Metrics for UniformSampleCone, z

analyze118.0ms (3.1%)

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: 62.0ms

ival-<=: 25.0ms (40.1% of total)

...c/correct-round.rkt:119:19: 16.0ms (25.7% of total)

ival-sub: 6.0ms (9.6% of total)

ival-mult: 6.0ms (9.6% of total)

ival-add: 4.0ms (6.4% of total)

ival-and: 4.0ms (6.4% of total)

const: 1.0ms (1.6% of total)

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

sample1.5s (38.8%)

Results

946.0ms	8256×	0	valid
19.0ms	60×	5	exit

Precisions

Click to see histograms. Total time spent on operations: 681.0ms

ival-<=: 276.0ms (40.5% of total)

...c/correct-round.rkt:119:19: 154.0ms (22.6% of total)

ival-mult: 91.0ms (13.4% of total)

ival-sub: 55.0ms (8.1% of total)

ival-add: 53.0ms (7.8% of total)

ival-and: 38.0ms (5.6% of total)

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

const: 7.0ms (1% of total)

Bogosity

preprocess119.0ms (3.1%)

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)

explain53.0ms (1.4%)

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

31.0ms

512×

valid

Compiler

Compiled 50 to 23 computations (54% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 5.0ms (44.1% of total)

ival-sub: 3.0ms (26.5% of total)

ival-add: 3.0ms (26.5% of total)

const: 1.0ms (8.8% 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)

simplify47.0ms (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)

localize30.0ms (0.8%)

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

21.0ms

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 (58.7% of total)

ival-mult: 2.0ms (39.1% 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)))

rewrite247.0ms (6.4%)

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)))

simplify133.0ms (3.4%)

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))

eval29.0ms (0.7%)

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

prune42.0ms (1.1%)

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
▶	97.9%	(-.f32 #s(literal 1 binary32) ux)
▶	100.0%	(+.f32 #s(literal 1 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 maxCos maxCos)) ux) (-.f32 #s(literal -1 binary32) maxCos)))
✓	100.0%	(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
▶	71.4%	#s(literal 1 binary32)

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify195.0ms (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 #s(literal 1 binary32) (*.f32 maxCos maxCos))
✓	cost-diff	0	(.f32 (-.f32 #s(literal 1 binary32) (.f32 maxCos maxCos)) ux)
✓	cost-diff	192	(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 maxCos maxCos)) ux) (-.f32 #s(literal -1 binary32) maxCos))
✓	cost-diff	192	(+.f32 #s(literal 1 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 maxCos maxCos)) ux) (-.f32 #s(literal -1 binary32) maxCos)))

Rules

1548×	`fma-lowering-fma.f32`
1548×	`fma-lowering-fma.f64`
1436×	`fmsub-define`
1426×	`fnmsub-define`
1198×	`--lowering--.f32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	25	51
2	45	47
3	102	47
4	297	47
5	717	41
6	2414	37
7	5579	37
0	8122	37

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize55.0ms (1.4%)

Localize:

Found 5 expressions of interest:

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

Results

34.0ms

256×

valid

Compiler

Compiled 56 to 13 computations (76.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sub: 4.0ms (36.9% of total)

ival-mult: 4.0ms (36.9% of total)

ival-div: 2.0ms (18.5% of total)

ival-add: 1.0ms (9.2% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Counts

5 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite279.0ms (7.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4484×	`-lowering-.f32`
4484×	`-lowering-.f64`
3498×	`/-lowering-/.f32`
3498×	`/-lowering-/.f64`
1650×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	77	27
2	687	24
0	8846	24

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 323

Calls

Call 1

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

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

simplify187.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

2108×	`-lowering-.f32`
2108×	`-lowering-.f64`
1752×	`sum4-define`
1192×	`sum3-define`
1052×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	687
1	199	586
2	583	577
3	1569	563
4	5241	563
0	8056	563

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval35.0ms (0.9%)

Compiler: Compiled 9345 to 1151 computations (87.7% saved)

prune46.0ms (1.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	419	0	419
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	419	4	423

Accuracy

100.0%

Counts

423 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(-.f32 #s(literal 1 binary32) ux)
✓	100.0%	(+.f32 #s(literal 1 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 maxCos maxCos)) ux) (-.f32 #s(literal -1 binary32) maxCos)))
✓	100.0%	(+.f32 #s(literal 1 binary32) (*.f32 ux (+.f32 maxCos #s(literal -1 binary32))))
✓	71.4%	#s(literal 1 binary32)

Compiler

Compiled 70 to 45 computations (35.7% saved)

regimes12.0ms (0.3%)

Counts

5 → 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 #s(literal 1 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 maxCos maxCos)) ux) (-.f32 #s(literal -1 binary32) maxCos)))

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

Calls

4 calls:

4.0ms	ux
2.0ms	(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
2.0ms	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)

regimes9.0ms (0.2%)

Counts

4 → 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))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
97.9%	1	`ux`
97.9%	1	`uy`
97.9%	1	`maxCos`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (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:

2.0ms	uy
1.0ms	maxCos
1.0ms	ux

Results

Accuracy	Segments	Branch
71.4%	1	`ux`
71.4%	1	`uy`
71.4%	1	`maxCos`

Compiler

Compiled 12 to 9 computations (25% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	30	24
2	40	24
3	46	24
4	49	24

Stop Event

1×

saturated

Calls

Call 1

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

soundness683.0ms (17.6%)

Rules

2300×	`-lowering-.f32`
2300×	`-lowering-.f64`
1786×	`-lowering-.f32`
1786×	`-lowering-.f64`
1686×	`fma-lowering-fma.f32`

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	7	15
1	43	14
2	362	14
3	4077	13
0	8036	13
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×	node limit
1×	iter limit
1×	saturated

Compiler

Compiled 93 to 67 computations (28% saved)

preprocess22.0ms (0.6%)

Remove: (abs uy)
Compiler: Compiled 138 to 88 computations (36.2% saved)

UniformSampleCone, z

analyze118.0ms (3.1%)

sample1.5s (38.8%)

preprocess119.0ms (3.1%)

explain53.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify47.0ms (1.2%)

localize30.0ms (0.8%)

series3.0ms (0.1%)

rewrite247.0ms (6.4%)

simplify133.0ms (3.4%)

eval29.0ms (0.7%)

prune42.0ms (1.1%)

simplify195.0ms (5%)

localize55.0ms (1.4%)

series8.0ms (0.2%)

rewrite279.0ms (7.2%)

simplify187.0ms (4.8%)

eval35.0ms (0.9%)

prune46.0ms (1.2%)

regimes12.0ms (0.3%)

regimes9.0ms (0.2%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

simplify8.0ms (0.2%)

soundness683.0ms (17.6%)

preprocess22.0ms (0.6%)

end0.0ms (0%)

Profiling