Metrics for Given's Rotation SVD example, simplified

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 14 to 10 computations (28.6% saved)

Precisions

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

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

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

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

ival-mult: 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)

compiled-spec: 0.0ms (0% of total)

sample9.0s (54.2%)

Results

6.5s	8153×	5	exit
905.0ms	8256×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.9s

compiled-spec: 1.4s (20.2% of total)

ival-sqrt: 1.4s (19.7% of total)

backward-pass: 1.1s (16.4% of total)

ival-mult: 1.0s (14.6% of total)

ival-div: 682.0ms (9.8% of total)

ival-add: 667.0ms (9.6% of total)

ival-sub: 467.0ms (6.7% of total)

const: 204.0ms (2.9% of total)

Bogosity

preprocess28.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

128×	`fnmsub-define`
128×	`fmsub-define`
128×	`fnmadd-define`
78×	`sum3-define`
76×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	51	30
2	91	30
3	144	30
4	235	30
5	382	30
6	490	30
7	536	30
8	550	30
0	12	11
1	29	10
2	37	10
3	45	10
4	53	10
5	66	10
6	83	10
7	97	10
8	109	10
9	110	10
0	110	10

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))

Outputs

(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))

(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Call 2

Inputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x)))))))
(neg (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x))))))))

Outputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x)))))))
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
(neg (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x))))))))
(+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) -1)

Symmetry

(abs x)

explain139.0ms (0.8%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
2	-	-	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
0	-	-	`x`
0	-	-	`#s(literal 1/2 binary64)`
0	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
0	-	-	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
0	-	-	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
0	-	-	`(hypot.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`

Results

90.0ms

512×

valid

Compiler

Compiled 115 to 29 computations (74.8% saved)

Precisions

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

ival-div: 19.0ms (29.5% of total)

compiled-spec: 17.0ms (26.4% of total)

ival-mult: 11.0ms (17.1% of total)

ival-sqrt: 8.0ms (12.4% of total)

ival-add: 5.0ms (7.8% of total)

ival-sub: 3.0ms (4.7% of total)

const: 1.0ms (1.6% of total)

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

eval0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓	cost-diff	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Rules

32×	`sum3-define`
32×	`+-lowering-+.f64`
32×	`+-lowering-+.f32`
18×	`--lowering--.f32`
18×	`--lowering--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	19	36
2	24	36
3	30	36
4	38	36
5	51	36
6	68	36
7	82	36
8	94	36
9	95	36
0	95	36

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))
1
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))))
(+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))
1/2
(/ 1/2 (sqrt (+ (* 1 1) (* x x))))
(sqrt (+ (* 1 1) (* x x)))
x

Outputs
(- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
1/2
#s(literal 1/2 binary64)
(/ 1/2 (sqrt (+ (* 1 1) (* x x))))
(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(sqrt (+ (* 1 1) (* x x)))
(hypot.f64 #s(literal 1 binary64) x)
x

localize55.0ms (0.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓	accuracy	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Results

37.0ms

256×

valid

Compiler

Compiled 38 to 9 computations (76.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

compiled-spec: 8.0ms (31.4% of total)

ival-div: 5.0ms (19.6% of total)

ival-mult: 4.0ms (15.7% of total)

ival-sqrt: 4.0ms (15.7% of total)

ival-add: 3.0ms (11.8% of total)

ival-sub: 1.0ms (3.9% of total)

const: 0.0ms (0% of total)

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

series46.0ms (0.3%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))>
#<alt (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))))>
#<alt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))>
#<alt (/ 1/2 (sqrt (+ (* 1 1) (* x x))))>

Outputs
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt 1>
#<alt (+ 1 (* -1/4 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt (- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))>

Calls

12 calls:

Time	Variable		Point	Expression
43.0ms	x	@	inf	(- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))
1.0ms	x	@	0	(- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))
0.0ms	x	@	-inf	(- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))
0.0ms	x	@	inf	(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))))
0.0ms	x	@	-inf	(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))))

rewrite217.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1894×	`fnmadd-define`
1480×	`fnmsub-define`
1466×	`fmsub-define`
1374×	`fmm-def`
1250×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	31	30
2	77	30
3	212	30
4	483	30
5	954	30
6	3612	30
0	8178	30

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 129

Calls

Call 1

Inputs
(- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))))
(+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))
(/ 1/2 (sqrt (+ (* 1 1) (* x x))))

Outputs
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 0 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 0 binary64)))
(-.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal -1 binary64))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 0 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 0 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 0 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 0 binary64))
(exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) #s(literal 1/2 binary64))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64) #s(literal 0 binary64))
(neg.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(neg.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(+.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (E.f64))) (log.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(exp.f64 (neg.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (E.f64))) (log.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (E.f64))) (log.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (E.f64))) (log.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (E.f64))) (.f64 #s(literal 1/2 binary64) (log1p.f64 (*.f64 x x)))) (log.f64 #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log1p.f64 (.f64 x x))) (log.f64 #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (log.f64 #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (log.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (E.f64))) (.f64 #s(literal 1/2 binary64) (log1p.f64 (*.f64 x x))))))
(exp.f64 (+.f64 (log.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log1p.f64 (.f64 x x)))))
(exp.f64 (+.f64 (log.f64 #s(literal -1/2 binary64)) (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) #s(literal 0 binary64))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -2 binary64)))))
(/.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(/.f64 (pow.f64 (E.f64) (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (E.f64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (log.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(pow.f64 (E.f64) (log.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(pow.f64 (exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (E.f64)))) (log.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (pow.f64 (E.f64) (.f64 #s(literal 1 binary64) (log.f64 #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (pow.f64 (E.f64) (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (exp.f64 (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (pow.f64 (E.f64) (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (.f64 (log.f64 #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (pow.f64 (E.f64) (.f64 #s(literal 1 binary64) (log.f64 #s(literal -1/2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (exp.f64 (.f64 (log.f64 #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(*.f64 (pow.f64 (E.f64) (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (.f64 (log.f64 #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (E.f64) (.f64 #s(literal 1 binary64) (log.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (E.f64) (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (E.f64) (.f64 (log.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (pow.f64 (E.f64) (*.f64 (log.f64 #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 (E.f64) (.f64 (log.f64 #s(literal -1/2 binary64)) #s(literal 1 binary64))) (pow.f64 (E.f64) (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(.f64 (pow.f64 (E.f64) (.f64 #s(literal 1 binary64) (log.f64 #s(literal -1/2 binary64)))) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(.f64 (exp.f64 (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(.f64 (exp.f64 (.f64 (log.f64 #s(literal -1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))

simplify311.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2628×	`-lowering-.f32`
2628×	`-lowering-.f64`
1676×	`+-lowering-+.f64`
1676×	`+-lowering-+.f32`
1572×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	619
1	503	526
2	1468	510
3	4231	508
0	8068	508

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
1/2
(+ 1/2 (* -1/4 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))

Outputs
(* 1/8 (pow x 2))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64))))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (.f64 (.f64 x x) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)) x))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x #s(literal 3/16 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 3/16 binary64) (.f64 (.f64 x x) #s(literal -5/32 binary64)))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64)))
(+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x #s(literal 3/16 binary64))))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 3/16 binary64) (.f64 (.f64 x x) #s(literal -5/32 binary64)))))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal -5/32 binary64) (pow.f64 x #s(literal 6 binary64))))) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal -5/32 binary64) (pow.f64 x #s(literal 6 binary64))))) x)

eval23.0ms (0.1%)

Compiler: Compiled 2502 to 671 computations (73.2% saved)

prune31.0ms (0.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	162	15	177
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	162	16	178

Accuracy

98.4%

Counts

178 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.3%	(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
	97.1%	(-.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)))))
▶	4.1%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))))
	1.3%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
	4.3%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
▶	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
	96.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
▶	3.1%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
	96.7%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
	1.5%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
	4.1%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
▶	1.3%	(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
	4.3%	(.f64 #s(literal 1/8 binary64) (.f64 x x))

Compiler

Compiled 439 to 292 computations (33.5% saved)

simplify261.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))))
✓	cost-diff	256	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))))
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
✓	cost-diff	128	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	cost-diff	6400	(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))

Rules

1924×	`+-lowering-+.f64`
1924×	`+-lowering-+.f32`
1848×	`fnmsub-define`
1648×	`sum3-define`
1542×	`--lowering--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	188
1	92	173
2	282	172
3	775	171
4	2323	171
5	7957	171
0	8741	171

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (- 0 (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)
(- 0 (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))
0
(sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))
(+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))
1
(/ 1 (sqrt (+ (* 1 1) (* x x))))
(sqrt (+ (* 1 1) (* x x)))
x
(sqrt 1/2)
1/2
(- 1 1)
1
(* x (* x (+ 1/8 (* (* x x) -11/128))))
x
(* x (+ 1/8 (* (* x x) -11/128)))
(+ 1/8 (* (* x x) -11/128))
1/8
(* (* x x) -11/128)
(* x x)
-11/128
(- 1 (+ 1 (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))))
1
(+ 1 (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))))
(* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))
(* x x)
x
(+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))
-1/8
(* (* x x) (+ 11/128 (* (* x x) -69/1024)))
(+ 11/128 (* (* x x) -69/1024))
11/128
(* (* x x) -69/1024)
-69/1024
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
1
(sqrt (+ 1/2 (/ 1/2 x)))
(+ 1/2 (/ 1/2 x))
1/2
(/ 1/2 x)
x

Outputs
(+ (* (- 0 (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)
(-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64))))
(- 0 (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
0
#s(literal 0 binary64)
(sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
1
#s(literal 1 binary64)
(/ 1 (sqrt (+ (* 1 1) (* x x))))
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
(sqrt (+ (* 1 1) (* x x)))
(hypot.f64 #s(literal 1 binary64) x)
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(- 1 1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
(* x (* x (+ 1/8 (* (* x x) -11/128))))
(.f64 x (.f64 x (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))
x
(* x (+ 1/8 (* (* x x) -11/128)))
(.f64 x (-.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 11/128 binary64))))
(+ 1/8 (* (* x x) -11/128))
(-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))
1/8
#s(literal 1/8 binary64)
(* (* x x) -11/128)
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* x x)
(*.f64 x x)
-11/128
#s(literal -11/128 binary64)
(- 1 (+ 1 (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (-.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))))
(* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))
(* x x)
(*.f64 x x)
x
(+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))
(+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
-1/8
#s(literal -1/8 binary64)
(* (* x x) (+ 11/128 (* (* x x) -69/1024)))
(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
(+ 11/128 (* (* x x) -69/1024))
(+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))
11/128
#s(literal 11/128 binary64)
(* (* x x) -69/1024)
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
-69/1024
#s(literal -69/1024 binary64)
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (/ 1/2 x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(+ 1/2 (/ 1/2 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
x

localize239.0ms (1.4%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	98.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
✓	accuracy	99.9%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))))
✓	accuracy	99.2%	(.f64 (.f64 x x) #s(literal -69/1024 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64))))
✓	accuracy	99.9%	(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
✓	accuracy	99.5%	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓	accuracy	98.3%	(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))

Results

191.0ms

256×

valid

Compiler

Compiled 223 to 34 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-mult: 32.0ms (28.9% of total)

compiled-spec: 26.0ms (23.5% of total)

ival-sqrt: 17.0ms (15.4% of total)

ival-div: 15.0ms (13.6% of total)

ival-add: 10.0ms (9% of total)

ival-sub: 9.0ms (8.1% of total)

const: 2.0ms (1.8% of total)

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

series17.0ms (0.1%)

Counts

20 → 228

Calls

Call 1

Inputs
#<alt (+ (* (- 0 (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)>
#<alt (- 0 (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))>
#<alt (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))>
#<alt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))>
#<alt (- 1 1)>
#<alt (* x (* x (+ 1/8 (* (* x x) -11/128))))>
#<alt (* x (+ 1/8 (* (* x x) -11/128)))>
#<alt (+ 1/8 (* (* x x) -11/128))>
#<alt (* (* x x) -11/128)>
#<alt (- 1 (+ 1 (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))))>
#<alt (+ 1 (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))))>
#<alt (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))>
#<alt (* x x)>
#<alt (- 1 (sqrt (+ 1/2 (/ 1/2 x))))>
#<alt (sqrt (+ 1/2 (/ 1/2 x)))>
#<alt (+ 1/2 (/ 1/2 x))>
#<alt (/ 1/2 x)>
#<alt (/ 1 (sqrt (+ (* 1 1) (* x x))))>
#<alt (* (* x x) -69/1024)>
#<alt (* (* x x) (+ 11/128 (* (* x x) -69/1024)))>

Outputs
#<alt (+ 1 (* -1 (* (sqrt 1/2) (sqrt 2))))>
#<alt (+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))))>
#<alt (+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/4 (/ (sqrt 1/2) (sqrt 2)))))))>
#<alt (+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2)))))))))>
#<alt (+ 1 (* -1 (sqrt 1/2)))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))>
#<alt (+ 1 (* -1 (sqrt 1/2)))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* 1/2 (/ (sqrt 1/2) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* -1/8 (/ (sqrt 1/2) x))) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* -3/16 (/ (sqrt 1/2) x)) (* 1/8 (sqrt 1/2))) x)) (* -1/2 (sqrt 1/2))) x))))>
#<alt (* -1 (sqrt 2))>
#<alt (- (* 1/4 (/ (pow x 2) (sqrt 2))) (sqrt 2))>
#<alt (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))>
#<alt (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))>
#<alt -1>
#<alt (* -1 (+ 1 (* 1/2 (/ 1 x))))>
#<alt (- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))>
#<alt (- (+ (/ 1/8 (pow x 2)) (* 3/16 (/ 1 (pow x 3)))) (+ 1 (* 1/2 (/ 1 x))))>
#<alt -1>
#<alt (- (* 1/2 (/ 1 x)) 1)>
#<alt (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)>
#<alt (- (* -1 (/ (- (* -1 (/ (- 1/8 (* 3/16 (/ 1 x))) x)) 1/2) x)) 1)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/4 (/ (pow x 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))>
#<alt (+ 1 (+ (* -1 (/ (+ 1/8 (* 3/16 (/ 1 x))) (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt 1>
#<alt (- 1 (* 1/2 (/ 1 x)))>
#<alt (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))>
#<alt (+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 3/16 (/ 1 x)) 1/8) x))) x)))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))>
#<alt 1>
#<alt (+ 1 (/ 1 x))>
#<alt (- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))>
#<alt (- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))>
#<alt 1>
#<alt (- 1 (/ 1 x))>
#<alt (+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* 1/8 x)>
#<alt (* x (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* x (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* x (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))>
#<alt (* -69/1024 (pow x 6))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 11/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 69/1024 (/ 1/8 (pow x 4)))))>
#<alt (* -69/1024 (pow x 6))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 11/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 69/1024 (/ 1/8 (pow x 4)))))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))>
#<alt (* -69/1024 (pow x 6))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))>
#<alt (* -69/1024 (pow x 6))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))>
#<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 (* -1 (* (sqrt (/ 1 x)) (sqrt 1/2)))>
#<alt (/ (- x (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt 1/2)))))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (/ (- (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 x)) (sqrt 1/2))>
#<alt (/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 5))))))))) x)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* 11/128 (pow x 2))>
#<alt (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))>
#<alt (* -69/1024 (pow x 4))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* -69/1024 (pow x 4))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>

Calls

57 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+ (* (- 0 (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)
1.0ms	x	@	inf	(* (* x x) -11/128)
1.0ms	x	@	inf	(- 1 (+ 1 (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))))
1.0ms	x	@	inf	(* x (* x (+ 1/8 (* (* x x) -11/128))))
0.0ms	x	@	0	(- 1 (sqrt (+ 1/2 (/ 1/2 x))))

rewrite256.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2052×	`-lowering-.f32`
2052×	`-lowering-.f64`
1880×	`fma-lowering-fma.f32`
1880×	`fma-lowering-fma.f64`
1812×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	148
1	114	136
2	373	135
3	1069	134
4	3497	134
0	8077	134

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 790

Calls

Call 1

Inputs
(+ (* (- 0 (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)
(- 0 (sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))
(sqrt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))
(+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))
(- 1 1)
(* x (* x (+ 1/8 (* (* x x) -11/128))))
(* x (+ 1/8 (* (* x x) -11/128)))
(+ 1/8 (* (* x x) -11/128))
(* (* x x) -11/128)
(- 1 (+ 1 (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))))
(+ 1 (* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))))
(* (* x x) (+ -1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))
(* x x)
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
(sqrt (+ 1/2 (/ 1/2 x)))
(+ 1/2 (/ 1/2 x))
(/ 1/2 x)
(/ 1 (sqrt (+ (* 1 1) (* x x))))
(* (* x x) -69/1024)
(* (* x x) (+ 11/128 (* (* x x) -69/1024)))

Outputs
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 0 binary64))
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 0 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log1p.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 0 binary64))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64) #s(literal 0 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(+.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(exp.f64 (log1p.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
#s(literal 0 binary64)
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))))))
(+.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) (.f64 (neg.f64 (.f64 x (.f64 x (.f64 x #s(literal 11/128 binary64))))) x))
(+.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal 1/8 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal 11/128 binary64)))))))
(-.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 11/128 binary64))))))
(-.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))))
(-.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/8 binary64))))
(-.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/8 binary64))))
(-.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64))) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 x (.f64 x #s(literal 1/8 binary64)) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(fma.f64 x (.f64 (.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64)) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 (.f64 x x) #s(literal 1/8 binary64) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -11/128 binary64))) (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(fma.f64 #s(literal 1/8 binary64) (.f64 x x) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) (.f64 x x) (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(fma.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64))) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/8 binary64))) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -1/8 binary64)) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) #s(literal -1 binary64) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 (.f64 x #s(literal 1/8 binary64)) x (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))) x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(fma.f64 (.f64 x #s(literal -11/128 binary64)) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -1/8 binary64) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x #s(literal -1/8 binary64)) (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) #s(literal 1 binary64) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -11/128 binary64)) (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -11/128 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(fma.f64 (.f64 (.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64)) x (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 (.f64 (.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(neg.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal 11/128 binary64)))))))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))))))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x #s(literal -11/128 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))))) #s(literal 1 binary64))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))))) #s(literal -1 binary64))
(/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64))))) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 x #s(literal 1/8 binary64)) (.f64 x (.f64 x (.f64 x #s(literal 11/128 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/8 binary64))) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) x)) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (.f64 x #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))))) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (.f64 x #s(literal 1/8 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x (*.f64 x #s(literal -11/128 binary64))))))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x #s(literal 1/8 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 x (.f64 x (*.f64 x #s(literal -11/128 binary64)))) (-.f64 #s(literal 0 binary64) x)))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))) (-.f64 #s(literal 0 binary64) x)))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x #s(literal -11/128 binary64)))))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/8 binary64))) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 11/128 binary64)))))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/8 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/8 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))) (-.f64 #s(literal 0 binary64) x)))) #s(literal 1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x #s(literal -11/128 binary64)))))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 11/128 binary64)))))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64)) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))) (-.f64 #s(literal 0 binary64) x)))) #s(literal 1 binary64))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))) (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x #s(literal 1/8 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
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(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))) #s(literal 1 binary64))
(-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64))
(neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(*.f64 (exp.f64 (log1p.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/2 binary64) x))
(exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) x))
(neg.f64 (/.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) x)
(/.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -2 binary64))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 x #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(exp.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 (.f64 x x))))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 (*.f64 x x))) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/2 binary64) (log1p.f64 (*.f64 x x)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 (log.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (+.f64 (log.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (neg.f64 (log1p.f64 (*.f64 x x))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64)))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (log1p.f64 (.f64 x x))))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 #s(literal 1/2 binary64) (log1p.f64 (.f64 x x))))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (log1p.f64 (*.f64 x x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (log1p.f64 (.f64 x x))))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log1p.f64 (*.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log1p.f64 (*.f64 x x)))
(pow.f64 (exp.f64 (neg.f64 (log1p.f64 (*.f64 x x)))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 (.f64 #s(literal -1 binary64) (log1p.f64 (.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -69/1024 binary64))))
(neg.f64 (.f64 (.f64 x #s(literal -69/1024 binary64)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (.f64 x x) #s(literal -69/1024 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 x #s(literal -69/1024 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -69/1024 binary64))) #s(literal -1 binary64))
(/.f64 (.f64 (.f64 x #s(literal -69/1024 binary64)) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))
(.f64 x (.f64 x #s(literal -69/1024 binary64)))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(.f64 #s(literal -69/1024 binary64) (.f64 x x))
(.f64 (.f64 (*.f64 x x) #s(literal -69/1024 binary64)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x #s(literal -69/1024 binary64))))
(.f64 (.f64 x #s(literal -69/1024 binary64)) x)
(.f64 (.f64 (*.f64 x #s(literal -69/1024 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(+.f64 (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal 11/128 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 11/128 binary64))) (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (.f64 x x)))))
(-.f64 (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal -11/128 binary64))))
(-.f64 (.f64 x (.f64 x #s(literal 11/128 binary64))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 69/1024 binary64)))
(fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (.f64 x (*.f64 x #s(literal 11/128 binary64))))
(fma.f64 x (.f64 x #s(literal 11/128 binary64)) (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) #s(literal 11/128 binary64) (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -69/1024 binary64)) (.f64 x (*.f64 x #s(literal 11/128 binary64))))
(fma.f64 #s(literal 11/128 binary64) (.f64 x x) (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 11/128 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal -69/1024 binary64)) (.f64 x x) (.f64 x (*.f64 x #s(literal 11/128 binary64))))
(fma.f64 (.f64 x #s(literal -69/1024 binary64)) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal 11/128 binary64))))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64))) x (.f64 x (*.f64 x #s(literal 11/128 binary64))))
(fma.f64 (.f64 x #s(literal 11/128 binary64)) x (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -69/1024 binary64)) (.f64 x (*.f64 x #s(literal 11/128 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -69/1024 binary64) (.f64 x (*.f64 x #s(literal 11/128 binary64))))
(neg.f64 (.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))) #s(literal 1 binary64))
(/.f64 (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (.f64 x (*.f64 x #s(literal -11/128 binary64)))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (.f64 x #s(literal 11/128 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x #s(literal -11/128 binary64))))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal 11/128 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x #s(literal 11/128 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 69/1024 binary64)) #s(literal -1 binary64)) (.f64 x (*.f64 x #s(literal 11/128 binary64)))) #s(literal 1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 69/1024 binary64)) #s(literal 1 binary64)) (.f64 x (*.f64 x #s(literal -11/128 binary64)))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 69/1024 binary64)) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 binary64) (*.f64 x #s(literal 11/128 binary64)))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal -69/1024 binary64))))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal -1 binary64)) (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1 binary64))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x #s(literal 11/128 binary64))) (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x #s(literal 11/128 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 69/1024 binary64)))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 x #s(literal 11/128 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 (.f64 (.f64 x #s(literal 11/128 binary64)) (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (.f64 (.f64 x #s(literal 11/128 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 69/1024 binary64)))) (/.f64 #s(literal -1 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))))
(.f64 x (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
(.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (.f64 x x))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(.f64 (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))) x)
(.f64 (.f64 (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))

simplify307.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

4026×	`-lowering-.f32`
4026×	`-lowering-.f64`
3702×	`+-lowering-+.f64`
3702×	`+-lowering-+.f32`
1560×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	2364
1	1234	1968
2	3947	1926
0	8153	1926

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(+ 1 (* -1 (* (sqrt 1/2) (sqrt 2))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/4 (/ (sqrt 1/2) (sqrt 2)))))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2)))))))))
(+ 1 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))
(+ 1 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* 1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* -1/8 (/ (sqrt 1/2) x))) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* -3/16 (/ (sqrt 1/2) x)) (* 1/8 (sqrt 1/2))) x)) (* -1/2 (sqrt 1/2))) x))))
(* -1 (sqrt 2))
(- (* 1/4 (/ (pow x 2) (sqrt 2))) (sqrt 2))
(- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))
-1
(* -1 (+ 1 (* 1/2 (/ 1 x))))
(- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))
(- (+ (/ 1/8 (pow x 2)) (* 3/16 (/ 1 (pow x 3)))) (+ 1 (* 1/2 (/ 1 x))))
-1
(- (* 1/2 (/ 1 x)) 1)
(- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)
(- (* -1 (/ (- (* -1 (/ (- 1/8 (* 3/16 (/ 1 x))) x)) 1/2) x)) 1)
(sqrt 2)
(+ (sqrt 2) (* -1/4 (/ (pow x 2) (sqrt 2))))
(+ (sqrt 2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))))
1
(+ 1 (* 1/2 (/ 1 x)))
(- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))
(+ 1 (+ (* -1 (/ (+ 1/8 (* 3/16 (/ 1 x))) (pow x 2))) (* 1/2 (/ 1 x))))
1
(- 1 (* 1/2 (/ 1 x)))
(+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))
(+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 3/16 (/ 1 x)) 1/8) x))) x)))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
1
(+ 1 (/ 1 x))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
1
(- 1 (/ 1 x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 3))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(* -69/1024 (pow x 6))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))
(* (pow x 6) (- (+ (* 11/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 69/1024 (/ 1/8 (pow x 4)))))
(* -69/1024 (pow x 6))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))
(* (pow x 6) (- (+ (* 11/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 69/1024 (/ 1/8 (pow x 4)))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 11/128 (pow x 2)) 1/8))
(* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))
(* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8))
(* -69/1024 (pow x 6))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))
(* -69/1024 (pow x 6))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))
(* (pow x 6) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4)))))
(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)
(* -1 (* (sqrt (/ 1 x)) (sqrt 1/2)))
(/ (- x (* (sqrt x) (sqrt 1/2))) x)
(/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt 1/2)))))) (* (sqrt x) (sqrt 1/2))) x)
(/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))) (* (sqrt x) (sqrt 1/2))) x)
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (+ (* -1 (/ (- (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* (sqrt (/ 1 x)) (sqrt 1/2))
(/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 5))))))))) x)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(/ 1 x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)
(/ -1 x)
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* 11/128 (pow x 2))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(* -69/1024 (pow x 4))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* -69/1024 (pow x 4))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))

Outputs
(+ 1 (* -1 (* (sqrt 1/2) (sqrt 2))))
(-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))))
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(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/4 (/ (sqrt 1/2) (sqrt 2)))))))
(+.f64 (-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2)))))))))
(+.f64 (-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x (.f64 x (+.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 69/256 binary64))))) (sqrt.f64 #s(literal 2 binary64)))))))))
(+ 1 (* -1 (sqrt 1/2)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))
(+.f64 #s(literal 1 binary64) (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) (.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))))
(+ 1 (* -1 (sqrt 1/2)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* 1/2 (/ (sqrt 1/2) x))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (sqrt.f64 #s(literal 1/2 binary64))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* -1/8 (/ (sqrt 1/2) x))) x))))
(-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) x)) x))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* -3/16 (/ (sqrt 1/2) x)) (* 1/8 (sqrt 1/2))) x)) (* -1/2 (sqrt 1/2))) x))))
(-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (/.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -3/16 binary64)) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/8 binary64))) x)) x))
(* -1 (sqrt 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))
(- (* 1/4 (/ (pow x 2) (sqrt 2))) (sqrt 2))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))
(-.f64 (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal -11/64 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))
(-.f64 (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal 69/512 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 2 binary64))))))) (sqrt.f64 #s(literal 2 binary64)))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (* 1/2 (/ 1 x))))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))
(- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(- (+ (/ 1/8 (pow x 2)) (* 3/16 (/ 1 (pow x 3)))) (+ 1 (* 1/2 (/ 1 x))))
(+.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) (/.f64 #s(literal 3/16 binary64) (.f64 x (*.f64 x x))))
-1
#s(literal -1 binary64)
(- (* 1/2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(- (* -1 (/ (- (* -1 (/ (- 1/8 (* 3/16 (/ 1 x))) x)) 1/2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)) x)) x))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -1/4 (/ (pow x 2) (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 11/64 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -69/512 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ 1 x)))
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(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* -1 (/ (+ (* -1 (/ (- (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/128 binary64) (*.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(* (sqrt (/ 1 x)) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 x)) (.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 x)) (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 x) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 5))))))))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 x)) (.f64 x (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))))) x)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)) x))
(- (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)) x) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1/128 binary64) (.f64 x (.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)) x))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/128 binary64) (*.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 3/8 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 3/8 binary64) (.f64 (.f64 x x) #s(literal -5/16 binary64))))))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (/.f64 #s(literal -5/16 binary64) (pow.f64 x #s(literal 6 binary64))))) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))
(/.f64 (+.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (/.f64 #s(literal -5/16 binary64) (pow.f64 x #s(literal 6 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* 11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal 11/128 binary64))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
(* -69/1024 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -69/1024 binary64))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal -69/1024 binary64)))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal -69/1024 binary64)))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal -69/1024 binary64)))
(* -69/1024 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -69/1024 binary64))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal -69/1024 binary64)))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal -69/1024 binary64)))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal -69/1024 binary64)))

eval150.0ms (0.9%)

Compiler: Compiled 22321 to 2954 computations (86.8% saved)

prune167.0ms (1%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	1114	9	1123
Fresh	4	6	10
Picked	3	2	5
Done	0	1	1
Total	1121	18	1139

Accuracy

98.4%

Counts

1139 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.0%	(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
	97.1%	(fma.f64 (+.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) (/.f64 #s(literal 3/16 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
▶	98.3%	(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
▶	4.1%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
	1.3%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
	4.3%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
▶	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
	96.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	96.7%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
	4.1%	(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
▶	1.3%	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
	1.5%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
	4.3%	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	1.3%	(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
▶	3.1%	#s(literal 0 binary64)

Compiler

Compiled 474 to 321 computations (32.3% saved)

simplify180.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))))
✓	cost-diff	256	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 x #s(literal -11/128 binary64))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -11/128 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64))))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓	cost-diff	6400	(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))

Rules

2190×	`+-lowering-+.f64`
2190×	`+-lowering-+.f32`
1924×	`fnmadd-define`
1520×	`fmsub-define`
1512×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	226
1	90	212
2	231	200
3	647	200
4	1787	200
5	4296	200
6	7664	200
0	8384	200

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (neg (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)
(neg (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x)))))))
(sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x))))))
(- 1 (/ -1 (sqrt (+ (* 1 1) (* x x)))))
1
(/ -1 (sqrt (+ (* 1 1) (* x x))))
-1
(sqrt (+ (* 1 1) (* x x)))
x
(sqrt 1/2)
1/2
0
(* (+ 1/8 (* x (* x -11/128))) (* x x))
(+ 1/8 (* x (* x -11/128)))
1/8
(* x (* x -11/128))
x
(* x -11/128)
-11/128
(* x x)
(- (+ 1 (* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))) 1)
(+ 1 (* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))))
1
(* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))
(* x x)
x
(- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))
1/8
(* (* x x) (+ 11/128 (* (* x x) -69/1024)))
(+ 11/128 (* (* x x) -69/1024))
11/128
(* (* x x) -69/1024)
-69/1024
(- 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
1
(sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
(+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
1/2
(/ (+ 1/2 (/ -1/4 (* x x))) x)
(+ 1/2 (/ -1/4 (* x x)))
(/ -1/4 (* x x))
-1/4
(* x x)
x

Outputs
(+ (* (neg (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)
(-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64))))
(neg (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x)))))))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(- 1 (/ -1 (sqrt (+ (* 1 1) (* x x)))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
1
#s(literal 1 binary64)
(/ -1 (sqrt (+ (* 1 1) (* x x))))
(/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))
-1
#s(literal -1 binary64)
(sqrt (+ (* 1 1) (* x x)))
(hypot.f64 #s(literal 1 binary64) x)
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
0
#s(literal 0 binary64)
(* (+ 1/8 (* x (* x -11/128))) (* x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))))
(+ 1/8 (* x (* x -11/128)))
(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64))))
1/8
#s(literal 1/8 binary64)
(* x (* x -11/128))
(.f64 x (.f64 x #s(literal -11/128 binary64)))
x
(* x -11/128)
(*.f64 x #s(literal -11/128 binary64))
-11/128
#s(literal -11/128 binary64)
(* x x)
(*.f64 x x)
(- (+ 1 (* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))) 1)
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))))))
(+ 1 (* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))))
1
#s(literal 1 binary64)
(* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))))))
(* x x)
(*.f64 x x)
x
(- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))
(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
1/8
#s(literal 1/8 binary64)
(* (* x x) (+ 11/128 (* (* x x) -69/1024)))
(.f64 x (.f64 x (-.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))))
(+ 11/128 (* (* x x) -69/1024))
(-.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))
11/128
#s(literal 11/128 binary64)
(* (* x x) -69/1024)
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
-69/1024
#s(literal -69/1024 binary64)
(- 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
(+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
1/2
#s(literal 1/2 binary64)
(/ (+ 1/2 (/ -1/4 (* x x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(+ 1/2 (/ -1/4 (* x x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(/ -1/4 (* x x))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
-1/4
#s(literal -1/4 binary64)
(* x x)
(*.f64 x x)
x

localize184.0ms (1.1%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
✓	accuracy	98.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
✓	accuracy	97.8%	(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
✓	accuracy	99.2%	(.f64 (.f64 x x) #s(literal -69/1024 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 x #s(literal -11/128 binary64))
✓	accuracy	99.9%	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
✓	accuracy	99.9%	(.f64 x (.f64 x #s(literal -11/128 binary64)))
✓	accuracy	100.0%	(neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	accuracy	100.0%	(/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓	accuracy	98.5%	(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))

Results

132.0ms	253×	0	valid
1.0ms	3×	0	invalid

Compiler

Compiled 252 to 36 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-mult: 22.0ms (31.9% of total)

compiled-spec: 13.0ms (18.8% of total)

ival-add: 10.0ms (14.5% of total)

ival-sqrt: 8.0ms (11.6% of total)

ival-sub: 7.0ms (10.1% of total)

ival-div: 6.0ms (8.7% of total)

const: 1.0ms (1.4% of total)

ival-neg: 1.0ms (1.4% of total)

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

series13.0ms (0.1%)

Counts

20 → 240

Calls

Call 1

Inputs
#<alt (+ (* (neg (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)>
#<alt (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x))))))>
#<alt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x)))))>
#<alt (/ -1 (sqrt (+ (* 1 1) (* x x))))>
#<alt (* (+ 1/8 (* x (* x -11/128))) (* x x))>
#<alt (+ 1/8 (* x (* x -11/128)))>
#<alt (* x (* x -11/128))>
#<alt (* x -11/128)>
#<alt (- (+ 1 (* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))) 1)>
#<alt (+ 1 (* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))))>
#<alt (* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))>
#<alt (* x x)>
#<alt (- 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))>
#<alt (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))>
#<alt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))>
#<alt (/ (+ 1/2 (/ -1/4 (* x x))) x)>
#<alt (neg (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x)))))))>
#<alt (* (* x x) -69/1024)>
#<alt (* (* x x) (+ 11/128 (* (* x x) -69/1024)))>
#<alt (/ -1/4 (* x x))>

Outputs
#<alt (+ 1 (* -1 (* (sqrt 1/2) (sqrt 2))))>
#<alt (+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))))>
#<alt (+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/4 (/ (sqrt 1/2) (sqrt 2)))))))>
#<alt (+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2)))))))))>
#<alt (+ 1 (* -1 (sqrt 1/2)))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))>
#<alt (+ 1 (* -1 (sqrt 1/2)))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* 1/2 (/ (sqrt 1/2) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* -1/8 (/ (sqrt 1/2) x))) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* -3/16 (/ (sqrt 1/2) x)) (* 1/8 (sqrt 1/2))) x)) (* -1/2 (sqrt 1/2))) x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/4 (/ (pow x 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))>
#<alt (+ 1 (+ (* -1 (/ (+ 1/8 (* 3/16 (/ 1 x))) (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt 1>
#<alt (- 1 (* 1/2 (/ 1 x)))>
#<alt (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))>
#<alt (+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 3/16 (/ 1 x)) 1/8) x))) x)))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))>
#<alt 1>
#<alt (+ 1 (/ 1 x))>
#<alt (- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))>
#<alt (- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))>
#<alt 1>
#<alt (- 1 (/ 1 x))>
#<alt (+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))>
#<alt -1>
#<alt (- (* 1/2 (pow x 2)) 1)>
#<alt (- (* (pow x 2) (+ 1/2 (* -3/8 (pow x 2)))) 1)>
#<alt (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 5/16 (pow x 2)) 3/8)))) 1)>
#<alt (/ -1 x)>
#<alt (/ (- (* 1/2 (/ 1 (pow x 2))) 1) x)>
#<alt (/ (- (* 1/2 (/ 1 (pow x 2))) (+ 1 (/ 3/8 (pow x 4)))) x)>
#<alt (/ (- (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6)))) (+ 1 (/ 3/8 (pow x 4)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* 1/2 (/ 1 (pow x 2))) 1) x))>
#<alt (* -1 (/ (- (* 1/2 (/ 1 (pow x 2))) (+ 1 (/ 3/8 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6)))) (+ 1 (/ 3/8 (pow x 4)))) x))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* -11/128 x)>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (+ (/ 1/8 (pow x 4)) (/ 1 (pow x 6)))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (+ (/ 1/8 (pow x 4)) (/ 1 (pow x 6)))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (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 (* -1 (* (sqrt (/ 1 (pow x 3))) (sqrt -1/4)))>
#<alt (/ (- (pow x 2) (* (sqrt x) (sqrt -1/4))) (pow x 2))>
#<alt (/ (- (* (pow x 2) (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))))) (* (sqrt x) (sqrt -1/4))) (pow x 2))>
#<alt (/ (- (* (pow x 2) (+ 1 (* x (- (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))))))) (* (sqrt x) (sqrt -1/4))) (pow x 2))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))>
#<alt (/ (+ (* 1/4 (* (sqrt (pow x 5)) (/ 1 (sqrt -1/4)))) (* (sqrt x) (sqrt -1/4))) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/4) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (/ -1/4 (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))>
#<alt (/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))>
#<alt (/ -1/4 (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (sqrt 2))>
#<alt (- (* 1/4 (/ (pow x 2) (sqrt 2))) (sqrt 2))>
#<alt (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))>
#<alt (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))>
#<alt -1>
#<alt (* -1 (+ 1 (* 1/2 (/ 1 x))))>
#<alt (- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))>
#<alt (- (+ (/ 1/8 (pow x 2)) (* 3/16 (/ 1 (pow x 3)))) (+ 1 (* 1/2 (/ 1 x))))>
#<alt -1>
#<alt (- (* 1/2 (/ 1 x)) 1)>
#<alt (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)>
#<alt (- (* -1 (/ (- (* -1 (/ (- 1/8 (* 3/16 (/ 1 x))) x)) 1/2) x)) 1)>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* 11/128 (pow x 2))>
#<alt (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))>
#<alt (* -69/1024 (pow x 4))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* -69/1024 (pow x 4))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>

Calls

60 calls:

Time	Variable		Expression
3.0ms	x	@	(/ -1/4 (* x x))
2.0ms	x	@	(/ (+ 1/2 (/ -1/4 (* x x))) x)
0.0ms	x	@	(- 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
0.0ms	x	@	(sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
0.0ms	x	@	(+ (* (neg (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)

rewrite236.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1886×	`-lowering-.f32`
1886×	`-lowering-.f64`
1654×	`sum5-define`
1630×	`fnmadd-define`
1566×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	177
1	117	161
2	384	154
3	1293	154
4	4585	154
0	8260	154

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 618

Calls

Call 1

Inputs
(+ (* (neg (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x))))))) (sqrt 1/2)) 1)
(sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x))))))
(- 1 (/ -1 (sqrt (+ (* 1 1) (* x x)))))
(/ -1 (sqrt (+ (* 1 1) (* x x))))
(* (+ 1/8 (* x (* x -11/128))) (* x x))
(+ 1/8 (* x (* x -11/128)))
(* x (* x -11/128))
(* x -11/128)
(- (+ 1 (* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))) 1)
(+ 1 (* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))))
(* (* x x) (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))))
(* x x)
(- 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
(sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
(+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
(/ (+ 1/2 (/ -1/4 (* x x))) x)
(neg (sqrt (- 1 (/ -1 (sqrt (+ (* 1 1) (* x x)))))))
(* (* x x) -69/1024)
(* (* x x) (+ 11/128 (* (* x x) -69/1024)))
(/ -1/4 (* x x))

Outputs
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64)))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(+.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(exp.f64 (log1p.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64) #s(literal 1 binary64))
(neg.f64 (+.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(+.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
(-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (.f64 x x) #s(literal -11/128 binary64))))
(-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) #s(literal 11/128 binary64)) (.f64 x x)))
(-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 11/128 binary64))))
(-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -11/128 binary64))) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/8 binary64))))
(-.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1/8 binary64)))
(-.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(-.f64 (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 x (.f64 x #s(literal 1/8 binary64)) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/8 binary64) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(fma.f64 #s(literal 1/8 binary64) (.f64 x x) (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(fma.f64 (.f64 x #s(literal 1/8 binary64)) x (.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -11/128 binary64)) (.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -11/128 binary64) (.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(fma.f64 (.f64 x #s(literal -11/128 binary64)) (.f64 x (.f64 x x)) (.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal -11/128 binary64))) x (.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))))))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(neg.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))) #s(literal 1 binary64))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))))) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))) #s(literal -1 binary64))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1 binary64))
(/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64))))))
(.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))))
(.f64 (.f64 x x) (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))) x)
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64)))) #s(literal 1 binary64))
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(.f64 (.f64 x #s(literal 69/1024 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (*.f64 x #s(literal -69/1024 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64)))) (.f64 (.f64 x x) #s(literal 11/128 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal 11/128 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
(-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64)))) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
(-.f64 (.f64 (.f64 x x) #s(literal 11/128 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64)))) (.f64 (.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 69/1024 binary64))) (.f64 (.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
(fma.f64 x (.f64 x #s(literal 11/128 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))))
(fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (.f64 x x) #s(literal 11/128 binary64) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -69/1024 binary64)) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 #s(literal -11/128 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))))
(fma.f64 #s(literal 11/128 binary64) (.f64 x x) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))))
(fma.f64 #s(literal -69/1024 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal -69/1024 binary64)) (.f64 x x) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 (.f64 x x) #s(literal 69/1024 binary64))) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -11/128 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))))
(fma.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64)))) #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 11/128 binary64)) #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
(fma.f64 (.f64 x #s(literal -69/1024 binary64)) (.f64 x (.f64 x x)) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (.f64 x #s(literal 11/128 binary64)) x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal -69/1024 binary64))) x (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -69/1024 binary64)) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -69/1024 binary64) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 69/1024 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 69/1024 binary64))) (-.f64 #s(literal 0 binary64) x) (.f64 (*.f64 x x) #s(literal 11/128 binary64)))
(fma.f64 (.f64 x #s(literal -11/128 binary64)) (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))))
(neg.f64 (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
(/.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) #s(literal 1 binary64))
(/.f64 (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))) #s(literal -1 binary64))
(/.f64 (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (*.f64 x x) #s(literal -69/1024 binary64))))))
(.f64 #s(literal -1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (*.f64 x x) #s(literal 69/1024 binary64))))))
(.f64 x (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
(.f64 (.f64 x x) (.f64 #s(literal 1 binary64) (+.f64 #s(literal 11/128 binary64) (.f64 (*.f64 x x) #s(literal -69/1024 binary64)))))
(.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) (.f64 x x))
(.f64 (.f64 x (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (*.f64 x x) #s(literal -69/1024 binary64))))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))))
(.f64 (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))) x)
(.f64 (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) #s(literal 1 binary64)) (*.f64 x x))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 x (/.f64 #s(literal -1/4 binary64) x)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(neg.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal -1/4 binary64) x)))
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x)))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1 binary64))
(/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal -1/4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -4 binary64))
(/.f64 (/.f64 #s(literal -1/4 binary64) x) x)
(/.f64 (/.f64 #s(literal 1/4 binary64) x) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x #s(literal 1/4 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 4 binary64))
(/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal -1/4 binary64) x)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 x (/.f64 #s(literal -1/4 binary64) x)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/4 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/4 binary64))
(*.f64 (/.f64 #s(literal -1/4 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1/4 binary64) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1/4 binary64))
(.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1 binary64))

simplify281.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

4054×	`-lowering-.f32`
4054×	`-lowering-.f64`
3778×	`+-lowering-+.f64`
3778×	`+-lowering-+.f32`
1238×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	407	2487
1	1321	2067
2	4338	2017
0	8106	2017

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(+ 1 (* -1 (* (sqrt 1/2) (sqrt 2))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/4 (/ (sqrt 1/2) (sqrt 2)))))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2)))))))))
(+ 1 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))
(+ 1 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* 1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* -1/8 (/ (sqrt 1/2) x))) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* -3/16 (/ (sqrt 1/2) x)) (* 1/8 (sqrt 1/2))) x)) (* -1/2 (sqrt 1/2))) x))))
(sqrt 2)
(+ (sqrt 2) (* -1/4 (/ (pow x 2) (sqrt 2))))
(+ (sqrt 2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))))
1
(+ 1 (* 1/2 (/ 1 x)))
(- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))
(+ 1 (+ (* -1 (/ (+ 1/8 (* 3/16 (/ 1 x))) (pow x 2))) (* 1/2 (/ 1 x))))
1
(- 1 (* 1/2 (/ 1 x)))
(+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))
(+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 3/16 (/ 1 x)) 1/8) x))) x)))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
1
(+ 1 (/ 1 x))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
1
(- 1 (/ 1 x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))
-1
(- (* 1/2 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/2 (* -3/8 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 5/16 (pow x 2)) 3/8)))) 1)
(/ -1 x)
(/ (- (* 1/2 (/ 1 (pow x 2))) 1) x)
(/ (- (* 1/2 (/ 1 (pow x 2))) (+ 1 (/ 3/8 (pow x 4)))) x)
(/ (- (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6)))) (+ 1 (/ 3/8 (pow x 4)))) x)
(/ 1 x)
(* -1 (/ (- (* 1/2 (/ 1 (pow x 2))) 1) x))
(* -1 (/ (- (* 1/2 (/ 1 (pow x 2))) (+ 1 (/ 3/8 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6)))) (+ 1 (/ 3/8 (pow x 4)))) x))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* -11/128 x)
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (+ (/ 1/8 (pow x 4)) (/ 1 (pow x 6)))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (+ (/ 1/8 (pow x 4)) (/ 1 (pow x 6)))) (* 11/128 (/ 1 (pow x 2)))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (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)
(* -1 (* (sqrt (/ 1 (pow x 3))) (sqrt -1/4)))
(/ (- (pow x 2) (* (sqrt x) (sqrt -1/4))) (pow x 2))
(/ (- (* (pow x 2) (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))))) (* (sqrt x) (sqrt -1/4))) (pow x 2))
(/ (- (* (pow x 2) (+ 1 (* x (- (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))))))) (* (sqrt x) (sqrt -1/4))) (pow x 2))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))
(/ (+ (* 1/4 (* (sqrt (pow x 5)) (/ 1 (sqrt -1/4)))) (* (sqrt x) (sqrt -1/4))) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/4) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(/ -1/4 (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))
(/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(/ -1/4 (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (sqrt 2))
(- (* 1/4 (/ (pow x 2) (sqrt 2))) (sqrt 2))
(- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))
-1
(* -1 (+ 1 (* 1/2 (/ 1 x))))
(- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))
(- (+ (/ 1/8 (pow x 2)) (* 3/16 (/ 1 (pow x 3)))) (+ 1 (* 1/2 (/ 1 x))))
-1
(- (* 1/2 (/ 1 x)) 1)
(- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)
(- (* -1 (/ (- (* -1 (/ (- 1/8 (* 3/16 (/ 1 x))) x)) 1/2) x)) 1)
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* 11/128 (pow x 2))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(* -69/1024 (pow x 4))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* -69/1024 (pow x 4))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))

Outputs
(+ 1 (* -1 (* (sqrt 1/2) (sqrt 2))))
(-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))))
(+.f64 (-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) (sqrt.f64 #s(literal 2 binary64))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/4 (/ (sqrt 1/2) (sqrt 2)))))))
(+.f64 (-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2)))))))))
(+.f64 (-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x (.f64 x (+.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) #s(literal 69/256 binary64))) (sqrt.f64 #s(literal 2 binary64)))))))))
(+ 1 (* -1 (sqrt 1/2)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))
(+.f64 #s(literal 1 binary64) (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))) (.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))))
(+ 1 (* -1 (sqrt 1/2)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* 1/2 (/ (sqrt 1/2) x))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (sqrt.f64 #s(literal 1/2 binary64))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* -1/8 (/ (sqrt 1/2) x))) x))))
(-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/8 binary64))) x))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* -3/16 (/ (sqrt 1/2) x)) (* 1/8 (sqrt 1/2))) x)) (* -1/2 (sqrt 1/2))) x))))
(-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (/.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -3/16 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/8 binary64))) x)) x))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -1/4 (/ (pow x 2) (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 11/64 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal -69/512 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(+ 1 (+ (* -1 (/ (+ 1/8 (* 3/16 (/ 1 x))) (pow x 2))) (* 1/2 (/ 1 x))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -3/16 binary64) x)) (*.f64 x x)))
1
#s(literal 1 binary64)
(- 1 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x))
(+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))
(+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 3/16 (/ 1 x)) 1/8) x))) x)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)) x)) x))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 3/8 binary64))))))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 (.f64 x x) #s(literal -5/16 binary64))))))))
1
#s(literal 1 binary64)
(+ 1 (/ 1 x))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)))
1
#s(literal 1 binary64)
(- 1 (/ 1 x))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/8 binary64) (.f64 (.f64 x (.f64 x x)) x)))) x))
-1
#s(literal -1 binary64)
(- (* 1/2 (pow x 2)) 1)
(+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(- (* (pow x 2) (+ 1/2 (* -3/8 (pow x 2)))) 1)
(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -3/8 binary64)))))
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 5/16 (pow x 2)) 3/8)))) 1)
(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -3/8 binary64) (.f64 (.f64 x x) #s(literal 5/16 binary64)))))))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ (- (* 1/2 (/ 1 (pow x 2))) 1) x)
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(/ (- (* 1/2 (/ 1 (pow x 2))) (+ 1 (/ 3/8 (pow x 4)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/8 binary64) (.f64 (.f64 x (.f64 x x)) x)))) x)
(/ (- (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6)))) (+ 1 (/ 3/8 (pow x 4)))) x)
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/8 binary64) (.f64 (.f64 x (.f64 x x)) x)))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 1/2 (/ 1 (pow x 2))) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* 1/2 (/ 1 (pow x 2))) (+ 1 (/ 3/8 (pow x 4)))) x))
(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/8 binary64) (.f64 (.f64 x (.f64 x x)) x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6)))) (+ 1 (/ 3/8 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/8 binary64) (.f64 (.f64 x (.f64 x x)) x)))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))))
(* -11/128 (pow x 4))
(.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal -11/128 binary64))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64)))
(* -11/128 (pow x 4))
(.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal -11/128 binary64))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64)))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -11/128 (pow x 2)))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
(+ 1/8 (* -11/128 (pow x 2)))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
(+ 1/8 (* -11/128 (pow x 2)))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64))))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64))))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64))))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64))))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64))))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -11/128 binary64))))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 (pow x 2))
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
(*.f64 x #s(literal -11/128 binary64))
(* -11/128 x)
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(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)
(* -1 (sqrt 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))
(- (* 1/4 (/ (pow x 2) (sqrt 2))) (sqrt 2))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))
(-.f64 (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -11/64 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))) (sqrt 2))
(-.f64 (.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal 69/512 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (* 1/2 (/ 1 x))))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(- (+ (/ 1/8 (pow x 2)) (* 3/16 (/ 1 (pow x 3)))) (+ 1 (* 1/2 (/ 1 x))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (*.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))))
-1
#s(literal -1 binary64)
(- (* 1/2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)
(+.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(- (* -1 (/ (- (* -1 (/ (- 1/8 (* 3/16 (/ 1 x))) x)) 1/2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -3/16 binary64) x)) x)) x))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* 11/128 (pow x 2))
(.f64 x (.f64 x #s(literal 11/128 binary64)))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
(* -69/1024 (pow x 4))
(.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal -69/1024 binary64))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal -69/1024 binary64)))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal -69/1024 binary64)))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal -69/1024 binary64)))
(* -69/1024 (pow x 4))
(.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal -69/1024 binary64))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal -69/1024 binary64)))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal -69/1024 binary64)))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 #s(literal 11/128 binary64) (*.f64 x x)) #s(literal -69/1024 binary64)))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))

eval168.0ms (1%)

Compiler: Compiled 18972 to 2889 computations (84.8% saved)

prune111.0ms (0.7%)

Pruning

19 alts after pruning (11 fresh and 8 done)

	Pruned	Kept	Total
New	1010	4	1014
Fresh	3	7	10
Picked	0	5	5
Done	0	3	3
Total	1013	19	1032

Accuracy

98.4%

Counts

1032 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.1%	(fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (*.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
	97.0%	(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	98.3%	(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
▶	1.3%	(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	4.1%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
	4.3%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64)))) #s(literal 1 binary64))
	1.3%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
✓	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
▶	96.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	96.7%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
▶	4.1%	(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
✓	1.3%	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
	1.5%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
▶	4.3%	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	1.3%	(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
✓	3.1%	#s(literal 0 binary64)

Compiler

Compiled 437 to 292 computations (33.2% saved)

simplify177.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
✓	cost-diff	0	(-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64)))))
✓	cost-diff	0	(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
✓	cost-diff	128	(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
✓	cost-diff	0	(+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (*.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓	cost-diff	6272	(fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (*.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))

Rules

1788×	`fma-lowering-fma.f32`
1788×	`fma-lowering-fma.f64`
1524×	`fma-define`
1498×	`-lowering-.f32`
1498×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	172
1	87	160
2	236	158
3	724	158
4	2173	158
5	5905	158
0	8066	158

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (+ (/ 1/8 (* x x)) (+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x)))) (sqrt 1/2)) 1)
(+ (/ 1/8 (* x x)) (+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x))))
(/ 1/8 (* x x))
1/8
(* x x)
x
(+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x)))
(/ 3/16 (* x (* x x)))
3/16
(* x (* x x))
(- -1 (/ 1/2 x))
-1
(/ 1/2 x)
1/2
(sqrt 1/2)
1
(* (* x x) 1/8)
(* x x)
x
1/8
(/ (+ 1/8 (* (* x x) -11/128)) (/ 1 (* x x)))
(+ 1/8 (* (* x x) -11/128))
1/8
(* (* x x) -11/128)
(* x x)
x
-11/128
(/ 1 (* x x))
1
(* (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))) (* x x))
(- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))
1/8
(* (* x x) (+ 11/128 (* (* x x) -69/1024)))
(* x x)
x
(+ 11/128 (* (* x x) -69/1024))
11/128
(* (* x x) -69/1024)
-69/1024
(- 1 (sqrt 1/2))
1
(sqrt 1/2)
1/2

Outputs
(+ (* (+ (/ 1/8 (* x x)) (+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x)))) (sqrt 1/2)) 1)
(+.f64 (.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) x))) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(+ (/ 1/8 (* x x)) (+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x))))
(+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)))
(/ 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
(+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x)))
(+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(/ 3/16 (* x (* x x)))
(/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x)))
3/16
#s(literal 3/16 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(- -1 (/ 1/2 x))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))
-1
#s(literal -1 binary64)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(* (* x x) 1/8)
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(* x x)
(*.f64 x x)
x
1/8
#s(literal 1/8 binary64)
(/ (+ 1/8 (* (* x x) -11/128)) (/ 1 (* x x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))))
(+ 1/8 (* (* x x) -11/128))
(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64))))
1/8
#s(literal 1/8 binary64)
(* (* x x) -11/128)
(.f64 x (.f64 x #s(literal -11/128 binary64)))
(* x x)
(*.f64 x x)
x
-11/128
#s(literal -11/128 binary64)
(/ 1 (* x x))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
1
#s(literal 1 binary64)
(* (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))) (* x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))))))
(- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))
(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
1/8
#s(literal 1/8 binary64)
(* (* x x) (+ 11/128 (* (* x x) -69/1024)))
(.f64 (.f64 x x) (-.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))
(* x x)
(*.f64 x x)
x
(+ 11/128 (* (* x x) -69/1024))
(-.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))
11/128
#s(literal 11/128 binary64)
(* (* x x) -69/1024)
(.f64 x (.f64 x #s(literal -69/1024 binary64)))
-69/1024
#s(literal -69/1024 binary64)
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize204.0ms (1.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	98.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))
✓	accuracy	99.2%	(.f64 (.f64 x x) #s(literal -69/1024 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	accuracy	99.5%	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	accuracy	97.6%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.6%	(/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x)))
✓	accuracy	98.5%	(fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (*.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	97.8%	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))

Results

161.0ms

256×

valid

Compiler

Compiled 208 to 31 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 27.0ms (46.8% of total)

ival-div: 12.0ms (20.8% of total)

ival-add: 7.0ms (12.1% of total)

ival-sub: 4.0ms (6.9% of total)

compiled-spec: 4.0ms (6.9% of total)

ival-sqrt: 2.0ms (3.5% of total)

const: 1.0ms (1.7% of total)

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

series8.0ms (0%)

Counts

17 → 180

Calls

Call 1

Inputs
#<alt (+ (* (+ (/ 1/8 (* x x)) (+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x)))) (sqrt 1/2)) 1)>
#<alt (+ (/ 1/8 (* x x)) (+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x))))>
#<alt (/ 1/8 (* x x))>
#<alt (* x x)>
#<alt (* (* x x) 1/8)>
#<alt (/ (+ 1/8 (* (* x x) -11/128)) (/ 1 (* x x)))>
#<alt (+ 1/8 (* (* x x) -11/128))>
#<alt (* (* x x) -11/128)>
#<alt (* (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))) (* x x))>
#<alt (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))>
#<alt (* (* x x) (+ 11/128 (* (* x x) -69/1024)))>
#<alt (- 1 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (/ 3/16 (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (/ 1 (* x x))>
#<alt (* (* x x) -69/1024)>

Outputs
#<alt (* 3/16 (/ (sqrt 1/2) (pow x 3)))>
#<alt (/ (+ (* 1/8 (* x (sqrt 1/2))) (* 3/16 (sqrt 1/2))) (pow x 3))>
#<alt (/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* -1/2 (* x (sqrt 1/2))) (* 1/8 (sqrt 1/2))))) (pow x 3))>
#<alt (/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ 1 (* -1 (sqrt 1/2))))))))) (pow x 3))>
#<alt (+ 1 (* -1 (sqrt 1/2)))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))>
#<alt (+ 1 (* -1 (sqrt 1/2)))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ (+ 3/16 (* 1/8 x)) (pow x 3))>
#<alt (/ (+ 3/16 (* x (+ 1/8 (* -1/2 x)))) (pow x 3))>
#<alt (/ (+ 3/16 (* x (+ 1/8 (* x (- (* -1 x) 1/2))))) (pow x 3))>
#<alt -1>
#<alt (* -1 (+ 1 (* 1/2 (/ 1 x))))>
#<alt (- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))>
#<alt (- (+ (/ 1/8 (pow x 2)) (* 3/16 (/ 1 (pow x 3)))) (+ 1 (* 1/2 (/ 1 x))))>
#<alt -1>
#<alt (* -1 (+ 1 (* 1/2 (/ 1 x))))>
#<alt (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 1)>
#<alt (- (* -1 (/ (+ 1/2 (* -1 (/ (+ 1/8 (* 3/16 (/ 1 x))) x))) x)) 1)>
#<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 (* 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 (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))>
#<alt (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))>
#<alt (* 69/1024 (pow x 4))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 69/1024 (pow x 4))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 11/128 (pow x 2))>
#<alt (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))>
#<alt (* -69/1024 (pow x 4))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* -69/1024 (pow x 4))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (pow x 3))>
#<alt (/ 3/16 (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 (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>
#<alt (* -69/1024 (pow x 2))>

Calls

45 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))
1.0ms	x	@	0	(/ 3/16 (* x (* x x)))
0.0ms	x	@	0	(+ (* (+ (/ 1/8 (* x x)) (+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x)))) (sqrt 1/2)) 1)
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	0	(/ 1/8 (* x x))

rewrite230.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2536×	`-lowering-.f32`
2536×	`-lowering-.f64`
1682×	`/-lowering-/.f32`
1682×	`/-lowering-/.f64`
1400×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	121
1	124	111
2	565	109
3	4725	109
0	8165	109

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 451

Calls

Call 1

Inputs
(+ (* (+ (/ 1/8 (* x x)) (+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x)))) (sqrt 1/2)) 1)
(+ (/ 1/8 (* x x)) (+ (/ 3/16 (* x (* x x))) (- -1 (/ 1/2 x))))
(/ 1/8 (* x x))
(* x x)
(* (* x x) 1/8)
(/ (+ 1/8 (* (* x x) -11/128)) (/ 1 (* x x)))
(+ 1/8 (* (* x x) -11/128))
(* (* x x) -11/128)
(* (- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024)))) (* x x))
(- 1/8 (* (* x x) (+ 11/128 (* (* x x) -69/1024))))
(* (* x x) (+ 11/128 (* (* x x) -69/1024)))
(- 1 (sqrt 1/2))
(sqrt 1/2)
(/ 3/16 (* x (* x x)))
(* x (* x x))
(/ 1 (* x x))
(* (* x x) -69/1024)

Outputs
(+.f64 (.f64 (+.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (+.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x)) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/8 binary64))) #s(literal 1 binary64)))
(+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 x x) #s(literal 1/8 binary64))) (+.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (*.f64 x x))) x)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))) (+.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 x x) #s(literal 1/8 binary64)))) (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (*.f64 x x))) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x))))) (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (+.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))) #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x)))
(+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)))
(+.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))))
(+.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x)) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(+.f64 #s(literal -1 binary64) (-.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)))
(+.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x))))
(+.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x)) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(+.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/16 binary64) (.f64 x (.f64 x x)))) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)))
(+.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/16 binary64) (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(+.f64 (+.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))) (/.f64 #s(literal -1/2 binary64) x))
(+.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x))))
(+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x)))
(+.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64))
(-.f64 #s(literal -1 binary64) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))))
(-.f64 #s(literal -1 binary64) (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x)) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/16 binary64) (.f64 x (.f64 x x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 (+.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))) (/.f64 #s(literal 1/2 binary64) x))
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (/.f64 #s(literal -3/16 binary64) (.f64 x (.f64 x x))))
(-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x))
(-.f64 (+.f64 (+.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)))) #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x)))
(fma.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x x))) x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)))
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(.f64 #s(literal -3/16 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))
(.f64 #s(literal -3/16 binary64) (pow.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 3/16 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (/.f64 (.f64 x x) #s(literal 3/16 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) #s(literal 3/16 binary64))
(.f64 (/.f64 #s(literal 3/16 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal -3/16 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 (.f64 x x) #s(literal -3/16 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))) #s(literal -3/16 binary64))
(.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1 binary64))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (pow.f64 (/.f64 (.f64 x x) #s(literal -3/16 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/16 binary64) x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 3 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -3 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x x) (exp.f64 (log.f64 x)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(exp.f64 (*.f64 #s(literal -2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal -2 binary64) (log.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 x) #s(literal -1 binary64)) (.f64 (log.f64 x) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(/.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) x)
(pow.f64 x #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -2 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (/.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (exp.f64 (log.f64 x)) #s(literal -1 binary64)) (pow.f64 (exp.f64 (log.f64 x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal -69/1024 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (.f64 x (.f64 x #s(literal -69/1024 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 69/1024 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -69/1024 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 #s(literal -69/1024 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1 binary64))
(.f64 x (.f64 x #s(literal -69/1024 binary64)))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -69/1024 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -69/1024 binary64))))
(.f64 #s(literal -69/1024 binary64) (.f64 x x))
(.f64 (.f64 x (*.f64 x #s(literal -69/1024 binary64))) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal -69/1024 binary64)) x)
(.f64 #s(literal 69/1024 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))

simplify238.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

2400×	`-lowering-.f32`
2400×	`-lowering-.f64`
1882×	`+-lowering-+.f64`
1882×	`+-lowering-+.f32`
1190×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1312
1	412	1115
2	1152	1090
3	3244	1081
4	7595	1081
0	8047	1081

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* 3/16 (/ (sqrt 1/2) (pow x 3)))
(/ (+ (* 1/8 (* x (sqrt 1/2))) (* 3/16 (sqrt 1/2))) (pow x 3))
(/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* -1/2 (* x (sqrt 1/2))) (* 1/8 (sqrt 1/2))))) (pow x 3))
(/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ 1 (* -1 (sqrt 1/2))))))))) (pow x 3))
(+ 1 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))
(+ 1 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))))
(/ 3/16 (pow x 3))
(/ (+ 3/16 (* 1/8 x)) (pow x 3))
(/ (+ 3/16 (* x (+ 1/8 (* -1/2 x)))) (pow x 3))
(/ (+ 3/16 (* x (+ 1/8 (* x (- (* -1 x) 1/2))))) (pow x 3))
-1
(* -1 (+ 1 (* 1/2 (/ 1 x))))
(- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))
(- (+ (/ 1/8 (pow x 2)) (* 3/16 (/ 1 (pow x 3)))) (+ 1 (* 1/2 (/ 1 x))))
-1
(* -1 (+ 1 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 1)
(- (* -1 (/ (+ 1/2 (* -1 (/ (+ 1/8 (* 3/16 (/ 1 x))) x))) x)) 1)
(/ 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)
(* 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))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 11/128 (pow x 2))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2))))
(* -69/1024 (pow x 4))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* -69/1024 (pow x 4))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(* (pow x 4) (- (* 11/128 (/ 1 (pow x 2))) 69/1024))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (pow x 3))
(/ 3/16 (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)
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))
(* -69/1024 (pow x 2))

Outputs
(* 3/16 (/ (sqrt 1/2) (pow x 3)))
(/.f64 (.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (*.f64 x x)))
(/ (+ (* 1/8 (* x (sqrt 1/2))) (* 3/16 (sqrt 1/2))) (pow x 3))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 1/8 binary64)))) (.f64 x (.f64 x x)))
(/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* -1/2 (* x (sqrt 1/2))) (* 1/8 (sqrt 1/2))))) (pow x 3))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 3/16 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal -1/2 binary64)))))) (.f64 x (*.f64 x x)))
(/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ 1 (* -1 (sqrt 1/2))))))))) (pow x 3))
(/.f64 (+.f64 (.f64 (+.f64 x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1/2 binary64) x))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 1/8 binary64))))) (.f64 x (*.f64 x x)))
(+ 1 (* -1 (sqrt 1/2)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))
(+.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(+ 1 (* -1 (sqrt 1/2)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))))
(+.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(/ 3/16 (pow x 3))
(/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x)))
(/ (+ 3/16 (* 1/8 x)) (pow x 3))
(/.f64 (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 1/8 binary64))) (.f64 x (*.f64 x x)))
(/ (+ 3/16 (* x (+ 1/8 (* -1/2 x)))) (pow x 3))
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(* -69/1024 (pow x 2))
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(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
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(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal -69/1024 binary64))
(* -69/1024 (pow x 2))
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eval163.0ms (1%)

Compiler: Compiled 18777 to 2296 computations (87.8% saved)

prune210.0ms (1.3%)

Pruning

28 alts after pruning (17 fresh and 11 done)

	Pruned	Kept	Total
New	989	12	1001
Fresh	1	5	6
Picked	2	3	5
Done	0	8	8
Total	992	28	1020

Accuracy

98.5%

Counts

1020 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.1%	(fma.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)) x)) x)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	98.3%	(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
	26.8%	(/.f64 (+.f64 (.f64 (+.f64 x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1/2 binary64) x))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 1/8 binary64))))) (.f64 x (*.f64 x x)))
	1.3%	(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
	4.3%	(/.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	4.1%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
	4.3%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64)))) #s(literal 1 binary64))
	1.3%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
✓	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	97.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓	96.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	97.1%	(+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 x x) #s(literal 1/8 binary64))) (+.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (*.f64 x x))) x)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
	96.7%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
	97.0%	(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))))
	4.3%	(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
	4.3%	(.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 x (*.f64 x x)))
	2.3%	(.f64 (-.f64 (-.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -69/1024 binary64)))))) (.f64 x (.f64 x #s(literal 11/128 binary64)))) (.f64 x x))
✓	4.1%	(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
✓	1.3%	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
	4.3%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal 1/8 binary64))
	4.3%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/8 binary64))
	4.3%	(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
	1.5%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
✓	4.3%	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	1.3%	(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
✓	3.1%	#s(literal 0 binary64)

Compiler

Compiled 970 to 460 computations (52.6% saved)

regimes82.0ms (0.5%)

Counts

42 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(/.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
(.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 x (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64)))) #s(literal 1 binary64))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/8 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal 1/8 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
(.f64 (-.f64 (-.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -69/1024 binary64)))))) (.f64 x (.f64 x #s(literal 11/128 binary64)))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/16 binary64) x)) x)) x)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (+.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) (/.f64 #s(literal 3/16 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (*.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 x x) #s(literal 1/8 binary64))) (+.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (*.f64 x x))) x)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 (+.f64 (.f64 (+.f64 x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1/2 binary64) x))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 1/8 binary64))))) (.f64 x (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)))))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))

Outputs
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Calls

7 calls:

13.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
12.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
12.0ms	(hypot.f64 #s(literal 1 binary64) x)
12.0ms	x
10.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
98.3%	1	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
98.3%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.3%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.3%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.3%	1	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes12.0ms (0.1%)

Counts

29 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(/.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
(.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 x (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64)))) #s(literal 1 binary64))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/8 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal 1/8 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
(.f64 (-.f64 (-.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -69/1024 binary64)))))) (.f64 x (.f64 x #s(literal 11/128 binary64)))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))

Outputs

(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) x))))

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
97.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes12.0ms (0.1%)

Counts

28 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(/.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
(.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 x (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64)))) #s(literal 1 binary64))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/8 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal 1/8 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
(.f64 (-.f64 (-.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -69/1024 binary64)))))) (.f64 x (.f64 x #s(literal 11/128 binary64)))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))

Outputs
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))))

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
97.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes10.0ms (0.1%)

Counts

26 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(/.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
(.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 x (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64)))) #s(literal 1 binary64))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/8 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal 1/8 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
(.f64 (-.f64 (-.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -69/1024 binary64)))))) (.f64 x (.f64 x #s(literal 11/128 binary64)))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))

Outputs
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
97.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes11.0ms (0.1%)

Counts

25 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(/.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
(.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 x (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64)))) #s(literal 1 binary64))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/8 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal 1/8 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
(.f64 (-.f64 (-.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -69/1024 binary64)))))) (.f64 x (.f64 x #s(literal 11/128 binary64)))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

Outputs
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
96.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes9.0ms (0.1%)

Counts

24 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(/.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
(.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 x (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64)))) #s(literal 1 binary64))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/8 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x #s(literal -11/128 binary64)))) (.f64 x x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal 1/8 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))) (.f64 x x))
(.f64 (-.f64 (-.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -69/1024 binary64)))))) (.f64 x (.f64 x #s(literal 11/128 binary64)))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))))))) #s(literal 1 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
4.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

8 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(/.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
(.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 x (*.f64 x x)))

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
4.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

6 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(/.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
4.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Outputs
#s(literal 0 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
3.1%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

48×	`+-commutative_binary64`
36×	`*-commutative_binary64`
30×	`sub-neg_binary64`
20×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	84
1	74	84
2	93	84
3	115	84
4	137	84
5	144	84
6	148	84
7	149	84

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
#s(literal 0 binary64)

Outputs
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) x) (*.f64 x x))
(.f64 (.f64 x x) (*.f64 x (/.f64 #s(literal 1/8 binary64) x)))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
#s(literal 0 binary64)

soundness2.7s (16.2%)

Rules

4054×	`-lowering-.f32`
4054×	`-lowering-.f64`
4026×	`-lowering-.f32`
4026×	`-lowering-.f64`
3778×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	148
1	114	136
2	373	135
3	1069	134
4	3497	134
0	8077	134
0	12	11
1	29	10
2	37	10
3	45	10
4	53	10
5	66	10
6	83	10
7	97	10
8	109	10
9	110	10
0	110	10
0	145	1312
1	412	1115
2	1152	1090
3	3244	1081
4	7595	1081
0	8047	1081
0	407	2487
1	1321	2067
2	4338	2017
0	8106	2017
0	385	2364
1	1234	1968
2	3947	1926
0	8153	1926
0	169	619
1	503	526
2	1468	510
3	4231	508
0	8068	508
0	31	121
1	124	111
2	565	109
3	4725	109
0	8165	109
0	11	30
1	31	30
2	77	30
3	212	30
4	483	30
5	954	30
6	3612	30
0	8178	30

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit

Compiler

Compiled 288 to 192 computations (33.3% saved)

preprocess82.0ms (0.5%)

Remove: (abs x)
Compiler: Compiled 284 to 172 computations (39.4% saved)

Iter	Nodes	Cost
0	17	35
1	51	30
2	91	30
3	144	30
4	235	30
5	382	30
6	490	30
7	536	30
8	550	30
0	12	11
1	29	10
2	37	10
3	45	10
4	53	10
5	66	10
6	83	10
7	97	10
8	109	10
9	110	10
0	110	10

Iter	Nodes	Cost
0	17	35
1	51	30
2	91	30
3	144	30
4	235	30
5	382	30
6	490	30
7	536	30
8	550	30
0	12	11
1	29	10
2	37	10
3	45	10
4	53	10
5	66	10
6	83	10
7	97	10
8	109	10
9	110	10
0	110	10

analyze1.0ms (0%)

sample9.0s (54.2%)

preprocess28.0ms (0.2%)

explain139.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0%)

localize55.0ms (0.3%)

series46.0ms (0.3%)

rewrite217.0ms (1.3%)

simplify311.0ms (1.9%)

eval23.0ms (0.1%)

prune31.0ms (0.2%)

simplify261.0ms (1.6%)

localize239.0ms (1.4%)

series17.0ms (0.1%)

rewrite256.0ms (1.5%)

simplify307.0ms (1.9%)

eval150.0ms (0.9%)

prune167.0ms (1%)

simplify180.0ms (1.1%)

localize184.0ms (1.1%)

series13.0ms (0.1%)

rewrite236.0ms (1.4%)

simplify281.0ms (1.7%)

eval168.0ms (1%)

prune111.0ms (0.7%)

simplify177.0ms (1.1%)

localize204.0ms (1.2%)

series8.0ms (0%)

rewrite230.0ms (1.4%)

simplify238.0ms (1.4%)

eval163.0ms (1%)

prune210.0ms (1.3%)

regimes82.0ms (0.5%)

regimes12.0ms (0.1%)

regimes12.0ms (0.1%)

regimes10.0ms (0.1%)

regimes11.0ms (0.1%)

regimes9.0ms (0.1%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify12.0ms (0.1%)

soundness2.7s (16.2%)

preprocess82.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	17	35
1	51	30
2	91	30
3	144	30
4	235	30
5	382	30
6	490	30
7	536	30
8	550	30
0	12	11
1	29	10
2	37	10
3	45	10
4	53	10
5	66	10
6	83	10
7	97	10
8	109	10
9	110	10
0	110	10