Metrics for Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

analyze36.0ms (1%)

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
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 34.0ms (99.6% of total)

ival-sub: 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)

sample747.0ms (20.1%)

Results

568.0ms	8256×	0	valid
0.0ms	3×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 294.0ms

ival-mult: 136.0ms (46.2% of total)

ival-sqrt: 92.0ms (31.2% of total)

ival-sub: 51.0ms (17.3% of total)

const: 12.0ms (4.1% of total)

backward-pass: 3.0ms (1% of total)

Bogosity

preprocess424.0ms (11.4%)

Algorithm

2×	egg-herbie

Rules

2210×	`sum3-define`
2022×	`+-lowering-+.f64`
2022×	`+-lowering-+.f32`
1796×	`sum3-define`
1706×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	30	16
2	50	16
3	100	16
4	172	16
5	325	16
6	557	16
7	969	16
8	2606	16
9	4826	16
0	5	5
1	13	5
2	20	5
3	32	5
4	51	5
5	89	5
6	148	5
7	377	5
8	1739	5
9	3818	5
10	6818	5
0	8187	5

Stop Event

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

Calls

Call 1

Inputs
(sqrt (- 1 (* x x)))

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

Call 2

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

Outputs
(sqrt (- 1 (* x x)))
(sqrt (fnmsub x x -1))
(sqrt (- 1 (* (neg x) (neg x))))
(sqrt (fnmsub x x -1))
(neg (sqrt (- 1 (* (neg x) (neg x)))))
(neg (sqrt (fnmsub x x -1)))

Symmetry

(abs x)

explain77.0ms (2.1%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
-	-	`(*.f64 x x)`
-	-	`#s(literal 1 binary64)`
-	-	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`

Results

41.0ms

512×

valid

Compiler

Compiled 43 to 17 computations (60.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 5.0ms (38.7% of total)

ival-sqrt: 4.0ms (31% of total)

ival-sub: 3.0ms (23.2% of total)

const: 1.0ms (7.7% of total)

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

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify294.0ms (7.9%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

2022×	`+-lowering-+.f64`
2022×	`+-lowering-+.f32`
1796×	`sum3-define`
1374×	`sum4-define`
1248×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	13	13
2	20	13
3	32	13
4	51	13
5	89	13
6	148	13
7	377	13
8	1739	13
9	3818	13
10	6818	13
0	8187	13

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (- 1 (* x x)))
(- 1 (* x x))
1
(* x x)
x

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

localize28.0ms (0.8%)

Localize:

Found 3 expressions of interest:

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

Results

21.0ms

256×

valid

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sqrt: 4.0ms (44.1% of total)

ival-mult: 3.0ms (33.1% of total)

ival-sub: 1.0ms (11% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Counts

3 → 36

Calls

Call 1

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

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

Calls

9 calls:

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

rewrite318.0ms (8.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3418×	`/-lowering-/.f32`
3418×	`/-lowering-/.f64`
3212×	`-lowering-.f32`
3212×	`-lowering-.f64`
1494×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	30	11
2	188	11
3	1517	9
0	9350	9

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 308

Calls

Call 1

Inputs
(sqrt (- 1 (* x x)))
(- 1 (* x x))
(* x x)

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

simplify190.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

1960×	`sum4-define`
1860×	`fma-define`
1740×	`sum5-define`
1600×	`-lowering-.f32`
1600×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	292
1	160	241
2	470	229
3	1582	220
4	5772	220
0	8098	220

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 2))
(* (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)
(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)

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64))))))))
(* x (sqrt -1))
(*.f64 x (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) (.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))) x))
(* -1 (* x (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (-.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 #s(literal -1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64)))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval51.0ms (1.4%)

Compiler: Compiled 13851 to 1076 computations (92.2% saved)

prune75.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	340	4	344
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	341	4	345

Accuracy

100.0%

Counts

345 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64))))))))
▶	100.0%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
▶	99.7%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
▶	99.2%	#s(literal 1 binary64)

Compiler

Compiled 44 to 30 computations (31.8% saved)

simplify36.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64))))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64)))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64))))))))
✓	cost-diff	(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 #s(literal -1/2 binary64) (.f64 x x))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))

Rules

856×	`fma-define`
672×	`fma-lowering-fma.f32`
672×	`fma-lowering-fma.f64`
242×	`-lowering-.f32`
242×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	122
1	61	108
2	203	108
3	473	108
4	776	108
5	954	108
6	980	108
0	980	108

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (* x x)))
1
(* -1/2 (* x x))
-1/2
(* x x)
x
(+ 1 (* (* x x) (+ -1/2 (* (* x x) -1/8))))
1
(* (* x x) (+ -1/2 (* (* x x) -1/8)))
(* x x)
x
(+ -1/2 (* (* x x) -1/8))
-1/2
(* (* x x) -1/8)
-1/8
(+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16)))))))
1
(* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16))))))
(* x x)
x
(+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16)))))
-1/2
(* (* x x) (+ -1/8 (* x (* x -1/16))))
(+ -1/8 (* x (* x -1/16)))
-1/8
(* x (* x -1/16))
(* x -1/16)
-1/16

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* x x)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
1
#s(literal 1 binary64)
(* -1/2 (* x x))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
x
(+ 1 (* (* x x) (+ -1/2 (* (* x x) -1/8))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64)))))))
1
#s(literal 1 binary64)
(* (* x x) (+ -1/2 (* (* x x) -1/8)))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64))))))
(* x x)
(*.f64 x x)
x
(+ -1/2 (* (* x x) -1/8))
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64))))
-1/2
#s(literal -1/2 binary64)
(* (* x x) -1/8)
(.f64 x (.f64 x #s(literal -1/8 binary64)))
-1/8
#s(literal -1/8 binary64)
(+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16)))))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64))))))))
1
#s(literal 1 binary64)
(* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))))
(* x x)
(*.f64 x x)
x
(+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16)))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))
-1/2
#s(literal -1/2 binary64)
(* (* x x) (+ -1/8 (* x (* x -1/16))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64))))
(+ -1/8 (* x (* x -1/16)))
(+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))
-1/8
#s(literal -1/8 binary64)
(* x (* x -1/16))
(.f64 (.f64 x x) #s(literal -1/16 binary64))
(* x -1/16)
(*.f64 x #s(literal -1/16 binary64))
-1/16
#s(literal -1/16 binary64)

localize113.0ms (3.1%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 x #s(literal -1/16 binary64))
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64)))))
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64)))))))
✓	accuracy	100.0%	(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal -1/8 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal -1/2 binary64) (.f64 x x))

Results

83.0ms

256×

valid

Compiler

Compiled 147 to 20 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 24.0ms (74.7% of total)

ival-add: 7.0ms (21.8% of total)

const: 1.0ms (3.1% of total)

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

series8.0ms (0.2%)

Counts

12 → 144

Calls

Call 1

Inputs
#<alt (+ 1 (* -1/2 (* x x)))>
#<alt (* -1/2 (* x x))>
#<alt (* x x)>
#<alt (+ 1 (* (* x x) (+ -1/2 (* (* x x) -1/8))))>
#<alt (* (* x x) (+ -1/2 (* (* x x) -1/8)))>
#<alt (+ -1/2 (* (* x x) -1/8))>
#<alt (+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16)))))))>
#<alt (* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16))))))>
#<alt (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16)))))>
#<alt (* (* x x) -1/8)>
#<alt (* (* x x) (+ -1/8 (* x (* x -1/16))))>
#<alt (* x -1/16)>

Outputs
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (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>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (* -1/8 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1/8 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))>
#<alt (* -1/8 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1/8 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt -1/2>
#<alt (- (* -1/8 (pow x 2)) 1/2)>
#<alt (- (* -1/8 (pow x 2)) 1/2)>
#<alt (- (* -1/8 (pow x 2)) 1/2)>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* -1/16 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<alt (* (pow x 6) (- (/ 1 (pow x 6)) (+ 1/16 (+ (/ 1/2 (pow x 4)) (* 1/8 (/ 1 (pow x 2)))))))>
#<alt (* -1/16 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<alt (* (pow x 6) (- (/ 1 (pow x 6)) (+ 1/16 (+ (/ 1/2 (pow x 4)) (* 1/8 (/ 1 (pow x 2)))))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))>
#<alt (* -1/16 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<alt (* -1/16 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<alt -1/2>
#<alt (- (* -1/8 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)>
#<alt (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)>
#<alt (* -1/16 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<alt (* -1/16 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))>
#<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) (- (* -1/16 (pow x 2)) 1/8))>
#<alt (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8))>
#<alt (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8))>
#<alt (* -1/16 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/16 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>
#<alt (* -1/16 x)>

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16)))))))
0.0ms	x	@	inf	(+ 1 (* (* x x) (+ -1/2 (* (* x x) -1/8))))
0.0ms	x	@	inf	(+ 1 (* -1/2 (* x x)))
0.0ms	x	@	inf	(* (* x x) -1/8)
0.0ms	x	@	inf	(* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16))))))

rewrite362.0ms (9.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3916×	`-lowering-.f32`
3916×	`-lowering-.f64`
2788×	`/-lowering-/.f32`
2788×	`/-lowering-/.f64`
2328×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	95
1	133	82
2	1290	82
0	8112	82

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 382

Calls

Call 1

Inputs
(+ 1 (* -1/2 (* x x)))
(* -1/2 (* x x))
(* x x)
(+ 1 (* (* x x) (+ -1/2 (* (* x x) -1/8))))
(* (* x x) (+ -1/2 (* (* x x) -1/8)))
(+ -1/2 (* (* x x) -1/8))
(+ 1 (* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16)))))))
(* (* x x) (+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16))))))
(+ -1/2 (* (* x x) (+ -1/8 (* x (* x -1/16)))))
(* (* x x) -1/8)
(* (* x x) (+ -1/8 (* x (* x -1/16))))
(* x -1/16)

Outputs
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal -1/2 binary64) x))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
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(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/16 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))) (neg.f64 (-.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -1/16 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/4096 binary64))))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/16 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal -1/16 binary64)) #s(literal -1/8 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/256 binary64))))) (neg.f64 (-.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/4096 binary64))) (.f64 x x))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/16 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal -1/16 binary64)) #s(literal -1/8 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/256 binary64))) (.f64 x x))) (neg.f64 (-.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/4096 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/16 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/16 binary64)))) (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/16 binary64))) (.f64 x (.f64 x #s(literal -1/8 binary64)))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64))))
(.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))) x)
(*.f64 x #s(literal -1/16 binary64))
(*.f64 #s(literal -1/16 binary64) x)

simplify222.0ms (6%)

Algorithm

1×	egg-herbie

Rules

2374×	`-lowering-.f32`
2374×	`-lowering-.f64`
2194×	`+-lowering-+.f64`
2194×	`+-lowering-+.f32`
1276×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	1124
1	167	960
2	541	922
3	1544	894
4	3935	894
0	8152	894

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (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)
(pow x 2)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(* -1/8 (pow x 4))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1/8 (pow x 4))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))
(* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))
(* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))
(* -1/8 (pow x 4))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1/8 (pow x 4))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
-1/2
(- (* -1/8 (pow x 2)) 1/2)
(- (* -1/8 (pow x 2)) 1/2)
(- (* -1/8 (pow x 2)) 1/2)
(* -1/8 (pow x 2))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1/8 (pow x 2))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* -1/16 (pow x 6))
(* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(* (pow x 6) (- (/ 1 (pow x 6)) (+ 1/16 (+ (/ 1/2 (pow x 4)) (* 1/8 (/ 1 (pow x 2)))))))
(* -1/16 (pow x 6))
(* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(* (pow x 6) (- (/ 1 (pow x 6)) (+ 1/16 (+ (/ 1/2 (pow x 4)) (* 1/8 (/ 1 (pow x 2)))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))
(* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))
(* -1/16 (pow x 6))
(* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(* -1/16 (pow x 6))
(* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
-1/2
(- (* -1/8 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)
(- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)
(* -1/16 (pow x 4))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(* -1/16 (pow x 4))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(* -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) (- (* -1/16 (pow x 2)) 1/8))
(* (pow x 2) (- (* -1/16 (pow x 2)) 1/8))
(* (pow x 2) (- (* -1/16 (pow x 2)) 1/8))
(* -1/16 (pow x 4))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* -1/16 (pow x 4))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)
(* -1/16 x)

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+ 1 (* (pow x 2) (- (* -1/8 (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 -1/8 binary64))))))
(+ 1 (* (pow x 2) (- (* -1/8 (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 -1/8 binary64))))))
(* -1/8 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))))
(* -1/8 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* -1/8 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* -1/8 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
-1/2
#s(literal -1/2 binary64)
(- (* -1/8 (pow x 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(- (* -1/8 (pow x 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(- (* -1/8 (pow x 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+ 1 (* (pow x 2) (- (* -1/8 (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 -1/8 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64))))))))
(* -1/16 (pow x 6))
(*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64)))
(* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 x x))))
(* (pow x 6) (- (/ 1 (pow x 6)) (+ 1/16 (+ (/ 1/2 (pow x 4)) (* 1/8 (/ 1 (pow x 2)))))))
(+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* -1/16 (pow x 6))
(*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64)))
(* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 x x))))
(* (pow x 6) (- (/ 1 (pow x 6)) (+ 1/16 (+ (/ 1/2 (pow x 4)) (* 1/8 (/ 1 (pow x 2)))))))
(+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))))
(* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))))
(* -1/16 (pow x 6))
(*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64)))
(* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 x x))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 x x))))
(* -1/16 (pow x 6))
(*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64)))
(* -1 (* (pow x 6) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 x x))))
(* (pow x 6) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 x x))))
-1/2
#s(literal -1/2 binary64)
(- (* -1/8 (pow x 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))
(- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64)))))
(* -1/16 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/16 binary64))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 x x))))
(* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 x x))))
(* -1/16 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/16 binary64))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 x x))))
(* (pow x 4) (- (* -1 (/ (+ 1/8 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/16))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 x x))))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* (pow x 2) (- (* -1/16 (pow x 2)) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64))))
(* (pow x 2) (- (* -1/16 (pow x 2)) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64))))
(* (pow x 2) (- (* -1/16 (pow x 2)) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/16 binary64))))
(* -1/16 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/16 binary64))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(* -1/16 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/16 binary64))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(* -1 (* (pow x 4) (+ 1/16 (* 1/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))
(* -1/16 x)
(*.f64 x #s(literal -1/16 binary64))

eval230.0ms (6.2%)

Compiler: Compiled 18522 to 1357 computations (92.7% saved)

prune59.0ms (1.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	598	0	598
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	598	4	602

Accuracy

100.0%

Counts

602 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64))))))))
✓	100.0%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
✓	99.7%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	99.2%	#s(literal 1 binary64)

Compiler

Compiled 91 to 51 computations (44% saved)

regimes26.0ms (0.7%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64))))))))

Calls

4 calls:

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

Results

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes3.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs

#s(literal 1 binary64)

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

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

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

Calls

2 calls:

2.0ms	x
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes3.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	x
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(*.f64 x x)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	35	40

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64))))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
#s(literal 1 binary64)

Outputs
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/16 binary64))))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(literal 1 binary64)

soundness356.0ms (9.6%)

Rules

1960×	`sum4-define`
1860×	`fma-define`
1740×	`sum5-define`
1600×	`-lowering-.f32`
1600×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	292
1	160	241
2	470	229
3	1582	220
4	5772	220
0	8098	220

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 85 to 49 computations (42.4% saved)

preprocess31.0ms (0.8%)

Remove: (abs x)
Compiler: Compiled 176 to 100 computations (43.2% saved)

Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

analyze36.0ms (1%)

sample747.0ms (20.1%)

preprocess424.0ms (11.4%)

explain77.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify294.0ms (7.9%)

localize28.0ms (0.8%)

series2.0ms (0.1%)

rewrite318.0ms (8.6%)

simplify190.0ms (5.1%)

eval51.0ms (1.4%)

prune75.0ms (2%)

simplify36.0ms (1%)

localize113.0ms (3.1%)

series8.0ms (0.2%)

rewrite362.0ms (9.8%)

simplify222.0ms (6%)

eval230.0ms (6.2%)

prune59.0ms (1.6%)

regimes26.0ms (0.7%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes1.0ms (0%)

simplify9.0ms (0.2%)

soundness356.0ms (9.6%)

preprocess31.0ms (0.8%)

end0.0ms (0%)

Profiling