Metrics for invcot (example 3.9)

analyze7.0ms (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: 4.0ms

...c/correct-round.rkt:119:19: 2.0ms (47.5% of total)

ival-div: 1.0ms (23.8% of total)

ival-tan: 1.0ms (23.8% of total)

ival-<: 1.0ms (23.8% 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)

sample7.7s (60.6%)

Results

4.8s	4546×	2	valid
1.5s	1387×	3	valid
868.0ms	2274×	1	valid
5.0ms	49×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.1s

ival-tan: 4.7s (76.7% of total)

ival-div: 562.0ms (9.2% of total)

...c/correct-round.rkt:119:19: 323.0ms (5.3% of total)

backward-pass: 233.0ms (3.8% of total)

ival-sub: 180.0ms (2.9% of total)

ival-<: 99.0ms (1.6% of total)

const: 17.0ms (0.3% of total)

ival-and: 11.0ms (0.2% of total)

Bogosity

preprocess40.0ms (0.3%)

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)

explain518.0ms (4.1%)

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

347.0ms	280×	2	valid
91.0ms	90×	3	valid
22.0ms	136×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 378.0ms

ival-tan: 203.0ms (53.6% of total)

ival-div: 152.0ms (40.2% of total)

backward-pass: 14.0ms (3.7% of total)

ival-sub: 8.0ms (2.1% of total)

const: 2.0ms (0.5% 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
▶	6.8%	(-.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)

localize200.0ms (1.6%)

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	6.9%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

99.0ms	140×	2	valid
45.0ms	68×	1	valid
44.0ms	45×	3	valid
0.0ms	3×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-tan: 97.0ms (64.7% of total)

backward-pass: 21.0ms (14% of total)

ival-sub: 18.0ms (12% of total)

ival-div: 12.0ms (8% of total)

const: 1.0ms (0.7% 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))

rewrite225.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2434×	`-lowering-.f32`
2434×	`-lowering-.f64`
2300×	`/-lowering-/.f32`
2300×	`/-lowering-/.f64`
1480×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	47	13
2	485	13
3	6201	13
0	8254	13

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 222

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 #s(literal -1 binary64) (tan.f64 x)) (+.f64 (/.f64 #s(literal -1 binary64) (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 #s(literal -1 binary64) (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 0 binary64) (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))) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1 binary64) (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) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #s(literal 1 binary64)))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))) (+.f64 (+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (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) (+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(+.f64 (+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(+.f64 (/.f64 (tan.f64 x) (.f64 (tan.f64 x) x)) (neg.f64 (/.f64 x (.f64 (tan.f64 x) x))))
(+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x))))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.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 #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 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x))
(-.f64 (/.f64 (tan.f64 x) (.f64 (tan.f64 x) x)) (/.f64 x (.f64 (tan.f64 x) x)))
(-.f64 (/.f64 (tan.f64 x) (.f64 (tan.f64 x) x)) (-.f64 (/.f64 x (.f64 (tan.f64 x) x)) (+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x)))) (-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x)))) (+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 x x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 x x))) (-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) (+.f64 (/.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)))
(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))) (+.f64 (/.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) (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 #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 (-.f64 (tan.f64 x) x) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) x) (+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x)))) (+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (/.f64 #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) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(neg.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(neg.f64 (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x)))
(neg.f64 (/.f64 (-.f64 (tan.f64 x) x) (*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) x)))
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x))))))
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x))))
(neg.f64 (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) x) (*.f64 (tan.f64 x) x)))
(neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x)))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (tan.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1 binary64) (/.f64 (tan.f64 x) (/.f64 (-.f64 (tan.f64 x) x) x)))
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(/.f64 (tan.f64 x) #s(literal 1 binary64))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (sin.f64 x) (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (sin.f64 x) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal -1 binary64))
(/.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 #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 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (cos.f64 x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (/.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (cos.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (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 (tan.f64 x) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (sin.f64 x) (.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 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

simplify218.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

2522×	`-lowering-.f32`
2522×	`-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	1807	266
4	2716	266
5	4431	266
6	6050	266
7	6596	266
0	8084	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 x (*.f64 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 (.f64 x 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 x (.f64 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 (.f64 x 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 (*.f64 x 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))

eval38.0ms (0.3%)

Compiler: Compiled 5571 to 674 computations (87.9% saved)

prune30.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	268	3	271

Accuracy

99.4%

Counts

271 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.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)))))))
▶	99.2%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
▶	98.5%	(*.f64 #s(literal 1/3 binary64) x)

Status

Accuracy

Program

▶

99.4%

(*.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)))))))

▶

99.2%

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

▶

98.5%

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

Compiler

Compiled 30 to 21 computations (30% saved)

simplify116.0ms (0.9%)

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 x (.f64 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 x (.f64 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 x (*.f64 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

1976×	`sum3-define`
1920×	`sum4-define`
1820×	`fma-define`
1616×	`fma-lowering-fma.f32`
1616×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	80
1	43	76
2	133	72
3	428	72
4	1209	72
5	2366	72
6	5316	72
0	8042	72

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

localize100.0ms (0.8%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -2/945 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64)))))
✓	accuracy	99.4%	(.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)))))))
✓	accuracy	99.4%	(*.f64 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	99.7%	(.f64 (.f64 x x) #s(literal -1/45 binary64))
✓	accuracy	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) x)

Results

72.0ms

256×

valid

Compiler

Compiled 95 to 16 computations (83.2% saved)

Precisions

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

...c/correct-round.rkt:119:19: 15.0ms (46.2% of total)

ival-mult: 13.0ms (40% of total)

ival-sub: 2.0ms (6.2% of total)

ival-add: 1.0ms (3.1% of total)

const: 0.0ms (0% of total)

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

series22.0ms (0.2%)

Counts

10 → 120

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 -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 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<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

30 calls:

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

rewrite286.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

5384×	`-lowering-.f32`
5384×	`-lowering-.f64`
2582×	`/-lowering-/.f32`
2582×	`/-lowering-/.f64`
1428×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	84	60
2	680	56
0	8182	56

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 287

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 -2/945)
(* x (* x -2/945))

Outputs
(*.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 (.f64 x x) #s(literal 1/45 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))) (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))))
(/.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))))) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64)))) (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))))) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(/.f64 (.f64 x (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
(/.f64 (.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) x) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64))) x)
(.f64 (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x))))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))) x))
(.f64 (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x))))) (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) x))
(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))))
(.f64 (/.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+.f64 (/.f64 #s(literal 1/27 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))))
(+.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))))
(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(-.f64 (/.f64 #s(literal 1/27 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(-.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x 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))
(fma.f64 #s(literal -1/45 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) #s(literal 1/3 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal 1/3 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x #s(literal -1/45 binary64)) #s(literal 1/3 binary64))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(neg.f64 (/.f64 (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))))
(neg.f64 (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(neg.f64 (/.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))))
(/.f64 (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))
(/.f64 (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/135 binary64) (.f64 x x)))))
(/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))))
(/.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
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(/.f64 (.f64 x (.f64 x (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64))))))) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))))
(/.f64 (neg.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))) (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (.f64 (.f64 x x) #s(literal -1/45 binary64))))
(/.f64 (.f64 (.f64 x x) (+.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))) #s(literal 1/91125 binary64))) (+.f64 (neg.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))) #s(literal -1/2025 binary64)))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/2025 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64))))) (+.f64 #s(literal 1/45 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(/.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(/.f64 (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) #s(literal -1/2025 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))
(/.f64 (.f64 (+.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))) #s(literal 1/91125 binary64)) (.f64 x x)) (+.f64 (neg.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))) #s(literal -1/2025 binary64)))
(/.f64 (.f64 (+.f64 #s(literal -1/2025 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64)))) (.f64 x x)) (+.f64 #s(literal 1/45 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) #s(literal -1/2025 binary64)) (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))
(.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (.f64 x x))
(.f64 (+.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))))) (.f64 x x)))
(.f64 (+.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))) (/.f64 (.f64 x x) (+.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))))))
(.f64 (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) (*.f64 x x)))
(.f64 (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 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 -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))) x)
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (.f64 (.f64 x x) #s(literal -1/45 binary64)))))))
(.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))))))
(.f64 (.f64 x (.f64 x (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(.f64 (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64))))) (+.f64 #s(literal 1/8303765625 binary64) (.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))))) (+.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))) (-.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))) #s(literal 1/2025 binary64)))))
(.f64 (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64))))) (-.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))))) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))))
(.f64 (/.f64 (.f64 x (.f64 x (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64))))))) (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))))) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))
(.f64 (/.f64 (.f64 x (.f64 x (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64))))))) (-.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64))))) (+.f64 #s(literal 1/2025 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))))
(*.f64 x #s(literal -2/945 binary64))
(*.f64 #s(literal -2/945 binary64) x)
(.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 #s(literal -2/945 binary64)) x)

simplify159.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2644×	`-lowering-.f32`
2644×	`-lowering-.f64`
1732×	`fma-define`
1206×	`fma-lowering-fma.f32`
1206×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	753
1	161	604
2	475	604
3	1240	600
4	2907	598
5	7687	598
0	8029	598

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

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

eval72.0ms (0.6%)

Compiler: Compiled 15010 to 1069 computations (92.9% saved)

prune52.0ms (0.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	421	4	425
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	421	7	428

Accuracy

100.0%

Counts

428 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 x (/.f64 #s(literal 1 binary64) (-.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)))))))
▶	99.8%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
▶	99.4%	(+.f64 (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
▶	99.2%	(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 #s(literal 1/3 binary64) x))
✓	99.4%	(.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)))))))
✓	99.2%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	98.5%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 90 to 61 computations (32.2% saved)

simplify185.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

2488×	`sum5-define`
2004×	`sum4-define`
1742×	`fma-lowering-fma.f32`
1742×	`fma-lowering-fma.f64`
1644×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	169
1	80	155
2	246	151
3	637	151
4	1283	151
5	2197	151
6	4309	151
0	8057	151

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

localize147.0ms (1.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))
✓	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	99.7%	(.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	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/45 binary64))
✓	accuracy	99.8%	(.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (*.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 2/945 binary64))
✓	accuracy	99.6%	(.f64 x (+.f64 (.f64 (*.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) x)
✓	accuracy	100.0%	(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 #s(literal 1/3 binary64) x))
✓	accuracy	99.9%	(.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/45 binary64))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) x)

Results

104.0ms

256×

valid

Compiler

Compiled 210 to 27 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-add: 20.0ms (33.2% of total)

ival-mult: 16.0ms (26.5% of total)

...c/correct-round.rkt:119:19: 16.0ms (26.5% of total)

ival-div: 7.0ms (11.6% of total)

ival-sub: 1.0ms (1.7% of total)

const: 0.0ms (0% of total)

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

series11.0ms (0.1%)

Counts

18 → 216

Calls

Call 1

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

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 (* 1/45 (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 (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 (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* (pow x 3) (+ 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 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 2/945 (* 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 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* 1/45 x)>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* 2/945 (pow x 3))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* 2/945 (pow x 3))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<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 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))>
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (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 (* 1/3 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 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))>
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (- (* 13/7875 (pow x 2)) 1/175)) 1/5)))>
#<alt (/ 945/2 (pow x 4))>
#<alt (/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))>
#<alt (/ 945/2 (pow x 4))>
#<alt (/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))>
#<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 (* 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 (* 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))>
#<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))>
#<alt -1/45>
#<alt (- (* -2/945 (pow x 2)) 1/45)>
#<alt (- (* -2/945 (pow x 2)) 1/45)>
#<alt (- (* -2/945 (pow x 2)) 1/45)>
#<alt (* -2/945 (pow x 2))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>

Calls

54 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(* (* x x) 1/45)
0.0ms	x	@	inf	(+ (* (* x x) (* x (+ (* (* x x) 2/945) 1/45))) (* 1/3 x))
0.0ms	x	@	inf	(+ (* x (* (* x x) 1/45)) (* 1/3 x))
0.0ms	x	@	inf	(* x (* (* x x) 1/45))
0.0ms	x	@	0	(/ 1 (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))

rewrite345.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3278×	`-lowering-.f32`
3278×	`-lowering-.f64`
3150×	`/-lowering-/.f32`
3150×	`/-lowering-/.f64`
1710×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	136
1	183	121
2	1591	117
0	8148	117

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 601

Calls

Call 1

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

Outputs
(+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64))) (.f64 x #s(literal 1/3 binary64)))
(+.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64))))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal 1/3 binary64))))) #s(literal -1 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 (.f64 x x) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/3 binary64) (.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 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64))))) (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64))))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal 1/45 binary64))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) x (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (.f64 (.f64 x x) (*.f64 x #s(literal 1/45 binary64))))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(neg.f64 (.f64 x (-.f64 #s(literal -1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal 1/3 binary64))))
(/.f64 (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal 1/3 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (.f64 x (.f64 x #s(literal 1/3 binary64)))))) (+.f64 (.f64 #s(literal 1/27 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.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 x (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)))) (-.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))))))
(/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal 1/3 binary64)) (/.f64 #s(literal 1 binary64) x))
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(.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64)))))))
(.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))))
(.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))))
(.f64 (.f64 (-.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 (*.f64 x #s(literal 2/945 binary64)) (/.f64 #s(literal 1 binary64) x))
(.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 #s(literal 2/945 binary64)) x)
(/.f64 (*.f64 x #s(literal -2/945 binary64)) (/.f64 #s(literal 1 binary64) x))
(.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 #s(literal -2/945 binary64)) x)
(+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))
(+.f64 (/.f64 #s(literal 1/2025 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))))
(-.f64 (/.f64 #s(literal 1/2025 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))) (/.f64 #s(literal 1/2025 binary64) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))
(fma.f64 x (*.f64 x #s(literal -2/945 binary64)) #s(literal -1/45 binary64))
(fma.f64 (*.f64 x x) #s(literal -2/945 binary64) #s(literal -1/45 binary64))
(fma.f64 #s(literal -2/945 binary64) (*.f64 x x) #s(literal -1/45 binary64))
(fma.f64 (*.f64 x #s(literal -2/945 binary64)) x #s(literal -1/45 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (-.f64 #s(literal 1/2025 binary64) (.f64 #s(literal 2/42525 binary64) (.f64 x x)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) #s(literal -1/2025 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64)) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64)) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (-.f64 #s(literal 1/2025 binary64) (.f64 #s(literal 2/42525 binary64) (.f64 x x)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) #s(literal -1/2025 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))
(/.f64 (-.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64))) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) #s(literal -1/2025 binary64))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64))) (neg.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (-.f64 #s(literal 1/2025 binary64) (.f64 #s(literal 2/42525 binary64) (.f64 x x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 1/2025 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) (.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)))) (.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2025 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1/2025 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) (/.f64 #s(literal 1/2025 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))) (+.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))) (.f64 (/.f64 #s(literal 1/2025 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) (-.f64 #s(literal 1/2025 binary64) (.f64 #s(literal 2/42525 binary64) (*.f64 x x))))))
(.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)) #s(literal -1/2025 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64))))
(.f64 (-.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal -1/91125 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) #s(literal 1/45 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4/893025 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))

simplify212.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

2428×	`-lowering-.f32`
2428×	`-lowering-.f64`
1878×	`fma-define`
1570×	`fma-lowering-fma.f32`
1570×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1663
1	369	1387
2	1056	1377
3	2832	1356
4	6943	1356
0	8385	1356

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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)))))
(* 1/45 (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))
(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)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(* (pow x 3) (+ 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 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* 1/45 x)
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* 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)))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (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)))))
(* 1/3 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)))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (- (* 13/7875 (pow x 2)) 1/175)) 1/5)))
(/ 945/2 (pow x 4))
(/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))
(/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))
(/ 945/2 (pow x 4))
(/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))
(/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))
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))))))
(* 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)
(* 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))
(* -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))
-1/45
(- (* -2/945 (pow x 2)) 1/45)
(- (* -2/945 (pow x 2)) 1/45)
(- (* -2/945 (pow x 2)) 1/45)
(* -2/945 (pow x 2))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 2))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))

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 x (.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)))))
(* (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 x (.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)))))
(* (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 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 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 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 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x 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 (*.f64 x x) #s(literal 2/945 binary64)))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x 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 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 2/945 binary64) (/.f64 (+.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) (*.f64 x x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 2/945 binary64) (/.f64 (+.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* 2/945 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/945 binary64)))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* 2/945 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/945 binary64)))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 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 (* 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 x (.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)))))
(* (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 x (.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)))))
(* (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)))))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal 1/75 binary64)))))))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/75 binary64) (.f64 x (.f64 x #s(literal -1/1125 binary64))))))))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -675 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -151875 binary64) (pow.f64 x #s(literal 6 binary64))))) (*.f64 x x))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -675 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -151875 binary64) (pow.f64 x #s(literal 6 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 x (.f64 x #s(literal 1/45 binary64))))
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.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)
(* 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 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x 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 (*.f64 x x) #s(literal 2/945 binary64)))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x 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 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 2/945 binary64) (/.f64 (+.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) (*.f64 x x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 2/945 binary64) (/.f64 (+.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) (*.f64 x x))))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64))))))
(+ 3 (* (pow x 2) (- (* (pow x 2) (- (* 13/7875 (pow x 2)) 1/175)) 1/5)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/175 binary64) (.f64 (.f64 x x) #s(literal 13/7875 binary64)))))))
(/ 945/2 (pow x 4))
(/.f64 #s(literal 945/2 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))
(/.f64 (-.f64 #s(literal 945/2 binary64) (/.f64 #s(literal 19845/4 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
(/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/.f64 (+.f64 #s(literal 945/2 binary64) (/.f64 (+.f64 #s(literal -19845/4 binary64) (/.f64 #s(literal -178605/8 binary64) (.f64 x x))) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))
(/.f64 (+.f64 (+.f64 #s(literal 945/2 binary64) (+.f64 (/.f64 #s(literal 16253055/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -19845/4 binary64) (.f64 x x)))) (/.f64 (/.f64 #s(literal -178605/8 binary64) (.f64 x x)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
(/ 945/2 (pow x 4))
(/.f64 #s(literal 945/2 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))
(/.f64 (-.f64 #s(literal 945/2 binary64) (/.f64 #s(literal 19845/4 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
(/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/.f64 (+.f64 #s(literal 945/2 binary64) (/.f64 (+.f64 #s(literal -19845/4 binary64) (/.f64 #s(literal -178605/8 binary64) (.f64 x x))) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))
(/.f64 (+.f64 (+.f64 #s(literal 945/2 binary64) (+.f64 (/.f64 #s(literal 16253055/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -19845/4 binary64) (.f64 x x)))) (/.f64 (/.f64 #s(literal -178605/8 binary64) (.f64 x x)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 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 (.f64 x 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 (.f64 x x) #s(literal 2/945 binary64))))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x 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 (.f64 x 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 (.f64 x 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 (.f64 x x) #s(literal 2/945 binary64))))))
(* 2/945 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x 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 (.f64 x 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 (.f64 x 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 (.f64 x x) #s(literal 2/945 binary64))))))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(.f64 (.f64 x 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 (.f64 x 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 (.f64 x 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 (.f64 x 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 (.f64 x 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 (.f64 x 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 (.f64 x 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 (.f64 x 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 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 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)
(* 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))
(* -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))
-1/45
#s(literal -1/45 binary64)
(- (* -2/945 (pow x 2)) 1/45)
(-.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))
(- (* -2/945 (pow x 2)) 1/45)
(-.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))
(- (* -2/945 (pow x 2)) 1/45)
(-.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))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(-.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(-.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(-.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))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(-.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(-.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(-.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))

eval110.0ms (0.9%)

Compiler: Compiled 25800 to 2203 computations (91.5% saved)

prune75.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	946	3	949
Fresh	0	0	0
Picked	4	0	4
Done	3	0	3
Total	953	3	956

Accuracy

100.0%

Counts

956 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

99.8%

(/.f64 x (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) #s(literal -1/5 binary64))))

▶

100.0%

(/.f64 x (+.f64 #s(literal 3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/5 binary64) (*.f64 (*.f64 x x) #s(literal -1/175 binary64)))))))

▶

99.1%

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

Compiler

Compiled 30 to 21 computations (30% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) #s(literal -1/5 binary64))
✓	cost-diff	(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
✓	cost-diff	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
✓	cost-diff	(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
✓	cost-diff	(.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))
✓	cost-diff	(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64))))))
✓	cost-diff	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))))
✓	cost-diff	(/.f64 x #s(literal 3 binary64))

Rules

140×	`fma-define`
104×	`fma-lowering-fma.f32`
104×	`fma-lowering-fma.f64`
76×	`-lowering-.f32`
76×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	85
1	33	76
2	81	76
3	146	76
4	188	76
5	191	76
0	191	76

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x 3)
x
3
(/ x (+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175))))))
x
(+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175)))))
3
(* x (* x (+ -1/5 (* (* x x) -1/175))))
(* x (+ -1/5 (* (* x x) -1/175)))
(+ -1/5 (* (* x x) -1/175))
-1/5
(* (* x x) -1/175)
(* x x)
-1/175
(/ x (+ 3 (* (* x x) -1/5)))
x
(+ 3 (* (* x x) -1/5))
3
(* (* x x) -1/5)
(* x x)
-1/5

Outputs
(/ x 3)
(/.f64 x #s(literal 3 binary64))
x
3
#s(literal 3 binary64)
(/ x (+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175))))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64))))))
x
(+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175)))))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))
3
#s(literal 3 binary64)
(* x (* x (+ -1/5 (* (* x x) -1/175))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64))))
(* x (+ -1/5 (* (* x x) -1/175)))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
(+ -1/5 (* (* x x) -1/175))
(+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))
-1/5
#s(literal -1/5 binary64)
(* (* x x) -1/175)
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* x x)
(*.f64 x x)
-1/175
#s(literal -1/175 binary64)
(/ x (+ 3 (* (* x x) -1/5)))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
x
(+ 3 (* (* x x) -1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
3
#s(literal 3 binary64)
(* (* x x) -1/5)
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* x x)
(*.f64 x x)
-1/5
#s(literal -1/5 binary64)

localize69.0ms (0.5%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal -1/5 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal -1/175 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))
✓	accuracy	99.4%	(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
✓	accuracy	100.0%	(/.f64 x #s(literal 3 binary64))

Results

47.0ms

256×

valid

Compiler

Compiled 101 to 16 computations (84.2% saved)

Precisions

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

ival-mult: 9.0ms (36% of total)

...c/correct-round.rkt:119:19: 7.0ms (28% of total)

ival-div: 6.0ms (24% of total)

ival-add: 4.0ms (16% of total)

const: 0.0ms (0% of total)

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

series9.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (/ x 3)>
#<alt (/ x (+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175))))))>
#<alt (+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175)))))>
#<alt (* x (* x (+ -1/5 (* (* x x) -1/175))))>
#<alt (* x (+ -1/5 (* (* x x) -1/175)))>
#<alt (/ x (+ 3 (* (* x x) -1/5)))>
#<alt (+ 3 (* (* x x) -1/5))>
#<alt (* (* x x) -1/5)>
#<alt (* x x)>
#<alt (* (* x x) -1/175)>

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 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 13/70875 (pow x 2))))))))>
#<alt (/ -175 (pow x 3))>
#<alt (/ (- (* 6125 (/ 1 (pow x 2))) 175) (pow x 3))>
#<alt (/ (- (* 6125 (/ 1 (pow x 2))) (+ 175 (/ 306250 (pow x 4)))) (pow x 3))>
#<alt (/ (- (+ (* 6125 (/ 1 (pow x 2))) (* 13934375 (/ 1 (pow x 6)))) (+ 175 (/ 306250 (pow x 4)))) (pow x 3))>
#<alt (/ -175 (pow x 3))>
#<alt (* -1 (/ (- 175 (* 6125 (/ 1 (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ 175 (/ 306250 (pow x 4))) (* 6125 (/ 1 (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ 175 (/ 306250 (pow x 4))) (+ (* 6125 (/ 1 (pow x 2))) (* 13934375 (/ 1 (pow x 6))))) (pow x 3)))>
#<alt 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))>
#<alt (+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))>
#<alt (* -1/175 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1/175 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1/5 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))>
#<alt (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))>
#<alt (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))>
#<alt (* -1/175 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1/175 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1/5 x)>
#<alt (* x (- (* -1/175 (pow x 2)) 1/5))>
#<alt (* x (- (* -1/175 (pow x 2)) 1/5))>
#<alt (* x (- (* -1/175 (pow x 2)) 1/5))>
#<alt (* -1/175 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1/175 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (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 (* 1/675 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)>
#<alt (/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))>
#<alt 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (* -1/5 (pow x 2))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* -1/5 (pow x 2))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (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 (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>
#<alt (* -1/175 (pow x 2))>

Calls

30 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(* (* x x) -1/5)
1.0ms	x	@	inf	(/ x (+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175))))))
0.0ms	x	@	inf	(/ x (+ 3 (* (* x x) -1/5)))
0.0ms	x	@	0	(/ x (+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175))))))
0.0ms	x	@	inf	(* (* x x) -1/175)

rewrite284.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

5078×	`-lowering-.f32`
5078×	`-lowering-.f64`
2990×	`/-lowering-/.f32`
2990×	`/-lowering-/.f64`
1430×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	68
1	95	60
2	733	60
3	7993	60
0	8150	60

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 391

Calls

Call 1

Inputs
(/ x 3)
(/ x (+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175))))))
(+ 3 (* x (* x (+ -1/5 (* (* x x) -1/175)))))
(* x (* x (+ -1/5 (* (* x x) -1/175))))
(* x (+ -1/5 (* (* x x) -1/175)))
(/ x (+ 3 (* (* x x) -1/5)))
(+ 3 (* (* x x) -1/5))
(* (* x x) -1/5)
(* x x)
(* (* x x) -1/175)

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 3 binary64) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal -3 binary64)))
(neg.f64 (/.f64 x #s(literal -3 binary64)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 x #s(literal -3 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 3 binary64) x)))
(/.f64 x #s(literal 3 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -3 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -3 binary64) x))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -3 binary64))
(pow.f64 (/.f64 #s(literal 3 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 (/.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/3 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 3 binary64)))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 x #s(literal -3 binary64)))
(*.f64 #s(literal -1/3 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (pow.f64 (/.f64 #s(literal 3 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 3 binary64) x) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -1/3 binary64))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))))) #s(literal 9 binary64)) (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))))) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))) (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (*.f64 x #s(literal -1/175 binary64))))) #s(literal -3 binary64)))))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))))) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))) (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))) #s(literal -3 binary64)))) (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (*.f64 x #s(literal -1/175 binary64))))))))))) #s(literal 9 binary64)))
(+.f64 (.f64 (/.f64 x (-.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))) #s(literal 3 binary64)) (.f64 (/.f64 x (-.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (-.f64 #s(literal 0 binary64) (.f64 x x)))))
(+.f64 (.f64 #s(literal 9 binary64) (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))))))))))) (.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))) (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))) #s(literal -3 binary64))) (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (*.f64 x #s(literal -1/175 binary64)))))))))))))
(+.f64 (.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))) (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))) #s(literal -3 binary64))) (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))))))))))) (.f64 #s(literal 9 binary64) (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (*.f64 x #s(literal -1/175 binary64)))))))))))))
(+.f64 (.f64 #s(literal 3 binary64) (/.f64 x (-.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))))))))) (.f64 (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (-.f64 #s(literal 0 binary64) (.f64 x x))) (/.f64 x (-.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))))))))))
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (*.f64 x #s(literal -1/175 binary64)))))) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x (-.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))) (/.f64 x (-.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))
(neg.f64 (/.f64 x (-.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (*.f64 x #s(literal -1/175 binary64)))))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))))) x)))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))))) x))
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))))) x))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))) (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (*.f64 x #s(literal -1/175 binary64))))) #s(literal -3 binary64))))))
(/.f64 (/.f64 x (-.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64)))) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal -1/175 binary64))))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (*.f64 x #s(literal -1/175 binary64))))))))
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(/.f64 (-.f64 (.f64 (/.f64 #s(literal 9 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))) (/.f64 #s(literal 9 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64))))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))))) (+.f64 (/.f64 #s(literal 9 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal 19683 binary64) (.f64 (.f64 #s(literal -1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal 1/15625 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))) (+.f64 #s(literal 729 binary64) (.f64 (.f64 #s(literal -1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 #s(literal -1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 27 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 729 binary64) (.f64 #s(literal 1/15625 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))) (+.f64 #s(literal 27 binary64) (.f64 #s(literal 1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 (-.f64 #s(literal 729 binary64) (.f64 #s(literal 1/15625 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64))))) (+.f64 #s(literal 81 binary64) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64))))))))
(/.f64 (.f64 (-.f64 #s(literal 81 binary64) (.f64 #s(literal 1/625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64))))) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/25 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 3 binary64) (.f64 x (*.f64 x #s(literal -1/5 binary64)))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 27 binary64) (.f64 #s(literal -1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))))
(.f64 (+.f64 #s(literal 27 binary64) (.f64 #s(literal -1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))) #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (*.f64 x #s(literal -1/5 binary64)))))
(.f64 (-.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64)))))
(.f64 (-.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64)))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (+.f64 #s(literal -3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64))))
(.f64 (+.f64 (neg.f64 (.f64 #s(literal -1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -27 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -3 binary64) (neg.f64 (.f64 (*.f64 x x) #s(literal 1/5 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))) (+.f64 #s(literal 27 binary64) (.f64 #s(literal -1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))) (-.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/25 binary64))))))
(.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))) #s(literal -9 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64))))) (-.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))))) (+.f64 #s(literal 3 binary64) (.f64 x (*.f64 x #s(literal -1/5 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 27 binary64) (.f64 #s(literal -1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 729 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))))) (+.f64 #s(literal 81 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) #s(literal 9 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 27 binary64) (.f64 #s(literal -1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 81 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))) (-.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64))))) (+.f64 #s(literal 27 binary64) (.f64 #s(literal 1/125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(.f64 #s(literal -1/5 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(.f64 (.f64 x #s(literal -1/5 binary64)) x)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 x (.f64 x #s(literal -1/175 binary64)))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(.f64 #s(literal -1/175 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/175 binary64)) x)

simplify241.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2812×	`-lowering-.f32`
2812×	`-lowering-.f64`
2534×	`+-lowering-+.f64`
2534×	`+-lowering-+.f32`
1370×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	912
1	394	779
2	1298	755
3	4031	754
0	8215	754

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

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 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 13/70875 (pow x 2))))))))
(/ -175 (pow x 3))
(/ (- (* 6125 (/ 1 (pow x 2))) 175) (pow x 3))
(/ (- (* 6125 (/ 1 (pow x 2))) (+ 175 (/ 306250 (pow x 4)))) (pow x 3))
(/ (- (+ (* 6125 (/ 1 (pow x 2))) (* 13934375 (/ 1 (pow x 6)))) (+ 175 (/ 306250 (pow x 4)))) (pow x 3))
(/ -175 (pow x 3))
(* -1 (/ (- 175 (* 6125 (/ 1 (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ 175 (/ 306250 (pow x 4))) (* 6125 (/ 1 (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ 175 (/ 306250 (pow x 4))) (+ (* 6125 (/ 1 (pow x 2))) (* 13934375 (/ 1 (pow x 6))))) (pow x 3)))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))
(* -1/175 (pow x 4))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1/175 (pow x 4))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))
(* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))
(* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))
(* -1/175 (pow x 4))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1/175 (pow x 4))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1/5 x)
(* x (- (* -1/175 (pow x 2)) 1/5))
(* x (- (* -1/175 (pow x 2)) 1/5))
(* x (- (* -1/175 (pow x 2)) 1/5))
(* -1/175 (pow x 3))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1/175 (pow x 3))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 1/675 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (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)
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (pow x 2))
(* -1/175 (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 (* (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 (* 13/70875 (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 13/70875 binary64))))))))
(/ -175 (pow x 3))
(/.f64 (/.f64 #s(literal -175 binary64) (*.f64 x x)) x)
(/ (- (* 6125 (/ 1 (pow x 2))) 175) (pow x 3))
(/.f64 (+.f64 #s(literal -175 binary64) (/.f64 #s(literal 6125 binary64) (.f64 x x))) (.f64 x (*.f64 x x)))
(/ (- (* 6125 (/ 1 (pow x 2))) (+ 175 (/ 306250 (pow x 4)))) (pow x 3))
(/.f64 (-.f64 #s(literal -175 binary64) (+.f64 (/.f64 #s(literal 306250 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -6125 binary64) (.f64 x x)))) (.f64 x (.f64 x x)))
(/ (- (+ (* 6125 (/ 1 (pow x 2))) (* 13934375 (/ 1 (pow x 6)))) (+ 175 (/ 306250 (pow x 4)))) (pow x 3))
(/.f64 (+.f64 (+.f64 #s(literal -175 binary64) (/.f64 #s(literal 6125 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 13934375 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 306250 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x x)))
(/ -175 (pow x 3))
(/.f64 (/.f64 #s(literal -175 binary64) (*.f64 x x)) x)
(* -1 (/ (- 175 (* 6125 (/ 1 (pow x 2)))) (pow x 3)))
(/.f64 (+.f64 #s(literal -175 binary64) (/.f64 #s(literal 6125 binary64) (.f64 x x))) (.f64 x (*.f64 x x)))
(* -1 (/ (- (+ 175 (/ 306250 (pow x 4))) (* 6125 (/ 1 (pow x 2)))) (pow x 3)))
(/.f64 (-.f64 #s(literal -175 binary64) (+.f64 (/.f64 #s(literal 306250 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -6125 binary64) (.f64 x x)))) (.f64 x (.f64 x x)))
(* -1 (/ (- (+ 175 (/ 306250 (pow x 4))) (+ (* 6125 (/ 1 (pow x 2))) (* 13934375 (/ 1 (pow x 6))))) (pow x 3)))
(/.f64 (+.f64 (+.f64 #s(literal -175 binary64) (/.f64 #s(literal 6125 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 13934375 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 306250 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x x)))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64))))))
(+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64))))))
(* -1/175 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/175 binary64))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 (/.f64 #s(literal 3 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 (/.f64 #s(literal 3 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))
(* -1/175 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/175 binary64))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 (/.f64 #s(literal 3 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (/ 3 (pow x 4)) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 (/.f64 #s(literal 3 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))
(.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))
(* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))
(.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))
(* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))
(.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))
(* -1/175 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/175 binary64))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* -1/175 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/175 binary64))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* -1 (* (pow x 4) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/175 binary64) (/.f64 #s(literal -1/5 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* x (- (* -1/175 (pow x 2)) 1/5))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
(* x (- (* -1/175 (pow x 2)) 1/5))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
(* x (- (* -1/175 (pow x 2)) 1/5))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
(* -1/175 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/175 binary64)))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
(* -1/175 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/175 binary64)))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 binary64))))
(* -1 (* (pow x 3) (+ 1/175 (* 1/5 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (*.f64 x x) #s(literal -1/175 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 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 1/675 (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 1/675 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (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 (+.f64 #s(literal 1/675 binary64) (.f64 (*.f64 x x) #s(literal 1/10125 binary64)))))))))
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 (-.f64 #s(literal -75 binary64) (/.f64 #s(literal 1125 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 #s(literal -5 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1125 binary64) (/.f64 #s(literal -16875 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -75 binary64) (*.f64 x x)))) x)
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (.f64 x x))) (/.f64 #s(literal -1125 binary64) (.f64 x (.f64 x (.f64 x x))))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (.f64 x x))) (/.f64 #s(literal -16875 binary64) (pow.f64 x #s(literal 6 binary64))))) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 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)
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))
(* -1/175 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/175 binary64))

eval63.0ms (0.5%)

Compiler: Compiled 16945 to 1411 computations (91.7% saved)

prune89.0ms (0.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	527	2	529
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	527	5	532

Accuracy

100.0%

Counts

532 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))) (/.f64 #s(literal 1 binary64) x))
✓	99.8%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
✓	100.0%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))))
✓	99.1%	(/.f64 x #s(literal 3 binary64))
	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))) x))

Compiler

Compiled 199 to 99 computations (50.3% saved)

regimes8.0ms (0.1%)

Counts

13 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 x #s(literal 3 binary64))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 #s(literal 1/3 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))) (/.f64 #s(literal 1 binary64) x))
(.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)))))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))))
(+.f64 (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (-.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 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Outputs
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))))

Calls

2 calls:

4.0ms	x
3.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	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)

regimes13.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 x #s(literal 3 binary64))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 #s(literal 1/3 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))) (/.f64 #s(literal 1 binary64) x))
(.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)))))))

Outputs
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))

Calls

1 calls:

13.0ms

Results

Accuracy	Segments	Branch
99.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

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

2.0ms

Results

Accuracy	Segments	Branch
99.2%	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 #s(literal 3 binary64))

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.1%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (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
98.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
16×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	36	39
2	51	39
3	59	39
4	65	39
5	67	39

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 x #s(literal 3 binary64))
(*.f64 #s(literal 1/3 binary64) x)

Outputs
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal -1/175 binary64)))))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 #s(literal -1/5 binary64) (.f64 x x))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 x #s(literal 3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))

soundness931.0ms (7.4%)

Rules

5384×	`-lowering-.f32`
5384×	`-lowering-.f64`
2582×	`/-lowering-/.f32`
2582×	`/-lowering-/.f64`
2522×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	84	60
2	680	56
0	8182	56
0	128	1663
1	369	1387
2	1056	1377
3	2832	1356
4	6943	1356
0	8385	1356
0	67	302
1	186	269
2	560	266
3	1807	266
4	2716	266
5	4431	266
6	6050	266
7	6596	266
0	8084	266

Stop Event

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

Compiler

Compiled 130 to 86 computations (33.8% saved)

preprocess50.0ms (0.4%)

Remove: (negabs x)
Compiler: Compiled 244 to 154 computations (36.9% saved)

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

analyze7.0ms (0.1%)

sample7.7s (60.6%)

preprocess40.0ms (0.3%)

explain518.0ms (4.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify19.0ms (0.2%)

localize200.0ms (1.6%)

series4.0ms (0%)

rewrite225.0ms (1.8%)

simplify218.0ms (1.7%)

eval38.0ms (0.3%)

prune30.0ms (0.2%)

simplify116.0ms (0.9%)

localize100.0ms (0.8%)

series22.0ms (0.2%)

rewrite286.0ms (2.3%)

simplify159.0ms (1.3%)

eval72.0ms (0.6%)

prune52.0ms (0.4%)

simplify185.0ms (1.5%)

localize147.0ms (1.2%)

series11.0ms (0.1%)

rewrite345.0ms (2.7%)

simplify212.0ms (1.7%)

eval110.0ms (0.9%)

prune75.0ms (0.6%)

simplify9.0ms (0.1%)

localize69.0ms (0.5%)

series9.0ms (0.1%)

rewrite284.0ms (2.3%)

simplify241.0ms (1.9%)

eval63.0ms (0.5%)

prune89.0ms (0.7%)

regimes8.0ms (0.1%)

regimes13.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

simplify9.0ms (0.1%)

soundness931.0ms (7.4%)

preprocess50.0ms (0.4%)

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