6) (E.f32)))) 1)))
(-.f32 (fma.f32 8/3 (.f32 (pow.f32 (PI.f32) 4) (.f32 (E.f32) (pow.f32 u2 4))) (E.f32)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (E.f32) (.f32 u2 u2))) (fma.f32 124/45 (.f32 (pow.f32 (PI.f32) 6) (*.f32 (E.f32) (pow.f32 u2 6))) 1)))
(-.f32 (fma.f32 8/3 (.f32 (E.f32) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 u2 4))) (E.f32)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (E.f32) u2) u2)) (fma.f32 124/45 (.f32 (E.f32) (*.f32 (pow.f32 (PI.f32) 6) (pow.f32 u2 6))) 1)))
(-.f32 (fma.f32 (pow.f32 (PI.f32) 4) (.f32 (E.f32) (.f32 (pow.f32 u2 4) 8/3)) (E.f32)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 (E.f32) (.f32 u2 u2))) (fma.f32 (.f32 (pow.f32 (PI.f32) 6) (*.f32 124/45 (pow.f32 u2 6))) (E.f32) 1)))
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
(expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))))
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
(expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))))
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
(expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))))
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
(expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))))
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
(expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))))
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
(expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))))
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
(expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))))
(-.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) 1)
(expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
(expm1.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
(.f32 2 (.f32 u2 (PI.f32)))
(.f32 2 (.f32 (PI.f32) u2))
(.f32 (PI.f32) (.f32 2 u2))
1
(-.f32 1 (.f32 2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (.f32 -2 (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2))))
(-.f32 1 (.f32 (pow.f32 (PI.f32) 2) (.f32 (*.f32 2 u2) u2)))
(fma.f32 (.f32 (.f32 u2 u2) -2) (pow.f32 (PI.f32) 2) 1)
(-.f32 (+.f32 1 (.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 (PI.f32) 4) (pow.f32 u2 4))) (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2)))))
(-.f32 (fma.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 u2 4)) 1) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 2 u2) u2)))
(fma.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) 2/3) (fma.f32 (.f32 (*.f32 u2 u2) -2) (pow.f32 (PI.f32) 2) 1))
(-.f32 (+.f32 1 (.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 (+.f32 1 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 u2 4)))) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2)) (.f32 4/45 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 u2 6)))))
(-.f32 (fma.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 u2 4)) 1) (fma.f32 4/45 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 u2 6)) (.f32 (pow.f32 (PI.f32) 2) (.f32 (*.f32 2 u2) u2))))
(+.f32 (fma.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) 2/3) (fma.f32 (.f32 (.f32 u2 u2) -2) (pow.f32 (PI.f32) 2) 1)) (.f32 (pow.f32 (PI.f32) 6) (*.f32 (pow.f32 u2 6) -4/45)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 (PI.f32) (.f32 2 u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 (PI.f32) (.f32 2 u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 (PI.f32) (.f32 2 u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 (PI.f32) (.f32 2 u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 (PI.f32) (.f32 2 u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 (PI.f32) (.f32 2 u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 (PI.f32) (.f32 2 u2)))
(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
(cos.f32 (.f32 (PI.f32) (.f32 2 u2)))
(.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))
(.f32 (cos.f32 (.f32 (PI.f32) (*.f32 2 u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))
(.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1))))
(+.f32 (.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) u1))))
(fma.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1))))
(fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) u1)) (.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))))
(fma.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) (/.f32 (.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) 1/2) u1) (.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))))
(-.f32 (+.f32 (.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 2)))))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (pow.f32 u1 2)))))
(+.f32 (fma.f32 (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1)) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (.f32 u1 u1)))))) (.f32 -1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (*.f32 u1 u1)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 3))))))
(+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) u1)) (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (.f32 u1 u1)) 1/4)))) (.f32 (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 u2))) (*.f32 u1 u1)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 3)))) -1/8))
(fma.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (sqrt.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1))) (fma.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1)) (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (.f32 u1 u1)) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)))) 1/4) (*.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 -1)) (log.f32 u1)) 3))) -1/8)))))
(-.f32 (+.f32 (.f32 (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) u1))) (+.f32 (.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 3)))) (+.f32 (.f32 1/16 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 5))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 3)))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 2)))))))) (+.f32 (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))) (/.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (pow.f32 u1 3)))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (pow.f32 u1 2))))))
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(.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 (PI.f32) (*.f32 2 u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

prune155.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	117	10	127

Error

0.1b

Counts

127 → 10

Alt Table

Status	Error	Program
	8.6b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2)))) 3))
	9.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 3/2) 1/3) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	14.0b	(.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)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (*.f32 (PI.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 (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))))
	1.9b	(-.f32 (.f32 (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (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))))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (fma.f32 (sqrt.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))) (sqrt.f32 (exp.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))) -1)))
	9.0b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1))

Compiler

Compiled 3401 to 2194 computations (35.5% saved)

localize42.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series125.0ms (1.7%)

Counts

1 → 20

Calls

6 calls:

Time	Variable		Point	Expression
53.0ms	u2	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1))
52.0ms	u2	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1))
6.0ms	u1	@	-inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1))
5.0ms	u1	@	0	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1))
5.0ms	u1	@	inf	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1))

rewrite38.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`prod-diff_binary32`
206×	`expm1-udef_binary32`
206×	`log1p-udef_binary32`
137×	`add-sqr-sqrt_binary32`
135×	`pow1_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	288	17
2	3342	17

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

Outputs

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

simplify32.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

545×	`fma-def_binary32`
356×	`associate-r_binary32`
342×	`associate-l_binary32`
300×	`cancel-sign-sub-inv_binary32`
262×	`associate-+l+_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	1250
1	366	1179
2	1248	1079

Stop Event

1×	node limit

Counts

35 → 41

Calls

Call 1

Inputs
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))))
(+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (.f32 1/4 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))))) (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))))))
(-.f32 (+.f32 (.f32 1/16 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 5))))) (+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 1/6 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (.f32 1/4 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))))))) (+.f32 (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))))) (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3)))))))
(.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 (.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 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)))))
(-.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 (.f32 1/16 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 5))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)))) (+.f32 (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)))) (+.f32 (.f32 1/6 (.f32 (sqrt.f32 (/.f32 1 (log.f32 (/.f32 -1 u1)))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)))) (.f32 (sqrt.f32 (log.f32 (/.f32 -1 u1))) (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))))) (+.f32 (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 3)))) (.f32 1/8 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (log.f32 (/.f32 -1 u1)) 3))) (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2))))))
(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
(-.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 2 (.f32 (pow.f32 u2 2) (*.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))))
(-.f32 (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))) (.f32 2 (.f32 (pow.f32 u2 2) (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))))
(-.f32 (+.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 2/3 (.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))) (+.f32 (.f32 2 (.f32 (pow.f32 u2 2) (.f32 (pow.f32 (PI.f32) 2) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))) (.f32 4/45 (.f32 (pow.f32 u2 6) (*.f32 (pow.f32 (PI.f32) 6) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (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 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (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 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (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 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

Outputs
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1))))
(.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1)))))
(+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))
(fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) u1) (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))) (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))))
(fma.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1)))) (.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) u1) (.f32 (sqrt.f32 (/.f32 1 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1))))) 1/2)))
(fma.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1)))) (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (.f32 (sqrt.f32 (/.f32 1 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1))))) 1/2)))
(-.f32 (+.f32 (.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (sqrt.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))) (.f32 1/4 (.f32 (/.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)))))))) (.f32 1/8 (.f32 (/.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (pow.f32 u1 2)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (log.f32 (/.f32 1 u1)) (log.f32 -1)) 3))))))
(+.f32 (fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) u1) (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))))) (fma.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (sqrt.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1))) (.f32 1/4 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)))) (/.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (.f32 u1 u1)))))) (.f32 -1/8 (.f32 (/.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (*.f32 u1 u1)) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (neg.f32 (log.f32 u1)) (log.f32 -1)) 3))))))
(+.f32 (fma.f32 1/2 (.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) u1) (sqrt.f32 (/.f32 1 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1)))))) (fma.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1)))) (.f32 (sqrt.f32 (/.f32 1 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1))))) (/.f32 (.f32 1/4 (cos.f32 (.f32 u2 (.f32 2 (PI.f32))))) (.f32 u1 u1))))) (.f32 (.f32 (/.f32 (cos.f32 (.f32 u2 (.f32 2 (PI.f32)))) u1) (/.f32 (sqrt.f32 (/.f32 1 (pow.f32 (neg.f32 (+.f32 (log.f32 u1) (log.f32 -1))) 3))) u1)) -1/8))
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(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 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 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 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 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 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 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 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 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 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 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 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 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 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 (PI.f32) u2))))
(.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))
(.f32 (cos.f32 (.f32 u2 (*.f32 2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
(.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

prune187.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	144	10	154

Error

0.1b

Counts

154 → 10

Alt Table

Status	Error	Program
	8.6b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2)))) 3))
	9.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 3/2) 1/3) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	14.0b	(.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)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (*.f32 (PI.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 (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))))
	1.9b	(-.f32 (.f32 (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (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))))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (fma.f32 (sqrt.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))) (sqrt.f32 (exp.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))) -1)))
	9.0b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1))

Compiler

Compiled 5094 to 3249 computations (36.2% saved)

localize52.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)
	0.3b	(*.f32 (PI.f32) u2)
✓	0.3b	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
✓	0.5b	(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)

series20.0ms (0.3%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	u2	@	0	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
3.0ms	u2	@	0	(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)
3.0ms	u2	@	-inf	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
2.0ms	u2	@	inf	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
2.0ms	u2	@	0	(pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)

rewrite51.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

897×	`log1p-expm1-u_binary32`
897×	`expm1-log1p-u_binary32`
107×	`add-sqr-sqrt_binary32`
106×	`pow1_binary32`
104×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	214	30
2	2634	30

Stop Event

1×	node limit

Counts

3 → 88

Calls

Call 1

Inputs
(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)
(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
(pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 1/2 (*.f32 1/2 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sin.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2) (*.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) (sin.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)) (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) (*.f32 (sqrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) (sin.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (sqrt.f32 (sin.f32 (*.f32 (PI.f32) u2)))) (sqrt.f32 (sin.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2)) (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (cos.f32 (-.f32 (*.f32 (PI.f32) u2) (*.f32 (PI.f32) u2))) (cos.f32 (+.f32 (*.f32 (PI.f32) u2) (*.f32 (PI.f32) u2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4) 3) (pow.f32 (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2) 3)) (+.f32 (*.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)) (-.f32 (*.f32 (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2) (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2)) (*.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (*.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)) (*.f32 (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2) (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2))) (-.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2) (pow.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sin.f32 (*.f32 (PI.f32) u2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.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) (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 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (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 2 (*.f32 (PI.f32) u2))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)) 1 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (fma.f32 (neg.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4) (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4) (*.f32 (neg.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 (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) (cbrt.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2)) (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 6) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 6)) (/.f32 1 (+.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.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))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4)) (-.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 6) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 1 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 6) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 6)) (+.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 6) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 6))) (neg.f32 (+.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4) 3) (pow.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4) 3)) (+.f32 (*.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4)) (+.f32 (*.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)) (*.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 6) (pow.f32 (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)) 3)) (+.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4) (-.f32 (*.f32 (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))) (*.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 (-.f32 (*.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4)) (*.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4))) (+.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4) (*.f32 (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))) (-.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 pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (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 fma.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2) (neg.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (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 fma.f32 (cbrt.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4)) (pow.f32 (cbrt.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 expm1.f32 (log1p.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 1/2 (*.f32 1/2 (cos.f32 (*.f32 2 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cos.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (cos.f32 (*.f32 (PI.f32) u2))) 2) (cbrt.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (cos.f32 (*.f32 (PI.f32) u2))) 2) (*.f32 (cbrt.f32 (cos.f32 (*.f32 (PI.f32) u2))) (cos.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4)) (pow.f32 (cbrt.f32 (cos.f32 (*.f32 (PI.f32) u2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (cos.f32 (*.f32 (PI.f32) u2))) (*.f32 (sqrt.f32 (cos.f32 (*.f32 (PI.f32) u2))) (cos.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (sqrt.f32 (cos.f32 (*.f32 (PI.f32) u2)))) (sqrt.f32 (cos.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (cos.f32 (*.f32 (PI.f32) u2)) (pow.f32 (cbrt.f32 (cos.f32 (*.f32 (PI.f32) u2))) 2)) (cbrt.f32 (cos.f32 (*.f32 (PI.f32) u2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (cos.f32 (+.f32 (*.f32 (PI.f32) u2) (*.f32 (PI.f32) u2))) (cos.f32 (-.f32 (*.f32 (PI.f32) u2) (*.f32 (PI.f32) u2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 2 (log.f32 (cos.f32 (*.f32 (PI.f32) u2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 2 (log.f32 (cos.f32 (*.f32 (PI.f32) u2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)))))))

simplify32.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-neg_binary32`
536×	`distribute-rgt-neg-in_binary32`
511×	`distribute-lft-neg-in_binary32`
367×	`unswap-sqr_binary32`
337×	`associate-r_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	489
1	166	477
2	530	471
3	2603	471

Stop Event

1×	node limit

Counts

112 → 115

Calls

Call 1

Inputs
(*.f32 (pow.f32 (PI.f32) 2) (pow.f32 u2 2))
(-.f32 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)) (.f32 1/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))
(-.f32 (+.f32 (.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))) (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (.f32 1/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))
(-.f32 (+.f32 (.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))) (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (+.f32 (.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 1/315 (*.f32 (pow.f32 u2 8) (pow.f32 (PI.f32) 8)))))
(pow.f32 (sin.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (sin.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (sin.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (sin.f32 (*.f32 u2 (PI.f32))) 2)
1
(-.f32 1 (.f32 2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(-.f32 (+.f32 1 (.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 (+.f32 1 (.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 (pow.f32 (cos.f32 (.f32 u2 (PI.f32))) 2) (pow.f32 (sin.f32 (.f32 u2 (PI.f32))) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 u2 (PI.f32))) 2) (pow.f32 (sin.f32 (.f32 u2 (PI.f32))) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 u2 (PI.f32))) 2) (pow.f32 (sin.f32 (.f32 u2 (PI.f32))) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 u2 (PI.f32))) 2) (pow.f32 (sin.f32 (.f32 u2 (PI.f32))) 2))
1
(-.f32 1 (*.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))
(-.f32 (+.f32 1 (.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)))) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 u2 2)))
(-.f32 (+.f32 1 (.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 u2 2)) (.f32 2/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)))))
(pow.f32 (cos.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (cos.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (cos.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (cos.f32 (*.f32 u2 (PI.f32))) 2)

Outputs
(*.f32 (pow.f32 (PI.f32) 2) (pow.f32 u2 2))
(.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2))
(-.f32 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)) (.f32 1/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))
(+.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2)) (.f32 -1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))
(fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 (*.f32 -1/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4)))
(fma.f32 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) -1/3 (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2)))
(.f32 (pow.f32 (PI.f32) 2) (fma.f32 u2 u2 (.f32 (pow.f32 (PI.f32) 2) (*.f32 (pow.f32 u2 4) -1/3))))
(-.f32 (+.f32 (.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))) (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (.f32 1/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))
(-.f32 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)))) (.f32 1/3 (*.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))))
(fma.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 (.f32 -1/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4))))
(fma.f32 (pow.f32 u2 6) (.f32 2/45 (pow.f32 (PI.f32) 6)) (fma.f32 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) -1/3 (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2))))
(fma.f32 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) -1/3 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)))))
(-.f32 (+.f32 (.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))) (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))) (+.f32 (.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 1/315 (*.f32 (pow.f32 u2 8) (pow.f32 (PI.f32) 8)))))
(-.f32 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)))) (fma.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 1/315 (.f32 (pow.f32 u2 8) (pow.f32 (PI.f32) 8)))))
(-.f32 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 (pow.f32 (PI.f32) 6) (.f32 2/45 (pow.f32 u2 6)))) (fma.f32 1/315 (.f32 (pow.f32 u2 8) (pow.f32 (PI.f32) 8)) (.f32 (pow.f32 (PI.f32) 4) (.f32 1/3 (pow.f32 u2 4)))))
(fma.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (fma.f32 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) -1/3 (.f32 (pow.f32 (PI.f32) 8) (*.f32 (pow.f32 u2 8) -1/315)))))
(fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (fma.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)) (fma.f32 (pow.f32 u2 8) (.f32 (pow.f32 (PI.f32) 8) -1/315) (.f32 (pow.f32 u2 4) (*.f32 (pow.f32 (PI.f32) 4) -1/3)))))
(pow.f32 (sin.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)
(pow.f32 (sin.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)
(pow.f32 (sin.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)
(pow.f32 (sin.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)
1
(-.f32 1 (.f32 2 (.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (.f32 -2 (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2))))
(+.f32 1 (.f32 (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2)) -2))
(fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2)) -2 1)
(fma.f32 (.f32 (pow.f32 (PI.f32) 2) -2) (.f32 u2 u2) 1)
(-.f32 (+.f32 1 (.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 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 2/3) (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2)))))
(+.f32 1 (fma.f32 (.f32 (pow.f32 u2 4) 2/3) (pow.f32 (PI.f32) 4) (.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2)) -2)))
(fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2)) -2 (fma.f32 (pow.f32 u2 4) (*.f32 (pow.f32 (PI.f32) 4) 2/3) 1))
(fma.f32 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 2/3 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) -2) (*.f32 u2 u2) 1))
(-.f32 (+.f32 1 (.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 (+.f32 1 (.f32 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 2/3)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2)) (.f32 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)) 4/45)))
(-.f32 (fma.f32 (.f32 (pow.f32 u2 4) 2/3) (pow.f32 (PI.f32) 4) 1) (fma.f32 (.f32 (pow.f32 u2 6) 4/45) (pow.f32 (PI.f32) 6) (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2)))))
(-.f32 (fma.f32 (pow.f32 u2 4) (.f32 (pow.f32 (PI.f32) 4) 2/3) 1) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 u2 6) 4/45) (.f32 2 (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2)))))
(+.f32 1 (fma.f32 (pow.f32 (PI.f32) 2) (fma.f32 (pow.f32 u2 4) (.f32 2/3 (pow.f32 (PI.f32) 2)) (.f32 (.f32 u2 u2) -2)) (.f32 (pow.f32 (PI.f32) 6) (*.f32 (pow.f32 u2 6) -4/45))))
(-.f32 (pow.f32 (cos.f32 (.f32 u2 (PI.f32))) 2) (pow.f32 (sin.f32 (.f32 u2 (PI.f32))) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 u2 (PI.f32))) 2) (pow.f32 (sin.f32 (.f32 u2 (PI.f32))) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 u2 (PI.f32))) 2) (pow.f32 (sin.f32 (.f32 u2 (PI.f32))) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 u2 (PI.f32))) 2) (pow.f32 (sin.f32 (.f32 u2 (PI.f32))) 2))
(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
1
(-.f32 1 (*.f32 (pow.f32 u2 2) (pow.f32 (PI.f32) 2)))
(-.f32 1 (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2)))
(fma.f32 (*.f32 u2 u2) (neg.f32 (pow.f32 (PI.f32) 2)) 1)
(-.f32 (+.f32 1 (.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)))) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 u2 2)))
(+.f32 1 (-.f32 (.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2))))
(-.f32 (fma.f32 (.f32 1/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2)))
(-.f32 (fma.f32 (pow.f32 u2 4) (.f32 1/3 (pow.f32 (PI.f32) 4)) 1) (.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2)))
(-.f32 (.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (fma.f32 (pow.f32 (PI.f32) 2) (*.f32 u2 u2) -1))
(-.f32 (+.f32 1 (.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)))) (+.f32 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 u2 2)) (.f32 2/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)))))
(+.f32 1 (-.f32 (.f32 1/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4))) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 2/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
(-.f32 (fma.f32 (.f32 1/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 (pow.f32 (PI.f32) 6) (.f32 2/45 (pow.f32 u2 6)))))
(-.f32 (fma.f32 (pow.f32 u2 4) (.f32 1/3 (pow.f32 (PI.f32) 4)) 1) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 (pow.f32 u2 6) (.f32 2/45 (pow.f32 (PI.f32) 6)))))
(-.f32 (fma.f32 (pow.f32 u2 4) (.f32 1/3 (pow.f32 (PI.f32) 4)) 1) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 u2 u2) (.f32 2/45 (.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6)))))
(pow.f32 (cos.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)
(pow.f32 (cos.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)
(pow.f32 (cos.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)
(pow.f32 (cos.f32 (*.f32 u2 (PI.f32))) 2)
(pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)

prune229.0ms (3.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	140	5	145
Fresh	1	7	8
Picked	1	0	1
Done	1	0	1
Total	143	12	155

Error

0.1b

Counts

155 → 12

Alt Table

Status	Error	Program
	1.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 1 (fma.f32 (pow.f32 (PI.f32) 2) (fma.f32 (pow.f32 u2 4) (.f32 2/3 (pow.f32 (PI.f32) 2)) (.f32 (.f32 u2 u2) -2)) (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 u2 6) -4/45)))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (fma.f32 (sqrt.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))) (sqrt.f32 (exp.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))) -1)))
	8.6b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2)))) 3))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (/.f32 (-.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 4) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 4)) (.f32 (pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) 2) (pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) 2))) (-.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 4) (pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) 2)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) u2))) 2) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4)))))
	9.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 3/2) 1/3) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	14.0b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (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 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))
	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 4))))
	9.0b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32)))) 2)))

Compiler

Compiled 4051 to 1795 computations (55.7% saved)

regimes2.8s (38.1%)

Accuracy

Total 0.2b remaining (63%)

Threshold costs 0.2b (63%)

Counts

244 → 1

Compiler

Compiled 57550 to 46202 computations (19.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary32`
7×	`neg-sub0_binary32`
7×	`neg-mul-1_binary32`
6×	`+-commutative_binary32`
6×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	28	26
2	40	26
3	52	26
4	57	26
5	60	26
6	61	26

Stop Event

1×

saturated

Calls

Call 1

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

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

end227.0ms (3.1%)

Stop Event

1×

fuel

Compiler

Compiled 402 to 286 computations (28.9% 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

analyze426.0ms (5.9%)

sample2.1s (28.3%)

preprocess37.0ms (0.5%)

simplify12.0ms (0.2%)

prune8.0ms (0.1%)

localize50.0ms (0.7%)

series156.0ms (2.2%)

rewrite54.0ms (0.7%)

simplify43.0ms (0.6%)

prune180.0ms (2.5%)

localize46.0ms (0.6%)

series137.0ms (1.9%)

rewrite53.0ms (0.7%)

simplify48.0ms (0.7%)

prune155.0ms (2.1%)

localize42.0ms (0.6%)

series125.0ms (1.7%)

rewrite38.0ms (0.5%)

simplify32.0ms (0.4%)

prune187.0ms (2.6%)

localize52.0ms (0.7%)

series20.0ms (0.3%)

rewrite51.0ms (0.7%)

simplify32.0ms (0.4%)

prune229.0ms (3.2%)

regimes2.8s (38.1%)

simplify3.0ms (0%)

end227.0ms (3.1%)

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