Metrics for UniformSampleCone, z

analyze122.0ms (2.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0.1%	99.9%	0%	0%	0%	0
0%	0%	0.1%	99.9%	0%	0%	0%	1
0%	0%	0.1%	99.9%	0%	0%	0%	2
25%	0%	0.1%	99.9%	0%	0%	0%	3
25%	0%	0.1%	99.9%	0%	0%	0%	4
37.5%	0%	0.1%	99.9%	0%	0%	0%	5
56.2%	0.1%	0%	99.9%	0%	0%	0%	6
56.2%	0.1%	0%	99.9%	0%	0%	0%	7
65.6%	0.1%	0%	99.9%	0%	0%	0%	8
76.6%	0.1%	0%	99.9%	0%	0%	0%	9
76.6%	0.1%	0%	99.9%	0%	0%	0%	10
82%	0.1%	0%	99.9%	0%	0%	0%	11
87.9%	0.1%	0%	99.9%	0%	0%	0%	12

Compiler

Compiled 33 to 20 computations (39.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-<=: 21.0ms (32.9% of total)

...c/correct-round.rkt:119:19: 18.0ms (28.2% of total)

ival-mult: 7.0ms (11% of total)

ival-sub: 6.0ms (9.4% of total)

ival-add: 6.0ms (9.4% of total)

ival-and: 4.0ms (6.3% of total)

const: 1.0ms (1.6% of total)

backward-pass: 0.0ms (0% of total)

sample1.5s (33.7%)

Results

990.0ms	8256×	0	valid
18.0ms	59×	5	exit

Precisions

Click to see histograms. Total time spent on operations: 689.0ms

ival-<=: 195.0ms (28.3% of total)

...c/correct-round.rkt:119:19: 172.0ms (24.9% of total)

ival-and: 134.0ms (19.4% of total)

ival-mult: 65.0ms (9.4% of total)

ival-add: 55.0ms (8% of total)

ival-sub: 53.0ms (7.7% of total)

const: 8.0ms (1.2% of total)

backward-pass: 7.0ms (1% of total)

Bogosity

preprocess112.0ms (2.5%)

Algorithm

2×	egg-herbie

Rules

2030×	`sum3-define`
1968×	`sum5-define`
1736×	`sum4-define`
1720×	`fnmsub-define`
1686×	`fnmadd-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	79
1	78	63
2	245	60
3	852	60
4	3104	60
5	6894	60
0	6	7
1	14	6
2	35	6
3	70	6
4	182	6
5	485	6
6	1531	6
7	2129	6
8	2264	6
9	2284	6
0	2284	6

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

Inputs
(+ (- 1 ux) (* ux maxCos))

Outputs
(+ (- 1 ux) (* ux maxCos))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))

Call 2

Inputs
(+ (- 1 ux) (* ux maxCos))
(+ (- 1 (neg ux)) (* (neg ux) maxCos))
(+ (- 1 ux) (* ux maxCos))
(+ (- 1 ux) (* ux (neg maxCos)))
(neg (+ (- 1 (neg ux)) (* (neg ux) maxCos)))
(neg (+ (- 1 ux) (* ux maxCos)))
(neg (+ (- 1 ux) (* ux (neg maxCos))))
(+ (- 1 uy) (* uy maxCos))
(+ (- 1 maxCos) (* maxCos ux))
(+ (- 1 ux) (* ux uy))

Outputs
(+ (- 1 ux) (* ux maxCos))
(+ 1 (fmsub ux maxCos ux))
(+ (- 1 (neg ux)) (* (neg ux) maxCos))
(+ 1 (fnmadd ux maxCos ux))
(+ (- 1 ux) (* ux maxCos))
(+ 1 (fmsub ux maxCos ux))
(+ (- 1 ux) (* ux (neg maxCos)))
(- 1 (fma ux maxCos ux))
(neg (+ (- 1 (neg ux)) (* (neg ux) maxCos)))
(+ -1 (fmsub ux maxCos ux))
(neg (+ (- 1 ux) (* ux maxCos)))
(+ ux (fnmsub ux maxCos 1))
(neg (+ (- 1 ux) (* ux (neg maxCos))))
(sum3 ux (* ux maxCos) -1)
(+ (- 1 uy) (* uy maxCos))
(+ 1 (fmsub maxCos uy uy))
(+ (- 1 maxCos) (* maxCos ux))
(fmsub ux maxCos (+ maxCos -1))
(+ (- 1 ux) (* ux uy))
(+ 1 (fmsub ux uy ux))

Symmetry

(abs uy)

explain54.0ms (1.2%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f32 #s(literal 1 binary32) ux)`
-	-	`(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))`
-	-	`ux`
-	-	`(*.f32 ux maxCos)`
-	-	`maxCos`
-	-	`#s(literal 1 binary32)`

Results

30.0ms

512×

valid

Compiler

Compiled 50 to 23 computations (54% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 4.0ms (38.5% of total)

ival-sub: 3.0ms (28.9% of total)

ival-add: 3.0ms (28.9% of total)

const: 1.0ms (9.6% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify52.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f32 maxCos #s(literal -1 binary32))
✓	cost-diff	(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
✓	cost-diff	(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))

Rules

968×	`sum5-define`
710×	`sum3-define`
664×	`fnmadd-define`
480×	`sum4-define`
456×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	18	18
2	37	18
3	54	17
4	77	17
5	123	17
6	237	17
7	513	17
8	1190	17
9	2314	17
10	2606	17
11	2707	17
12	2710	17
0	2710	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ 1 (* ux (+ maxCos -1)))
1
(* ux (+ maxCos -1))
ux
(+ maxCos -1)
maxCos
-1

Outputs
(+ 1 (* ux (+ maxCos -1)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
1
#s(literal 1 binary32)
(* ux (+ maxCos -1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
ux
(+ maxCos -1)
(+.f32 maxCos #s(literal -1 binary32))
maxCos
-1
#s(literal -1 binary32)

localize25.0ms (0.6%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f32 maxCos #s(literal -1 binary32))
✓	accuracy	100.0%	(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
✓	accuracy	99.9%	(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))

Results

16.0ms

256×

valid

Compiler

Compiled 23 to 9 computations (60.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-add: 3.0ms (56.2% of total)

ival-mult: 2.0ms (37.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (+ 1 (* ux (+ maxCos -1)))>
#<alt (* ux (+ maxCos -1))>
#<alt (+ maxCos -1)>

Outputs
#<alt 1>
#<alt (+ 1 (* ux (- maxCos 1)))>
#<alt (+ 1 (* ux (- maxCos 1)))>
#<alt (+ 1 (* ux (- maxCos 1)))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- (+ maxCos (/ 1 ux)) 1))>
#<alt (* ux (- (+ maxCos (/ 1 ux)) 1))>
#<alt (* ux (- (+ maxCos (/ 1 ux)) 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))>
#<alt (* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))>
#<alt (* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))>
#<alt (+ 1 (* -1 ux))>
#<alt (+ 1 (+ (* -1 ux) (* maxCos ux)))>
#<alt (+ 1 (+ (* -1 ux) (* maxCos ux)))>
#<alt (+ 1 (+ (* -1 ux) (* maxCos ux)))>
#<alt (* maxCos ux)>
#<alt (* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))>
#<alt (* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))>
#<alt (* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))>
#<alt (* maxCos ux)>
#<alt (* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* -1 ux)>
#<alt (+ (* -1 ux) (* maxCos ux))>
#<alt (+ (* -1 ux) (* maxCos ux))>
#<alt (+ (* -1 ux) (* maxCos ux))>
#<alt (* maxCos ux)>
#<alt (* maxCos (+ ux (* -1 (/ ux maxCos))))>
#<alt (* maxCos (+ ux (* -1 (/ ux maxCos))))>
#<alt (* maxCos (+ ux (* -1 (/ ux maxCos))))>
#<alt (* maxCos ux)>
#<alt (* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))>
#<alt -1>
#<alt (- maxCos 1)>
#<alt (- maxCos 1)>
#<alt (- maxCos 1)>
#<alt maxCos>
#<alt (* maxCos (- 1 (/ 1 maxCos)))>
#<alt (* maxCos (- 1 (/ 1 maxCos)))>
#<alt (* maxCos (- 1 (/ 1 maxCos)))>
#<alt maxCos>
#<alt (* -1 (* maxCos (- (/ 1 maxCos) 1)))>
#<alt (* -1 (* maxCos (- (/ 1 maxCos) 1)))>
#<alt (* -1 (* maxCos (- (/ 1 maxCos) 1)))>

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	maxCos	@	-inf	(+ 1 (* ux (+ maxCos -1)))
0.0ms	ux	@	inf	(+ 1 (* ux (+ maxCos -1)))
0.0ms	ux	@	-inf	(+ 1 (* ux (+ maxCos -1)))
0.0ms	maxCos	@	inf	(+ 1 (* ux (+ maxCos -1)))
0.0ms	ux	@	0	(+ 1 (* ux (+ maxCos -1)))

rewrite255.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2300×	`-lowering-.f32`
2300×	`-lowering-.f64`
1686×	`fma-lowering-fma.f32`
1686×	`fma-lowering-fma.f64`
1564×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	43	14
2	362	14
3	4077	13
0	8036	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 202

Calls

Call 1

Inputs
(+ 1 (* ux (+ maxCos -1)))
(* ux (+ maxCos -1))
(+ maxCos -1)

Outputs
(neg.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)))))))
(neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))))) (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))
(neg.f32 (/.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32))))))
(neg.f32 (/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))))) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(exp.f32 (.f32 (log.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) #s(literal -1 binary32)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1 binary32))
(+.f32 (*.f32 ux maxCos) (+.f32 #s(literal 1 binary32) (neg.f32 ux)))
(+.f32 (neg.f32 ux) (+.f32 #s(literal 1 binary32) (*.f32 ux maxCos)))
(+.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (neg.f32 (/.f32 (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))
(+.f32 (+.f32 #s(literal 1 binary32) (*.f32 ux maxCos)) (neg.f32 ux))
(+.f32 (+.f32 #s(literal 1 binary32) (neg.f32 ux)) (*.f32 ux maxCos))
(pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) #s(literal -1 binary32))
(pow.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)) (+.f32 (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))) #s(literal -1 binary32))) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1 binary32))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (neg.f32 (/.f32 (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))
(fma.f32 ux maxCos (+.f32 #s(literal 1 binary32) (neg.f32 ux)))
(fma.f32 ux (+.f32 maxCos #s(literal -1 binary32)) #s(literal 1 binary32))
(fma.f32 maxCos ux (+.f32 #s(literal 1 binary32) (neg.f32 ux)))
(fma.f32 (+.f32 maxCos #s(literal -1 binary32)) ux #s(literal 1 binary32))
(fma.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1 binary32) #s(literal 1 binary32))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))))) (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (neg.f32 (/.f32 (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (neg.f32 (/.f32 (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (/.f32 (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(-.f32 (+.f32 #s(literal 1 binary32) (*.f32 ux maxCos)) ux)
(-.f32 (/.f32 (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)) (+.f32 (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))) #s(literal -1 binary32))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)))))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))))) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(/.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32))))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32))))))) (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (.f32 (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 (.f32 ux (.f32 (.f32 ux (.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) #s(literal 1 binary32))))))
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(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos))) #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 maxCos (+.f32 #s(literal 1 binary32) maxCos))))
(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos maxCos)) #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) maxCos))
(/.f32 (neg.f32 (neg.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos))))) (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (*.f32 maxCos (+.f32 #s(literal 1 binary32) maxCos))))))
(/.f32 (neg.f32 (neg.f32 (+.f32 #s(literal -1 binary32) (*.f32 maxCos maxCos)))) (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) maxCos))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 maxCos maxCos))) (neg.f32 (-.f32 #s(literal -1 binary32) maxCos)))
(/.f32 (-.f32 (pow.f32 (/.f32 (.f32 maxCos maxCos) (+.f32 #s(literal 1 binary32) maxCos)) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos)) #s(literal 3 binary32))) (+.f32 (.f32 (/.f32 (.f32 maxCos maxCos) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 (.f32 maxCos maxCos) (+.f32 #s(literal 1 binary32) maxCos))) (+.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos))) (.f32 (/.f32 (*.f32 maxCos maxCos) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos))))))
(/.f32 (-.f32 (.f32 (/.f32 (.f32 maxCos maxCos) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 (.f32 maxCos maxCos) (+.f32 #s(literal 1 binary32) maxCos))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos)))) (+.f32 (/.f32 (*.f32 maxCos maxCos) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos))))
(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 maxCos (.f32 maxCos maxCos)) (.f32 (.f32 maxCos (.f32 maxCos maxCos)) (.f32 maxCos (.f32 maxCos maxCos))))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 maxCos (+.f32 #s(literal 1 binary32) maxCos))))) (+.f32 (.f32 (.f32 maxCos (.f32 maxCos maxCos)) (.f32 maxCos (.f32 maxCos maxCos))) (-.f32 #s(literal 1 binary32) (.f32 maxCos (.f32 (.f32 maxCos maxCos) #s(literal -1 binary32))))))
(/.f32 (.f32 (+.f32 (.f32 (.f32 maxCos (.f32 maxCos maxCos)) (.f32 maxCos (.f32 maxCos maxCos))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 maxCos (+.f32 #s(literal 1 binary32) maxCos))))) (+.f32 (.f32 maxCos (*.f32 maxCos maxCos)) #s(literal 1 binary32)))
(/.f32 (.f32 (+.f32 (.f32 (.f32 maxCos (.f32 maxCos maxCos)) (.f32 maxCos (.f32 maxCos maxCos))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos))) (+.f32 (.f32 maxCos (.f32 maxCos (.f32 maxCos maxCos))) (+.f32 #s(literal 1 binary32) (.f32 maxCos maxCos))))
(/.f32 (.f32 (+.f32 (.f32 maxCos (.f32 maxCos (.f32 maxCos maxCos))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos))) (+.f32 #s(literal 1 binary32) (*.f32 maxCos maxCos)))
(*.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32)))
(*.f32 (+.f32 maxCos #s(literal -1 binary32)) #s(literal 1 binary32))
(.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 maxCos (+.f32 #s(literal 1 binary32) maxCos)))))
(.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos maxCos)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (+.f32 #s(literal 1 binary32) maxCos) (.f32 (+.f32 maxCos #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos))))
(*.f32 (+.f32 #s(literal 1 binary32) maxCos) (/.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (neg.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos)))) (/.f32 #s(literal 1 binary32) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 maxCos (+.f32 #s(literal 1 binary32) maxCos))))))
(.f32 (neg.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos maxCos))) (/.f32 #s(literal 1 binary32) (neg.f32 (+.f32 #s(literal 1 binary32) maxCos))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos)) (+.f32 #s(literal -1 binary32) (.f32 maxCos maxCos)))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 maxCos (+.f32 #s(literal 1 binary32) maxCos)))) (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos))))
(.f32 (-.f32 #s(literal 1 binary32) (.f32 maxCos maxCos)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) maxCos)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos)))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 maxCos (+.f32 #s(literal 1 binary32) maxCos)))))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (*.f32 maxCos maxCos))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos maxCos)) (+.f32 #s(literal -1 binary32) (*.f32 maxCos maxCos))) (+.f32 maxCos #s(literal -1 binary32)))
(.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos))) (+.f32 (.f32 (.f32 maxCos (.f32 maxCos maxCos)) (.f32 maxCos (.f32 maxCos maxCos))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal 1 binary32) maxCos)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal 1 binary32) maxCos)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal 1 binary32) maxCos)))))) (+.f32 (.f32 maxCos (.f32 maxCos (.f32 maxCos maxCos))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal 1 binary32) maxCos)) (-.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal 1 binary32) maxCos)) (.f32 maxCos maxCos)))))
(.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 maxCos (+.f32 #s(literal 1 binary32) maxCos))) (+.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos maxCos)) (neg.f32 maxCos)))) (+.f32 (+.f32 #s(literal -1 binary32) (*.f32 maxCos maxCos)) (neg.f32 maxCos)))
(.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos maxCos)) (+.f32 (.f32 maxCos (.f32 maxCos maxCos)) #s(literal 1 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 maxCos maxCos) maxCos)))

simplify140.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1786×	`-lowering-.f32`
1786×	`-lowering-.f64`
1342×	`sum4-define`
1182×	`sum3-define`
1152×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	290
1	131	271
2	410	248
3	1040	248
4	3466	248
5	6550	248
0	8123	248

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
1
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* ux (- maxCos 1)))
(* ux (- maxCos 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* ux (- maxCos 1))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(+ 1 (* -1 ux))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(* maxCos ux)
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(* maxCos ux)
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* -1 ux)
(+ (* -1 ux) (* maxCos ux))
(+ (* -1 ux) (* maxCos ux))
(+ (* -1 ux) (* maxCos ux))
(* maxCos ux)
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(* maxCos ux)
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
-1
(- maxCos 1)
(- maxCos 1)
(- maxCos 1)
maxCos
(* maxCos (- 1 (/ 1 maxCos)))
(* maxCos (- 1 (/ 1 maxCos)))
(* maxCos (- 1 (/ 1 maxCos)))
maxCos
(* -1 (* maxCos (- (/ 1 maxCos) 1)))
(* -1 (* maxCos (- (/ 1 maxCos) 1)))
(* -1 (* maxCos (- (/ 1 maxCos) 1)))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* ux (- maxCos 1)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (* ux (- maxCos 1)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (* ux (- maxCos 1)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* maxCos ux)
(*.f32 ux maxCos)
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* maxCos ux)
(*.f32 ux maxCos)
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 ux)
(neg.f32 ux)
(+ (* -1 ux) (* maxCos ux))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(+ (* -1 ux) (* maxCos ux))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(+ (* -1 ux) (* maxCos ux))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos ux)
(*.f32 ux maxCos)
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos ux)
(*.f32 ux maxCos)
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
-1
#s(literal -1 binary32)
(- maxCos 1)
(+.f32 maxCos #s(literal -1 binary32))
(- maxCos 1)
(+.f32 maxCos #s(literal -1 binary32))
(- maxCos 1)
(+.f32 maxCos #s(literal -1 binary32))
maxCos
(* maxCos (- 1 (/ 1 maxCos)))
(+.f32 maxCos #s(literal -1 binary32))
(* maxCos (- 1 (/ 1 maxCos)))
(+.f32 maxCos #s(literal -1 binary32))
(* maxCos (- 1 (/ 1 maxCos)))
(+.f32 maxCos #s(literal -1 binary32))
maxCos
(* -1 (* maxCos (- (/ 1 maxCos) 1)))
(+.f32 maxCos #s(literal -1 binary32))
(* -1 (* maxCos (- (/ 1 maxCos) 1)))
(+.f32 maxCos #s(literal -1 binary32))
(* -1 (* maxCos (- (/ 1 maxCos) 1)))
(+.f32 maxCos #s(literal -1 binary32))

eval27.0ms (0.6%)

Compiler: Compiled 5709 to 685 computations (88% saved)

prune40.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	259	4	263

Accuracy

100.0%

Counts

263 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.9%	(-.f32 #s(literal 1 binary32) ux)
▶	99.9%	(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))))))
✓	100.0%	(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
▶	72.9%	#s(literal 1 binary32)

Compiler

Compiled 44 to 30 computations (31.8% saved)

simplify202.0ms (4.5%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f32 #s(literal 1 binary32) ux)
✓	cost-diff	0	(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
✓	cost-diff	320	(/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))))
✓	cost-diff	448	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)))))
✓	cost-diff	448	(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))))))

Rules

2120×	`-lowering-.f32`
2120×	`-lowering-.f64`
1786×	`fma-lowering-fma.f32`
1786×	`fma-lowering-fma.f64`
1444×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	105
1	47	104
2	195	53
3	1074	48
4	5568	48
5	7257	48
0	8064	48

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
1
(+ 1 (/ 1 (/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))))
1
(/ 1 (/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos)))))
(/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))
(* ux (+ 1 maxCos))
ux
(+ 1 maxCos)
maxCos
(* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos)))
(* ux (+ maxCos -1))
(+ maxCos -1)
-1
(- 1 ux)
1
ux

Outputs
1
#s(literal 1 binary32)
(+ 1 (/ 1 (/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
1
#s(literal 1 binary32)
(/ 1 (/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos)))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))
(/.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
ux
(+ 1 maxCos)
(+.f32 #s(literal 1 binary32) maxCos)
maxCos
(* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos)))
(.f32 (+.f32 #s(literal 1 binary32) maxCos) (.f32 (+.f32 maxCos #s(literal -1 binary32)) (*.f32 ux ux)))
(* ux (+ maxCos -1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(+ maxCos -1)
(+.f32 maxCos #s(literal -1 binary32))
-1
#s(literal -1 binary32)
(- 1 ux)
(-.f32 #s(literal 1 binary32) ux)
1
#s(literal 1 binary32)
ux

localize112.0ms (2.5%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f32 #s(literal 1 binary32) ux)
✓	accuracy	99.9%	(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
✓	accuracy	99.8%	(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
✓	accuracy	99.4%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)))))
✓	accuracy	99.3%	(/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))))

Results

92.0ms	250×	0	valid
3.0ms	6×	5	exit

Compiler

Compiled 98 to 15 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-add: 37.0ms (48.4% of total)

ival-mult: 25.0ms (32.7% of total)

ival-sub: 9.0ms (11.8% of total)

ival-div: 4.0ms (5.2% of total)

backward-pass: 1.0ms (1.3% of total)

const: 0.0ms (0% of total)

series6.0ms (0.1%)

Counts

6 → 132

Calls

Call 1

Inputs
#<alt (+ 1 (/ 1 (/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))))>
#<alt (/ 1 (/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos)))))>
#<alt (/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))>
#<alt (* ux (+ 1 maxCos))>
#<alt (- 1 ux)>
#<alt (* ux (+ maxCos -1))>

Outputs
#<alt 1>
#<alt (+ 1 (* ux (- maxCos 1)))>
#<alt (+ 1 (* ux (- maxCos 1)))>
#<alt (+ 1 (* ux (- maxCos 1)))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- (+ maxCos (/ 1 ux)) 1))>
#<alt (* ux (- (+ maxCos (/ 1 ux)) 1))>
#<alt (* ux (- (+ maxCos (/ 1 ux)) 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))>
#<alt (* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))>
#<alt (* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))>
#<alt (+ 1 (* -1 ux))>
#<alt (+ 1 (+ (* -1 ux) (* maxCos ux)))>
#<alt (+ 1 (+ (* -1 ux) (* maxCos ux)))>
#<alt (+ 1 (+ (* -1 ux) (* maxCos ux)))>
#<alt (* maxCos ux)>
#<alt (* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))>
#<alt (* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))>
#<alt (* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))>
#<alt (* maxCos ux)>
#<alt (* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* -1 ux)>
#<alt (+ (* -1 ux) (* maxCos ux))>
#<alt (+ (* -1 ux) (* maxCos ux))>
#<alt (+ (* -1 ux) (* maxCos ux))>
#<alt (* maxCos ux)>
#<alt (* maxCos (+ ux (* -1 (/ ux maxCos))))>
#<alt (* maxCos (+ ux (* -1 (/ ux maxCos))))>
#<alt (* maxCos (+ ux (* -1 (/ ux maxCos))))>
#<alt (* maxCos ux)>
#<alt (* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ 1 (* ux (- maxCos 1)))>
#<alt (/ -1 ux)>
#<alt (- (* -1 (/ maxCos ux)) (/ 1 ux))>
#<alt (- (* maxCos (- (* -1 (/ maxCos ux)) (/ 1 ux))) (/ 1 ux))>
#<alt (- (* maxCos (- (* maxCos (- (* -1 (/ maxCos ux)) (/ 1 ux))) (/ 1 ux))) (/ 1 ux))>
#<alt (/ 1 (* maxCos ux))>
#<alt (/ (+ (/ 1 ux) (/ 1 (* maxCos ux))) maxCos)>
#<alt (/ (+ (/ 1 ux) (+ (/ 1 (* maxCos ux)) (/ 1 (* (pow maxCos 2) ux)))) maxCos)>
#<alt (/ (+ (/ 1 ux) (+ (/ 1 (* maxCos ux)) (+ (/ 1 (* (pow maxCos 2) ux)) (/ 1 (* (pow maxCos 3) ux))))) maxCos)>
#<alt (/ 1 (* maxCos ux))>
#<alt (/ (+ (/ 1 ux) (/ 1 (* maxCos ux))) maxCos)>
#<alt (* -1 (/ (- (* -1 (/ (+ (/ 1 ux) (/ 1 (* maxCos ux))) maxCos)) (/ 1 ux)) maxCos))>
#<alt (* -1 (/ (- (* -1 (/ (+ (/ 1 ux) (+ (/ 1 (* maxCos ux)) (/ 1 (* (pow maxCos 2) ux)))) maxCos)) (/ 1 ux)) maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt (* ux (+ 1 maxCos))>
#<alt ux>
#<alt (+ ux (* maxCos ux))>
#<alt (+ ux (* maxCos ux))>
#<alt (+ ux (* maxCos ux))>
#<alt (* maxCos ux)>
#<alt (* maxCos (+ ux (/ ux maxCos)))>
#<alt (* maxCos (+ ux (/ ux maxCos)))>
#<alt (* maxCos (+ ux (/ ux maxCos)))>
#<alt (* maxCos ux)>
#<alt (* -1 (* maxCos (+ (* -1 ux) (* -1 (/ ux maxCos)))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (* -1 (/ ux maxCos)))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (* -1 (/ ux maxCos)))))>
#<alt 1>
#<alt (+ 1 (* -1 ux))>
#<alt (+ 1 (* -1 ux))>
#<alt (+ 1 (* -1 ux))>
#<alt (* -1 ux)>
#<alt (* ux (- (/ 1 ux) 1))>
#<alt (* ux (- (/ 1 ux) 1))>
#<alt (* ux (- (/ 1 ux) 1))>
#<alt (* -1 ux)>
#<alt (* -1 (* ux (- 1 (/ 1 ux))))>
#<alt (* -1 (* ux (- 1 (/ 1 ux))))>
#<alt (* -1 (* ux (- 1 (/ 1 ux))))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* ux (- maxCos 1))>
#<alt (* -1 ux)>
#<alt (+ (* -1 ux) (* maxCos ux))>
#<alt (+ (* -1 ux) (* maxCos ux))>
#<alt (+ (* -1 ux) (* maxCos ux))>
#<alt (* maxCos ux)>
#<alt (* maxCos (+ ux (* -1 (/ ux maxCos))))>
#<alt (* maxCos (+ ux (* -1 (/ ux maxCos))))>
#<alt (* maxCos (+ ux (* -1 (/ ux maxCos))))>
#<alt (* maxCos ux)>
#<alt (* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))>
#<alt (* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))>

Calls

33 calls:

Time	Variable		Point	Expression
1.0ms	maxCos	@	0	(/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))
0.0ms	ux	@	0	(/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))
0.0ms	ux	@	0	(* ux (+ 1 maxCos))
0.0ms	ux	@	inf	(/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))
0.0ms	ux	@	-inf	(/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))

rewrite244.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3852×	`-lowering-.f32`
3852×	`-lowering-.f64`
2778×	`/-lowering-/.f32`
2778×	`/-lowering-/.f64`
1886×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	81
1	103	78
2	967	30
0	9101	30

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 560

Calls

Call 1

Inputs
(+ 1 (/ 1 (/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))))
(/ 1 (/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos)))))
(/ (* ux (+ 1 maxCos)) (* (* ux (+ maxCos -1)) (* ux (+ 1 maxCos))))
(* ux (+ 1 maxCos))
(- 1 ux)
(* ux (+ maxCos -1))

Outputs
(neg.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)))))))
(neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (+.f32 #s(literal -1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(neg.f32 (/.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32))))))
(neg.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1 binary32))
(+.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (neg.f32 (/.f32 (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))
(pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1 binary32))
(fma.f32 ux (/.f32 (.f32 ux (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32))) (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) #s(literal 1 binary32))
(fma.f32 (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (+.f32 maxCos #s(literal -1 binary32)))) #s(literal 1 binary32))
(fma.f32 #s(literal -1 binary32) (neg.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) #s(literal 1 binary32))
(fma.f32 (+.f32 maxCos #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) ux)) #s(literal 1 binary32))
(fma.f32 (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) #s(literal 1 binary32))
(fma.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1 binary32) #s(literal 1 binary32))
(fma.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) ux) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) #s(literal 1 binary32))
(fma.f32 (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32))
(fma.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (.f32 ux ux)) #s(literal 1 binary32))
(fma.f32 (/.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 (.f32 ux (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32))) ux) #s(literal 1 binary32))
(fma.f32 (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) ux) (/.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) maxCos)) #s(literal 1 binary32))
(fma.f32 (/.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) ux) #s(literal 1 binary32))
(fma.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) ux)) (+.f32 maxCos #s(literal -1 binary32)) #s(literal 1 binary32))
(fma.f32 (/.f32 (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) ux) #s(literal 1 binary32))
(fma.f32 (pow.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1/2 binary32)) (pow.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1/2 binary32)) #s(literal 1 binary32))
(fma.f32 (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (+.f32 maxCos #s(literal -1 binary32)))) (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) #s(literal 1 binary32))
(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) ux) (.f32 ux (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32))) #s(literal 1 binary32))
(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) #s(literal 1 binary32))
(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (+.f32 #s(literal 1 binary32) maxCos) #s(literal 1 binary32))
(fma.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (.f32 (+.f32 maxCos #s(literal -1 binary32)) (.f32 (.f32 ux (-.f32 #s(literal -1 binary32) maxCos)) ux)) #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) (neg.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (/.f32 (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(-.f32 (/.f32 (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)) (+.f32 (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) #s(literal -1 binary32))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)))))
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (+.f32 (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(/.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32))))))
(/.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))) (neg.f32 (+.f32 (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))
(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (+.f32 #s(literal -1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(/.f32 (+.f32 (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) #s(literal -1 binary32)) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)))
(/.f32 (-.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
(/.f32 (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))))) (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal -1 binary32)))))))
(/.f32 (neg.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (neg.f32 (+.f32 #s(literal -1 binary32) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))))
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(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (/.f32 (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (*.f32 ux ux)) ux)))
(/.f32 ux (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))))
(/.f32 (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (+.f32 maxCos #s(literal -1 binary32))))
(/.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(/.f32 (+.f32 maxCos #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) ux))
(/.f32 (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (.f32 ux ux)) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)))
(/.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1 binary32))
(/.f32 (.f32 ux (-.f32 #s(literal -1 binary32) maxCos)) (.f32 (+.f32 #s(literal 1 binary32) maxCos) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) maxCos))))
(/.f32 (.f32 (+.f32 maxCos #s(literal -1 binary32)) (.f32 (.f32 ux (-.f32 #s(literal -1 binary32) maxCos)) ux)) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos)))
(/.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 (/.f32 #s(literal 1 binary32) ux) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(/.f32 (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) ux)
(/.f32 (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) ux)))
(/.f32 (.f32 ux (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) maxCos))
(/.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (.f32 ux ux))))
(/.f32 (+.f32 (.f32 (.f32 maxCos (.f32 maxCos maxCos)) (.f32 ux (.f32 ux ux))) (.f32 ux (-.f32 #s(literal 0 binary32) (.f32 ux ux)))) (+.f32 (.f32 (.f32 maxCos maxCos) (.f32 ux ux)) (.f32 (neg.f32 ux) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos)))))
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) ux) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) ux)
(/.f32 (.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (.f32 ux (-.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos)))
(/.f32 (neg.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) #s(literal -1 binary32))
(/.f32 (neg.f32 (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (neg.f32 ux))
(/.f32 (/.f32 #s(literal -1 binary32) ux) (/.f32 (/.f32 #s(literal -1 binary32) ux) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(/.f32 (.f32 (+.f32 maxCos #s(literal -1 binary32)) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (-.f32 #s(literal -1 binary32) maxCos))
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(/.f32 (.f32 ux (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos)))) (+.f32 (+.f32 (.f32 maxCos maxCos) #s(literal 1 binary32)) maxCos))
(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos))) ux) (+.f32 (+.f32 (.f32 maxCos maxCos) #s(literal 1 binary32)) maxCos))
(/.f32 (/.f32 (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (*.f32 ux ux)) ux) (+.f32 #s(literal 1 binary32) maxCos))
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(/.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) ux) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (neg.f32 ux))
(/.f32 (neg.f32 (/.f32 (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (*.f32 ux ux)) ux)) (-.f32 #s(literal -1 binary32) maxCos))
(/.f32 (+.f32 (.f32 ux (-.f32 #s(literal 0 binary32) (.f32 ux ux))) (.f32 (.f32 maxCos (.f32 maxCos maxCos)) (.f32 ux (.f32 ux ux)))) (+.f32 (.f32 ux ux) (-.f32 (.f32 (.f32 maxCos maxCos) (.f32 ux ux)) (.f32 (neg.f32 ux) (*.f32 ux maxCos)))))
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(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(.f32 ux (/.f32 (.f32 ux (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))))
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(.f32 #s(literal -1 binary32) (neg.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(*.f32 (+.f32 maxCos #s(literal -1 binary32)) ux)
(*.f32 (+.f32 maxCos #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) ux)))
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(.f32 (.f32 ux (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) ux))
(.f32 (.f32 ux (+.f32 (*.f32 maxCos maxCos) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (*.f32 ux ux)))
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(.f32 (/.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 (.f32 ux (+.f32 (*.f32 maxCos maxCos) #s(literal -1 binary32))) ux))
(.f32 (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) ux) (/.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (/.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) ux))
(*.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) ux)) (+.f32 maxCos #s(literal -1 binary32)))
(.f32 (/.f32 (.f32 ux (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (+.f32 #s(literal 1 binary32) maxCos)) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) ux))
(.f32 (+.f32 (.f32 (.f32 maxCos (.f32 maxCos maxCos)) (.f32 ux (.f32 ux ux))) (.f32 ux (-.f32 #s(literal 0 binary32) (.f32 ux ux)))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 maxCos maxCos) (.f32 ux ux)) (.f32 (neg.f32 ux) (*.f32 ux (-.f32 #s(literal -1 binary32) maxCos))))))
(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) ux) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) ux))
(.f32 (pow.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1/2 binary32)) (pow.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1/2 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (+.f32 maxCos #s(literal -1 binary32)))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (+.f32 maxCos #s(literal -1 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) #s(literal -1 binary32)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) ux) (.f32 ux (+.f32 (*.f32 maxCos maxCos) #s(literal -1 binary32))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (+.f32 #s(literal 1 binary32) maxCos))
(.f32 (.f32 ux (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos)))) (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (*.f32 maxCos maxCos) #s(literal 1 binary32)) maxCos)))
(.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 maxCos (.f32 maxCos maxCos))) ux) (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (*.f32 maxCos maxCos) #s(literal 1 binary32)) maxCos)))
(.f32 (/.f32 (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (.f32 ux ux)) ux) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (.f32 (+.f32 maxCos #s(literal -1 binary32)) (.f32 (*.f32 ux (-.f32 #s(literal -1 binary32) maxCos)) ux)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (pow.f32 (/.f32 #s(literal -1 binary32) (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (*.f32 ux ux))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) maxCos) ux) #s(literal -1 binary32)) (pow.f32 (/.f32 ux (.f32 ux (+.f32 (*.f32 maxCos maxCos) #s(literal -1 binary32)))) #s(literal -1 binary32)))
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(.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) #s(literal -1 binary32)) (pow.f32 (/.f32 ux (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (.f32 ux (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) #s(literal -1 binary32)) (pow.f32 (/.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) #s(literal -1 binary32)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (.f32 ux (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 #s(literal -1 binary32) maxCos))
(.f32 (.f32 (+.f32 maxCos #s(literal -1 binary32)) #s(literal 1 binary32)) ux)
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (+.f32 maxCos #s(literal -1 binary32)))) ux) (+.f32 #s(literal 1 binary32) maxCos))
(.f32 (.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (+.f32 #s(literal 1 binary32) maxCos))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (+.f32 #s(literal 1 binary32) maxCos)) (.f32 ux (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) (+.f32 maxCos #s(literal -1 binary32)))) (+.f32 #s(literal 1 binary32) maxCos)) ux)
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) ux) (.f32 (+.f32 maxCos #s(literal -1 binary32)) (*.f32 ux (-.f32 #s(literal -1 binary32) maxCos))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (neg.f32 (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (*.f32 ux (-.f32 #s(literal -1 binary32) maxCos)))
(.f32 (.f32 #s(literal 1 binary32) (/.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (/.f32 (.f32 ux (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32))) ux))
(.f32 (.f32 #s(literal 1 binary32) (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) ux)) (/.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (.f32 #s(literal 1 binary32) (/.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) maxCos))) (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) ux))
(.f32 (.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) ux))) (+.f32 maxCos #s(literal -1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (/.f32 (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (+.f32 #s(literal 1 binary32) maxCos))) (/.f32 (+.f32 #s(literal 1 binary32) maxCos) ux))
(.f32 (.f32 #s(literal 1 binary32) (pow.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1/2 binary32))) (pow.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) #s(literal 1/2 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) ux)) (.f32 ux (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32))))
(.f32 (.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (+.f32 (*.f32 maxCos maxCos) #s(literal -1 binary32)))) ux)
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos)))) (+.f32 maxCos #s(literal -1 binary32)))
(.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) ux) (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (+.f32 maxCos #s(literal -1 binary32)))
(.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) ux) (*.f32 (+.f32 maxCos #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) maxCos))) ux)
(.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))) (+.f32 #s(literal 1 binary32) maxCos)) ux)
(.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (+.f32 #s(literal 1 binary32) (.f32 maxCos (.f32 maxCos maxCos)))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 maxCos (+.f32 maxCos #s(literal -1 binary32))))))
(.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))) (.f32 ux (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (-.f32 #s(literal 1 binary32) (*.f32 maxCos maxCos))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) maxCos)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) #s(literal -1 binary32)) (.f32 (+.f32 (.f32 maxCos maxCos) #s(literal -1 binary32)) (.f32 ux ux)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (neg.f32 ux)) (.f32 ux (+.f32 (*.f32 maxCos maxCos) #s(literal -1 binary32))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (neg.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))))) (*.f32 ux (+.f32 #s(literal 1 binary32) maxCos)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 ux (-.f32 #s(literal -1 binary32) maxCos))) (neg.f32 (.f32 ux (*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))))) (+.f32 #s(literal 1 binary32) maxCos))

simplify212.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1734×	`sum4-define`
1570×	`-lowering-.f32`
1570×	`-lowering-.f64`
1380×	`sum3-define`
1216×	`--lowering--.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	84	738
1	260	684
2	738	626
3	2018	618
4	5978	617
0	8297	617

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
1
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* ux (- maxCos 1)))
(* ux (- maxCos 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* ux (- maxCos 1))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(+ 1 (* -1 ux))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(* maxCos ux)
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(* maxCos ux)
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* -1 ux)
(+ (* -1 ux) (* maxCos ux))
(+ (* -1 ux) (* maxCos ux))
(+ (* -1 ux) (* maxCos ux))
(* maxCos ux)
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(* maxCos ux)
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ 1 (* ux (- maxCos 1)))
(/ -1 ux)
(- (* -1 (/ maxCos ux)) (/ 1 ux))
(- (* maxCos (- (* -1 (/ maxCos ux)) (/ 1 ux))) (/ 1 ux))
(- (* maxCos (- (* maxCos (- (* -1 (/ maxCos ux)) (/ 1 ux))) (/ 1 ux))) (/ 1 ux))
(/ 1 (* maxCos ux))
(/ (+ (/ 1 ux) (/ 1 (* maxCos ux))) maxCos)
(/ (+ (/ 1 ux) (+ (/ 1 (* maxCos ux)) (/ 1 (* (pow maxCos 2) ux)))) maxCos)
(/ (+ (/ 1 ux) (+ (/ 1 (* maxCos ux)) (+ (/ 1 (* (pow maxCos 2) ux)) (/ 1 (* (pow maxCos 3) ux))))) maxCos)
(/ 1 (* maxCos ux))
(/ (+ (/ 1 ux) (/ 1 (* maxCos ux))) maxCos)
(* -1 (/ (- (* -1 (/ (+ (/ 1 ux) (/ 1 (* maxCos ux))) maxCos)) (/ 1 ux)) maxCos))
(* -1 (/ (- (* -1 (/ (+ (/ 1 ux) (+ (/ 1 (* maxCos ux)) (/ 1 (* (pow maxCos 2) ux)))) maxCos)) (/ 1 ux)) maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
(* ux (+ 1 maxCos))
ux
(+ ux (* maxCos ux))
(+ ux (* maxCos ux))
(+ ux (* maxCos ux))
(* maxCos ux)
(* maxCos (+ ux (/ ux maxCos)))
(* maxCos (+ ux (/ ux maxCos)))
(* maxCos (+ ux (/ ux maxCos)))
(* maxCos ux)
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ ux maxCos)))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ ux maxCos)))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ ux maxCos)))))
1
(+ 1 (* -1 ux))
(+ 1 (* -1 ux))
(+ 1 (* -1 ux))
(* -1 ux)
(* ux (- (/ 1 ux) 1))
(* ux (- (/ 1 ux) 1))
(* ux (- (/ 1 ux) 1))
(* -1 ux)
(* -1 (* ux (- 1 (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* ux (- maxCos 1))
(* -1 ux)
(+ (* -1 ux) (* maxCos ux))
(+ (* -1 ux) (* maxCos ux))
(+ (* -1 ux) (* maxCos ux))
(* maxCos ux)
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(* maxCos ux)
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* ux (- maxCos 1)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (* ux (- maxCos 1)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (* ux (- maxCos 1)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* -1 (* ux (- (* -1 (- maxCos 1)) (/ 1 ux))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+ 1 (+ (* -1 ux) (* maxCos ux)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* maxCos ux)
(*.f32 ux maxCos)
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* maxCos (+ ux (+ (* -1 (/ ux maxCos)) (/ 1 maxCos))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* maxCos ux)
(*.f32 ux maxCos)
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (+ 1 (* -1 ux)) maxCos)))))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 ux)
(neg.f32 ux)
(+ (* -1 ux) (* maxCos ux))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(+ (* -1 ux) (* maxCos ux))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(+ (* -1 ux) (* maxCos ux))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos ux)
(*.f32 ux maxCos)
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos ux)
(*.f32 ux maxCos)
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ 1 (* ux (- maxCos 1)))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 maxCos #s(literal -1 binary32))) ux)
(/ -1 ux)
(/.f32 #s(literal -1 binary32) ux)
(- (* -1 (/ maxCos ux)) (/ 1 ux))
(*.f32 (+.f32 #s(literal 1 binary32) maxCos) (/.f32 #s(literal -1 binary32) ux))
(- (* maxCos (- (* -1 (/ maxCos ux)) (/ 1 ux))) (/ 1 ux))
(+.f32 (*.f32 (/.f32 maxCos ux) (+.f32 (neg.f32 maxCos) #s(literal -1 binary32))) (/.f32 #s(literal -1 binary32) ux))
(- (* maxCos (- (* maxCos (- (* -1 (/ maxCos ux)) (/ 1 ux))) (/ 1 ux))) (/ 1 ux))
(.f32 (+.f32 (.f32 maxCos maxCos) #s(literal 1 binary32)) (*.f32 (+.f32 #s(literal 1 binary32) maxCos) (/.f32 #s(literal -1 binary32) ux)))
(/ 1 (* maxCos ux))
(/.f32 #s(literal 1 binary32) (*.f32 ux maxCos))
(/ (+ (/ 1 ux) (/ 1 (* maxCos ux))) maxCos)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (*.f32 ux maxCos))) maxCos)
(/ (+ (/ 1 ux) (+ (/ 1 (* maxCos ux)) (/ 1 (* (pow maxCos 2) ux)))) maxCos)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (*.f32 ux maxCos))) maxCos)) maxCos)
(/ (+ (/ 1 ux) (+ (/ 1 (* maxCos ux)) (+ (/ 1 (* (pow maxCos 2) ux)) (/ 1 (* (pow maxCos 3) ux))))) maxCos)
(/.f32 (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (.f32 ux maxCos))) maxCos)) (/.f32 #s(literal 1 binary32) (.f32 maxCos (.f32 ux (.f32 maxCos maxCos))))) maxCos)
(/ 1 (* maxCos ux))
(/.f32 #s(literal 1 binary32) (*.f32 ux maxCos))
(/ (+ (/ 1 ux) (/ 1 (* maxCos ux))) maxCos)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (*.f32 ux maxCos))) maxCos)
(* -1 (/ (- (* -1 (/ (+ (/ 1 ux) (/ 1 (* maxCos ux))) maxCos)) (/ 1 ux)) maxCos))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (*.f32 ux maxCos))) maxCos)) maxCos)
(* -1 (/ (- (* -1 (/ (+ (/ 1 ux) (+ (/ 1 (* maxCos ux)) (/ 1 (* (pow maxCos 2) ux)))) maxCos)) (/ 1 ux)) maxCos))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 (-.f32 (/.f32 #s(literal -1 binary32) ux) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (*.f32 ux maxCos))) maxCos)) maxCos)) maxCos)
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* ux (+ 1 maxCos))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
ux
(+ ux (* maxCos ux))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(+ ux (* maxCos ux))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(+ ux (* maxCos ux))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* maxCos ux)
(*.f32 ux maxCos)
(* maxCos (+ ux (/ ux maxCos)))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* maxCos (+ ux (/ ux maxCos)))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* maxCos (+ ux (/ ux maxCos)))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* maxCos ux)
(*.f32 ux maxCos)
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ ux maxCos)))))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ ux maxCos)))))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ ux maxCos)))))
(*.f32 ux (+.f32 #s(literal 1 binary32) maxCos))
1
#s(literal 1 binary32)
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(* -1 ux)
(neg.f32 ux)
(* ux (- (/ 1 ux) 1))
(-.f32 #s(literal 1 binary32) ux)
(* ux (- (/ 1 ux) 1))
(-.f32 #s(literal 1 binary32) ux)
(* ux (- (/ 1 ux) 1))
(-.f32 #s(literal 1 binary32) ux)
(* -1 ux)
(neg.f32 ux)
(* -1 (* ux (- 1 (/ 1 ux))))
(-.f32 #s(literal 1 binary32) ux)
(* -1 (* ux (- 1 (/ 1 ux))))
(-.f32 #s(literal 1 binary32) ux)
(* -1 (* ux (- 1 (/ 1 ux))))
(-.f32 #s(literal 1 binary32) ux)
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* ux (- maxCos 1))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 ux)
(neg.f32 ux)
(+ (* -1 ux) (* maxCos ux))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(+ (* -1 ux) (* maxCos ux))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(+ (* -1 ux) (* maxCos ux))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos ux)
(*.f32 ux maxCos)
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos (+ ux (* -1 (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* maxCos ux)
(*.f32 ux maxCos)
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))
(* -1 (* maxCos (+ (* -1 ux) (/ ux maxCos))))
(*.f32 ux (+.f32 maxCos #s(literal -1 binary32)))

eval67.0ms (1.5%)

Compiler: Compiled 18140 to 2225 computations (87.7% saved)

prune97.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	775	1	776
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	776	4	780

Accuracy

100.0%

Counts

780 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.9%	(-.f32 #s(literal 1 binary32) ux)
✓	100.0%	(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
▶	97.6%	(.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)))
✓	72.9%	#s(literal 1 binary32)

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify118.0ms (2.6%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux))
✓	cost-diff	0	(*.f32 ux ux)
✓	cost-diff	0	(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
✓	cost-diff	256	(.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)))

Rules

1862×	`fnmsub-define`
1666×	`sum3-define`
1548×	`fma-define`
1224×	`-lowering-.f32`
1224×	`-lowering-.f64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	7	27
1	19	26
2	35	24
3	82	24
4	214	24
5	362	24
6	580	19
7	1290	19
8	5533	19
0	8128	19

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (- 1 (* ux ux)) (/ 1 (+ 1 ux)))
(- 1 (* ux ux))
1
(* ux ux)
ux
(/ 1 (+ 1 ux))
(+ 1 ux)

Outputs
(* (- 1 (* ux ux)) (/ 1 (+ 1 ux)))
(-.f32 #s(literal 1 binary32) ux)
(- 1 (* ux ux))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
1
#s(literal 1 binary32)
(* ux ux)
(*.f32 ux ux)
ux
(/ 1 (+ 1 ux))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux))
(+ 1 ux)
(+.f32 #s(literal 1 binary32) ux)

localize53.0ms (1.2%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f32 ux ux)
✓	accuracy	100.0%	(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
✓	accuracy	99.6%	(.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux))

Results

34.0ms	247×	0	valid
10.0ms	9×	5	exit

Compiler

Compiled 33 to 10 computations (69.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 4.0ms (39.9% of total)

ival-div: 2.0ms (20% of total)

ival-add: 1.0ms (10% of total)

backward-pass: 1.0ms (10% of total)

ival-sub: 1.0ms (10% of total)

const: 0.0ms (0% of total)

series2.0ms (0%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (* (- 1 (* ux ux)) (/ 1 (+ 1 ux)))>
#<alt (- 1 (* ux ux))>
#<alt (* ux ux)>
#<alt (/ 1 (+ 1 ux))>

Outputs
#<alt 1>
#<alt (+ 1 (* -1 ux))>
#<alt (+ 1 (* -1 ux))>
#<alt (+ 1 (* -1 ux))>
#<alt (* -1 ux)>
#<alt (* ux (- (/ 1 ux) 1))>
#<alt (* ux (- (/ 1 ux) 1))>
#<alt (* ux (- (/ 1 ux) 1))>
#<alt (* -1 ux)>
#<alt (* -1 (* ux (- 1 (/ 1 ux))))>
#<alt (* -1 (* ux (- 1 (/ 1 ux))))>
#<alt (* -1 (* ux (- 1 (/ 1 ux))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow ux 2)))>
#<alt (+ 1 (* -1 (pow ux 2)))>
#<alt (+ 1 (* -1 (pow ux 2)))>
#<alt (* -1 (pow ux 2))>
#<alt (* (pow ux 2) (- (/ 1 (pow ux 2)) 1))>
#<alt (* (pow ux 2) (- (/ 1 (pow ux 2)) 1))>
#<alt (* (pow ux 2) (- (/ 1 (pow ux 2)) 1))>
#<alt (* -1 (pow ux 2))>
#<alt (* (pow ux 2) (- (/ 1 (pow ux 2)) 1))>
#<alt (* (pow ux 2) (- (/ 1 (pow ux 2)) 1))>
#<alt (* (pow ux 2) (- (/ 1 (pow ux 2)) 1))>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt (pow ux 2)>
#<alt 1>
#<alt (+ 1 (* -1 ux))>
#<alt (+ 1 (* ux (- ux 1)))>
#<alt (+ 1 (* ux (- (* ux (+ 1 (* -1 ux))) 1)))>
#<alt (/ 1 ux)>
#<alt (/ (- 1 (/ 1 ux)) ux)>
#<alt (/ (- (+ 1 (/ 1 (pow ux 2))) (/ 1 ux)) ux)>
#<alt (/ (- (+ 1 (/ 1 (pow ux 2))) (+ (/ 1 ux) (/ 1 (pow ux 3)))) ux)>
#<alt (/ 1 ux)>
#<alt (* -1 (/ (- (/ 1 ux) 1) ux))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ 1 ux) 1) ux)) 1) ux))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 ux) 1) ux)) 1) ux)) 1) ux))>

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	ux	@	0	(* (- 1 (* ux ux)) (/ 1 (+ 1 ux)))
0.0ms	ux	@	inf	(* (- 1 (* ux ux)) (/ 1 (+ 1 ux)))
0.0ms	ux	@	-inf	(* (- 1 (* ux ux)) (/ 1 (+ 1 ux)))
0.0ms	ux	@	0	(* ux ux)
0.0ms	ux	@	inf	(/ 1 (+ 1 ux))

rewrite243.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2474×	`-lowering-.f32`
2474×	`-lowering-.f64`
2246×	`/-lowering-/.f32`
2246×	`/-lowering-/.f64`
1612×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	51	15
2	389	14
3	4812	14
0	8128	14

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 370

Calls

Call 1

Inputs
(* (- 1 (* ux ux)) (/ 1 (+ 1 ux)))
(- 1 (* ux ux))
(* ux ux)
(/ 1 (+ 1 ux))

Outputs
(neg.f32 (neg.f32 (-.f32 #s(literal 1 binary32) ux)))
(+.f32 #s(literal 1 binary32) (neg.f32 ux))
(+.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(+.f32 (neg.f32 ux) #s(literal 1 binary32))
(+.f32 (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)))
(+.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (.f32 (.f32 ux (+.f32 ux #s(literal -1 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux))))))
(+.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) #s(literal 1 binary32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (*.f32 ux (+.f32 ux #s(literal -1 binary32)))))
(+.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (*.f32 ux ux)))) #s(literal 1 binary32)))
(+.f32 (.f32 (.f32 ux (+.f32 ux #s(literal -1 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))))
(pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) ux)) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) ux)) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (-.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) ux)) #s(literal -1 binary32) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (pow.f32 (+.f32 #s(literal 1 binary32) ux) #s(literal -1/2 binary32)) (pow.f32 (+.f32 #s(literal 1 binary32) ux) #s(literal -1/2 binary32)) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (pow.f32 (+.f32 #s(literal 1 binary32) ux) #s(literal -1/2 binary32)) (.f32 (pow.f32 (+.f32 #s(literal 1 binary32) ux) #s(literal -1/2 binary32)) #s(literal 1 binary32)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (-.f32 #s(literal 1 binary32) ux) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32))))) #s(literal -1 binary32)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) #s(literal 1 binary32)) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) #s(literal 1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))) (-.f32 #s(literal 1 binary32) ux)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (/.f32 (-.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (.f32 (-.f32 #s(literal 1 binary32) ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (/.f32 (-.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) #s(literal 1 binary32)) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) #s(literal 1 binary32)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) ux) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux))) (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (.f32 #s(literal 1 binary32) (pow.f32 (+.f32 #s(literal 1 binary32) ux) #s(literal -1/2 binary32))) (pow.f32 (+.f32 #s(literal 1 binary32) ux) #s(literal -1/2 binary32)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux))))) (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal -1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (neg.f32 (-.f32 #s(literal 1 binary32) ux)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32))))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (+.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (.f32 ux ux)) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux))))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (.f32 ux ux)) (-.f32 (.f32 ux (.f32 ux ux)) #s(literal 1 binary32)))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) ux) (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux))))))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux))))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) ux) (+.f32 #s(literal -1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (+.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 0 binary32) (*.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux)))) (neg.f32 (-.f32 #s(literal 1 binary32) ux)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux))))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32))))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 ux ux) #s(literal -1 binary32))) (+.f32 ux #s(literal -1 binary32)) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) ux)))
(-.f32 #s(literal 1 binary32) ux)
(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (/.f32 (*.f32 ux ux) (+.f32 #s(literal 1 binary32) ux)))
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(.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))) (-.f32 #s(literal 1 binary32) ux)))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (/.f32 (-.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (*.f32 ux ux)))))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (.f32 (-.f32 #s(literal 1 binary32) ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (/.f32 (-.f32 #s(literal 1 binary32) ux) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux ux)))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))))
(.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) #s(literal 1 binary32)) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (.f32 ux ux))))
(.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) #s(literal 1 binary32)))
(.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (*.f32 ux ux)))))))
(.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 ux ux)))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 ux ux))) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) ux))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux))) (-.f32 #s(literal 1 binary32) (.f32 ux ux)))
(.f32 (.f32 #s(literal 1 binary32) (pow.f32 (+.f32 #s(literal 1 binary32) ux) #s(literal -1/2 binary32))) (pow.f32 (+.f32 #s(literal 1 binary32) ux) #s(literal -1/2 binary32)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux))))) (+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 ux #s(literal -1 binary32)))))
(.f32 (/.f32 #s(literal -1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (neg.f32 (-.f32 #s(literal 1 binary32) ux)))
(.f32 (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux)))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32))))))
(.f32 (/.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (*.f32 ux ux)))))
(.f32 (/.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (+.f32 #s(literal 1 binary32) (*.f32 ux ux)))
(.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux)))))) (-.f32 #s(literal 1 binary32) (.f32 ux (*.f32 ux ux))))
(.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (.f32 ux ux)) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux))))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux (.f32 ux ux)) (-.f32 (.f32 ux (*.f32 ux ux)) #s(literal 1 binary32)))))
(.f32 (/.f32 (-.f32 #s(literal 1 binary32) ux) (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (.f32 ux (.f32 ux (.f32 ux ux))))))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 ux ux) (+.f32 #s(literal 1 binary32) (*.f32 ux ux))))))
(.f32 (/.f32 (-.f32 #s(literal 1 binary32) ux) (+.f32 #s(literal -1 binary32) (.f32 ux (.f32 ux (.f32 ux ux))))) (+.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 binary32) (*.f32 ux ux))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux)))) (neg.f32 (-.f32 #s(literal 1 binary32) ux)))
(.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (.f32 ux ux))))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 ux (+.f32 ux #s(literal -1 binary32))))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 ux ux) #s(literal -1 binary32))) (+.f32 ux #s(literal -1 binary32)))

simplify176.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

2014×	`fnmadd-define`
1794×	`sum4-define`
1792×	`sum3-define`
1692×	`fma-lowering-fma.f32`
1692×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	233
1	122	198
2	291	196
3	877	195
4	2919	195
0	8020	195

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
1
(+ 1 (* -1 ux))
(+ 1 (* -1 ux))
(+ 1 (* -1 ux))
(* -1 ux)
(* ux (- (/ 1 ux) 1))
(* ux (- (/ 1 ux) 1))
(* ux (- (/ 1 ux) 1))
(* -1 ux)
(* -1 (* ux (- 1 (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
1
(+ 1 (* -1 (pow ux 2)))
(+ 1 (* -1 (pow ux 2)))
(+ 1 (* -1 (pow ux 2)))
(* -1 (pow ux 2))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(* -1 (pow ux 2))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(pow ux 2)
(pow ux 2)
(pow ux 2)
(pow ux 2)
(pow ux 2)
(pow ux 2)
(pow ux 2)
(pow ux 2)
(pow ux 2)
(pow ux 2)
(pow ux 2)
(pow ux 2)
1
(+ 1 (* -1 ux))
(+ 1 (* ux (- ux 1)))
(+ 1 (* ux (- (* ux (+ 1 (* -1 ux))) 1)))
(/ 1 ux)
(/ (- 1 (/ 1 ux)) ux)
(/ (- (+ 1 (/ 1 (pow ux 2))) (/ 1 ux)) ux)
(/ (- (+ 1 (/ 1 (pow ux 2))) (+ (/ 1 ux) (/ 1 (pow ux 3)))) ux)
(/ 1 ux)
(* -1 (/ (- (/ 1 ux) 1) ux))
(* -1 (/ (- (* -1 (/ (- (/ 1 ux) 1) ux)) 1) ux))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 ux) 1) ux)) 1) ux)) 1) ux))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(* -1 ux)
(neg.f32 ux)
(* ux (- (/ 1 ux) 1))
(-.f32 #s(literal 1 binary32) ux)
(* ux (- (/ 1 ux) 1))
(-.f32 #s(literal 1 binary32) ux)
(* ux (- (/ 1 ux) 1))
(-.f32 #s(literal 1 binary32) ux)
(* -1 ux)
(neg.f32 ux)
(* -1 (* ux (- 1 (/ 1 ux))))
(-.f32 #s(literal 1 binary32) ux)
(* -1 (* ux (- 1 (/ 1 ux))))
(-.f32 #s(literal 1 binary32) ux)
(* -1 (* ux (- 1 (/ 1 ux))))
(-.f32 #s(literal 1 binary32) ux)
1
#s(literal 1 binary32)
(+ 1 (* -1 (pow ux 2)))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
(+ 1 (* -1 (pow ux 2)))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
(+ 1 (* -1 (pow ux 2)))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
(* -1 (pow ux 2))
(-.f32 #s(literal 0 binary32) (*.f32 ux ux))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
(* -1 (pow ux 2))
(-.f32 #s(literal 0 binary32) (*.f32 ux ux))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
(* (pow ux 2) (- (/ 1 (pow ux 2)) 1))
(-.f32 #s(literal 1 binary32) (*.f32 ux ux))
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
(pow ux 2)
(*.f32 ux ux)
1
#s(literal 1 binary32)
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(+ 1 (* ux (- ux 1)))
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 #s(literal -1 binary32) ux)))
(+ 1 (* ux (- (* ux (+ 1 (* -1 ux))) 1)))
(.f32 (-.f32 #s(literal 1 binary32) ux) (+.f32 #s(literal 1 binary32) (.f32 ux ux)))
(/ 1 ux)
(/.f32 #s(literal 1 binary32) ux)
(/ (- 1 (/ 1 ux)) ux)
(/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)) ux)
(/ (- (+ 1 (/ 1 (pow ux 2))) (/ 1 ux)) ux)
(/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) ux)) ux)) ux)
(/ (- (+ 1 (/ 1 (pow ux 2))) (+ (/ 1 ux) (/ 1 (pow ux 3)))) ux)
(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) ux)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (.f32 ux ux)))) ux)
(/ 1 ux)
(/.f32 #s(literal 1 binary32) ux)
(* -1 (/ (- (/ 1 ux) 1) ux))
(/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)) ux)
(* -1 (/ (- (* -1 (/ (- (/ 1 ux) 1) ux)) 1) ux))
(/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) ux)) ux)) ux)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 ux) 1) ux)) 1) ux)) 1) ux))
(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) ux)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (.f32 ux ux)))) ux)

eval52.0ms (1.2%)

Compiler: Compiled 11470 to 959 computations (91.6% saved)

prune70.0ms (1.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	418	0	418
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	418	4	422

Accuracy

100.0%

Counts

422 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.9%	(-.f32 #s(literal 1 binary32) ux)
✓	100.0%	(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
✓	97.6%	(.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)))
✓	72.9%	#s(literal 1 binary32)

Compiler

Compiled 87 to 48 computations (44.8% saved)

regimes12.0ms (0.3%)

Counts

6 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(-.f32 #s(literal 1 binary32) ux)
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
(.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) ux)))
(+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (.f32 ux (+.f32 #s(literal 1 binary32) maxCos)) (.f32 (.f32 ux (+.f32 maxCos #s(literal -1 binary32))) (.f32 ux (+.f32 #s(literal 1 binary32) maxCos))))))

Outputs
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))

Calls

4 calls:

3.0ms	ux
3.0ms	(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
3.0ms	uy
2.0ms	maxCos

Results

Accuracy	Segments	Branch
100.0%	1	`ux`
100.0%	1	`uy`
100.0%	1	`maxCos`
100.0%	1	`(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))`

Compiler

Compiled 22 to 16 computations (27.3% saved)

regimes5.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(-.f32 #s(literal 1 binary32) ux)

Outputs
(-.f32 #s(literal 1 binary32) ux)

Calls

3 calls:

2.0ms	maxCos
2.0ms	uy
2.0ms	ux

Results

Accuracy	Segments	Branch
98.9%	1	`ux`
98.9%	1	`uy`
98.9%	1	`maxCos`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)

Outputs
#s(literal 1 binary32)

Calls

3 calls:

1.0ms	uy
1.0ms	maxCos
1.0ms	ux

Results

Accuracy	Segments	Branch
72.9%	1	`ux`
72.9%	1	`uy`
72.9%	1	`maxCos`

Compiler

Compiled 12 to 9 computations (25% saved)

simplify21.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary32`
4×	`*-commutative_binary32`
4×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	19	11
3	21	11
4	22	11

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(-.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)

Outputs
(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
(-.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)

soundness446.0ms (9.9%)

Rules

1786×	`-lowering-.f32`
1786×	`-lowering-.f64`
1342×	`sum4-define`
1182×	`sum3-define`
1152×	`sum5-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	14	6
2	35	6
3	70	6
4	182	6
5	485	6
6	1531	6
7	2129	6
8	2264	6
9	2284	6
0	2284	6
0	41	290
1	131	271
2	410	248
3	1040	248
4	3466	248
5	6550	248
0	8123	248

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated

Compiler

Compiled 54 to 42 computations (22.2% saved)

preprocess22.0ms (0.5%)

Remove: (abs uy)
Compiler: Compiled 88 to 64 computations (27.3% saved)

UniformSampleCone, z

analyze122.0ms (2.7%)

sample1.5s (33.7%)

preprocess112.0ms (2.5%)

explain54.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify52.0ms (1.2%)

localize25.0ms (0.6%)

series3.0ms (0.1%)

rewrite255.0ms (5.6%)

simplify140.0ms (3.1%)

eval27.0ms (0.6%)

prune40.0ms (0.9%)

simplify202.0ms (4.5%)

localize112.0ms (2.5%)

series6.0ms (0.1%)

rewrite244.0ms (5.4%)

simplify212.0ms (4.7%)

eval67.0ms (1.5%)

prune97.0ms (2.1%)

simplify118.0ms (2.6%)

localize53.0ms (1.2%)

series2.0ms (0%)

rewrite243.0ms (5.4%)

simplify176.0ms (3.9%)

eval52.0ms (1.2%)

prune70.0ms (1.5%)

regimes12.0ms (0.3%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify21.0ms (0.5%)

soundness446.0ms (9.9%)

preprocess22.0ms (0.5%)

end0.0ms (0%)

Profiling