Metrics for bug333 (missed optimization)

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 17 to 11 computations (35.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-sub: 0.0ms (0% of total)

ival-add: 0.0ms (0% of total)

ival-and: 0.0ms (0% of total)

const: 0.0ms (0% of total)

ival-sqrt: 0.0ms (0% of total)

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

ival-<=: 0.0ms (0% of total)

sample1.9s (37.1%)

Results

1.6s	8072×	1	valid
12.0ms	184×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-sqrt: 331.0ms (30.9% of total)

backward-pass: 187.0ms (17.5% of total)

ival-sub: 175.0ms (16.3% of total)

ival-add: 174.0ms (16.2% of total)

ival-<=: 153.0ms (14.3% of total)

ival-and: 33.0ms (3.1% of total)

const: 19.0ms (1.8% of total)

Bogosity

preprocess39.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

200×	`fnmadd-define`
172×	`fmsub-define`
168×	`fnmsub-define`
166×	`sum3-define`
156×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	31	27
2	62	27
3	132	27
4	264	27
5	480	27
6	677	27
7	781	27
8	787	27
0	7	9
1	14	9
2	21	9
3	34	9
4	52	9
5	97	9
6	170	9
7	271	9
8	372	9
9	480	9
10	558	9
11	564	9
0	564	9

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))

Outputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Call 2

Inputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(- (sqrt (+ 1 (neg x))) (sqrt (- 1 (neg x))))
(neg (- (sqrt (+ 1 (neg x))) (sqrt (- 1 (neg x)))))

Outputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(- (sqrt (+ 1 (neg x))) (sqrt (- 1 (neg x))))
(- (sqrt (- 1 x)) (sqrt (+ 1 x)))
(neg (- (sqrt (+ 1 (neg x))) (sqrt (- 1 (neg x)))))
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))

Symmetry

(negabs x)

explain164.0ms (3.2%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
256	-	1	(0.012958257044675172)	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`
0	-	0	-	`x`
0	-	0	-	`(sqrt.f64 (-.f64 #s(literal 1 binary64) x))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(-.f64 #s(literal 1 binary64) x)`
0	-	0	-	`(sqrt.f64 (+.f64 #s(literal 1 binary64) x))`
0	-	0	-	`(+.f64 #s(literal 1 binary64) x)`

Results

127.0ms	506×	1	valid
1.0ms	6×	0	valid

Compiler

Compiled 64 to 23 computations (64.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-sqrt: 17.0ms (34.9% of total)

backward-pass: 12.0ms (24.6% of total)

ival-sub: 11.0ms (22.6% of total)

ival-add: 8.0ms (16.4% of total)

const: 1.0ms (2.1% of total)

eval0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.3%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Rules

166×	`sum3-define`
124×	`fnmadd-define`
92×	`fma-lowering-fma.f32`
92×	`fmsub-define`
92×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	25
1	14	25
2	21	25
3	34	25
4	52	25
5	97	25
6	170	25
7	271	25
8	372	25
9	480	25
10	558	25
11	564	25
0	564	25

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(sqrt (+ 1 x))
(+ 1 x)
1
x
(sqrt (- 1 x))
(- 1 x)

Outputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt (+ 1 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(sqrt (- 1 x))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)

localize66.0ms (1.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	accuracy	7.2%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

54.0ms	253×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 27 to 8 computations (70.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-sqrt: 8.0ms (32.4% of total)

ival-sub: 6.0ms (24.3% of total)

backward-pass: 6.0ms (24.3% of total)

ival-add: 4.0ms (16.2% of total)

const: 1.0ms (4.1% of total)

series5.0ms (0.1%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (- (sqrt (+ 1 x)) (sqrt (- 1 x)))>
#<alt (sqrt (+ 1 x))>
#<alt (+ 1 x)>
#<alt (sqrt (- 1 x))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
1.0ms	x	@	-inf	(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
0.0ms	x	@	0	(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
0.0ms	x	@	-inf	(sqrt (+ 1 x))
0.0ms	x	@	inf	(sqrt (- 1 x))

rewrite295.0ms (5.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3064×	`-lowering-.f32`
3064×	`-lowering-.f64`
2554×	`/-lowering-/.f32`
2554×	`/-lowering-/.f64`
1828×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	46	20
2	389	20
3	6209	20
0	8435	20

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 244

Calls

Call 1

Inputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(sqrt (+ 1 x))
(+ 1 x)
(sqrt (- 1 x))

Outputs
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(+.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(+.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (neg.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 0 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))))
(neg.f64 (/.f64 (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))))))
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(pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))))))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))))))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))

simplify244.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

4834×	`-lowering-.f32`
4834×	`-lowering-.f64`
4254×	`+-lowering-+.f64`
4254×	`+-lowering-+.f32`
1772×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	826
1	528	727
2	2050	693
0	8755	693

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (-.f64 (+.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(.f64 (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))) (-.f64 #s(literal 0 binary64) x))

eval36.0ms (0.7%)

Compiler: Compiled 7942 to 1076 computations (86.5% saved)

prune31.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	288	4	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	289	4	293

Accuracy

100.0%

Counts

293 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
▶	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
▶	99.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
▶	99.4%	x

Compiler

Compiled 50 to 32 computations (36% saved)

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal 7/128 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal 7/128 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64))))))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 #s(literal 1/8 binary64) (.f64 x x))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))

Rules

2824×	`fma-define`
1752×	`fma-lowering-fma.f32`
1752×	`fma-lowering-fma.f64`
614×	`-lowering-.f32`
614×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	166
1	81	145
2	272	142
3	778	142
4	1632	142
5	2749	142
6	3241	142
7	3310	142
8	3311	142
9	3311	142
10	3314	142
0	3314	142

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/8 (* x x))))
x
(+ 1 (* 1/8 (* x x)))
1
(* 1/8 (* x x))
1/8
(* x x)
(* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))
x
(+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))
1
(* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))
(* x x)
(+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))
1/8
(* x (* x (+ 7/128 (* (* x x) 33/1024))))
(* x (+ 7/128 (* (* x x) 33/1024)))
(+ 7/128 (* (* x x) 33/1024))
7/128
(* (* x x) 33/1024)
33/1024
(* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))
x
(+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128))))
1
(* (* x x) (+ 1/8 (* (* x x) 7/128)))
(* x x)
(+ 1/8 (* (* x x) 7/128))
1/8
(* (* x x) 7/128)
7/128

Outputs
x
(* x (+ 1 (* 1/8 (* x x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
x
(+ 1 (* 1/8 (* x x)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
1
#s(literal 1 binary64)
(* 1/8 (* x x))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
1/8
#s(literal 1/8 binary64)
(* x x)
(*.f64 x x)
(* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
x
(+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64))))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))
(* x x)
(*.f64 x x)
(+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))
(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64))))))
1/8
#s(literal 1/8 binary64)
(* x (* x (+ 7/128 (* (* x x) 33/1024))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* x (+ 7/128 (* (* x x) 33/1024)))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(+ 7/128 (* (* x x) 33/1024))
(+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))
7/128
#s(literal 7/128 binary64)
(* (* x x) 33/1024)
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
33/1024
#s(literal 33/1024 binary64)
(* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x #s(literal 7/128 binary64)))))))
x
(+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal 7/128 binary64))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1/8 (* (* x x) 7/128)))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal 7/128 binary64)))))
(* x x)
(*.f64 x x)
(+ 1/8 (* (* x x) 7/128))
(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal 7/128 binary64))))
1/8
#s(literal 1/8 binary64)
(* (* x x) 7/128)
(.f64 x (.f64 x #s(literal 7/128 binary64)))
7/128
#s(literal 7/128 binary64)

localize152.0ms (2.9%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal 7/128 binary64))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 7/128 binary64))
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 33/1024 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/8 binary64) (.f64 x x))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))

Results

68.0ms	236×	0	valid
12.0ms	10×	3	valid
5.0ms	8×	1	valid
2.0ms	2×	2	valid

Compiler

Compiled 198 to 23 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 19.0ms (61% of total)

ival-add: 8.0ms (25.7% of total)

backward-pass: 3.0ms (9.6% of total)

const: 1.0ms (3.2% of total)

series9.0ms (0.2%)

Counts

14 → 168

Calls

Call 1

Inputs
#<alt (* x (+ 1 (* 1/8 (* x x))))>
#<alt (+ 1 (* 1/8 (* x x)))>
#<alt (* 1/8 (* x x))>
#<alt (* x x)>
#<alt (* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))>
#<alt (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))>
#<alt (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))>
#<alt (* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))>
#<alt (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128))))>
#<alt (* (* x x) (+ 1/8 (* (* x x) 7/128)))>
#<alt (* x (* x (+ 7/128 (* (* x x) 33/1024))))>
#<alt (* (* x x) 33/1024)>
#<alt (* x (+ 7/128 (* (* x x) 33/1024)))>
#<alt (* (* x x) 7/128)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* 7/128 (pow x 5))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 7/128 (pow x 5))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))>
#<alt (* 7/128 (pow x 4))>
#<alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 7/128 (pow x 4))>
#<alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* 7/128 (pow x 4))>
#<alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 7/128 (pow x 4))>
#<alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 7/128 (pow x 2))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* 33/1024 (pow x 4))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 4))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 7/128 x)>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* 33/1024 (pow x 3))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 3))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>

Calls

42 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))
1.0ms	x	@	0	(* x (+ 1 (* 1/8 (* x x))))
0.0ms	x	@	inf	(* x (+ 1 (* 1/8 (* x x))))
0.0ms	x	@	inf	(* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))
0.0ms	x	@	inf	(* 1/8 (* x x))

rewrite320.0ms (6.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3868×	`-lowering-.f32`
3868×	`-lowering-.f64`
2744×	`/-lowering-/.f32`
2744×	`/-lowering-/.f64`
2192×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	126
1	154	109
2	1458	106
0	8365	106

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 406

Calls

Call 1

Inputs
(* x (+ 1 (* 1/8 (* x x))))
(+ 1 (* 1/8 (* x x)))
(* 1/8 (* x x))
(* x x)
(* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))
(+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))
(* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))
(* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))
(+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128))))
(* (* x x) (+ 1/8 (* (* x x) 7/128)))
(* x (* x (+ 7/128 (* (* x x) 33/1024))))
(* (* x x) 33/1024)
(* x (+ 7/128 (* (* x x) 33/1024)))
(* (* x x) 7/128)

Outputs
(+.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (/.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))
(fma.f64 x #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(fma.f64 #s(literal 1 binary64) x (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))
(fma.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)) x)
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/8 binary64)) x)
(fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x)
(fma.f64 (.f64 x #s(literal 1/8 binary64)) (.f64 x x) x)
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) x)
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))))) x)) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))) x)) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (*.f64 x x)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal 1/8 binary64)) x #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/8 binary64))) x #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(/.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (*.f64 x x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (*.f64 x x)))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (*.f64 x x)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1 binary64))))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (*.f64 x x)))))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal 1/8 binary64)) x)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/8 binary64))) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(+.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))))) (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64))))))))) (-.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))))))
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(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 343/2097152 binary64) (.f64 x (.f64 x x)))) (pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 33/1024 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))) (.f64 (.f64 x (.f64 x #s(literal 7/128 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 343/2097152 binary64) (.f64 x (.f64 x x)))) (pow.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) x) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) x) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) x)) (.f64 (.f64 x (.f64 x #s(literal 7/128 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) x)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 343/2097152 binary64) (.f64 x (.f64 x x)))) (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (.f64 x x)) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (.f64 x x))) (.f64 (.f64 x (.f64 x #s(literal 7/128 binary64))) (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 33/1024 binary64))) #s(literal 3 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 343/2097152 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))) (-.f64 (.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 x (.f64 x #s(literal 7/128 binary64)))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (.f64 x x)) #s(literal 3 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 343/2097152 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (.f64 x x))) (-.f64 (.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (.f64 x x)) (.f64 x (.f64 x #s(literal 7/128 binary64)))))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64))))
(.f64 (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))) x)
(.f64 x (.f64 x #s(literal 33/1024 binary64)))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(.f64 #s(literal 33/1024 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 33/1024 binary64)) x)
(+.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 x #s(literal 7/128 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x #s(literal 7/128 binary64))) (-.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))))) (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64)))) (-.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))))))
(fma.f64 x #s(literal 7/128 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 33/1024 binary64)) (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 #s(literal 7/128 binary64) x (.f64 x (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(fma.f64 #s(literal 33/1024 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) x (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 (.f64 x #s(literal 33/1024 binary64)) (.f64 x x) (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 33/1024 binary64) (*.f64 x #s(literal 7/128 binary64)))
(/.f64 (+.f64 (.f64 #s(literal 343/2097152 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 35937/1073741824 binary64))) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x #s(literal 7/128 binary64))) (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64)))) (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x #s(literal 7/128 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))))) (-.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 343/2097152 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 35937/1073741824 binary64))))) (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) #s(literal 7/128 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1089/1048576 binary64)))) (-.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 343/2097152 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 35937/1073741824 binary64)))) x) (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) #s(literal 7/128 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1089/1048576 binary64))) x) (-.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 343/2097152 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 35937/1073741824 binary64))) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x #s(literal 7/128 binary64))) (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64)))) (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x #s(literal 7/128 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))) (neg.f64 (-.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 343/2097152 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 35937/1073741824 binary64)))))) (neg.f64 (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) #s(literal 7/128 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1089/1048576 binary64))))) (neg.f64 (-.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 343/2097152 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 35937/1073741824 binary64)))) x)) (neg.f64 (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 33/1024 binary64)) #s(literal 7/128 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1089/1048576 binary64))) x)) (neg.f64 (-.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 35937/1073741824 binary64))) (.f64 x (.f64 x x))) (.f64 #s(literal 343/2097152 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64)))) (-.f64 (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x #s(literal 7/128 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 33/1024 binary64))) (*.f64 x #s(literal 7/128 binary64))))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(.f64 (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))) x)
(.f64 x (.f64 x #s(literal 7/128 binary64)))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(.f64 #s(literal 7/128 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 7/128 binary64)) x)

simplify225.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

3892×	`-lowering-.f32`
3892×	`-lowering-.f64`
2480×	`+-lowering-+.f64`
2480×	`+-lowering-+.f32`
1444×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1422
1	301	1128
2	918	1115
3	3677	1111
4	7451	1111
0	8297	1111

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 7/128 x)
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* 1/8 (pow x 3))
(.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* 1/8 (pow x 3))
(.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
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(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* 33/1024 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* 33/1024 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))
(* 7/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/128 binary64))

eval101.0ms (1.9%)

Compiler: Compiled 20459 to 1788 computations (91.3% saved)

prune51.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	652	2	654
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	653	5	658

Accuracy

100.0%

Counts

658 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))) x)
▶	99.7%	(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)
✓	99.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
✓	99.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
✓	99.4%	x

Compiler

Compiled 60 to 37 computations (38.3% saved)

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))
✓	cost-diff	(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
✓	cost-diff	(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))) x)
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 x (.f64 x x))
✓	cost-diff	(.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))
✓	cost-diff	(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)

Rules

2302×	`fma-define`
1752×	`fma-lowering-fma.f32`
1752×	`fma-lowering-fma.f64`
614×	`-lowering-.f32`
614×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	108
1	52	96
2	164	96
3	494	96
4	1251	96
5	2091	96
6	2508	96
7	2746	96
8	2774	96
9	2774	96
0	2774	96

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* 1/8 (* x (* x x))) x)
(* 1/8 (* x (* x x)))
1/8
(* x (* x x))
x
(* x x)
(+ (* x (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))) x)
(* x (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))
x
(* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))
(* x x)
(+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))
1/8
(* x (* x (+ 7/128 (* (* x x) 33/1024))))
(* x (+ 7/128 (* (* x x) 33/1024)))
(+ 7/128 (* (* x x) 33/1024))
7/128
(* (* x x) 33/1024)
33/1024

Outputs
(+ (* 1/8 (* x (* x x))) x)
(.f64 x (+.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(* 1/8 (* x (* x x)))
(.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))
1/8
#s(literal 1/8 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
(+ (* x (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))) x)
(.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))) #s(literal 1 binary64)))
(* x (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))
x
(* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64))))))
(* x x)
(*.f64 x x)
(+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
1/8
#s(literal 1/8 binary64)
(* x (* x (+ 7/128 (* (* x x) 33/1024))))
(.f64 (.f64 x x) (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64))))
(* x (+ 7/128 (* (* x x) 33/1024)))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(+ 7/128 (* (* x x) 33/1024))
(+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))
7/128
#s(literal 7/128 binary64)
(* (* x x) 33/1024)
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
33/1024
#s(literal 33/1024 binary64)

localize95.0ms (1.8%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 33/1024 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))

Results

54.0ms	236×	0	valid
8.0ms	10×	3	valid
4.0ms	2×	2	valid
3.0ms	8×	1	valid

Compiler

Compiled 137 to 17 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 14.0ms (62.1% of total)

ival-add: 6.0ms (26.6% of total)

backward-pass: 2.0ms (8.9% of total)

const: 1.0ms (4.4% of total)

series4.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (+ (* 1/8 (* x (* x x))) x)>
#<alt (* 1/8 (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (+ (* x (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))) x)>
#<alt (* x (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))>
#<alt (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))>
#<alt (* x (* x (+ 7/128 (* (* x x) 33/1024))))>
#<alt (* (* x x) 33/1024)>
#<alt (* x (+ 7/128 (* (* x x) 33/1024)))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (* 1/8 (pow x 3))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))>
#<alt (* (pow x 3) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* 7/128 (pow x 2))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* 33/1024 (pow x 4))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 4))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 7/128 x)>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* 33/1024 (pow x 3))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 3))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>

Calls

30 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	inf	(+ (* 1/8 (* x (* x x))) x)
0.0ms	x	@	-inf	(* 1/8 (* x (* x x)))
0.0ms	x	@	0	(+ (* 1/8 (* x (* x x))) x)
0.0ms	x	@	inf	(+ (* x (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))) x)

rewrite318.0ms (6.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4466×	`-lowering-.f32`
4466×	`-lowering-.f64`
2716×	`/-lowering-/.f32`
2716×	`/-lowering-/.f64`
2458×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	83
1	102	74
2	871	74
0	8204	74

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 318

Calls

Call 1

Inputs
(+ (* 1/8 (* x (* x x))) x)
(* 1/8 (* x (* x x)))
(* x (* x x))
(* x x)
(+ (* x (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))) x)
(* x (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))
(* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))
(* x (* x (+ 7/128 (* (* x x) 33/1024))))
(* (* x x) 33/1024)
(* x (+ 7/128 (* (* x x) 33/1024)))

Outputs
(+.f64 x (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(+.f64 (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(+.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 (.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x))) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))))
(-.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 (.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))))
(fma.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)) x)
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(fma.f64 (.f64 x x) (.f64 #s(literal 1/8 binary64) x) x)
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) x)
(fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x)
(fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) x)
(neg.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (+.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/8 binary64))))))))
(neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x))) x))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))))) (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (+.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x x))) (-.f64 (.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x))) x)))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (+.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/8 binary64))))))
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(fma.f64 x (.f64 x (.f64 x #s(literal 33/1024 binary64))) (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 33/1024 binary64)) (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 33/1024 binary64) (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 #s(literal 7/128 binary64) x (.f64 (.f64 x x) (*.f64 x #s(literal 33/1024 binary64))))
(fma.f64 #s(literal 33/1024 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) x (*.f64 x #s(literal 7/128 binary64)))
(fma.f64 (.f64 x #s(literal 33/1024 binary64)) (.f64 x x) (*.f64 x #s(literal 7/128 binary64)))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 7/128 binary64) (.f64 x (.f64 x #s(literal 33/1024 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 49/16384 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1089/1048576 binary64)) (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 (.f64 x x) (.f64 x #s(literal 33/1024 binary64)))))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 343/2097152 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64)))) (.f64 (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 x (.f64 x #s(literal 33/1024 binary64))))) (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) #s(literal -7/128 binary64)))) (.f64 x (+.f64 #s(literal 343/2097152 binary64) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64))) (.f64 x (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1089/1048576 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) #s(literal -7/128 binary64)))) (.f64 (+.f64 #s(literal 343/2097152 binary64) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64))) (.f64 (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1089/1048576 binary64))) x)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 343/2097152 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 (.f64 (.f64 x x) #s(literal 49/16384 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1089/1048576 binary64)) (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 (.f64 x x) (*.f64 x #s(literal 33/1024 binary64)))))))
(/.f64 (.f64 (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 x (.f64 x #s(literal 33/1024 binary64))))) (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64))))) (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 343/2097152 binary64) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) #s(literal -7/128 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1089/1048576 binary64)))) (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal -33/1024 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 343/2097152 binary64) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x) (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) #s(literal -7/128 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1089/1048576 binary64))) x) (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal -33/1024 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 343/2097152 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 49/16384 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1089/1048576 binary64)) (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 (.f64 x x) (*.f64 x #s(literal 33/1024 binary64))))))))
(/.f64 (neg.f64 (.f64 (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 x (.f64 x #s(literal 33/1024 binary64))))) (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64)))))) (neg.f64 (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 343/2097152 binary64) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) #s(literal -7/128 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1089/1048576 binary64))))) (+.f64 #s(literal -7/128 binary64) (neg.f64 (.f64 (*.f64 x x) #s(literal -33/1024 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 343/2097152 binary64) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) #s(literal -7/128 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1089/1048576 binary64))) x)) (+.f64 #s(literal -7/128 binary64) (neg.f64 (.f64 (*.f64 x x) #s(literal -33/1024 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) #s(literal 343/2097152 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1089/1048576 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 49/16384 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x #s(literal 33/1024 binary64))) (*.f64 x #s(literal 7/128 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1089/1048576 binary64)) (.f64 (.f64 x x) #s(literal 49/16384 binary64))) (-.f64 (.f64 (.f64 x x) (.f64 x #s(literal 33/1024 binary64))) (.f64 x #s(literal 7/128 binary64))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(.f64 (+.f64 #s(literal 7/128 binary64) (.f64 x (*.f64 x #s(literal 33/1024 binary64)))) x)
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 343/2097152 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 49/16384 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1089/1048576 binary64)) (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 (.f64 x x) (.f64 x #s(literal 33/1024 binary64))))))))
(.f64 (.f64 (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 x (.f64 x #s(literal 33/1024 binary64))))) (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal -33/1024 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 343/2097152 binary64) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) (+.f64 (.f64 x (*.f64 x #s(literal 33/1024 binary64))) #s(literal -7/128 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1089/1048576 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64)))))
(.f64 (.f64 (+.f64 #s(literal 343/2097152 binary64) (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x (.f64 x #s(literal 33/1024 binary64))) (+.f64 (.f64 x (*.f64 x #s(literal 33/1024 binary64))) #s(literal -7/128 binary64))))))
(.f64 (.f64 (+.f64 #s(literal 49/16384 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1089/1048576 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal -33/1024 binary64)))))

simplify170.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

2716×	`-lowering-.f32`
2716×	`-lowering-.f64`
1526×	`times-frac`
1396×	`fma-lowering-fma.f32`
1396×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	956
1	241	801
2	771	784
3	2354	780
4	6439	780
0	8124	780

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 3) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* (pow x 3) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 7/128 x)
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x #s(literal 7/128 binary64))))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(* 33/1024 (pow x 7))
(*.f64 #s(literal 33/1024 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 33/1024 binary64) (+.f64 (/.f64 #s(literal 7/128 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(* 33/1024 (pow x 7))
(*.f64 #s(literal 33/1024 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (/.f64 (/.f64 (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) x)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))))
(* 1/8 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(* (pow x 3) (+ 1/8 (* 7/128 (pow x 2))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x #s(literal 7/128 binary64))))))
(* (pow x 3) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
(* (pow x 3) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
(* 33/1024 (pow x 7))
(*.f64 #s(literal 33/1024 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* 33/1024 (pow x 7))
(*.f64 #s(literal 33/1024 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (/.f64 (/.f64 (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) x)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (/.f64 (/.f64 (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) x)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal 7/128 binary64))))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))))
(* 33/1024 (pow x 6))
(*.f64 #s(literal 33/1024 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* 33/1024 (pow x 6))
(*.f64 #s(literal 33/1024 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* 7/128 (pow x 2))
(.f64 x (.f64 x #s(literal 7/128 binary64)))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* 33/1024 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 33/1024 binary64)))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* 33/1024 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 33/1024 binary64)))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (.f64 x x) #s(literal 33/1024 binary64)))))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 33/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 33/1024 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* 33/1024 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 33/1024 binary64))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* 33/1024 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 33/1024 binary64))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))

eval53.0ms (1%)

Compiler: Compiled 17847 to 1466 computations (91.8% saved)

prune48.0ms (0.9%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	474	0	474
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	474	5	479

Accuracy

100.0%

Counts

479 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))) x)
✓	99.7%	(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)
✓	99.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
✓	99.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
✓	99.4%	x

Compiler

Compiled 146 to 69 computations (52.7% saved)

regimes5.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))) x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Outputs
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))) x)

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes2.0ms (0%)

Counts

5 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))

Outputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

4 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))

Outputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)

Outputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
14×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	67
1	45	67

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
x

Outputs
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))) x)
(+.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 7/128 binary64) (.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))) #s(literal 1 binary64)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/8 binary64))))
x

soundness583.0ms (11.2%)

Rules

4834×	`-lowering-.f32`
4834×	`-lowering-.f64`
4254×	`+-lowering-+.f64`
4254×	`+-lowering-+.f32`
3868×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	126
1	154	109
2	1458	106
0	8365	106
0	161	826
1	528	727
2	2050	693
0	8755	693

Stop Event

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

Compiler

Compiled 141 to 71 computations (49.6% saved)

preprocess66.0ms (1.3%)

Remove: (negabs x)
Compiler: Compiled 360 to 186 computations (48.3% saved)

bug333 (missed optimization)

analyze0.0ms (0%)

sample1.9s (37.1%)

preprocess39.0ms (0.8%)

explain164.0ms (3.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify17.0ms (0.3%)

localize66.0ms (1.3%)

series5.0ms (0.1%)

rewrite295.0ms (5.7%)

simplify244.0ms (4.7%)

eval36.0ms (0.7%)

prune31.0ms (0.6%)

simplify84.0ms (1.6%)

localize152.0ms (2.9%)

series9.0ms (0.2%)

rewrite320.0ms (6.2%)

simplify225.0ms (4.3%)

eval101.0ms (1.9%)

prune51.0ms (1%)

simplify74.0ms (1.4%)

localize95.0ms (1.8%)

series4.0ms (0.1%)

rewrite318.0ms (6.1%)

simplify170.0ms (3.3%)

eval53.0ms (1%)

prune48.0ms (0.9%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify7.0ms (0.1%)

soundness583.0ms (11.2%)

preprocess66.0ms (1.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	14	28
1	31	27
2	62	27
3	132	27
4	264	27
5	480	27
6	677	27
7	781	27
8	787	27
0	7	9
1	14	9
2	21	9
3	34	9
4	52	9
5	97	9
6	170	9
7	271	9
8	372	9
9	480	9
10	558	9
11	564	9
0	564	9

Iter	Nodes	Cost
0	7	25
1	14	25
2	21	25
3	34	25
4	52	25
5	97	25
6	170	25
7	271	25
8	372	25
9	480	25
10	558	25
11	564	25
0	564	25

Iter	Nodes	Cost
0	14	28
1	31	27
2	62	27
3	132	27
4	264	27
5	480	27
6	677	27
7	781	27
8	787	27
0	7	9
1	14	9
2	21	9
3	34	9
4	52	9
5	97	9
6	170	9
7	271	9
8	372	9
9	480	9
10	558	9
11	564	9
0	564	9

Iter	Nodes	Cost
0	7	25
1	14	25
2	21	25
3	34	25
4	52	25
5	97	25
6	170	25
7	271	25
8	372	25
9	480	25
10	558	25
11	564	25
0	564	25

Iter	Nodes	Cost
0	14	28
1	31	27
2	62	27
3	132	27
4	264	27
5	480	27
6	677	27
7	781	27
8	787	27
0	7	9
1	14	9
2	21	9
3	34	9
4	52	9
5	97	9
6	170	9
7	271	9
8	372	9
9	480	9
10	558	9
11	564	9
0	564	9

Iter	Nodes	Cost
0	7	25
1	14	25
2	21	25
3	34	25
4	52	25
5	97	25
6	170	25
7	271	25
8	372	25
9	480	25
10	558	25
11	564	25
0	564	25