Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 66 to 48 computations (27.3% saved)

sample2.5s (45%)

Results

2.5s

8256×

body

128

valid

preprocess29.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

696×	`associate-/l*_binary32`
691×	`associate-/l/_binary32`
677×	`times-frac_binary32`
373×	`associate-/r/_binary32`
359×	`associate-/r*_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	374
1	361	374
2	1272	352
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2
3
4

Outputs
0
1
0
2
3
2
4

Call 2

Inputs
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 cosTheta_i sinTheta_O) v))) (/.f32 (.f32 sinTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i cosTheta_i) v))) (/.f32 (.f32 sinTheta_O cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) cosTheta_i))) (/.f32 (.f32 v cosTheta_O) cosTheta_i)) (.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_i)) 2) cosTheta_i))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 cosTheta_O sinTheta_O) v))) (/.f32 (.f32 cosTheta_i sinTheta_i) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i cosTheta_O) v))) (/.f32 (.f32 cosTheta_i sinTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) cosTheta_O))) (/.f32 (.f32 cosTheta_i v) cosTheta_O)) (.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_O)) 2) cosTheta_O))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 v sinTheta_O) sinTheta_i))) (/.f32 (.f32 cosTheta_i cosTheta_O) sinTheta_i)) (.f32 (*.f32 (sinh.f32 (/.f32 1 sinTheta_i)) 2) sinTheta_i))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i v) sinTheta_O))) (/.f32 (.f32 cosTheta_i cosTheta_O) sinTheta_O)) (.f32 (*.f32 (sinh.f32 (/.f32 1 sinTheta_O)) 2) sinTheta_O))

Outputs
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_i sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) v))
(.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_O (.f32 v (/.f32 v cosTheta_i))))
(/.f32 (/.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (pow.f32 (exp.f32 (/.f32 sinTheta_O v)) sinTheta_i))) v)
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_i sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) v))
(.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_O (.f32 v (/.f32 v cosTheta_i))))
(/.f32 (/.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (pow.f32 (exp.f32 (/.f32 sinTheta_O v)) sinTheta_i))) v)
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 cosTheta_i sinTheta_O) v))) (/.f32 (.f32 sinTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_O cosTheta_i)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 sinTheta_i (/.f32 v cosTheta_O)) v))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 cosTheta_i) (/.f32 v sinTheta_O))) (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (.f32 sinTheta_i cosTheta_O) (.f32 v v)))
(/.f32 (/.f32 (/.f32 (/.f32 cosTheta_O (/.f32 v sinTheta_i)) (exp.f32 (.f32 (/.f32 sinTheta_O v) cosTheta_i))) (sinh.f32 (/.f32 1 v))) (.f32 v 2))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i cosTheta_i) v))) (/.f32 (.f32 sinTheta_O cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(.f32 (/.f32 (exp.f32 (neg.f32 (/.f32 cosTheta_i (/.f32 v sinTheta_i)))) (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 sinTheta_O (/.f32 v cosTheta_O)) v))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 cosTheta_i) (/.f32 v sinTheta_i))) (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_O (*.f32 v (/.f32 v sinTheta_O))))
(/.f32 (/.f32 (.f32 (/.f32 sinTheta_O v) cosTheta_O) (.f32 v (exp.f32 (.f32 (/.f32 cosTheta_i v) sinTheta_i)))) (.f32 (sinh.f32 (/.f32 1 v)) 2))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) cosTheta_i))) (/.f32 (.f32 v cosTheta_O) cosTheta_i)) (.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_i)) 2) cosTheta_i))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_i sinTheta_O)) cosTheta_i)) (*.f32 2 (sinh.f32 (/.f32 1 cosTheta_i)))) (/.f32 (/.f32 v (/.f32 cosTheta_i cosTheta_O)) cosTheta_i))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 cosTheta_i sinTheta_O))) (.f32 2 (sinh.f32 (/.f32 1 cosTheta_i)))) (/.f32 (*.f32 (/.f32 v cosTheta_i) cosTheta_O) cosTheta_i))
(/.f32 (/.f32 (.f32 v cosTheta_O) (pow.f32 (exp.f32 (/.f32 sinTheta_i cosTheta_i)) sinTheta_O)) (.f32 (.f32 (sinh.f32 (/.f32 1 cosTheta_i)) (.f32 cosTheta_i 2)) cosTheta_i))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 cosTheta_O sinTheta_O) v))) (/.f32 (.f32 cosTheta_i sinTheta_i) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_O cosTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 cosTheta_i (/.f32 v sinTheta_i)) v))
(.f32 (/.f32 (exp.f32 (/.f32 (.f32 cosTheta_O (neg.f32 sinTheta_O)) v)) (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 sinTheta_i (.f32 v (/.f32 v cosTheta_i))))
(/.f32 (/.f32 (.f32 (/.f32 cosTheta_i v) sinTheta_i) (.f32 2 (pow.f32 (exp.f32 (/.f32 sinTheta_O v)) cosTheta_O))) (*.f32 (sinh.f32 (/.f32 1 v)) v))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i cosTheta_O) v))) (/.f32 (.f32 cosTheta_i sinTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_i cosTheta_O)) v)) (/.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_i (/.f32 v sinTheta_O))))
(/.f32 (/.f32 sinTheta_O (/.f32 v cosTheta_i)) (/.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)) (exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 cosTheta_O)) v))))
(/.f32 (/.f32 (/.f32 (.f32 (/.f32 sinTheta_O v) cosTheta_i) (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) cosTheta_O)) (sinh.f32 (/.f32 1 v))) (.f32 v 2))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) cosTheta_O))) (/.f32 (.f32 cosTheta_i v) cosTheta_O)) (.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_O)) 2) cosTheta_O))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_i sinTheta_O)) cosTheta_O)) (*.f32 2 (sinh.f32 (/.f32 1 cosTheta_O)))) (/.f32 (/.f32 cosTheta_i (/.f32 cosTheta_O v)) cosTheta_O))
(/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i (neg.f32 sinTheta_O)) cosTheta_O)) (.f32 (/.f32 (.f32 (sinh.f32 (/.f32 1 cosTheta_O)) (.f32 cosTheta_O 2)) cosTheta_i) (/.f32 cosTheta_O v)))
(/.f32 (/.f32 (/.f32 cosTheta_i (/.f32 cosTheta_O v)) (pow.f32 (exp.f32 (/.f32 sinTheta_i cosTheta_O)) sinTheta_O)) (.f32 (sinh.f32 (/.f32 1 cosTheta_O)) (.f32 cosTheta_O 2)))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_i sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) v))
(.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_O (.f32 v (/.f32 v cosTheta_i))))
(/.f32 (/.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (pow.f32 (exp.f32 (/.f32 sinTheta_O v)) sinTheta_i))) v)
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 v sinTheta_O) sinTheta_i))) (/.f32 (.f32 cosTheta_i cosTheta_O) sinTheta_i)) (.f32 (*.f32 (sinh.f32 (/.f32 1 sinTheta_i)) 2) sinTheta_i))
(/.f32 (.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_O v)) sinTheta_i)) (/.f32 (.f32 cosTheta_i cosTheta_O) sinTheta_i)) (.f32 (sinh.f32 (/.f32 1 sinTheta_i)) (*.f32 2 sinTheta_i)))
(.f32 (/.f32 (.f32 (/.f32 cosTheta_i sinTheta_i) cosTheta_O) (sinh.f32 (/.f32 1 sinTheta_i))) (/.f32 (exp.f32 (/.f32 (.f32 v (neg.f32 sinTheta_O)) sinTheta_i)) (.f32 sinTheta_i 2)))
(/.f32 (.f32 (/.f32 cosTheta_i sinTheta_i) cosTheta_O) (.f32 (.f32 (sinh.f32 (/.f32 1 sinTheta_i)) (.f32 sinTheta_i 2)) (pow.f32 (exp.f32 (/.f32 v sinTheta_i)) sinTheta_O)))
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i v) sinTheta_O))) (/.f32 (.f32 cosTheta_i cosTheta_O) sinTheta_O)) (.f32 (*.f32 (sinh.f32 (/.f32 1 sinTheta_O)) 2) sinTheta_O))
(/.f32 (.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_i v)) sinTheta_O)) (/.f32 cosTheta_i (/.f32 sinTheta_O cosTheta_O))) (.f32 (sinh.f32 (/.f32 1 sinTheta_O)) (.f32 2 sinTheta_O)))
(.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_i v)) sinTheta_O)) (.f32 2 (sinh.f32 (/.f32 1 sinTheta_O)))) (/.f32 cosTheta_i (.f32 sinTheta_O (/.f32 sinTheta_O cosTheta_O))))
(/.f32 (.f32 (/.f32 cosTheta_i sinTheta_O) cosTheta_O) (.f32 (.f32 2 (.f32 (sinh.f32 (/.f32 1 sinTheta_O)) sinTheta_O)) (exp.f32 (/.f32 sinTheta_i (/.f32 sinTheta_O v)))))

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

914×	`times-frac_binary32`
551×	`associate-/l*_binary32`
460×	`associate-/l/_binary32`
360×	`associate-*l/_binary32`
311×	`associate-/r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	54	34
2	173	32
3	800	32

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Outputs
(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (exp.f32 (/.f32 (neg.f32 (.f32 sinTheta_i sinTheta_O)) v)) (/.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (sinh.f32 (/.f32 1 v))) (/.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (*.f32 v 2)))
(/.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)) (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) sinTheta_O)))
(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status

Error

Program

0.5b

(*.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (*.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))

▶

0.4b

(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 154 to 106 computations (31.2% saved)

localize59.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓	0.8b	(sinh.f32 (/.f32 1 v))

series17.0ms (0.3%)

Counts

4 → 24

Calls

24 calls:

Time	Variable		Point	Expression
2.0ms	sinTheta_i	@	0	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms	v	@	-inf	(sinh.f32 (/.f32 1 v))
1.0ms	v	@	inf	(sinh.f32 (/.f32 1 v))
1.0ms	v	@	0	(sinh.f32 (/.f32 1 v))
1.0ms	v	@	inf	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)

rewrite63.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

292×	`log1p-udef_binary32`
166×	`add-sqr-sqrt_binary32`
162×	`*-un-lft-identity_binary32`
162×	`pow1_binary32`
152×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	332	32
2	4359	32

Stop Event

1×	node limit

Counts

4 → 131

Calls

Call 1

Inputs
(sinh.f32 (/.f32 1 v))
(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (exp.f32 (/.f32 1 v)) 2) (/.f32 (exp.f32 (/.f32 -1 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (sinh.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sinh.f32 (/.f32 1 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2) (cbrt.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 2 (.f32 (sinh.f32 (/.f32 1 v)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sinh.f32 (/.f32 1 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (sinh.f32 (/.f32 1 v))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (sinh.f32 (/.f32 1 v))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (.f32 v 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 v) (.f32 (sinh.f32 (/.f32 1 v)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 v 3) (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) 3) (pow.f32 v 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (.f32 (/.f32 cosTheta_i v) cosTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 v) (.f32 cosTheta_i cosTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)) (cbrt.f32 (pow.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) 2)) (cbrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)) (sqrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (.f32 (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 v -1/2) (/.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 cosTheta_i (neg.f32 cosTheta_O)) (/.f32 -1 v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 cosTheta_i 1) (/.f32 cosTheta_O v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 cosTheta_O 1) (/.f32 cosTheta_i v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 cosTheta_i v) cosTheta_O)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) 1) (/.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) 1) (/.f32 (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (.f32 cosTheta_i cosTheta_O) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 v) 2)) (/.f32 cosTheta_O (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 cosTheta_O (pow.f32 (cbrt.f32 v) 2)) (/.f32 cosTheta_i (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 cosTheta_O (sqrt.f32 v)) (/.f32 cosTheta_i (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (sqrt.f32 v)) (/.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (.f32 cosTheta_i cosTheta_O) (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 v -1/2)) (pow.f32 v -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (/.f32 v cosTheta_O) cosTheta_i) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (.f32 cosTheta_i cosTheta_O) 3) (pow.f32 v 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 cosTheta_i cosTheta_O) 3) (/.f32 (pow.f32 v -2) v)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (.f32 (/.f32 sinTheta_i v) sinTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 v) (.f32 sinTheta_i sinTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 sinTheta_i (/.f32 1 (/.f32 v sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 sinTheta_i (.f32 sinTheta_O (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 sinTheta_O (.f32 sinTheta_i (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 sinTheta_i sinTheta_O) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (.f32 sinTheta_i sinTheta_O) 2)) (.f32 (cbrt.f32 (.f32 sinTheta_i sinTheta_O)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (cbrt.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 2)) (cbrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 sinTheta_i sinTheta_O)) (.f32 (sqrt.f32 (.f32 sinTheta_i sinTheta_O)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (sqrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 v -1/2) (/.f32 (.f32 sinTheta_i sinTheta_O) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 sinTheta_O (neg.f32 sinTheta_i)) (/.f32 -1 v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (.f32 sinTheta_i sinTheta_O) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_i 1) (/.f32 sinTheta_O v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_O 1) (/.f32 sinTheta_i v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_i v) sinTheta_O)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (cbrt.f32 (pow.f32 (.f32 sinTheta_i sinTheta_O) 2)) 1) (/.f32 (cbrt.f32 (.f32 sinTheta_i sinTheta_O)) v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (.f32 sinTheta_i sinTheta_O)) 1) (/.f32 (sqrt.f32 (.f32 sinTheta_i sinTheta_O)) v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_i (pow.f32 (cbrt.f32 v) 2)) (/.f32 sinTheta_O (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_O (pow.f32 (cbrt.f32 v) 2)) (/.f32 sinTheta_i (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (cbrt.f32 (pow.f32 (.f32 sinTheta_i sinTheta_O) 2)) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (.f32 sinTheta_i sinTheta_O)) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (sqrt.f32 (.f32 sinTheta_i sinTheta_O)) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_i (sqrt.f32 v)) (/.f32 sinTheta_O (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_O (sqrt.f32 v)) (/.f32 sinTheta_i (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (cbrt.f32 (pow.f32 (.f32 sinTheta_i sinTheta_O) 2)) (sqrt.f32 v)) (/.f32 (cbrt.f32 (.f32 sinTheta_i sinTheta_O)) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (.f32 sinTheta_i sinTheta_O) (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v -1/2)) (pow.f32 v -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (.f32 sinTheta_i sinTheta_O) 3) (pow.f32 v 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 sinTheta_i sinTheta_O) 3) (/.f32 (pow.f32 v -2) v)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))))

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

509×	`unswap-sqr_binary32`
478×	`times-frac_binary32`
370×	`fma-def_binary32`
327×	`associate-*l/_binary32`
298×	`associate-/r*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	408
1	121	392
2	270	392
3	624	392
4	1896	392

Stop Event

1×	node limit

Counts

155 → 149

Calls

Call 1

Inputs
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
2
(+.f32 2 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))))
(+.f32 2 (+.f32 (.f32 1/3 (/.f32 1 (pow.f32 v 2))) (.f32 1/60 (/.f32 1 (pow.f32 v 4)))))
(+.f32 (.f32 1/2520 (/.f32 1 (pow.f32 v 6))) (+.f32 2 (+.f32 (.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4))))))
2
(+.f32 2 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))))
(+.f32 2 (+.f32 (.f32 1/3 (/.f32 1 (pow.f32 v 2))) (.f32 1/60 (/.f32 1 (pow.f32 v 4)))))
(+.f32 (.f32 1/2520 (/.f32 1 (pow.f32 v 6))) (+.f32 2 (+.f32 (.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4))))))

Outputs
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))
(+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(+.f32 (/.f32 1 v) (+.f32 (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7))) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))) (+.f32 (/.f32 1/5040 (pow.f32 v 7)) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/5040 (pow.f32 v 7)) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5)))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))
(+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(+.f32 (/.f32 1 v) (+.f32 (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7))) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))) (+.f32 (/.f32 1/5040 (pow.f32 v 7)) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/5040 (pow.f32 v 7)) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5)))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
2
(+.f32 2 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))))
(+.f32 2 (/.f32 1/3 (*.f32 v v)))
(+.f32 2 (+.f32 (.f32 1/3 (/.f32 1 (pow.f32 v 2))) (.f32 1/60 (/.f32 1 (pow.f32 v 4)))))
(+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (/.f32 1/60 (pow.f32 v 4))))
(+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (/.f32 1/60 (pow.f32 v 4)))
(+.f32 (/.f32 1/3 (*.f32 v v)) (+.f32 2 (/.f32 1/60 (pow.f32 v 4))))
(+.f32 (.f32 1/2520 (/.f32 1 (pow.f32 v 6))) (+.f32 2 (+.f32 (.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4))))))
(+.f32 (+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (/.f32 1/60 (pow.f32 v 4)))) (/.f32 1/2520 (pow.f32 v 6)))
(+.f32 (+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (/.f32 1/60 (pow.f32 v 4))) (/.f32 1/2520 (pow.f32 v 6)))
(+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (+.f32 (/.f32 1/60 (pow.f32 v 4)) (/.f32 1/2520 (pow.f32 v 6)))))
(+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (+.f32 (/.f32 1/60 (pow.f32 v 4)) (/.f32 1/2520 (pow.f32 v 6))))
2
(+.f32 2 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))))
(+.f32 2 (/.f32 1/3 (*.f32 v v)))
(+.f32 2 (+.f32 (.f32 1/3 (/.f32 1 (pow.f32 v 2))) (.f32 1/60 (/.f32 1 (pow.f32 v 4)))))
(+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (/.f32 1/60 (pow.f32 v 4))))
(+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (/.f32 1/60 (pow.f32 v 4)))
(+.f32 (/.f32 1/3 (*.f32 v v)) (+.f32 2 (/.f32 1/60 (pow.f32 v 4))))
(+.f32 (.f32 1/2520 (/.f32 1 (pow.f32 v 6))) (+.f32 2 (+.f32 (.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4))))))
(+.f32 (+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (/.f32 1/60 (pow.f32 v 4)))) (/.f32 1/2520 (pow.f32 v 6)))
(+.f32 (+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (/.f32 1/60 (pow.f32 v 4))) (/.f32 1/2520 (pow.f32 v 6)))
(+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (+.f32 (/.f32 1/60 (pow.f32 v 4)) (/.f32 1/2520 (pow.f32 v 6)))))
(+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (+.f32 (/.f32 1/60 (pow.f32 v 4)) (/.f32 1/2520 (pow.f32 v 6))))

prune589.0ms (10.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	137	12	149
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	138	13	151

Error

0.1b

Counts

151 → 13

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (pow.f32 (cbrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)) 3)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (-.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 v -1/2)) (pow.f32 v -1/2))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	6.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (+.f32 2 (/.f32 1/3 (.f32 v v))) (+.f32 (/.f32 1/60 (pow.f32 v 4)) (/.f32 1/2520 (pow.f32 v 6)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (expm1.f32 (log1p.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))))

Compiler

Compiled 4818 to 2432 computations (49.5% saved)

localize82.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓	0.3b	(*.f32 cosTheta_O (/.f32 1 v))
	0.8b	(sinh.f32 (/.f32 1 v))

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	cosTheta_O	@	0	(*.f32 cosTheta_O (/.f32 1 v))
1.0ms	cosTheta_O	@	-inf	(*.f32 cosTheta_O (/.f32 1 v))
0.0ms	v	@	-inf	(*.f32 cosTheta_O (/.f32 1 v))
0.0ms	cosTheta_O	@	inf	(*.f32 cosTheta_O (/.f32 1 v))
0.0ms	v	@	0	(*.f32 cosTheta_O (/.f32 1 v))

rewrite31.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`pow1_binary32`
495×	`add-log-exp_binary32`
495×	`log1p-expm1-u_binary32`
495×	`expm1-log1p-u_binary32`
484×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	120	4
2	1424	4

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(*.f32 cosTheta_O (/.f32 1 v))

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

Outputs

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

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96

Stop Event

1×

saturated

Counts

48 → 24

Calls

Call 1

Inputs
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)

Outputs
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)

prune452.0ms (8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	119	8	127
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	124	16	140

Error

0.1b

Counts

140 → 16

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (pow.f32 (cbrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)) 3)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	7.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (pow.f32 (/.f32 cosTheta_O v) 3) 1/3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	3.0b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (log.f32 (+.f32 1 (expm1.f32 (sinh.f32 (/.f32 1 v))))) 2) v))
	8.0b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 cosTheta_O v))))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 4580 to 2792 computations (39% saved)

localize73.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
	0.3b	(*.f32 cosTheta_O (/.f32 1 v))
	0.8b	(sinh.f32 (/.f32 1 v))
✓	13.9b	(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)

series37.0ms (0.7%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
17.0ms	v	@	0	(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)
6.0ms	v	@	inf	(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)
4.0ms	sinTheta_O	@	0	(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)
2.0ms	sinTheta_i	@	0	(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)
2.0ms	sinTheta_i	@	-inf	(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)

rewrite43.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

905×	`expm1-log1p-u_binary32`
904×	`log1p-expm1-u_binary32`
95×	`add-sqr-sqrt_binary32`
93×	`pow1_binary32`
92×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	207	7
2	2465	7

Stop Event

1×	node limit

Counts

1 → 60

Calls

Call 1

Inputs
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)

Outputs

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

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

445×	`distribute-rgt-out_binary32`
287×	`fma-def_binary32`
214×	`associate-+r+_binary32`
214×	`times-frac_binary32`
204×	`+-commutative_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	1676
1	930	1198
2	4132	871

Stop Event

1×	node limit

Counts

96 → 103

Calls

Call 1

Inputs
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(+.f32 (.f32 (pow.f32 sinTheta_i 2) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(+.f32 (.f32 (pow.f32 sinTheta_i 2) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))))) (+.f32 (.f32 (pow.f32 sinTheta_i 3) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3))) (.f32 1/6 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3)))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(+.f32 (.f32 (pow.f32 sinTheta_i 2) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))))) (+.f32 (.f32 (pow.f32 sinTheta_i 4) (+.f32 (.f32 1/24 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4))) (+.f32 (.f32 1/8 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4))) (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4))))))) (+.f32 (.f32 (pow.f32 sinTheta_i 3) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3))) (.f32 1/6 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3)))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
(-.f32 (exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v)))) 1)
(-.f32 (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) (.f32 sinTheta_i sinTheta_O)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) 1)
(-.f32 (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) (.f32 sinTheta_i sinTheta_O)) (+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2)))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) (pow.f32 sinTheta_i 2)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v)))))) 1)
(-.f32 (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) (.f32 sinTheta_i sinTheta_O)) (+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2)))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) (pow.f32 sinTheta_i 2)) (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v)))) (/.f32 (.f32 (+.f32 (.f32 1/6 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (.f32 -1/2 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))))) (exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) (pow.f32 sinTheta_i 3))))) 1)
(-.f32 (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i))))) 1)
(-.f32 (+.f32 (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i))))) (/.f32 (.f32 v (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i)))))) (.f32 sinTheta_i sinTheta_O))) 1)
(-.f32 (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i))))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2))))) (pow.f32 sinTheta_i 2)) (+.f32 (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i))))) (/.f32 (.f32 v (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i)))))) (*.f32 sinTheta_i sinTheta_O)))) 1)
(-.f32 (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i))))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2))))) (pow.f32 sinTheta_i 2)) (+.f32 (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i))))) (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i)))))) (.f32 sinTheta_i sinTheta_O)) (.f32 -1 (/.f32 (.f32 (exp.f32 (+.f32 (log.f32 (.f32 -1 (/.f32 sinTheta_O v))) (.f32 -1 (log.f32 (/.f32 -1 sinTheta_i))))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (+.f32 (.f32 -1/6 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (.f32 -1/3 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3)))))) (pow.f32 sinTheta_i 3)))))) 1)
(-.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (.f32 sinTheta_i sinTheta_O)))) 1)
(-.f32 (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (.f32 sinTheta_i sinTheta_O)))) (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (.f32 sinTheta_i sinTheta_O)))) v) (.f32 sinTheta_i sinTheta_O))) 1)
(-.f32 (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (.f32 sinTheta_i sinTheta_O)))) (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (.f32 sinTheta_i sinTheta_O)))) v) (.f32 sinTheta_i sinTheta_O))) 1)
(-.f32 (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (.f32 sinTheta_i sinTheta_O)))) (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (.f32 sinTheta_i sinTheta_O)))) v) (.f32 sinTheta_i sinTheta_O))) 1)
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(+.f32 (.f32 1/3 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
(+.f32 (.f32 1/3 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (+.f32 (.f32 1/8 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (+.f32 (.f32 1/24 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))) (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (.f32 1/3 (/.f32 (*.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))))))))))))
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 -1 (/.f32 (+.f32 (.f32 -1/6 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))) (.f32 1/2 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))))) (pow.f32 v 3))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
(+.f32 (.f32 1/8 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 -1 (/.f32 (+.f32 (.f32 -1/6 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))) (.f32 1/2 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))))) (pow.f32 v 3))) (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.f32 (.f32 1/24 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))) (.f32 1/3 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))))))))))
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)))) (pow.f32 sinTheta_O 2)))
(+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)))) (pow.f32 sinTheta_O 2)) (.f32 (pow.f32 sinTheta_O 3) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))))))))
(+.f32 (.f32 (+.f32 (.f32 1/24 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4))) (.f32 1/8 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)))))) (pow.f32 sinTheta_O 4)) (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)))) (pow.f32 sinTheta_O 2)) (.f32 (pow.f32 sinTheta_O 3) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (*.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)))))))))
(-.f32 (exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) 1)
(-.f32 (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v))))) (.f32 sinTheta_i sinTheta_O))) 1)
(-.f32 (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))))) (pow.f32 sinTheta_O 2)) (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v))))) (.f32 sinTheta_i sinTheta_O)))) 1)
(-.f32 (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))))) (pow.f32 sinTheta_O 2)) (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3))) (.f32 1/6 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3)))))) (pow.f32 sinTheta_O 3)) (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v))))) (*.f32 sinTheta_i sinTheta_O))))) 1)
(-.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v))))) 1)
(-.f32 (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) (.f32 sinTheta_i sinTheta_O)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) 1)
(-.f32 (+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2)))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) (pow.f32 sinTheta_O 2)) (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) (.f32 sinTheta_i sinTheta_O)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (*.f32 -1 (/.f32 sinTheta_i v))))))) 1)
(-.f32 (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) (.f32 sinTheta_i sinTheta_O)) (+.f32 (.f32 -1 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v))))) (+.f32 (.f32 -1/6 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3))) (+.f32 (.f32 -1/3 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3))) (.f32 1/2 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3)))))) (pow.f32 sinTheta_O 3))) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v))))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))))) (pow.f32 sinTheta_O 2)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))))) 1)

Outputs
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(/.f32 sinTheta_i (/.f32 v sinTheta_O))
(*.f32 (/.f32 sinTheta_i v) sinTheta_O)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(+.f32 (.f32 (pow.f32 sinTheta_i 2) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(fma.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 v v)) 0) (/.f32 sinTheta_i (/.f32 v sinTheta_O)))
(fma.f32 (.f32 sinTheta_i sinTheta_i) 0 (.f32 (/.f32 sinTheta_i v) sinTheta_O))
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) 0)
(+.f32 (.f32 (pow.f32 sinTheta_i 2) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))))) (+.f32 (.f32 (pow.f32 sinTheta_i 3) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3))) (.f32 1/6 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3)))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(fma.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 v v)) 0) (/.f32 sinTheta_i (/.f32 v sinTheta_O)))
(fma.f32 (.f32 sinTheta_i sinTheta_i) 0 (.f32 (/.f32 sinTheta_i v) sinTheta_O))
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) 0)
(+.f32 (.f32 (pow.f32 sinTheta_i 2) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) (pow.f32 v 2))))) (+.f32 (.f32 (pow.f32 sinTheta_i 4) (+.f32 (.f32 1/24 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4))) (+.f32 (.f32 1/8 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4))) (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4))))))) (+.f32 (.f32 (pow.f32 sinTheta_i 3) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3))) (.f32 1/6 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3)))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
(fma.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 v v)) 0) (fma.f32 (pow.f32 sinTheta_i 4) (fma.f32 1/24 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4)) (fma.f32 1/8 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4)) (.f32 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4)) -1/6))) (fma.f32 (pow.f32 sinTheta_i 3) (fma.f32 1/3 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3)) (.f32 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3)) -1/3)) (/.f32 sinTheta_i (/.f32 v sinTheta_O)))))
(fma.f32 (.f32 sinTheta_i sinTheta_i) 0 (fma.f32 (pow.f32 sinTheta_i 4) (fma.f32 1/24 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4)) (.f32 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4)) -1/24)) (fma.f32 (pow.f32 sinTheta_i 3) (.f32 (/.f32 (pow.f32 sinTheta_O 3) (pow.f32 v 3)) 0) (.f32 (/.f32 sinTheta_i v) sinTheta_O))))
(fma.f32 (pow.f32 sinTheta_i 4) (fma.f32 1/24 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4)) (*.f32 (/.f32 (pow.f32 sinTheta_O 4) (pow.f32 v 4)) -1/24)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) 0))
(-.f32 (exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v)))) 1)
(expm1.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v))))
(fma.f32 (pow.f32 v -1) (*.f32 sinTheta_i sinTheta_O) -1)
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) -1)
(-.f32 (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) (.f32 sinTheta_i sinTheta_O)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) 1)
(+.f32 (*.f32 (/.f32 v sinTheta_i) (/.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))) sinTheta_O)) (expm1.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))))
(fma.f32 (pow.f32 v -1) (.f32 sinTheta_i sinTheta_O) (fma.f32 (/.f32 (pow.f32 v -1) (/.f32 sinTheta_i (.f32 sinTheta_i sinTheta_O))) (/.f32 v sinTheta_O) -1))
(+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(-.f32 (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) (.f32 sinTheta_i sinTheta_O)) (+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_O 2)))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v))))) (pow.f32 sinTheta_i 2)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_i))) (log.f32 (/.f32 sinTheta_O v)))))) 1)
(+.f32 (*.f32 (/.f32 v sinTheta_i) (/.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))) sinTheta_O)) (expm1.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))))
(fma.f32 (pow.f32 v -1) (.f32 sinTheta_i sinTheta_O) (fma.f32 (/.f32 (pow.f32 v -1) (/.f32 sinTheta_i (.f32 sinTheta_i sinTheta_O))) (/.f32 v sinTheta_O) -1))
(+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
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(fma.f32 (/.f32 sinTheta_i v) sinTheta_O (/.f32 0 v))
(+.f32 (.f32 1/8 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 -1 (/.f32 (+.f32 (.f32 -1/6 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))) (.f32 1/2 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))))) (pow.f32 v 3))) (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.f32 (.f32 1/24 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))) (.f32 1/3 (/.f32 (.f32 (pow.f32 sinTheta_i 4) (pow.f32 sinTheta_O 4)) (pow.f32 v 4))))))))))
(fma.f32 1/8 (/.f32 (pow.f32 sinTheta_i 4) (/.f32 (pow.f32 v 4) (pow.f32 sinTheta_O 4))) (fma.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O))) (fma.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 4) (/.f32 (pow.f32 v 4) (pow.f32 sinTheta_O 4))) (fma.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O))) (+.f32 (fma.f32 -1 (/.f32 (fma.f32 -1/6 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) 1/6)) (pow.f32 v 3)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (.f32 (/.f32 (pow.f32 sinTheta_i 4) (/.f32 (pow.f32 v 4) (pow.f32 sinTheta_O 4))) 3/8))))))
(fma.f32 1/8 (.f32 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (pow.f32 sinTheta_O 4)) (fma.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (/.f32 v sinTheta_O) (/.f32 v sinTheta_O))) (fma.f32 -1/2 (.f32 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (pow.f32 sinTheta_O 4)) (fma.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (/.f32 v sinTheta_O) (/.f32 v sinTheta_O))) (-.f32 (fma.f32 (.f32 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (pow.f32 sinTheta_O 4)) 3/8 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 (.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) 0) (pow.f32 v 3)))))))
(fma.f32 1/8 (.f32 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (pow.f32 sinTheta_O 4)) (fma.f32 -1/2 (.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (/.f32 sinTheta_O v) (/.f32 sinTheta_O v))) (fma.f32 -1/2 (.f32 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (pow.f32 sinTheta_O 4)) (+.f32 (fma.f32 (.f32 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (pow.f32 sinTheta_O 4)) 3/8 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (fma.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 (.f32 sinTheta_O sinTheta_O) 1/2) (*.f32 v v)) (/.f32 0 v))))))
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(/.f32 sinTheta_i (/.f32 v sinTheta_O))
(*.f32 (/.f32 sinTheta_i v) sinTheta_O)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)))) (pow.f32 sinTheta_O 2)))
(fma.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 v v)) 0) (/.f32 sinTheta_i (/.f32 v sinTheta_O)))
(fma.f32 (.f32 sinTheta_i sinTheta_i) 0 (.f32 (/.f32 sinTheta_i v) sinTheta_O))
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) 0)
(+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)))) (pow.f32 sinTheta_O 2)) (.f32 (pow.f32 sinTheta_O 3) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))))))))
(fma.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (.f32 v v)) 0) (/.f32 sinTheta_i (/.f32 v sinTheta_O)))
(fma.f32 (.f32 sinTheta_i sinTheta_i) 0 (.f32 (/.f32 sinTheta_i v) sinTheta_O))
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) 0)
(+.f32 (.f32 (+.f32 (.f32 1/24 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4))) (.f32 1/8 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)))))) (pow.f32 sinTheta_O 4)) (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))) (.f32 1/2 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)))) (pow.f32 sinTheta_O 2)) (.f32 (pow.f32 sinTheta_O 3) (+.f32 (.f32 1/3 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (*.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)))))))))
(fma.f32 (fma.f32 1/24 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (fma.f32 1/3 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (.f32 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) -3/8))) (pow.f32 sinTheta_O 4) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (fma.f32 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) 0) (.f32 sinTheta_O sinTheta_O) (.f32 (pow.f32 sinTheta_O 3) (fma.f32 1/3 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) (*.f32 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) -1/3))))))
(+.f32 (fma.f32 (.f32 sinTheta_O sinTheta_O) 0 (.f32 (pow.f32 sinTheta_O 3) (.f32 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) 0))) (fma.f32 (pow.f32 sinTheta_O 4) (fma.f32 1/24 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (.f32 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) -1/24)) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(fma.f32 (pow.f32 sinTheta_O 4) (fma.f32 1/24 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) (*.f32 (/.f32 (pow.f32 sinTheta_i 4) (pow.f32 v 4)) -1/24)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) 0))
(-.f32 (exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) 1)
(expm1.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v))))
(fma.f32 (pow.f32 v -1) (*.f32 sinTheta_i sinTheta_O) -1)
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) -1)
(-.f32 (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v))))) (.f32 sinTheta_i sinTheta_O))) 1)
(+.f32 (*.f32 (/.f32 v sinTheta_i) (/.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))) sinTheta_O)) (expm1.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))))
(fma.f32 (pow.f32 v -1) (.f32 sinTheta_i sinTheta_O) (fma.f32 (/.f32 (pow.f32 v -1) (/.f32 sinTheta_i (.f32 sinTheta_i sinTheta_O))) (/.f32 v sinTheta_O) -1))
(+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(-.f32 (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))))) (pow.f32 sinTheta_O 2)) (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v))))) (.f32 sinTheta_i sinTheta_O)))) 1)
(+.f32 (*.f32 (/.f32 v sinTheta_i) (/.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))) sinTheta_O)) (expm1.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))))
(fma.f32 (pow.f32 v -1) (.f32 sinTheta_i sinTheta_O) (fma.f32 (/.f32 (pow.f32 v -1) (/.f32 sinTheta_i (.f32 sinTheta_i sinTheta_O))) (/.f32 v sinTheta_O) -1))
(+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(-.f32 (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))))) (pow.f32 sinTheta_O 2)) (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3))) (.f32 1/6 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3)))))) (pow.f32 sinTheta_O 3)) (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 sinTheta_O))) (log.f32 (/.f32 sinTheta_i v))))) (*.f32 sinTheta_i sinTheta_O))))) 1)
(+.f32 (*.f32 (/.f32 v sinTheta_i) (/.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))) sinTheta_O)) (expm1.f32 (fma.f32 -1 (neg.f32 (log.f32 sinTheta_i)) (log.f32 (/.f32 sinTheta_O v)))))
(fma.f32 (pow.f32 v -1) (.f32 sinTheta_i sinTheta_O) (fma.f32 (/.f32 (pow.f32 v -1) (/.f32 sinTheta_i (.f32 sinTheta_i sinTheta_O))) (/.f32 v sinTheta_O) -1))
(+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(-.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v))))) 1)
(expm1.f32 (fma.f32 -1 (log.f32 (/.f32 -1 sinTheta_O)) (log.f32 (neg.f32 (/.f32 sinTheta_i v)))))
(fma.f32 (pow.f32 (/.f32 -1 sinTheta_O) -1) (/.f32 (neg.f32 sinTheta_i) v) -1)
(+.f32 -1 (/.f32 (/.f32 (neg.f32 sinTheta_i) v) (/.f32 -1 sinTheta_O)))
(-.f32 (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) (.f32 sinTheta_i sinTheta_O)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) 1)
(+.f32 (*.f32 (/.f32 v sinTheta_i) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 sinTheta_O)) (log.f32 (neg.f32 (/.f32 sinTheta_i v))))) sinTheta_O)) (expm1.f32 (fma.f32 -1 (log.f32 (/.f32 -1 sinTheta_O)) (log.f32 (neg.f32 (/.f32 sinTheta_i v))))))
(fma.f32 (/.f32 v sinTheta_i) (/.f32 (pow.f32 (/.f32 -1 sinTheta_O) -1) (/.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))) (fma.f32 (pow.f32 (/.f32 -1 sinTheta_O) -1) (/.f32 (neg.f32 sinTheta_i) v) -1))
(+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (/.f32 (/.f32 (neg.f32 sinTheta_i) v) (/.f32 -1 sinTheta_O))))
(-.f32 (+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2)))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) (pow.f32 sinTheta_O 2)) (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) (.f32 sinTheta_i sinTheta_O)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (*.f32 -1 (/.f32 sinTheta_i v))))))) 1)
(+.f32 (*.f32 (/.f32 v sinTheta_i) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 sinTheta_O)) (log.f32 (neg.f32 (/.f32 sinTheta_i v))))) sinTheta_O)) (expm1.f32 (fma.f32 -1 (log.f32 (/.f32 -1 sinTheta_O)) (log.f32 (neg.f32 (/.f32 sinTheta_i v))))))
(fma.f32 (/.f32 v sinTheta_i) (/.f32 (pow.f32 (/.f32 -1 sinTheta_O) -1) (/.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))) (fma.f32 (pow.f32 (/.f32 -1 sinTheta_O) -1) (/.f32 (neg.f32 sinTheta_i) v) -1))
(+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (/.f32 (/.f32 (neg.f32 sinTheta_i) v) (/.f32 -1 sinTheta_O))))
(-.f32 (+.f32 (/.f32 (.f32 v (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))) (.f32 sinTheta_i sinTheta_O)) (+.f32 (.f32 -1 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v))))) (+.f32 (.f32 -1/6 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3))) (+.f32 (.f32 -1/3 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3))) (.f32 1/2 (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_i 3)))))) (pow.f32 sinTheta_O 3))) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v))))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 v 2) (pow.f32 sinTheta_i 2))))) (pow.f32 sinTheta_O 2)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 sinTheta_O))) (log.f32 (.f32 -1 (/.f32 sinTheta_i v)))))))) 1)
(+.f32 (*.f32 (/.f32 v sinTheta_i) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 sinTheta_O)) (log.f32 (neg.f32 (/.f32 sinTheta_i v))))) sinTheta_O)) (expm1.f32 (fma.f32 -1 (log.f32 (/.f32 -1 sinTheta_O)) (log.f32 (neg.f32 (/.f32 sinTheta_i v))))))
(fma.f32 (/.f32 v sinTheta_i) (/.f32 (pow.f32 (/.f32 -1 sinTheta_O) -1) (/.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))) (fma.f32 (pow.f32 (/.f32 -1 sinTheta_O) -1) (/.f32 (neg.f32 sinTheta_i) v) -1))
(+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (/.f32 (/.f32 (neg.f32 sinTheta_i) v) (/.f32 -1 sinTheta_O))))

prune582.0ms (10.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	185	15	200

Error

0.1b

Counts

200 → 15

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (pow.f32 (cbrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)) 3)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	7.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (pow.f32 (/.f32 cosTheta_O v) 3) 1/3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	14.2b	(/.f32 (.f32 (exp.f32 (neg.f32 (+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (.f32 sinTheta_i (/.f32 sinTheta_O v)))))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	3.0b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (log.f32 (+.f32 1 (expm1.f32 (sinh.f32 (/.f32 1 v))))) 2) v))
	8.0b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 cosTheta_O v))))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 8427 to 5528 computations (34.4% saved)

localize60.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.2b	(*.f32 cosTheta_i (/.f32 1 v))
	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
	0.8b	(sinh.f32 (/.f32 1 v))

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	cosTheta_i	@	0	(*.f32 cosTheta_i (/.f32 1 v))
0.0ms	v	@	inf	(*.f32 cosTheta_i (/.f32 1 v))
0.0ms	v	@	-inf	(*.f32 cosTheta_i (/.f32 1 v))
0.0ms	v	@	0	(*.f32 cosTheta_i (/.f32 1 v))
0.0ms	cosTheta_i	@	-inf	(*.f32 cosTheta_i (/.f32 1 v))

rewrite31.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`pow1_binary32`
495×	`add-log-exp_binary32`
495×	`log1p-expm1-u_binary32`
495×	`expm1-log1p-u_binary32`
484×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	120	4
2	1424	4

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(*.f32 cosTheta_i (/.f32 1 v))

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96

Stop Event

1×

saturated

Counts

48 → 24

Calls

Call 1

Inputs
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)

Outputs
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)
(/.f32 cosTheta_i v)

prune479.0ms (8.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	127	15	142

Error

0.1b

Counts

142 → 15

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (pow.f32 (sqrt.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))) 2))
✓	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	7.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (pow.f32 (/.f32 cosTheta_O v) 3) 1/3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	14.2b	(/.f32 (.f32 (exp.f32 (neg.f32 (+.f32 -1 (.f32 (+.f32 (/.f32 v (.f32 sinTheta_i sinTheta_O)) 1) (.f32 sinTheta_i (/.f32 sinTheta_O v)))))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	3.0b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (log.f32 (+.f32 1 (expm1.f32 (sinh.f32 (/.f32 1 v))))) 2) v))
	8.0b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 cosTheta_O v))))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 4063 to 2414 computations (40.6% saved)

regimes301.0ms (5.3%)

Accuracy

Total -25.0b remaining (-6772.8%)

Threshold costs -25.0b (-6772.8%)

Counts

64 → 1

Compiler

Compiled 1779 to 869 computations (51.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	37
1	35	37
2	46	37
3	53	37
4	57	37
5	58	37

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f32 (.f32 (exp.f32 (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Outputs

(/.f32 (*.f32 (exp.f32 (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

(/.f32 (*.f32 (exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))

(/.f32 (*.f32 (exp.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))

end41.0ms (0.7%)

Stop Event

1×

fuel

Remove

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 232 to 168 computations (27.6% saved)

Details

analyze1.0ms (0%)

sample2.5s (45%)

preprocess29.0ms (0.5%)

simplify14.0ms (0.3%)

prune4.0ms (0.1%)

localize59.0ms (1.1%)

series17.0ms (0.3%)

rewrite63.0ms (1.1%)

simplify30.0ms (0.5%)

prune589.0ms (10.4%)

localize82.0ms (1.5%)

series3.0ms (0.1%)

rewrite31.0ms (0.5%)

simplify12.0ms (0.2%)

prune452.0ms (8%)

localize73.0ms (1.3%)

series37.0ms (0.7%)

rewrite43.0ms (0.8%)

simplify52.0ms (0.9%)

prune582.0ms (10.3%)

localize60.0ms (1.1%)

series3.0ms (0%)

rewrite31.0ms (0.6%)

simplify7.0ms (0.1%)

prune479.0ms (8.5%)

regimes301.0ms (5.3%)

simplify3.0ms (0%)

end41.0ms (0.7%)

Profiling