Metrics for invcot (example 3.9)

analyze9.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.7%	50.3%	0%	0%	0%	0
0%	0%	49.7%	50.3%	0%	0%	0%	1
0%	0%	49.7%	50.3%	0%	0%	0%	2
25%	12.4%	37.3%	50.3%	0%	0%	0%	3
62.5%	31.1%	18.6%	50.3%	0%	0%	0%	4
81.3%	40.4%	9.3%	50.3%	0%	0%	0%	5
90.6%	45%	4.7%	50.3%	0%	0%	0%	6
95.3%	47.4%	2.3%	50.3%	0%	0%	0%	7
97.7%	48.5%	1.2%	50.3%	0%	0%	0%	8
98.8%	49.1%	0.6%	50.3%	0%	0%	0%	9
99.4%	49.4%	0.3%	50.3%	0%	0%	0%	10
99.7%	49.5%	0.1%	50.3%	0%	0%	0%	11
99.9%	49.6%	0.1%	50.3%	0%	0%	0%	12

Compiler

Compiled 16 to 11 computations (31.3% saved)

Precisions

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

...c/correct-round.rkt:119:19: 3.0ms (57.2% of total)

ival-div: 1.0ms (19.1% of total)

ival-tan: 1.0ms (19.1% of total)

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

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

const: 0.0ms (0% of total)

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

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

sample7.2s (65.7%)

Results

4.9s	4441×	2	valid
1.2s	1358×	3	valid
628.0ms	2409×	1	valid
7.0ms	48×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 5.9s

ival-tan: 4.4s (74% of total)

...c/correct-round.rkt:119:19: 529.0ms (9% of total)

ival-div: 488.0ms (8.3% of total)

backward-pass: 276.0ms (4.7% of total)

ival-sub: 131.0ms (2.2% of total)

ival-<: 73.0ms (1.2% of total)

const: 18.0ms (0.3% of total)

ival-and: 18.0ms (0.3% of total)

Bogosity

preprocess40.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

156×	`fnmadd-define`
138×	`sum3-define`
112×	`fma-lowering-fma.f32`
112×	`fnmsub-define`
112×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	29	19
2	64	18
3	146	18
4	300	18
5	464	18
6	507	18
7	515	18
0	6	6
1	12	6
2	20	6
3	31	6
4	45	6
5	82	6
6	152	6
7	248	6
8	350	6
9	486	6
10	607	6
11	639	6
0	639	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (/ 1 x) (/ 1 (tan x)))

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

Call 2

Inputs
(- (/ 1 x) (/ 1 (tan x)))
(- (/ 1 (neg x)) (/ 1 (tan (neg x))))
(neg (- (/ 1 (neg x)) (/ 1 (tan (neg x)))))

Outputs
(- (/ 1 x) (/ 1 (tan x)))
(- (recip x) (recip (tan x)))
(- (/ 1 (neg x)) (/ 1 (tan (neg x))))
(- (recip (tan x)) (recip x))
(neg (- (/ 1 (neg x)) (/ 1 (tan (neg x)))))
(- (recip x) (recip (tan x)))

Symmetry

(negabs x)

explain485.0ms (4.4%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`
0	-	-	`x`
0	-	-	`(/.f64 #s(literal 1 binary64) (tan.f64 x))`
0	-	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(tan.f64 x)`

Results

295.0ms	286×	2	valid
76.0ms	96×	3	valid
74.0ms	128×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 355.0ms

ival-tan: 254.0ms (71.5% of total)

ival-sub: 54.0ms (15.2% of total)

ival-div: 27.0ms (7.6% of total)

backward-pass: 19.0ms (5.4% of total)

const: 2.0ms (0.6% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.4%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

156×	`fnmadd-define`
138×	`sum3-define`
112×	`fma-lowering-fma.f32`
112×	`fnmsub-define`
112×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	12	15
2	20	15
3	31	15
4	45	15
5	82	15
6	152	15
7	248	15
8	350	15
9	486	15
10	607	15
11	639	15
0	639	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (/ 1 x) (/ 1 (tan x)))
(/ 1 x)
1
x
(/ 1 (tan x))
(tan x)

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

localize233.0ms (2.1%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(tan.f64 x)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (tan.f64 x))
✓	accuracy	6.4%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

153.0ms	143×	2	valid
40.0ms	48×	3	valid
14.0ms	64×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 167.0ms

ival-tan: 139.0ms (83% of total)

ival-div: 14.0ms (8.4% of total)

backward-pass: 9.0ms (5.4% of total)

ival-sub: 4.0ms (2.4% of total)

const: 1.0ms (0.6% of total)

series4.0ms (0%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (- (/ 1 x) (/ 1 (tan x)))>
#<alt (/ 1 x)>
#<alt (/ 1 (tan x))>
#<alt (tan x)>

Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/3 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- (/ 1 x) (/ 1 (tan x)))
1.0ms	x	@	-inf	(- (/ 1 x) (/ 1 (tan x)))
1.0ms	x	@	0	(- (/ 1 x) (/ 1 (tan x)))
0.0ms	x	@	-inf	(/ 1 (tan x))
0.0ms	x	@	inf	(/ 1 (tan x))

rewrite162.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2244×	`/-lowering-/.f32`
2244×	`/-lowering-/.f64`
2150×	`-lowering-.f32`
2150×	`-lowering-.f64`
752×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	34	13
2	184	13
3	1035	13
0	8029	13

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 476

Calls

Call 1

Inputs
(- (/ 1 x) (/ 1 (tan x)))
(/ 1 x)
(/ 1 (tan x))
(tan x)

Outputs
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) (-.f64 #s(literal 0 binary64) x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) (-.f64 #s(literal 0 binary64) (+.f64 x (.f64 x #s(literal 0 binary64))))))
(+.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (.f64 x #s(literal 0 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) #s(literal 0 binary64))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (fma.f64 (cos.f64 x) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) x)))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) x)))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (fma.f64 (/.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) x) x (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (fma.f64 (/.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) (.f64 x #s(literal 0 binary64))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 0 binary64)))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (.f64 (.f64 x #s(literal 0 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (.f64 (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 0 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x))))
(+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))))
(+.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(+.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(+.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) (.f64 x #s(literal 0 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(+.f64 (.f64 (.f64 x #s(literal 0 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x))) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 x (.f64 x #s(literal 0 binary64))) (.f64 x (tan.f64 x))))
(-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x))
(-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (-.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64)))
(-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))))
(-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x)))
(-.f64 #s(literal 0 binary64) (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x)) #s(literal 0 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x)))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x)))
(-.f64 (/.f64 (.f64 (tan.f64 x) (.f64 x (tan.f64 x))) (pow.f64 (.f64 x (tan.f64 x)) #s(literal 2 binary64))) (/.f64 (.f64 (tan.f64 x) (.f64 x x)) (pow.f64 (.f64 x (tan.f64 x)) #s(literal 2 binary64))))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (tan.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 (tan.f64 x) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (sin.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x (tan.f64 x))) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x)) #s(literal 0 binary64))
(fma.f64 (-.f64 (tan.f64 x) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (-.f64 x (tan.f64 x)) (/.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) x) #s(literal 0 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) (-.f64 (tan.f64 x) x) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (+.f64 (/.f64 (tan.f64 x) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (sin.f64 x) x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 (sin.f64 x) (tan.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (cos.f64 x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (+.f64 (/.f64 (tan.f64 x) x) #s(literal -1 binary64)) (sin.f64 x)) (cos.f64 x) #s(literal 0 binary64))
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(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 #s(literal -1 binary64) (.f64 (.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1 binary64) (.f64 (.f64 x (tan.f64 x)) (/.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))))
(/.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (/.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 x (cos.f64 x)) (.f64 x (sin.f64 x)))
(/.f64 (/.f64 x (tan.f64 x)) x)
(/.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) x) (tan.f64 x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) x) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (/.f64 x (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (/.f64 x (sin.f64 x)) (/.f64 x (cos.f64 x)))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x))) (/.f64 #s(literal -1 binary64) x))
(pow.f64 (tan.f64 x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (tan.f64 x)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 x (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) x))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x))))
(*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)) x)
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x))
(*.f64 (/.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 x (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (pow.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(*.f64 (/.f64 x (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(*.f64 (/.f64 x (sin.f64 x)) (/.f64 (cos.f64 x) x))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (cos.f64 x))
(*.f64 (/.f64 x (-.f64 #s(literal 0 binary64) (sin.f64 x))) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (sin.f64 x)))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (sin.f64 x)) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (/.f64 (cos.f64 x) x))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(+.f64 (tan.f64 x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (tan.f64 x))
(exp.f64 (log.f64 (tan.f64 x)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(-.f64 #s(literal 0 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal 0 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(tan.f64 x)
(fma.f64 #s(literal 1 binary64) (tan.f64 x) #s(literal 0 binary64))
(fma.f64 (tan.f64 x) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) #s(literal 0 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(neg.f64 (tan.f64 (-.f64 #s(literal 0 binary64) x)))
(neg.f64 (.f64 (.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) (/.f64 #s(literal 1 binary64) x)))
(neg.f64 (.f64 (.f64 x (tan.f64 x)) (/.f64 #s(literal -1 binary64) x)))
(neg.f64 (/.f64 (*.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) x))
(neg.f64 (/.f64 (*.f64 x (tan.f64 x)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 x (/.f64 x (tan.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 x)))
(/.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (sin.f64 x) (*.f64 x (/.f64 (cos.f64 x) x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 (*.f64 x (tan.f64 x)) x)
(/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (*.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(/.f64 (*.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 x (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(/.f64 (.f64 x (sin.f64 x)) (.f64 x (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 (cos.f64 x) x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (sin.f64 x))) (/.f64 (.f64 x (cos.f64 x)) #s(literal -1 binary64)))
(/.f64 (/.f64 (tan.f64 x) x) (/.f64 #s(literal 1 binary64) x))
(/.f64 (exp.f64 (log.f64 (sin.f64 x))) (exp.f64 (log.f64 (cos.f64 x))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)))) (exp.f64 (log.f64 #s(literal -1 binary64))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (.f64 (.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(/.f64 (/.f64 (*.f64 x (tan.f64 x)) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(/.f64 (.f64 (.f64 x (sin.f64 x)) (/.f64 #s(literal 1 binary64) x)) (cos.f64 x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (sin.f64 x))) (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(pow.f64 (tan.f64 x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 x (/.f64 (tan.f64 x) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (tan.f64 x)))
(*.f64 (tan.f64 x) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (sin.f64 x) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(.f64 (sin.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 (sin.f64 x) (.f64 (/.f64 x (cos.f64 x)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (sin.f64 x) (/.f64 (/.f64 x (cos.f64 x)) x))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(.f64 #s(literal -1 binary64) (.f64 (*.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) (/.f64 #s(literal 1 binary64) x)))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) x))
(.f64 (.f64 x (tan.f64 x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal -1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (/.f64 (-.f64 #s(literal 0 binary64) x) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) x))
(.f64 (.f64 x (-.f64 #s(literal 0 binary64) (tan.f64 x))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(.f64 (.f64 x (sin.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) x))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (sin.f64 x))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(*.f64 (exp.f64 (log.f64 (sin.f64 x))) (exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (.f64 (*.f64 x (tan.f64 x)) (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(.f64 (/.f64 (.f64 x (tan.f64 x)) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))

simplify183.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

2512×	`-lowering-.f32`
2512×	`-lowering-.f64`
2470×	`sum3-define`
1924×	`+-lowering-+.f64`
1924×	`+-lowering-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	302
1	186	269
2	560	266
3	1806	266
4	2709	266
5	4422	266
6	6045	266
7	6589	266
0	8077	266

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/3 binary64)))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))))) x)
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 2/15 binary64)))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

eval57.0ms (0.5%)

Compiler: Compiled 7695 to 1240 computations (83.9% saved)

prune59.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	521	3	524
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	522	3	525

Accuracy

99.5%

Counts

525 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
▶	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
▶	99.0%	(*.f64 #s(literal 1/3 binary64) x)

Status

Accuracy

Program

▶

99.5%

(*.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/45 binary64) (*.f64 (*.f64 x x) #s(literal -2/945 binary64))))))

▶

99.4%

(*.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))))

▶

99.0%

(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify116.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))
✓	cost-diff	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
✓	cost-diff	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) #s(literal -1/45 binary64))
✓	cost-diff	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
✓	cost-diff	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	cost-diff	(*.f64 #s(literal 1/3 binary64) x)

Rules

2142×	`sum3-define`
2072×	`sum4-define`
1540×	`fnmsub-define`
1424×	`fmsub-define`
1386×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	77
1	42	73
2	131	69
3	417	69
4	1198	69
5	2396	69
6	5132	69
7	7879	69
0	8039	69

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* 1/3 x)
1/3
x
(* x (- 1/3 (* (* x x) -1/45)))
x
(- 1/3 (* (* x x) -1/45))
1/3
(* (* x x) -1/45)
(* x x)
-1/45
(* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))
x
(- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))
1/3
(* (* x x) (+ -1/45 (* (* x x) -2/945)))
(* x x)
(+ -1/45 (* (* x x) -2/945))
-1/45
(* (* x x) -2/945)
-2/945

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
1/3
#s(literal 1/3 binary64)
x
(* x (- 1/3 (* (* x x) -1/45)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
x
(- 1/3 (* (* x x) -1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))
1/3
#s(literal 1/3 binary64)
(* (* x x) -1/45)
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* x x)
(*.f64 x x)
-1/45
#s(literal -1/45 binary64)
(* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
x
(- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
1/3
#s(literal 1/3 binary64)
(* (* x x) (+ -1/45 (* (* x x) -2/945)))
(.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* x x)
(*.f64 x x)
(+ -1/45 (* (* x x) -2/945))
(-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))
-1/45
#s(literal -1/45 binary64)
(* (* x x) -2/945)
(.f64 x (.f64 x #s(literal -2/945 binary64)))
-2/945
#s(literal -2/945 binary64)

localize85.0ms (0.8%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal -2/945 binary64))
✓	accuracy	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal -1/45 binary64))
✓	accuracy	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	accuracy	99.5%	(*.f64 #s(literal 1/3 binary64) x)

Results

63.0ms

256×

valid

Compiler

Compiled 92 to 15 computations (83.7% saved)

Precisions

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

ival-mult: 12.0ms (47% of total)

...c/correct-round.rkt:119:19: 10.0ms (39.1% of total)

ival-sub: 2.0ms (7.8% of total)

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

const: 0.0ms (0% of total)

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

series10.0ms (0.1%)

Counts

9 → 108

Calls

Call 1

Inputs
#<alt (* 1/3 x)>
#<alt (* x (- 1/3 (* (* x x) -1/45)))>
#<alt (- 1/3 (* (* x x) -1/45))>
#<alt (* (* x x) -1/45)>
#<alt (* x x)>
#<alt (* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))>
#<alt (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))>
#<alt (* (* x x) (+ -1/45 (* (* x x) -2/945)))>
#<alt (* (* x x) -2/945)>

Outputs
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt 1/3>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (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 (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt 1/3>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))>
#<alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1/45 (pow x 2))>
#<alt (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* (* x x) (+ -1/45 (* (* x x) -2/945)))
1.0ms	x	@	0	(- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))
1.0ms	x	@	0	(* 1/3 x)
1.0ms	x	@	inf	(* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))
0.0ms	x	@	inf	(* x (- 1/3 (* (* x x) -1/45)))

rewrite123.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2100×	`fnmadd-define`
1858×	`sum3-define`
1428×	`fma-define`
1410×	`fma-lowering-fma.f32`
1410×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	44	57
2	136	53
3	436	53
4	1673	53
5	5627	53
0	8590	53

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 297

Calls

Call 1

Inputs
(* 1/3 x)
(* x (- 1/3 (* (* x x) -1/45)))
(- 1/3 (* (* x x) -1/45))
(* (* x x) -1/45)
(* x x)
(* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))
(- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))
(* (* x x) (+ -1/45 (* (* x x) -2/945)))
(* (* x x) -2/945)

Outputs
(+.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 0 binary64))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/3 binary64)))
(neg.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
(+.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal -1/3 binary64) x)))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1/45 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x #s(literal -1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x #s(literal -1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) #s(literal -1 binary64) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal -1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(neg.f64 (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(neg.f64 (+.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal -1/3 binary64) x)))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(neg.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 0 binary64) x)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))) x)
(.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(.f64 (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)) (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) #s(literal 0 binary64))
(+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal 1/3 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(-.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))
(-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
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(.f64 (+.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) #s(literal -1/3 binary64)) (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)))
(+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)) (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x))))))
(+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))) #s(literal 0 binary64))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal 1/3 binary64))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) (+.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)) (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/3 binary64)))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) (+.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (.f64 x (.f64 x #s(literal -1/45 binary64)))) #s(literal 1/3 binary64)))
(+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64))))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64))) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(-.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x)))))
(-.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))) #s(literal 0 binary64))
(-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal -1/3 binary64))
(-.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (+.f64 (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/3 binary64)))
(-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(-.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64))) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal -1/3 binary64)))
(fma.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) #s(literal 1/3 binary64))
(fma.f64 x (.f64 x #s(literal 1/45 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 x (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))) #s(literal 1/3 binary64))
(fma.f64 (.f64 x x) #s(literal 1/45 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 #s(literal -1/45 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 #s(literal -2/945 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))) (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 1/3 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -1/45 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x #s(literal -2/945 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))) #s(literal 1/3 binary64))
(fma.f64 (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 (.f64 x #s(literal -2/945 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) (-.f64 #s(literal 0 binary64) x) #s(literal 1/3 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 #s(literal -1 binary64) (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(fma.f64 #s(literal -1 binary64) (+.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal -1/3 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal 1/3 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -1/45 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) #s(literal 1/3 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (.f64 x x) (.f64 x #s(literal -2/945 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 1/45 binary64) (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) x #s(literal 1/3 binary64))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
(fma.f64 (.f64 (.f64 x x) (.f64 x #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 2/945 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))) x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal -2/945 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x #s(literal 2/945 binary64)) (.f64 x (.f64 x x)) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 x #s(literal -2/945 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal -1 binary64) #s(literal 1/3 binary64))
(neg.f64 (+.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal -1/3 binary64)))
(.f64 #s(literal -1 binary64) (+.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) #s(literal -1/3 binary64)))
(+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(+.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal 0 binary64))
(+.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(+.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(-.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)))
(-.f64 (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(-.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal 0 binary64))
(fma.f64 x (.f64 x #s(literal -1/45 binary64)) (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) #s(literal 0 binary64))
(fma.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -2/945 binary64))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x x) #s(literal -1/45 binary64) (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -2/945 binary64))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))) #s(literal 0 binary64))
(fma.f64 #s(literal -1/45 binary64) (.f64 x x) (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) (.f64 x x) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))) (*.f64 x x) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x #s(literal 2/945 binary64))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x #s(literal -2/945 binary64)) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) x #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)) #s(literal -1 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 (.f64 x x) (.f64 x #s(literal -2/945 binary64))) x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -2/945 binary64)) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -2/945 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(fma.f64 #s(literal 2/945 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))) (-.f64 #s(literal 0 binary64) x) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 2/945 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (.f64 x #s(literal 2/945 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 x #s(literal 2/945 binary64)) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(.f64 x (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(.f64 (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))) (.f64 x x))
(.f64 (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) x)
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(neg.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(.f64 #s(literal -2/945 binary64) (.f64 x x))
(.f64 (.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 2/945 binary64))
(.f64 (.f64 x #s(literal -2/945 binary64)) x)
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 2/945 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64))))
(.f64 #s(literal 2/945 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal -1 binary64))
(.f64 (.f64 x #s(literal 2/945 binary64)) (-.f64 #s(literal 0 binary64) x))

simplify167.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1974×	`-lowering-.f32`
1974×	`-lowering-.f64`
1746×	`fma-lowering-fma.f32`
1746×	`fma-lowering-fma.f64`
1464×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	717
1	159	568
2	476	568
3	1228	568
4	2571	562
5	6227	562
0	8081	562

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (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)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* -1/45 (pow x 2))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(* -2/945 (pow x 4))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 4))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(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)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(* 2/945 (pow x 4))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(* 2/945 (pow x 4))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(* -2/945 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(* -2/945 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))
(* -2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal -2/945 binary64))

eval50.0ms (0.5%)

Compiler: Compiled 7011 to 862 computations (87.7% saved)

prune38.0ms (0.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	469	2	471
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	469	5	474

Accuracy

99.5%

Counts

474 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
▶	99.4%	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
✓	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	99.0%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 64 to 42 computations (34.4% saved)

simplify144.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
✓	cost-diff	384	(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	cost-diff	0	(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) x)
✓	cost-diff	128	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))

Rules

2516×	`sum3-define`
1948×	`fma-lowering-fma.f32`
1948×	`fma-lowering-fma.f64`
1794×	`fmsub-define`
1756×	`sum5-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	98
1	51	82
2	147	82
3	382	79
4	666	79
5	1214	79
6	2218	79
7	5686	79
0	8075	79

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(- (* 1/3 x) (* x (* x (* x -1/45))))
(* 1/3 x)
1/3
x
(* x (* x (* x -1/45)))
(* x (* x -1/45))
(* x -1/45)
-1/45
(- (* x (+ 1/3 (* (* x (* x (* x x))) 2/945))) (* x (* x (* x -1/45))))
(* x (+ 1/3 (* (* x (* x (* x x))) 2/945)))
x
(+ 1/3 (* (* x (* x (* x x))) 2/945))
1/3
(* (* x (* x (* x x))) 2/945)
(* x (* x (* x x)))
(* x (* x x))
(* x x)
2/945
(* x (* x (* x -1/45)))
(* x (* x -1/45))
(* x -1/45)
-1/45

Outputs
(- (* 1/3 x) (* x (* x (* x -1/45))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
1/3
#s(literal 1/3 binary64)
x
(* x (* x (* x -1/45)))
(.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x x)))
(* x (* x -1/45))
(.f64 #s(literal -1/45 binary64) (.f64 x x))
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(- (* x (+ 1/3 (* (* x (* x (* x x))) 2/945))) (* x (* x (* x -1/45))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* (* x (* x (* x x))) 2/945)))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -2/945 binary64))))
x
(+ 1/3 (* (* x (* x (* x x))) 2/945))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
1/3
#s(literal 1/3 binary64)
(* (* x (* x (* x x))) 2/945)
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* x (* x (* x x)))
(.f64 x (.f64 x (*.f64 x x)))
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
2/945
#s(literal 2/945 binary64)
(* x (* x (* x -1/45)))
(.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x x)))
(* x (* x -1/45))
(.f64 #s(literal -1/45 binary64) (.f64 x x))
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)

localize236.0ms (2.2%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.9%	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.5%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64))))
✓	accuracy	99.9%	(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
✓	accuracy	99.9%	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.5%	(*.f64 #s(literal 1/3 binary64) x)

Results

79.0ms

256×

valid

Compiler

Compiled 122 to 17 computations (86.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 14.0ms (49% of total)

...c/correct-round.rkt:119:19: 10.0ms (35% of total)

ival-sub: 2.0ms (7% of total)

ival-add: 1.0ms (3.5% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (- (* 1/3 x) (* x (* x (* x -1/45))))>
#<alt (* 1/3 x)>
#<alt (* x (* x (* x -1/45)))>
#<alt (* x (* x -1/45))>
#<alt (- (* x (+ 1/3 (* (* x (* x (* x x))) 2/945))) (* x (* x (* x -1/45))))>
#<alt (* x (+ 1/3 (* (* x (* x (* x x))) 2/945)))>
#<alt (+ 1/3 (* (* x (* x (* x x))) 2/945))>
#<alt (* (* x (* x (* x x))) 2/945)>
#<alt (* x -1/45)>
#<alt (* x (* x x))>

Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 2/945 (pow x 4))))>
#<alt (* x (+ 1/3 (* 2/945 (pow x 4))))>
#<alt (* x (+ 1/3 (* 2/945 (pow x 4))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt 1/3>
#<alt (+ 1/3 (* 2/945 (pow x 4)))>
#<alt (+ 1/3 (* 2/945 (pow x 4)))>
#<alt (+ 1/3 (* 2/945 (pow x 4)))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* 2/945 (pow x 4))>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<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)>

Calls

30 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(- (* 1/3 x) (* x (* x (* x -1/45))))
0.0ms	x	@	-inf	(- (* x (+ 1/3 (* (* x (* x (* x x))) 2/945))) (* x (* x (* x -1/45))))
0.0ms	x	@	inf	(* x (+ 1/3 (* (* x (* x (* x x))) 2/945)))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	inf	(- (* x (+ 1/3 (* (* x (* x (* x x))) 2/945))) (* x (* x (* x -1/45))))

rewrite145.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1768×	`sum4-define`
1150×	`sum3-define`
944×	`fma-define`
910×	`+-lowering-+.f64`
910×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	71
1	61	58
2	210	58
3	1098	55
4	4482	55
0	8185	55

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 392

Calls

Call 1

Inputs
(- (* 1/3 x) (* x (* x (* x -1/45))))
(* 1/3 x)
(* x (* x (* x -1/45)))
(* x (* x -1/45))
(- (* x (+ 1/3 (* (* x (* x (* x x))) 2/945))) (* x (* x (* x -1/45))))
(* x (+ 1/3 (* (* x (* x (* x x))) 2/945)))
(+ 1/3 (* (* x (* x (* x x))) 2/945))
(* (* x (* x (* x x))) 2/945)
(* x -1/45)
(* x (* x x))

Outputs
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 2/45 binary64)))))
(+.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))) #s(literal 0 binary64))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (+.f64 (.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (neg.f64 (+.f64 (.f64 x #s(literal -1/3 binary64)) (*.f64 #s(literal 1/3 binary64) x))))
(+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)) (.f64 #s(literal 1/3 binary64) x))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 2/45 binary64))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 2/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 x (.f64 (.f64 x x) #s(literal 2/45 binary64))))
(+.f64 (+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 2/45 binary64)))) (.f64 (.f64 x (.f64 x x)) #s(literal -2/45 binary64))) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(-.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (-.f64 (.f64 x #s(literal -1/3 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 2/45 binary64)))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))) #s(literal 0 binary64))
(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (+.f64 (.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (+.f64 (.f64 x #s(literal -1/3 binary64)) (*.f64 #s(literal 1/3 binary64) x)))
(-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)) (.f64 x #s(literal -1/3 binary64)))
(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 2/45 binary64)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)))
(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 (.f64 x (.f64 x x)) #s(literal -2/45 binary64)))
(-.f64 (+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 2/45 binary64)))) (.f64 (.f64 x (.f64 x x)) #s(literal -2/45 binary64))) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 #s(literal 1/3 binary64) x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)))
(fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 x #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(fma.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) #s(literal 0 binary64))
(fma.f64 #s(literal -1/45 binary64) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(fma.f64 #s(literal -1/45 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(fma.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) #s(literal -1 binary64) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x x) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
(fma.f64 #s(literal 2 binary64) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x #s(literal -1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x #s(literal -1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) x #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal -1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(neg.f64 (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(.f64 x (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -2/45 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))) x)
(+.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 0 binary64))
(+.f64 (.f64 #s(literal 1/3 binary64) x) (+.f64 (.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (-.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/3 binary64) x))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))
(+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -2/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 2/45 binary64)))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)))
(+.f64 (+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (.f64 (.f64 x (.f64 x x)) #s(literal -2/45 binary64))) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)))
(+.f64 (+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 x (.f64 (*.f64 x x) #s(literal 2/45 binary64))))
(-.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 0 binary64))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (+.f64 (.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (+.f64 (.f64 x #s(literal -1/3 binary64)) (*.f64 #s(literal 1/3 binary64) x)))
(-.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/3 binary64)))
(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)))
(-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
(-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -2/45 binary64)) (-.f64 (.f64 x #s(literal -1/3 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 2/45 binary64)))))
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(fma.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal 0 binary64))
(fma.f64 x #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(fma.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(fma.f64 #s(literal -1/45 binary64) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x x) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(fma.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(fma.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(fma.f64 (.f64 x x) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x #s(literal 2/945 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x #s(literal 2/945 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x #s(literal 2/945 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x)))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))) x #s(literal 0 binary64))
(fma.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(fma.f64 (.f64 (.f64 x x) (.f64 x #s(literal 2/945 binary64))) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 2/945 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal 2/945 binary64)) (.f64 x (.f64 x (.f64 x x))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) (.f64 x (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(neg.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))) x)
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))) #s(literal 1/3 binary64))
(+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(+.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))) #s(literal 1/3 binary64))
(+.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(+.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal 1/3 binary64)) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))
(+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(+.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(+.f64 (+.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal 1/3 binary64))
(-.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (-.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal 1/3 binary64)))
(-.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/3 binary64) (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(-.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(-.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal 1/3 binary64)) (.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(-.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(fma.f64 x (.f64 (.f64 x x) (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/3 binary64))
(fma.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/3 binary64))
(fma.f64 (.f64 x (.f64 x x)) (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/3 binary64))
(fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64) #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/3 binary64))
(fma.f64 (.f64 (.f64 x x) (*.f64 x #s(literal 2/945 binary64))) x #s(literal 1/3 binary64))
(fma.f64 (.f64 x #s(literal 2/945 binary64)) (.f64 x (*.f64 x x)) #s(literal 1/3 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) (*.f64 x x) #s(literal 1/3 binary64))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))) #s(literal 0 binary64))
(.f64 x (.f64 (.f64 x x) (.f64 x #s(literal 2/945 binary64))))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 2/945 binary64)))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64))
(.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 (.f64 (.f64 x x) (.f64 x #s(literal 2/945 binary64))) x)
(.f64 (.f64 x #s(literal 2/945 binary64)) (.f64 x (.f64 x x)))
(.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) (.f64 x x))
(+.f64 (*.f64 x #s(literal -1/45 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/45 binary64)))
(+.f64 (.f64 x #s(literal -2/45 binary64)) (.f64 x #s(literal 1/45 binary64)))
(-.f64 (*.f64 x #s(literal -1/45 binary64)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal 1/45 binary64)))
(-.f64 (.f64 x #s(literal -2/45 binary64)) (.f64 x #s(literal -1/45 binary64)))
(fma.f64 x #s(literal -1/45 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1/45 binary64) x #s(literal 0 binary64))
(neg.f64 (*.f64 x #s(literal 1/45 binary64)))
(*.f64 x #s(literal -1/45 binary64))
(*.f64 #s(literal -1/45 binary64) x)
(.f64 (.f64 x #s(literal -1/45 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/45 binary64))
(.f64 (.f64 x #s(literal 1/45 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/45 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/45 binary64)))
(*.f64 #s(literal 1/45 binary64) (-.f64 #s(literal 0 binary64) x))
(+.f64 (.f64 x (.f64 x x)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 3 binary64))) (log.f64 x)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (+.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 x)))
(-.f64 (.f64 x (.f64 x x)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(fma.f64 x (*.f64 x x) #s(literal 0 binary64))
(fma.f64 (*.f64 x x) x #s(literal 0 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 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) (.f64 x (*.f64 x x))) #s(literal -1 binary64))

simplify237.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

2384×	`-lowering-.f32`
2384×	`-lowering-.f64`
1292×	`fma-lowering-fma.f32`
1292×	`fma-lowering-fma.f64`
1214×	`fmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	684
1	157	608
2	416	608
3	963	608
4	1962	606
5	5298	606
0	8261	606

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* 1/3 x)
(* x (+ 1/3 (* 2/945 (pow x 4))))
(* x (+ 1/3 (* 2/945 (pow x 4))))
(* x (+ 1/3 (* 2/945 (pow x 4))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
1/3
(+ 1/3 (* 2/945 (pow x 4)))
(+ 1/3 (* 2/945 (pow x 4)))
(+ 1/3 (* 2/945 (pow x 4)))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* 2/945 (pow x 4))
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(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)

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(* 2/945 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x #s(literal 2/945 binary64)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(* 2/945 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x #s(literal 2/945 binary64)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 2/945 (pow x 4))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* x (+ 1/3 (* 2/945 (pow x 4))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* x (+ 1/3 (* 2/945 (pow x 4))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* 2/945 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x #s(literal 2/945 binary64)))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* 2/945 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x #s(literal 2/945 binary64)))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 2/945 (pow x 4)))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(+ 1/3 (* 2/945 (pow x 4)))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(+ 1/3 (* 2/945 (pow x 4)))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

eval73.0ms (0.7%)

Compiler: Compiled 12766 to 1025 computations (92% saved)

prune67.0ms (0.6%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	635	0	635
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	635	5	640

Accuracy

99.5%

Counts

640 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
✓	99.4%	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
✓	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	99.0%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 132 to 72 computations (45.5% saved)

regimes5.0ms (0%)

Counts

6 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 2/945 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Outputs
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs

(*.f64 #s(literal 1/3 binary64) x)

(*.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))))

(-.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 x (*.f64 x (*.f64 x #s(literal -1/45 binary64)))))

Outputs
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))

Outputs
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)

Outputs
(*.f64 #s(literal 1/3 binary64) x)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative_binary64`
30×	`+-commutative_binary64`
28×	`sub-neg_binary64`
26×	`distribute-lft-neg-in_binary64`
26×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	42	38
2	74	38
3	98	38
4	124	38
5	133	38
6	137	38
7	138	38

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(*.f64 #s(literal 1/3 binary64) x)

Outputs
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(-.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))

soundness913.0ms (8.4%)

Rules

2512×	`-lowering-.f32`
2512×	`-lowering-.f64`
2470×	`sum3-define`
2100×	`fnmadd-define`
1924×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	302
1	186	269
2	560	266
3	1806	266
4	2709	266
5	4422	266
6	6045	266
7	6589	266
0	8077	266
0	14	60
1	44	57
2	136	53
3	436	53
4	1673	53
5	5627	53
0	8590	53

Stop Event

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

Compiler

Compiled 76 to 44 computations (42.1% saved)

preprocess61.0ms (0.6%)

Remove: (negabs x)
Compiler: Compiled 242 to 142 computations (41.3% saved)

invcot (example 3.9)

analyze9.0ms (0.1%)

sample7.2s (65.7%)

preprocess40.0ms (0.4%)

explain485.0ms (4.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify19.0ms (0.2%)

localize233.0ms (2.1%)

series4.0ms (0%)

rewrite162.0ms (1.5%)

simplify183.0ms (1.7%)

eval57.0ms (0.5%)

prune59.0ms (0.5%)

simplify116.0ms (1.1%)

localize85.0ms (0.8%)

series10.0ms (0.1%)

rewrite123.0ms (1.1%)

simplify167.0ms (1.5%)

eval50.0ms (0.5%)

prune38.0ms (0.3%)

simplify144.0ms (1.3%)

localize236.0ms (2.2%)

series6.0ms (0.1%)

rewrite145.0ms (1.3%)

simplify237.0ms (2.2%)

eval73.0ms (0.7%)

prune67.0ms (0.6%)

regimes5.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify11.0ms (0.1%)

soundness913.0ms (8.4%)

preprocess61.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	20
1	29	19
2	64	18
3	146	18
4	300	18
5	464	18
6	507	18
7	515	18
0	6	6
1	12	6
2	20	6
3	31	6
4	45	6
5	82	6
6	152	6
7	248	6
8	350	6
9	486	6
10	607	6
11	639	6
0	639	6

Iter	Nodes	Cost
0	6	15
1	12	15
2	20	15
3	31	15
4	45	15
5	82	15
6	152	15
7	248	15
8	350	15
9	486	15
10	607	15
11	639	15
0	639	15

Iter	Nodes	Cost
0	12	20
1	29	19
2	64	18
3	146	18
4	300	18
5	464	18
6	507	18
7	515	18
0	6	6
1	12	6
2	20	6
3	31	6
4	45	6
5	82	6
6	152	6
7	248	6
8	350	6
9	486	6
10	607	6
11	639	6
0	639	6

Iter	Nodes	Cost
0	6	15
1	12	15
2	20	15
3	31	15
4	45	15
5	82	15
6	152	15
7	248	15
8	350	15
9	486	15
10	607	15
11	639	15
0	639	15

Iter	Nodes	Cost
0	12	20
1	29	19
2	64	18
3	146	18
4	300	18
5	464	18
6	507	18
7	515	18
0	6	6
1	12	6
2	20	6
3	31	6
4	45	6
5	82	6
6	152	6
7	248	6
8	350	6
9	486	6
10	607	6
11	639	6
0	639	6

Iter	Nodes	Cost
0	6	15
1	12	15
2	20	15
3	31	15
4	45	15
5	82	15
6	152	15
7	248	15
8	350	15
9	486	15
10	607	15
11	639	15
0	639	15