Metrics for invcot (example 3.9)

analyze15.0ms (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: 9.0ms

...c/correct-round.rkt:119:19: 3.0ms (33.7% of total)

ival-div: 2.0ms (22.5% of total)

ival-sub: 1.0ms (11.2% of total)

ival-tan: 1.0ms (11.2% of total)

ival-<: 1.0ms (11.2% of total)

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

const: 0.0ms (0% of total)

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

sample10.1s (36.5%)

Results

5.7s	4452×	2	valid
1.9s	1372×	3	valid
1.6s	2379×	1	valid
10.0ms	53×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.4s

ival-tan: 5.0s (59.1% of total)

ival-div: 1.6s (19.1% of total)

...c/correct-round.rkt:119:19: 486.0ms (5.8% of total)

backward-pass: 451.0ms (5.4% of total)

ival-<: 439.0ms (5.2% of total)

ival-sub: 402.0ms (4.8% of total)

const: 30.0ms (0.4% of total)

ival-and: 25.0ms (0.3% of total)

Bogosity

preprocess83.0ms (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)

explain544.0ms (2%)

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

329.0ms	276×	2	valid
74.0ms	78×	3	valid
62.0ms	152×	1	valid
1.0ms	6×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 352.0ms

ival-tan: 248.0ms (70.4% of total)

ival-div: 53.0ms (15% of total)

backward-pass: 32.0ms (9.1% of total)

ival-sub: 16.0ms (4.5% of total)

const: 3.0ms (0.9% of total)

eval1.0ms (0%)

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

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.9%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify49.0ms (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)

localize277.0ms (1%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(tan.f64 x)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (tan.f64 x))
✓	accuracy	6.9%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

185.0ms	138×	2	valid
38.0ms	39×	3	valid
28.0ms	76×	1	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: 191.0ms

ival-tan: 141.0ms (73.8% of total)

ival-div: 27.0ms (14.1% of total)

backward-pass: 14.0ms (7.3% of total)

ival-sub: 8.0ms (4.2% of total)

const: 1.0ms (0.5% of total)

series11.0ms (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
2.0ms	x	@	inf	(- (/ 1 x) (/ 1 (tan x)))
2.0ms	x	@	-inf	(- (/ 1 x) (/ 1 (tan x)))
2.0ms	x	@	0	(- (/ 1 x) (/ 1 (tan x)))
1.0ms	x	@	inf	(/ 1 (tan x))
1.0ms	x	@	-inf	(/ 1 (tan x))

rewrite485.0ms (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	483	13
3	6182	13
0	8127	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 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x))) (.f64 x (*.f64 x x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x))))))
(+.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 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 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x))) (.f64 x (*.f64 x x)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) 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 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (tan.f64 x))) (.f64 x (*.f64 x x)))) (-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) 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 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 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 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 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 #s(literal 1 binary64) (*.f64 (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 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) 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 (/.f64 #s(literal 1 binary64) 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 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) 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 (/.f64 #s(literal 1 binary64) 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 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) 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 (/.f64 #s(literal 1 binary64) 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 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (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 0 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(exp.f64 (log.f64 (tan.f64 x)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(tan.f64 x)
(neg.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.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))

simplify440.0ms (1.6%)

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	287
2	559	281
3	1807	281
4	2717	281
5	4432	281
6	6049	281
7	6591	281
0	8079	281

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 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 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 x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 2/15 binary64)))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 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))

eval74.0ms (0.3%)

Compiler: Compiled 5571 to 677 computations (87.8% saved)

prune73.0ms (0.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	266	4	270
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	267	4	271

Accuracy

99.5%

Counts

271 → 4

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))))
▶	99.5%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))))
▶	98.5%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 52 to 36 computations (30.8% saved)

simplify374.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 13 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 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64)))))))
✓	cost-diff	(.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (.f64 x x) #s(literal 1/4725 binary64))))))))
✓	cost-diff	(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (.f64 x x) #s(literal 1/4725 binary64)))))))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))))
✓	cost-diff	(*.f64 #s(literal 1/3 binary64) x)

Rules

2172×	`-lowering-.f32`
2172×	`-lowering-.f64`
970×	`fnmsub-define`
964×	`fma-define`
910×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	218
1	84	199
2	261	195
3	844	195
4	2501	195
5	5153	195
6	7288	195
0	8042	195

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 (* x (+ 2/945 (* (* x x) 1/4725)))))))))
x
(+ 1/3 (* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725))))))))
1/3
(* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))))
(* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725))))))
(+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))
1/45
(* x (* x (+ 2/945 (* (* x x) 1/4725))))
(* x (+ 2/945 (* (* x x) 1/4725)))
(+ 2/945 (* (* x x) 1/4725))
2/945
(* (* x x) 1/4725)
(* x x)
1/4725
(* 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 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))))))
(.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 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64)))))))))
x
(+ 1/3 (* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725))))))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (.f64 x x) #s(literal 1/4725 binary64))))))))
1/3
#s(literal 1/3 binary64)
(* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (.f64 x x) #s(literal 1/4725 binary64)))))))
(* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725))))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64)))))))
(+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))
(+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (.f64 x x) #s(literal 1/4725 binary64))))))
1/45
#s(literal 1/45 binary64)
(* x (* x (+ 2/945 (* (* x x) 1/4725))))
(.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (.f64 x x) #s(literal 1/4725 binary64)))))
(* x (+ 2/945 (* (* x x) 1/4725)))
(.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))
(+ 2/945 (* (* x x) 1/4725))
(+.f64 #s(literal 2/945 binary64) (.f64 (.f64 x x) #s(literal 1/4725 binary64)))
2/945
#s(literal 2/945 binary64)
(* (* x x) 1/4725)
(.f64 (.f64 x x) #s(literal 1/4725 binary64))
(* x x)
(*.f64 x x)
1/4725
#s(literal 1/4725 binary64)
(* x (- 1/3 (* (* x x) -1/45)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
x
(- 1/3 (* (* x x) -1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
1/3
#s(literal 1/3 binary64)
(* (* x x) -1/45)
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* x x)
(*.f64 x x)
-1/45
#s(literal -1/45 binary64)
(* x (- 1/3 (* (* x x) (+ -1/45 (* x (* x -2/945))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
x
(- 1/3 (* (* x x) (+ -1/45 (* x (* x -2/945)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
1/3
#s(literal 1/3 binary64)
(* (* x x) (+ -1/45 (* x (* x -2/945))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64)))))
(* x x)
(*.f64 x x)
(+ -1/45 (* x (* x -2/945)))
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
-1/45
#s(literal -1/45 binary64)
(* x (* x -2/945))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* x -2/945)
(*.f64 x #s(literal -2/945 binary64))
-2/945
#s(literal -2/945 binary64)

localize354.0ms (1.3%)

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -2/945 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64)))))
✓	accuracy	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
✓	accuracy	99.3%	(*.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	99.8%	(.f64 (.f64 x x) #s(literal -1/45 binary64))
✓	accuracy	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/4725 binary64))
✓	accuracy	99.7%	(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64)))))))
✓	accuracy	99.5%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))))
✓	accuracy	99.3%	(.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))
✓	accuracy	99.5%	(*.f64 #s(literal 1/3 binary64) x)

Results

252.0ms

256×

valid

Compiler

Compiled 220 to 28 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 149.0ms

ival-mult: 92.0ms (61.9% of total)

...c/correct-round.rkt:119:19: 39.0ms (26.2% of total)

ival-add: 12.0ms (8.1% of total)

ival-sub: 6.0ms (4% of total)

const: 0.0ms (0% of total)

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

series33.0ms (0.1%)

Counts

16 → 192

Calls

Call 1

Inputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))))))>
#<alt (+ 1/3 (* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725))))))))>
#<alt (* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))))>
#<alt (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725))))))>
#<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 (* (* x x) 1/4725)))>
#<alt (* (* x x) 1/4725)>
#<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 (* (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 (* 1/4725 (pow x 7))>
#<alt (* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))>
#<alt (* 1/4725 (pow x 7))>
#<alt (* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))))>
#<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 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))>
#<alt (* 1/4725 (pow x 6))>
#<alt (* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))>
#<alt (* 1/4725 (pow x 6))>
#<alt (* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))>
#<alt (* 1/4725 (pow x 6))>
#<alt (* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))>
#<alt (* 1/4725 (pow x 6))>
#<alt (* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))>
#<alt (* 1/45 x)>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* x (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))>
#<alt (* x (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))>
#<alt (* 1/4725 (pow x 5))>
#<alt (* (pow x 5) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))>
#<alt (* 1/4725 (pow x 5))>
#<alt (* (pow x 5) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))>
#<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 (* x (+ 2/945 (* 1/4725 (pow x 2))))>
#<alt (* x (+ 2/945 (* 1/4725 (pow x 2))))>
#<alt (* x (+ 2/945 (* 1/4725 (pow x 2))))>
#<alt (* 1/4725 (pow x 3))>
#<alt (* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* 1/4725 (pow x 3))>
#<alt (* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (pow x 2))>
#<alt (* 1/4725 (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

48 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(* x (- 1/3 (* (* x x) -1/45)))
2.0ms	x	@	0	(* 1/3 x)
2.0ms	x	@	inf	(* x (+ 1/3 (* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))))))
1.0ms	x	@	inf	(* x (- 1/3 (* (* x x) -1/45)))
1.0ms	x	@	inf	(* x (- 1/3 (* (* x x) (+ -1/45 (* x (* x -2/945))))))

rewrite854.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3976×	`-lowering-.f32`
3976×	`-lowering-.f64`
3252×	`/-lowering-/.f32`
3252×	`/-lowering-/.f64`
2070×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	160
1	162	146
2	1364	142
0	8168	142

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 369

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))))))
(+ 1/3 (* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725))))))))
(* x (* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725)))))))
(* x (+ 1/45 (* x (* x (+ 2/945 (* (* x x) 1/4725))))))
(* 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) 1/4725)))
(* (* x x) 1/4725)
(* 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) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64)))))))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64)))))))) (.f64 #s(literal 1/3 binary64) x))
(-.f64 (/.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64)))))))))) (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64)))))))) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64))))))))) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64)))))))))))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (*.f64 x #s(literal 1/4725 binary64)))))))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (*.f64 x #s(literal 1/4725 binary64)))))))))
(fma.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64))))))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64))))))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64))))))) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64))))))) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64)))))) (*.f64 #s(literal 1/3 binary64) x))
(/.f64 (+.f64 (.f64 #s(literal 1/27 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64)))))) (.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64)))))) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64))))))))) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64)))))))) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x #s(literal 1/4725 binary64))))))))) (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 x (*.f64 x #s(literal 1/4725 binary64))))))))))))
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(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/105488578125 binary64))) (.f64 x (.f64 x x))) (.f64 #s(literal 8/843908625 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 #s(literal 1/4725 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/4725 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 (.f64 x #s(literal 2/945 binary64)) (.f64 x #s(literal 2/945 binary64))) (.f64 (.f64 #s(literal 1/4725 binary64) (.f64 x (.f64 x x))) (*.f64 x #s(literal 2/945 binary64))))))
(.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 x (*.f64 x #s(literal 1/4725 binary64)))))
(.f64 (+.f64 #s(literal 2/945 binary64) (.f64 x (*.f64 x #s(literal 1/4725 binary64)))) x)
(.f64 x (.f64 x #s(literal 1/4725 binary64)))
(.f64 (.f64 x x) #s(literal 1/4725 binary64))
(.f64 #s(literal 1/4725 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/4725 binary64)) x)
(*.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)

simplify564.0ms (2%)

Algorithm

1×	egg-herbie

Rules

2724×	`-lowering-.f32`
2724×	`-lowering-.f64`
1742×	`fma-lowering-fma.f32`
1742×	`fma-lowering-fma.f64`
1336×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1531
1	361	1445
2	1111	1438
3	3128	1424
4	6486	1424
0	8169	1424

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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 (* 1/4725 (pow x 2))))))))
(* 1/4725 (pow x 7))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 1/4725 (pow x 7))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))))
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 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))
(* 1/4725 (pow x 6))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 1/4725 (pow x 6))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))
(* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))
(* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))
(* 1/4725 (pow x 6))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* 1/4725 (pow x 6))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* 1/45 x)
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))
(* x (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))
(* 1/4725 (pow x 5))
(* (pow x 5) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* 1/4725 (pow x 5))
(* (pow x 5) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))
(* 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)
(* x (+ 2/945 (* 1/4725 (pow x 2))))
(* x (+ 2/945 (* 1/4725 (pow x 2))))
(* x (+ 2/945 (* 1/4725 (pow x 2))))
(* 1/4725 (pow x 3))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* 1/4725 (pow x 3))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (pow x 2))
(* 1/4725 (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 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))
(* 1/4725 (pow x 7))
(*.f64 #s(literal 1/4725 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (/.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (*.f64 x x))) (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 6 binary64))))))
(* 1/4725 (pow x 7))
(*.f64 #s(literal 1/4725 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/4725 binary64) (/.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (*.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (/.f64 (+.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1/3 binary64) (.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 #s(literal 1/45 binary64) (.f64 x x)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))
(+.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)))))))
(* 1/4725 (pow x 6))
(*.f64 #s(literal 1/4725 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (/.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(+.f64 #s(literal 1/3 binary64) (.f64 (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (/.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64))))
(* 1/4725 (pow x 6))
(*.f64 #s(literal 1/4725 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (/.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(+.f64 #s(literal 1/3 binary64) (.f64 (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (/.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64))))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))
(.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))))))
(* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))
(.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))))))
(* 1/4725 (pow x 6))
(*.f64 #s(literal 1/4725 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (/.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (/.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* 1/4725 (pow x 6))
(*.f64 #s(literal 1/4725 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))) (/.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
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eval200.0ms (0.7%)

Compiler: Compiled 21065 to 1761 computations (91.6% saved)

prune189.0ms (0.7%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	591	6	597
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	591	10	601

Accuracy

100.0%

Counts

601 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(/.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
▶	99.3%	(/.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
▶	99.2%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))) x)))
▶	99.2%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x)))
▶	99.4%	(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))) x))
	98.6%	(.f64 x (/.f64 (.f64 (-.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) #s(literal 1 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 (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))))
✓	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))))
✓	99.5%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))))
✓	98.5%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 456 to 246 computations (46.1% saved)

simplify411.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
✓	cost-diff	128	(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
✓	cost-diff	128	(/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x)))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))) x)
✓	cost-diff	128	(.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
✓	cost-diff	128	(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
✓	cost-diff	128	(/.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))) x))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))) x)))
✓	cost-diff	0	(.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))
✓	cost-diff	0	(-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))
✓	cost-diff	0	(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))) x)
✓	cost-diff	0	(/.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) x)
✓	cost-diff	128	(.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
✓	cost-diff	128	(.f64 (.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x))) x)
✓	cost-diff	256	(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))) x))

Rules

2288×	`sum3-define`
2208×	`sum5-define`
2032×	`fnmadd-define`
1736×	`-lowering-.f32`
1736×	`-lowering-.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	523
1	109	464
2	346	394
3	1217	394
4	3042	392
5	5495	392
0	8477	392

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* 1/3 x) (* (* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x))) x))
(* 1/3 x)
1/3
x
(* (* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x))) x)
(* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x)))
(+ -1/45 (* (* x x) -2/945))
-1/45
(* (* x x) -2/945)
(* x x)
-2/945
(- 0 (* x x))
0
(/ (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x) (+ 1/3 (* x (* x -1/45))))
(* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)
(- 1/9 (* 1/2025 (* (* x x) (* x x))))
1/9
(* 1/2025 (* (* x x) (* x x)))
1/2025
(* (* x x) (* x x))
(* x x)
x
(+ 1/3 (* x (* x -1/45)))
1/3
(* x (* x -1/45))
(* x -1/45)
-1/45
(/ 1 (/ (+ 1/3 (* x (* x -1/45))) (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)))
1
(/ (+ 1/3 (* x (* x -1/45))) (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x))
(+ 1/3 (* x (* x -1/45)))
1/3
(* x (* x -1/45))
x
(* x -1/45)
-1/45
(* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)
(- 1/9 (* 1/2025 (* (* x x) (* x x))))
1/9
(* 1/2025 (* (* x x) (* x x)))
1/2025
(* (* x x) (* x x))
(* x x)
(/ (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x) (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))))
(* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)
(+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x)))))
1/27
(* 1/91125 (* (* x x) (* (* x x) (* x x))))
1/91125
(* (* x x) (* (* x x) (* x x)))
(* x x)
x
(* (* x x) (* x x))
(+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45)))))
1/9
(* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))
(* x (* x -1/45))
(* x -1/45)
-1/45
(+ 1/3 (* x (* x -1/45)))
1/3
(/ 1 (/ (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))) (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)))
1
(/ (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))) (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x))
(+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45)))))
1/9
(* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))
(* x (* x -1/45))
x
(* x -1/45)
-1/45
(+ 1/3 (* x (* x -1/45)))
1/3
(* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)
(+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x)))))
1/27
(* 1/91125 (* (* x x) (* (* x x) (* x x))))
1/91125
(* (* x x) (* (* x x) (* x x)))
(* x x)
(* (* x x) (* x x))

Outputs
(+ (* 1/3 x) (* (* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x))) x))
(.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)))))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
1/3
#s(literal 1/3 binary64)
x
(* (* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x))) x)
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x)))
(.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(+ -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))
(* x x)
(*.f64 x x)
-2/945
#s(literal -2/945 binary64)
(- 0 (* x x))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
0
#s(literal 0 binary64)
(/ (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x) (+ 1/3 (* x (* x -1/45))))
(/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/2025 binary64)))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/45 binary64) (.f64 x x))) x))
(* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/2025 binary64)))))
(- 1/9 (* 1/2025 (* (* x x) (* x x))))
(+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/2025 binary64))))
1/9
#s(literal 1/9 binary64)
(* 1/2025 (* (* x x) (* x x)))
(.f64 x (.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x x))))
1/2025
#s(literal 1/2025 binary64)
(* (* x x) (* x x))
(.f64 x (.f64 x (*.f64 x x)))
(* x x)
(*.f64 x x)
x
(+ 1/3 (* x (* x -1/45)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/45 binary64) (.f64 x x)))
1/3
#s(literal 1/3 binary64)
(* x (* x -1/45))
(.f64 #s(literal -1/45 binary64) (.f64 x x))
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(/ 1 (/ (+ 1/3 (* x (* x -1/45))) (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)))
(/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/2025 binary64)))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/45 binary64) (.f64 x x))) x))
1
#s(literal 1 binary64)
(/ (+ 1/3 (* x (* x -1/45))) (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x))
(/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/45 binary64) (.f64 x x))) (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/2025 binary64))))))
(+ 1/3 (* x (* x -1/45)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/45 binary64) (.f64 x x)))
1/3
#s(literal 1/3 binary64)
(* x (* x -1/45))
(.f64 #s(literal -1/45 binary64) (.f64 x x))
x
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/2025 binary64)))))
(- 1/9 (* 1/2025 (* (* x x) (* x x))))
(+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/2025 binary64))))
1/9
#s(literal 1/9 binary64)
(* 1/2025 (* (* x x) (* x x)))
(.f64 x (.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x x))))
1/2025
#s(literal 1/2025 binary64)
(* (* x x) (* x x))
(.f64 x (.f64 x (*.f64 x x)))
(* x x)
(*.f64 x x)
(/ (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x) (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))))
(/.f64 x (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/2025 binary64))) #s(literal -1/135 binary64)))) (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x #s(literal 1/91125 binary64))))))))
(* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)
(.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal 1/91125 binary64)))))))
(+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x)))))
(+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x #s(literal 1/91125 binary64))))))
1/27
#s(literal 1/27 binary64)
(* 1/91125 (* (* x x) (* (* x x) (* x x))))
(.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x #s(literal 1/91125 binary64)))))
1/91125
#s(literal 1/91125 binary64)
(* (* x x) (* (* x x) (* x x)))
(.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))
(* x x)
(*.f64 x x)
x
(* (* x x) (* x x))
(.f64 x (.f64 x (*.f64 x x)))
(+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45)))))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/2025 binary64))) #s(literal -1/135 binary64))))
1/9
#s(literal 1/9 binary64)
(* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))
(.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/2025 binary64))) #s(literal -1/135 binary64)))
(* x (* x -1/45))
(.f64 #s(literal -1/45 binary64) (.f64 x x))
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(+ 1/3 (* x (* x -1/45)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/45 binary64) (.f64 x x)))
1/3
#s(literal 1/3 binary64)
(/ 1 (/ (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))) (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)))
(/.f64 x (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/2025 binary64))) #s(literal -1/135 binary64)))) (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x #s(literal 1/91125 binary64))))))))
1
#s(literal 1 binary64)
(/ (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))) (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x))
(/.f64 (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/2025 binary64))) #s(literal -1/135 binary64)))) x) (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x #s(literal 1/91125 binary64)))))))
(+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45)))))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/2025 binary64))) #s(literal -1/135 binary64))))
1/9
#s(literal 1/9 binary64)
(* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))
(.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/2025 binary64))) #s(literal -1/135 binary64)))
(* x (* x -1/45))
(.f64 #s(literal -1/45 binary64) (.f64 x x))
x
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(+ 1/3 (* x (* x -1/45)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/45 binary64) (.f64 x x)))
1/3
#s(literal 1/3 binary64)
(* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)
(.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal 1/91125 binary64)))))))
(+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x)))))
(+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x #s(literal 1/91125 binary64))))))
1/27
#s(literal 1/27 binary64)
(* 1/91125 (* (* x x) (* (* x x) (* x x))))
(.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x #s(literal 1/91125 binary64)))))
1/91125
#s(literal 1/91125 binary64)
(* (* x x) (* (* x x) (* x x)))
(.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))
(* x x)
(*.f64 x x)
(* (* x x) (* x x))
(.f64 x (.f64 x (*.f64 x x)))

localize658.0ms (2.4%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x)))
✓	accuracy	99.4%	(.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))) x)
✓	accuracy	99.3%	(/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x))
✓	accuracy	99.7%	(.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.4%	(.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))) x)
✓	accuracy	99.4%	(/.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))) x)))
✓	accuracy	99.4%	(/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))) x))
✓	accuracy	99.4%	(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))) x)
✓	accuracy	99.8%	(.f64 (.f64 x x) (*.f64 x x))
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.4%	(/.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
✓	accuracy	99.4%	(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))) x)
✓	accuracy	99.9%	(.f64 (.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x))) x)
✓	accuracy	99.8%	(.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
✓	accuracy	99.6%	(.f64 (.f64 x x) #s(literal -2/945 binary64))
✓	accuracy	99.5%	(*.f64 #s(literal 1/3 binary64) x)

Results

391.0ms

256×

valid

Compiler

Compiled 601 to 38 computations (93.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 178.0ms

ival-mult: 86.0ms (48.3% of total)

...c/correct-round.rkt:119:19: 48.0ms (27% of total)

ival-div: 23.0ms (12.9% of total)

ival-add: 14.0ms (7.9% of total)

ival-sub: 6.0ms (3.4% of total)

const: 1.0ms (0.6% of total)

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

series40.0ms (0.1%)

Counts

21 → 252

Calls

Call 1

Inputs
#<alt (+ (* 1/3 x) (* (* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x))) x))>
#<alt (* (* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x))) x)>
#<alt (* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x)))>
#<alt (* 1/3 x)>
#<alt (/ (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x) (+ 1/3 (* x (* x -1/45))))>
#<alt (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)>
#<alt (- 1/9 (* 1/2025 (* (* x x) (* x x))))>
#<alt (* 1/2025 (* (* x x) (* x x)))>
#<alt (/ 1 (/ (+ 1/3 (* x (* x -1/45))) (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)))>
#<alt (/ (+ 1/3 (* x (* x -1/45))) (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x))>
#<alt (+ 1/3 (* x (* x -1/45)))>
#<alt (* x (* x -1/45))>
#<alt (/ (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x) (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))))>
#<alt (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45)))))>
#<alt (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))>
#<alt (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)>
#<alt (/ 1 (/ (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))) (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)))>
#<alt (/ (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))) (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x))>
#<alt (* (* x x) -2/945)>
#<alt (* x -1/45)>
#<alt (* (* x x) (* x 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 (* 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 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* (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 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 2/945 (* 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 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (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 (* 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 (* 1/9 x)>
#<alt (* x (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* x (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* x (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* -1/2025 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* -1/2025 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))>
#<alt 1/9>
#<alt (+ 1/9 (* -1/2025 (pow x 4)))>
#<alt (+ 1/9 (* -1/2025 (pow x 4)))>
#<alt (+ 1/9 (* -1/2025 (pow x 4)))>
#<alt (* -1/2025 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* -1/2025 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<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 x)>
#<alt (/ (+ 3 (* -1/5 (pow x 2))) x)>
#<alt (/ (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) x)>
#<alt (/ (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) x)>
#<alt (/ 45 (pow x 3))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 3))>
#<alt (/ 45 (pow x 3))>
#<alt (* -1 (/ (- (* 675 (/ 1 (pow x 2))) 45) (pow x 3)))>
#<alt (* -1 (/ (- (* 675 (/ 1 (pow x 2))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6)))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))>
#<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) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* -1/45 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 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 1/9>
#<alt (+ 1/9 (* -1/135 (pow x 2)))>
#<alt (+ 1/9 (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135)))>
#<alt (+ 1/9 (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135)))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* -1/135 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))>
#<alt (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))>
#<alt (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* 1/27 x)>
#<alt (* x (+ 1/27 (* 1/91125 (pow x 6))))>
#<alt (* x (+ 1/27 (* 1/91125 (pow x 6))))>
#<alt (* x (+ 1/27 (* 1/91125 (pow x 6))))>
#<alt (* 1/91125 (pow x 7))>
#<alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))>
#<alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))>
#<alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))>
#<alt (* 1/91125 (pow x 7))>
#<alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))>
#<alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))>
#<alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))>
#<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 x)>
#<alt (/ (+ 3 (* -1/5 (pow x 2))) x)>
#<alt (/ (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) x)>
#<alt (/ (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) x)>
#<alt (/ 45 (pow x 3))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 3))>
#<alt (/ 45 (pow x 3))>
#<alt (* -1 (/ (- (* 675 (/ 1 (pow x 2))) 45) (pow x 3)))>
#<alt (* -1 (/ (- (* 675 (/ 1 (pow x 2))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6)))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))>
#<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 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>

Calls

63 calls:

Time	Variable		Point	Expression
9.0ms	x	@	0	(/ (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x) (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))))
3.0ms	x	@	inf	(/ (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x) (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))))
2.0ms	x	@	inf	(/ (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x) (+ 1/3 (* x (* x -1/45))))
2.0ms	x	@	0	(/ (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x) (+ 1/3 (* x (* x -1/45))))
2.0ms	x	@	inf	(* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)

rewrite1.3s (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3566×	`-lowering-.f32`
3566×	`-lowering-.f64`
2830×	`/-lowering-/.f32`
2830×	`/-lowering-/.f64`
2542×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	274
1	224	204
2	2007	196
0	9402	196

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 872

Calls

Call 1

Inputs
(+ (* 1/3 x) (* (* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x))) x))
(* (* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x))) x)
(* (+ -1/45 (* (* x x) -2/945)) (- 0 (* x x)))
(* 1/3 x)
(/ (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x) (+ 1/3 (* x (* x -1/45))))
(* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)
(- 1/9 (* 1/2025 (* (* x x) (* x x))))
(* 1/2025 (* (* x x) (* x x)))
(/ 1 (/ (+ 1/3 (* x (* x -1/45))) (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x)))
(/ (+ 1/3 (* x (* x -1/45))) (* (- 1/9 (* 1/2025 (* (* x x) (* x x)))) x))
(+ 1/3 (* x (* x -1/45)))
(* x (* x -1/45))
(/ (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x) (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))))
(+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45)))))
(* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))
(* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)
(/ 1 (/ (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))) (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x)))
(/ (+ 1/9 (* (* x (* x -1/45)) (+ 1/3 (* x (* x -1/45))))) (* (+ 1/27 (* 1/91125 (* (* x x) (* (* x x) (* x x))))) x))
(* (* x x) -2/945)
(* x -1/45)
(* (* x x) (* x x))

Outputs
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(.f64 (/.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/91125 binary64)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))) x) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.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 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) #s(literal 1/9 binary64))))) (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/91125 binary64))))))
(.f64 (/.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/91125 binary64)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))) (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.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 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))) #s(literal 1/9 binary64))))) x))
(.f64 (/.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))) x) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 (.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 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))) (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))) x))
(.f64 (/.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/91125 binary64)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.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 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) #s(literal 1/9 binary64))))) (.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64)))))))
(.f64 (/.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 (.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 x (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/91125 binary64)))))))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))) (neg.f64 (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64)))))))
(.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64))))) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.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 #s(literal 0 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/91125 binary64)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64)))))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.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 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) #s(literal 1/9 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64)))))) (-.f64 #s(literal 1/9 binary64) (.f64 (.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 #s(literal 1/9 binary64) (.f64 (.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 #s(literal 1/19683 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/756680642578125 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64))) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64)))) x))
(.f64 (/.f64 (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.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 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8303765625 binary64))))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/91125 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 x #s(literal -1/45 binary64))
(*.f64 #s(literal -1/45 binary64) x)
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (.f64 #s(literal 2 binary64) (log.f64 x))))
(-.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) x #s(literal 0 binary64))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64)) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 0 binary64)))))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64)) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64))) (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 0 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x))))))
(pow.f64 x #s(literal 4 binary64))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(.f64 x (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 x x))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(.f64 (.f64 x (*.f64 x x)) x)

simplify640.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

4016×	`-lowering-.f32`
4016×	`-lowering-.f64`
1500×	`/-lowering-/.f32`
1500×	`/-lowering-/.f64`
1300×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1941
1	399	1840
2	1101	1834
3	2955	1809
4	7523	1809
0	8068	1809

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

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 (* 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 (pow x 2))
(* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))
(* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))
(* (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 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (* 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 (* 1/45 (/ 1 (pow x 2)))))
(* (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)
(* 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)))))
(* 1/9 x)
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(* -1/2025 (pow x 5))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* -1/2025 (pow x 5))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
1/9
(+ 1/9 (* -1/2025 (pow x 4)))
(+ 1/9 (* -1/2025 (pow x 4)))
(+ 1/9 (* -1/2025 (pow x 4)))
(* -1/2025 (pow x 4))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* -1/2025 (pow x 4))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 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 x)
(/ (+ 3 (* -1/5 (pow x 2))) x)
(/ (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) x)
(/ (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) x)
(/ 45 (pow x 3))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 3))
(/ 45 (pow x 3))
(* -1 (/ (- (* 675 (/ 1 (pow x 2))) 45) (pow x 3)))
(* -1 (/ (- (* 675 (/ 1 (pow x 2))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))
(* -1 (/ (- (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6)))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))
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) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* -1/45 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 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)))))
1/9
(+ 1/9 (* -1/135 (pow x 2)))
(+ 1/9 (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135)))
(+ 1/9 (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135)))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))
(* -1/135 (pow x 2))
(* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))
(* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))
(* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* 1/27 x)
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(* 1/91125 (pow x 7))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* 1/91125 (pow x 7))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* 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 x)
(/ (+ 3 (* -1/5 (pow x 2))) x)
(/ (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) x)
(/ (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) x)
(/ 45 (pow x 3))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 3))
(/ 45 (pow x 3))
(* -1 (/ (- (* 675 (/ 1 (pow x 2))) 45) (pow x 3)))
(* -1 (/ (- (* 675 (/ 1 (pow x 2))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))
(* -1 (/ (- (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6)))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))
(* -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 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)

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 (* (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 #s(literal 2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* (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 #s(literal 2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 x (.f64 (.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 x (.f64 (.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 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* 2/945 (pow x 5))
(.f64 x (.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* 2/945 (pow x 5))
(.f64 x (.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 2) (+ 1/45 (* 2/945 (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 #s(literal 2/945 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* 2/945 (pow x 4))
(.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x 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)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/9 x)
(*.f64 x #s(literal 1/9 binary64))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
(* -1/2025 (pow x 5))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/2025 binary64))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
(* -1/2025 (pow x 5))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/2025 binary64))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* -1/2025 (pow x 4)))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))
(+ 1/9 (* -1/2025 (pow x 4)))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))
(+ 1/9 (* -1/2025 (pow x 4)))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))
(* -1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))
(* -1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 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 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
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(pow x 4)
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(pow x 4)
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(pow x 4)
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(pow x 4)
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(pow x 4)
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(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
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(pow x 4)
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(pow x 4)
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(pow x 4)
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eval659.0ms (2.4%)

Compiler: Compiled 66892 to 3393 computations (94.9% saved)

prune350.0ms (1.3%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	1768	8	1776
Fresh	1	0	1
Picked	5	0	5
Done	0	4	4
Total	1774	12	1786

Accuracy

100.0%

Counts

1786 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.6%	(/.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))) x) #s(literal 1/9 binary64))
	99.3%	(/.f64 (.f64 x #s(literal 1/9 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
▶	98.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
▶	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))
▶	99.4%	(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (.f64 x x))))
▶	99.4%	(.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
▶	99.3%	(.f64 (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.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 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64)))))
	98.8%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) 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 x (*.f64 x #s(literal -1/45 binary64))))))
✓	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))))
✓	99.5%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))))
✓	98.5%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 364 to 240 computations (34.1% saved)

simplify692.0ms (2.5%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
✓	cost-diff	128	(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))
✓	cost-diff	128	(/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))))
✓	cost-diff	128	(.f64 (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.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 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64)))))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))
✓	cost-diff	0	(/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))
✓	cost-diff	0	(.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) x)
✓	cost-diff	128	(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (.f64 x x))))
✓	cost-diff	0	(/.f64 #s(literal 3 binary64) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
✓	cost-diff	384	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))

Rules

2736×	`fma-lowering-fma.f32`
2736×	`fma-lowering-fma.f64`
2734×	`-lowering-.f32`
2734×	`-lowering-.f64`
1880×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	349
1	121	307
2	364	282
3	1076	278
4	2517	278
5	3366	278
6	4880	278
7	7120	278
0	8439	278

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (/ 1 (/ x (/ 1 (- 1/3 (* x (* x -1/45)))))))
1
(/ 1 (/ x (/ 1 (- 1/3 (* x (* x -1/45))))))
(/ x (/ 1 (- 1/3 (* x (* x -1/45)))))
x
(/ 1 (- 1/3 (* x (* x -1/45))))
(- 1/3 (* x (* x -1/45)))
1/3
(* x (* x -1/45))
(* x -1/45)
-1/45
(/ 1 (/ 3 x))
1
(/ 3 x)
3
x
(+ (* 1/3 x) (* (+ 1/45 (* (* x x) 2/945)) (* x (* x x))))
(* 1/3 x)
1/3
x
(* (+ 1/45 (* (* x x) 2/945)) (* x (* x x)))
(+ 1/45 (* (* x x) 2/945))
1/45
(* (* x x) 2/945)
(* x x)
2/945
(* x (* x x))
(* (/ x (+ 1/3 (* x (* x -1/45)))) (+ 1/9 (* (* x (* x (* x x))) -1/2025)))
(/ x (+ 1/3 (* x (* x -1/45))))
x
(+ 1/3 (* x (* x -1/45)))
1/3
(* x (* x -1/45))
(* x -1/45)
-1/45
(+ 1/9 (* (* x (* x (* x x))) -1/2025))
1/9
(* (* x (* x (* x x))) -1/2025)
(* x (* x (* x x)))
(* x (* x x))
(* x x)
-1/2025
(* (/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45))))))) (+ 1/27 (* x (* (* x (* x (* x (* x x)))) 1/91125))))
(/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45)))))))
x
(+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45))))))
1/9
(* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45)))))
(* x -1/45)
-1/45
(* x (+ 1/3 (* x (* x -1/45))))
(+ 1/3 (* x (* x -1/45)))
1/3
(* x (* x -1/45))
(+ 1/27 (* x (* (* x (* x (* x (* x x)))) 1/91125)))
1/27
(* x (* (* x (* x (* x (* x x)))) 1/91125))
(* (* x (* x (* x (* x x)))) 1/91125)
(* x (* x (* x (* x x))))
(* x (* x (* x x)))
(* x (* x x))
(* x x)
1/91125

Outputs
(/ 1 (/ 1 (/ x (/ 1 (- 1/3 (* x (* x -1/45)))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
1
#s(literal 1 binary64)
(/ 1 (/ x (/ 1 (- 1/3 (* x (* x -1/45))))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x))))
(/ x (/ 1 (- 1/3 (* x (* x -1/45)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
x
(/ 1 (- 1/3 (* x (* x -1/45))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x))))
(- 1/3 (* x (* x -1/45)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
1/3
#s(literal 1/3 binary64)
(* x (* x -1/45))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(/ 1 (/ 3 x))
(/.f64 x #s(literal 3 binary64))
1
#s(literal 1 binary64)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
3
#s(literal 3 binary64)
x
(+ (* 1/3 x) (* (+ 1/45 (* (* x x) 2/945)) (* x (* x 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))))))
(* 1/3 x)
(/.f64 x #s(literal 3 binary64))
1/3
#s(literal 1/3 binary64)
x
(* (+ 1/45 (* (* x x) 2/945)) (* x (* x x)))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(+ 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))
(* x x)
(*.f64 x x)
2/945
#s(literal 2/945 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(* (/ x (+ 1/3 (* x (* x -1/45)))) (+ 1/9 (* (* x (* x (* x x))) -1/2025)))
(/.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/2025 binary64))))))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(/ 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 -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(+ 1/9 (* (* x (* x (* x x))) -1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/2025 binary64))))))
1/9
#s(literal 1/9 binary64)
(* (* x (* x (* x x))) -1/2025)
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/2025 binary64)))))
(* x (* x (* x x)))
(.f64 x (.f64 x (*.f64 x x)))
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
-1/2025
#s(literal -1/2025 binary64)
(* (/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45))))))) (+ 1/27 (* x (* (* x (* x (* x (* x x)))) 1/91125))))
(/.f64 (.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x #s(literal 1/91125 binary64)))))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (*.f64 x x) #s(literal 1/2025 binary64))))))
(/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45)))))))
(/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))))
x
(+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45))))))
(+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))
1/9
#s(literal 1/9 binary64)
(* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(* x (+ 1/3 (* x (* x -1/45))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(+ 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)))
(+ 1/27 (* x (* (* x (* x (* x (* x x)))) 1/91125)))
(+.f64 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x #s(literal 1/91125 binary64)))))))
1/27
#s(literal 1/27 binary64)
(* x (* (* x (* x (* x (* x x)))) 1/91125))
(.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x #s(literal 1/91125 binary64))))))
(* (* x (* x (* x (* x x)))) 1/91125)
(.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x #s(literal 1/91125 binary64)))))
(* x (* x (* x (* x x))))
(.f64 x (.f64 x (.f64 x (.f64 x x))))
(* x (* x (* x x)))
(.f64 x (.f64 x (*.f64 x x)))
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
1/91125
#s(literal 1/91125 binary64)

localize1.0s (3.7%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
✓	accuracy	99.6%	(/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))))
✓	accuracy	99.5%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
✓	accuracy	99.4%	(.f64 (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.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 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64)))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	accuracy	99.7%	(/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.6%	(.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (*.f64 x x)))
✓	accuracy	99.6%	(.f64 (.f64 x x) #s(literal 2/945 binary64))
✓	accuracy	99.5%	(*.f64 #s(literal 1/3 binary64) x)
✓	accuracy	100.0%	(/.f64 #s(literal 3 binary64) x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))

Results

337.0ms	47×	3	valid
234.0ms	160×	0	valid
124.0ms	28×	2	valid
59.0ms	21×	1	valid

Compiler

Compiled 393 to 43 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 357.0ms

ival-mult: 113.0ms (31.7% of total)

...c/correct-round.rkt:119:19: 105.0ms (29.4% of total)

ival-div: 59.0ms (16.5% of total)

backward-pass: 46.0ms (12.9% of total)

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

ival-sub: 5.0ms (1.4% of total)

const: 1.0ms (0.3% of total)

series23.0ms (0.1%)

Counts

22 → 264

Calls

Call 1

Inputs
#<alt (/ 1 (/ 1 (/ x (/ 1 (- 1/3 (* x (* x -1/45)))))))>
#<alt (/ 1 (/ x (/ 1 (- 1/3 (* x (* x -1/45))))))>
#<alt (/ x (/ 1 (- 1/3 (* x (* x -1/45)))))>
#<alt (/ 1 (- 1/3 (* x (* x -1/45))))>
#<alt (/ 1 (/ 3 x))>
#<alt (/ 3 x)>
#<alt (+ (* 1/3 x) (* (+ 1/45 (* (* x x) 2/945)) (* x (* x x))))>
#<alt (* 1/3 x)>
#<alt (* (+ 1/45 (* (* x x) 2/945)) (* x (* x x)))>
#<alt (+ 1/45 (* (* x x) 2/945))>
#<alt (* (/ x (+ 1/3 (* x (* x -1/45)))) (+ 1/9 (* (* x (* x (* x x))) -1/2025)))>
#<alt (/ x (+ 1/3 (* x (* x -1/45))))>
#<alt (+ 1/3 (* x (* x -1/45)))>
#<alt (* x (* x -1/45))>
#<alt (* (/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45))))))) (+ 1/27 (* x (* (* x (* x (* x (* x x)))) 1/91125))))>
#<alt (/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45)))))))>
#<alt (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45))))))>
#<alt (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45)))))>
#<alt (* x -1/45)>
#<alt (* (* x x) 2/945)>
#<alt (* x (* x x))>
#<alt (* x (+ 1/3 (* x (* x -1/45))))>

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 (/ 3 x)>
#<alt (/ (+ 3 (* -1/5 (pow x 2))) x)>
#<alt (/ (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) x)>
#<alt (/ (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) x)>
#<alt (/ 45 (pow x 3))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 3))>
#<alt (/ 45 (pow x 3))>
#<alt (* -1 (/ (- (* 675 (/ 1 (pow x 2))) 45) (pow x 3)))>
#<alt (* -1 (/ (- (* 675 (/ 1 (pow x 2))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6)))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))>
#<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 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 (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 3 x)>
#<alt (/ 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 (* 2/945 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/45 (pow x 3))>
#<alt (* (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>
#<alt (+ 1/45 (* 2/945 (pow x 2)))>
#<alt (+ 1/45 (* 2/945 (pow x 2)))>
#<alt (+ 1/45 (* 2/945 (pow x 2)))>
#<alt (* 2/945 (pow x 2))>
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* 2/945 (pow x 2))>
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 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 x)>
#<alt (* x (+ 3 (* 1/5 (pow x 2))))>
#<alt (* x (+ 3 (* (pow x 2) (+ 1/5 (* 1/75 (pow x 2))))))>
#<alt (* x (+ 3 (* (pow x 2) (+ 1/5 (* (pow x 2) (+ 1/75 (* 1/1125 (pow x 2))))))))>
#<alt (/ -45 x)>
#<alt (* -1 (/ (+ 45 (* 675 (/ 1 (pow x 2)))) x))>
#<alt (/ (- (* -1 (/ (+ 675 (* 10125 (/ 1 (pow x 2)))) (pow x 2))) 45) x)>
#<alt (/ (- (* -1 (/ (+ 10125 (* 151875 (/ 1 (pow x 2)))) (pow x 4))) (+ 45 (* 675 (/ 1 (pow x 2))))) x)>
#<alt (/ -45 x)>
#<alt (* -1 (/ (+ 45 (* 675 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 45 (+ (* 675 (/ 1 (pow x 2))) (/ 10125 (pow x 4)))) x))>
#<alt (* -1 (/ (+ 45 (+ (* 675 (/ 1 (pow x 2))) (+ (* 151875 (/ 1 (pow x 6))) (/ 10125 (pow x 4))))) x))>
#<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) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* -1/45 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 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 (* 9 x)>
#<alt (* x (+ 9 (* 3/5 (pow x 2))))>
#<alt (* x (+ 9 (* (pow x 2) (+ 3/5 (* -1/375 (pow x 4))))))>
#<alt (* x (+ 9 (* (pow x 2) (+ 3/5 (* (pow x 4) (- (* -1/5625 (pow x 2)) 1/375))))))>
#<alt (/ 2025 (pow x 3))>
#<alt (/ (+ 2025 (* 30375 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 2025 (* 30375 (/ 1 (pow x 2)))) (/ 6834375 (pow x 6))) (pow x 3))>
#<alt (/ (+ 2025 (+ (* -1 (/ (+ 6834375 (* 102515625 (/ 1 (pow x 2)))) (pow x 6))) (* 30375 (/ 1 (pow x 2))))) (pow x 3))>
#<alt (/ 2025 (pow x 3))>
#<alt (/ (+ 2025 (* 30375 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (* -1 (/ (- (/ 6834375 (pow x 6)) (+ 2025 (* 30375 (/ 1 (pow x 2))))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* 102515625 (/ 1 (pow x 8))) (/ 6834375 (pow x 6))) (+ 2025 (* 30375 (/ 1 (pow x 2))))) (pow x 3)))>
#<alt 1/9>
#<alt (+ 1/9 (* -1/135 (pow x 2)))>
#<alt (+ 1/9 (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135)))>
#<alt (+ 1/9 (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135)))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* -1/135 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))>
#<alt (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))>
#<alt (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* 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 (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 1/3 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) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 (pow x 2))) 1/45))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/45 (* 1/3 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/45 (* 1/3 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/45 (* 1/3 (/ 1 (pow x 2))))))>

Calls

66 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* (/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45))))))) (+ 1/27 (* x (* (* x (* x (* x (* x x)))) 1/91125))))
1.0ms	x	@	-inf	(* x (* x x))
1.0ms	x	@	0	(* (/ x (+ 1/3 (* x (* x -1/45)))) (+ 1/9 (* (* x (* x (* x x))) -1/2025)))
1.0ms	x	@	0	(/ 3 x)
1.0ms	x	@	-inf	(/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45)))))))

rewrite1.3s (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3438×	`-lowering-.f32`
3438×	`-lowering-.f64`
2700×	`fma-lowering-fma.f32`
2700×	`fma-lowering-fma.f64`
2408×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	195
1	252	176
2	2135	171
0	8757	171

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1178

Calls

Call 1

Inputs
(/ 1 (/ 1 (/ x (/ 1 (- 1/3 (* x (* x -1/45)))))))
(/ 1 (/ 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))
(/ 3 x)
(+ (* 1/3 x) (* (+ 1/45 (* (* x x) 2/945)) (* x (* x x))))
(* 1/3 x)
(* (+ 1/45 (* (* x x) 2/945)) (* x (* x x)))
(+ 1/45 (* (* x x) 2/945))
(* (/ x (+ 1/3 (* x (* x -1/45)))) (+ 1/9 (* (* x (* x (* x x))) -1/2025)))
(/ x (+ 1/3 (* x (* x -1/45))))
(+ 1/3 (* x (* x -1/45)))
(* x (* x -1/45))
(* (/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45))))))) (+ 1/27 (* x (* (* x (* x (* x (* x x)))) 1/91125))))
(/ x (+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45)))))))
(+ 1/9 (* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45))))))
(* (* x -1/45) (* x (+ 1/3 (* x (* x -1/45)))))
(* x -1/45)
(* (* x x) 2/945)
(* x (* x x))
(* x (+ 1/3 (* x (* x -1/45))))

Outputs
(+.f64 (/.f64 x #s(literal 3 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(+.f64 (/.f64 x #s(literal 3 binary64)) (.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) x))
(+.f64 (/.f64 #s(literal 1/27 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))) x)) (/.f64 (.f64 x (.f64 x (.f64 (.f64 #s(literal 1/91125 binary64) (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 #s(literal 1/91125 binary64) (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))) (/.f64 #s(literal 1/27 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))) x)))
(exp.f64 (log.f64 (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))
(exp.f64 (.f64 (log.f64 (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 x #s(literal 3 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 x #s(literal 3 binary64)) (.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) x))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) x))
(fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))) #s(literal 1/27 binary64)) (/.f64 (.f64 x (.f64 x (.f64 (.f64 #s(literal 1/91125 binary64) (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))))
(fma.f64 x (.f64 (.f64 (.f64 #s(literal 1/91125 binary64) (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))))) (/.f64 #s(literal 1/27 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))) x)))
(fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))) (.f64 x (.f64 (.f64 #s(literal 1/91125 binary64) (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1/27 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))) x)))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 #s(literal 1/3 binary64) x (.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) x))
(fma.f64 (/.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 (/.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) x))
(fma.f64 (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))) #s(literal 1/27 binary64) (/.f64 (.f64 x (.f64 x (.f64 (.f64 #s(literal 1/91125 binary64) (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))))))
(fma.f64 (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))) (.f64 x (.f64 (.f64 #s(literal 1/91125 binary64) (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/27 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))) x)))
(fma.f64 #s(literal 1/27 binary64) (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 #s(literal 1/91125 binary64) (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))))))
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(fma.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (/.f64 x #s(literal 3 binary64)) (.f64 x #s(literal -1/45 binary64)) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/2025 binary64)))
(fma.f64 (.f64 x x) (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x #s(literal -1/45 binary64))) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (.f64 x x) (.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x #s(literal -1/45 binary64)) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x #s(literal -1/45 binary64))) (.f64 x x) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 x #s(literal -1/45 binary64))) x (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 x x)) #s(literal -1/45 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/45 binary64))) x (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)))
(fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal -1/45 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8303765625 binary64)) (.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64)))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))) (.f64 (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal 1/3 binary64))))
(/.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64)))) (+.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 (.f64 (.f64 x (.f64 x #s(literal -1/45 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 x (*.f64 x #s(literal -1/45 binary64)))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8303765625 binary64)) (.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)) (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))) (.f64 (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))) (neg.f64 (.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 (neg.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64))))) (neg.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 (neg.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))
(.f64 x (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (*.f64 x #s(literal -1/45 binary64))))
(.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))
(.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(.f64 (.f64 x x) (.f64 #s(literal -1/45 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (*.f64 x #s(literal -1/45 binary64)))
(.f64 (.f64 #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))) x)
(.f64 (.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))) x) #s(literal -1/45 binary64))
(*.f64 x #s(literal -1/45 binary64))
(*.f64 #s(literal -1/45 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)
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))
(/.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(/.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 3 binary64)) #s(literal -1 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(+.f64 (/.f64 x #s(literal 3 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(+.f64 (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))) (/.f64 x #s(literal 3 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 x #s(literal 3 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))) (/.f64 x #s(literal 3 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x x) (/.f64 x #s(literal 3 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) x (/.f64 x #s(literal 3 binary64)))
(fma.f64 (/.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/45 binary64)) (/.f64 x #s(literal 3 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/45 binary64) (/.f64 x #s(literal 3 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -3 binary64) x)) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.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 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(fma.f64 #s(literal -1/3 binary64) (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 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 x (*.f64 x #s(literal -1/45 binary64)))))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 (/.f64 x #s(literal 3 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (-.f64 (/.f64 x #s(literal 3 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))))
(/.f64 (.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64)))) (+.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 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64))) x) (+.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 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))) x) (-.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 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 #s(literal 0 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 (/.f64 x #s(literal 3 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))))) (neg.f64 (-.f64 (/.f64 x #s(literal 3 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64))))) (neg.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 (neg.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/91125 binary64))) x)) (neg.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 (neg.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))) x)) (-.f64 #s(literal 0 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 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))) x)

simplify720.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

2890×	`-lowering-.f32`
2890×	`-lowering-.f64`
1882×	`+-lowering-+.f64`
1882×	`+-lowering-+.f32`
1842×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	2049
1	633	1935
2	1917	1918
3	5442	1914
0	8063	1914

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

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)))))
(/ 3 x)
(/ (+ 3 (* -1/5 (pow x 2))) x)
(/ (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) x)
(/ (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) x)
(/ 45 (pow x 3))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 3))
(/ 45 (pow x 3))
(* -1 (/ (- (* 675 (/ 1 (pow x 2))) 45) (pow x 3)))
(* -1 (/ (- (* 675 (/ 1 (pow x 2))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))
(* -1 (/ (- (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6)))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))
(* 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 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)
(/ 3 x)
(/ 3 x)
(/ 3 x)
(/ 3 x)
(/ 3 x)
(/ 3 x)
(/ 3 x)
(/ 3 x)
(/ 3 x)
(/ 3 x)
(/ 3 x)
(/ 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 (* 2/945 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/45 (pow x 3))
(* (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
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 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 x)
(* x (+ 3 (* 1/5 (pow x 2))))
(* x (+ 3 (* (pow x 2) (+ 1/5 (* 1/75 (pow x 2))))))
(* x (+ 3 (* (pow x 2) (+ 1/5 (* (pow x 2) (+ 1/75 (* 1/1125 (pow x 2))))))))
(/ -45 x)
(* -1 (/ (+ 45 (* 675 (/ 1 (pow x 2)))) x))
(/ (- (* -1 (/ (+ 675 (* 10125 (/ 1 (pow x 2)))) (pow x 2))) 45) x)
(/ (- (* -1 (/ (+ 10125 (* 151875 (/ 1 (pow x 2)))) (pow x 4))) (+ 45 (* 675 (/ 1 (pow x 2))))) x)
(/ -45 x)
(* -1 (/ (+ 45 (* 675 (/ 1 (pow x 2)))) x))
(* -1 (/ (+ 45 (+ (* 675 (/ 1 (pow x 2))) (/ 10125 (pow x 4)))) x))
(* -1 (/ (+ 45 (+ (* 675 (/ 1 (pow x 2))) (+ (* 151875 (/ 1 (pow x 6))) (/ 10125 (pow x 4))))) x))
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) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* -1/45 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 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)))))
(* 9 x)
(* x (+ 9 (* 3/5 (pow x 2))))
(* x (+ 9 (* (pow x 2) (+ 3/5 (* -1/375 (pow x 4))))))
(* x (+ 9 (* (pow x 2) (+ 3/5 (* (pow x 4) (- (* -1/5625 (pow x 2)) 1/375))))))
(/ 2025 (pow x 3))
(/ (+ 2025 (* 30375 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 2025 (* 30375 (/ 1 (pow x 2)))) (/ 6834375 (pow x 6))) (pow x 3))
(/ (+ 2025 (+ (* -1 (/ (+ 6834375 (* 102515625 (/ 1 (pow x 2)))) (pow x 6))) (* 30375 (/ 1 (pow x 2))))) (pow x 3))
(/ 2025 (pow x 3))
(/ (+ 2025 (* 30375 (/ 1 (pow x 2)))) (pow x 3))
(* -1 (/ (- (/ 6834375 (pow x 6)) (+ 2025 (* 30375 (/ 1 (pow x 2))))) (pow x 3)))
(* -1 (/ (- (+ (* 102515625 (/ 1 (pow x 8))) (/ 6834375 (pow x 6))) (+ 2025 (* 30375 (/ 1 (pow x 2))))) (pow x 3)))
1/9
(+ 1/9 (* -1/135 (pow x 2)))
(+ 1/9 (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135)))
(+ 1/9 (* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135)))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/2025 (/ 1/9 (pow x 4))) (* 1/135 (/ 1 (pow x 2)))))
(* -1/135 (pow x 2))
(* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))
(* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))
(* (pow x 2) (- (* 1/2025 (pow x 2)) 1/135))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* 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))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/3 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) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 3) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 3) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* -1/45 (pow x 3))
(* -1 (* (pow x 3) (- 1/45 (* 1/3 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/45 (* 1/3 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/45 (* 1/3 (/ 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 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ (+ 3 (* -1/5 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))) x)
(/ (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) x)
(/.f64 (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) #s(literal 1/75 binary64)))))) x)
(/ (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) x)
(/.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/75 binary64) (.f64 x (.f64 x #s(literal -1/1125 binary64))))))))) x)
(/ 45 (pow x 3))
(/.f64 #s(literal 45 binary64) (.f64 x (.f64 x x)))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 3))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (.f64 x (*.f64 x x)))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 3))
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 3))
(/.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal -151875 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 x (.f64 x x)))
(/ 45 (pow x 3))
(/.f64 #s(literal 45 binary64) (.f64 x (.f64 x x)))
(* -1 (/ (- (* 675 (/ 1 (pow x 2))) 45) (pow x 3)))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (.f64 x (*.f64 x x)))
(* -1 (/ (- (* 675 (/ 1 (pow x 2))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))
(* -1 (/ (- (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6)))) (+ 45 (/ 10125 (pow x 4)))) (pow x 3)))
(/.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal -151875 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 x (.f64 x x)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
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) (- (* 1/75 (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 1/75 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 x (.f64 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 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.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 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.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 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.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 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal -151875 binary64) (pow.f64 x #s(literal 6 binary64))))) (*.f64 x 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)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 3 binary64) x)
(/ 3 x)
(/.f64 #s(literal 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 x (*.f64 x #s(literal 2/945 binary64)))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64)))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.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 1/45 binary64) (.f64 x x)) (+.f64 #s(literal 2/945 binary64) (/.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 1/45 binary64) (.f64 x x)) (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 2/945 binary64)))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 (+.f64 #s(literal -1/45 binary64) (/.f64 #s(literal -1/3 binary64) (.f64 x x))) (*.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 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 (+.f64 #s(literal -1/45 binary64) (/.f64 #s(literal -1/3 binary64) (.f64 x x))) (*.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)
(* 1/45 (pow x 3))
(.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 3) (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
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(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.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 (* -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 (.f64 x (*.f64 x x)) #s(literal -1/45 binary64))
(* (pow x 3) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(* (pow x 3) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(* (pow x 3) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(* -1/45 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/45 binary64))
(* -1 (* (pow x 3) (- 1/45 (* 1/3 (/ 1 (pow x 2))))))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 #s(literal 1/3 binary64) x)))
(* -1 (* (pow x 3) (- 1/45 (* 1/3 (/ 1 (pow x 2))))))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 #s(literal 1/3 binary64) x)))
(* -1 (* (pow x 3) (- 1/45 (* 1/3 (/ 1 (pow x 2))))))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 #s(literal 1/3 binary64) x)))

eval879.0ms (3.2%)

Compiler: Compiled 68288 to 3374 computations (95.1% saved)

prune364.0ms (1.3%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	1602	2	1604
Fresh	2	1	3
Picked	3	2	5
Done	1	3	4
Total	1608	8	1616

Accuracy

100.0%

Counts

1616 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(/.f64 (.f64 x #s(literal 1/9 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
	99.0%	(/.f64 x #s(literal 3 binary64))
✓	98.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
	98.5%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))
✓	99.4%	(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (.f64 x 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))))
✓	99.5%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))))

Compiler

Compiled 507 to 178 computations (64.9% saved)

regimes21.0ms (0.1%)

Counts

21 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 x #s(literal 3 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 (.f64 x #s(literal 1/9 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 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (.f64 x x))))
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))) x))
(/.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))) x) #s(literal 1/9 binary64))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))))
(.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))) x)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) 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 x (*.f64 x #s(literal -1/45 binary64))))))
(.f64 (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.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 #s(literal 1/27 binary64) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal 1/91125 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) x)))
(.f64 x (/.f64 (.f64 (-.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/91125 binary64) (.f64 x (.f64 x x)))))) #s(literal 1 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 (.f64 x #s(literal -1/45 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

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

Calls

2 calls:

10.0ms	x
8.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes6.0ms (0%)

Counts

7 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 x #s(literal 3 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 (.f64 x #s(literal 1/9 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 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))

Outputs
(.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)))))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

6 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 x #s(literal 3 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 (.f64 x #s(literal 1/9 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))

Outputs
(/.f64 (.f64 x #s(literal 1/9 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

5 → 1

Calls

Call 1

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

4.0ms

Results

Accuracy	Segments	Branch
99.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (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:

2.0ms

Results

Accuracy	Segments	Branch
98.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify29.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

42×	`*-commutative_binary64`
32×	`+-commutative_binary64`
28×	`sub-neg_binary64`
26×	`distribute-lft-neg-in_binary64`
26×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	56
1	58	56
2	89	56
3	112	56
4	132	56
5	144	56
6	149	56
7	152	56
8	153	56

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.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 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(/.f64 (.f64 x #s(literal 1/9 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 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 x #s(literal 3 binary64))
(*.f64 #s(literal 1/3 binary64) x)

Outputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.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 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(/.f64 (.f64 x #s(literal 1/9 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 (*.f64 x x) #s(literal -1/45 binary64))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(/.f64 x #s(literal 3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))

soundness3.7s (13.4%)

Rules

4016×	`-lowering-.f32`
4016×	`-lowering-.f64`
3976×	`-lowering-.f32`
3976×	`-lowering-.f64`
3566×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	195
1	252	176
2	2135	171
0	8757	171
0	144	1941
1	399	1840
2	1101	1834
3	2955	1809
4	7523	1809
0	8068	1809
0	67	302
1	186	287
2	559	281
3	1807	281
4	2717	281
5	4432	281
6	6049	281
7	6591	281
0	8079	281
0	27	160
1	162	146
2	1364	142
0	8168	142
0	37	274
1	224	204
2	2007	196
0	9402	196

Stop Event

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

Compiler

Compiled 128 to 82 computations (35.9% saved)

preprocess141.0ms (0.5%)

Remove: (negabs x)
Compiler: Compiled 278 to 170 computations (38.8% 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

analyze15.0ms (0.1%)

sample10.1s (36.5%)

preprocess83.0ms (0.3%)

explain544.0ms (2%)

eval1.0ms (0%)

prune2.0ms (0%)

simplify49.0ms (0.2%)

localize277.0ms (1%)

series11.0ms (0%)

rewrite485.0ms (1.8%)

simplify440.0ms (1.6%)

eval74.0ms (0.3%)

prune73.0ms (0.3%)

simplify374.0ms (1.4%)

localize354.0ms (1.3%)

series33.0ms (0.1%)

rewrite854.0ms (3.1%)

simplify564.0ms (2%)

eval200.0ms (0.7%)

prune189.0ms (0.7%)

simplify411.0ms (1.5%)

localize658.0ms (2.4%)

series40.0ms (0.1%)

rewrite1.3s (4.6%)

simplify640.0ms (2.3%)

eval659.0ms (2.4%)

prune350.0ms (1.3%)

simplify692.0ms (2.5%)

localize1.0s (3.7%)

series23.0ms (0.1%)

rewrite1.3s (4.7%)

simplify720.0ms (2.6%)

eval879.0ms (3.2%)

prune364.0ms (1.3%)

regimes21.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify29.0ms (0.1%)

soundness3.7s (13.4%)

preprocess141.0ms (0.5%)

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