Metrics for invcot (example 3.9)

analyze8.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 16 to 11 computations (31.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

...c/correct-round.rkt:119:19: 2.0ms (46.8% of total)

ival-div: 1.0ms (23.4% of total)

ival-tan: 1.0ms (23.4% of total)

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

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

const: 0.0ms (0% of total)

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

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

sample7.3s (57.8%)

Results

4.9s	4502×	2	valid
1.3s	1303×	3	valid
687.0ms	2409×	1	valid
5.0ms	42×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.2s

ival-tan: 4.8s (78.1% of total)

ival-div: 592.0ms (9.5% of total)

...c/correct-round.rkt:119:19: 286.0ms (4.6% of total)

backward-pass: 242.0ms (3.9% of total)

ival-sub: 127.0ms (2% of total)

ival-<: 78.0ms (1.3% of total)

const: 19.0ms (0.3% of total)

ival-and: 17.0ms (0.3% of total)

Bogosity

preprocess67.0ms (0.5%)

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	17
1	37	16
2	72	15
3	156	15
4	311	15
5	480	15
6	523	15
7	531	15
0	6	5
1	16	5
2	24	5
3	36	5
4	50	5
5	87	5
6	158	5
7	255	5
8	356	5
9	499	5
10	621	5
11	653	5
0	653	5

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

Symmetry

(negabs x)

explain660.0ms (5.2%)

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

288.0ms	282×	2	valid
67.0ms	76×	3	valid
33.0ms	152×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 313.0ms

ival-tan: 259.0ms (82.7% of total)

ival-div: 26.0ms (8.3% of total)

backward-pass: 19.0ms (6.1% of total)

ival-sub: 8.0ms (2.6% of total)

const: 2.0ms (0.6% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify21.0ms (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	13
1	16	13
2	24	13
3	36	13
4	50	13
5	87	13
6	158	13
7	255	13
8	356	13
9	499	13
10	621	13
11	653	13
0	653	13

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)

localize201.0ms (1.6%)

Localize:

Found 4 expressions of interest:

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

Results

138.0ms	141×	2	valid
33.0ms	38×	3	valid
16.0ms	76×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

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

ival-tan: 122.0ms (81.4% of total)

ival-div: 14.0ms (9.3% of total)

backward-pass: 9.0ms (6% of total)

ival-sub: 4.0ms (2.7% of total)

const: 1.0ms (0.7% of total)

series4.0ms (0%)

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite208.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2426×	`-lowering-.f32`
2426×	`-lowering-.f64`
2310×	`/-lowering-/.f32`
2310×	`/-lowering-/.f64`
1480×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	51	11
2	475	11
3	6216	11
0	8036	11

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 225

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

simplify196.0ms (1.5%)

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	189	269
2	564	266
3	1805	266
4	2707	266
5	4420	266
6	6039	266
7	6587	266
0	8075	266

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval35.0ms (0.3%)

Compiler: Compiled 5633 to 680 computations (87.9% saved)

prune28.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	270	3	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	271	3	274

Accuracy

99.5%

Counts

274 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
▶	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
▶	98.7%	(*.f64 #s(literal 1/3 binary64) x)

Status

Accuracy

Program

▶

99.5%

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

▶

99.4%

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

▶

98.7%

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

Compiler

Compiled 30 to 21 computations (30% saved)

simplify117.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize91.0ms (0.7%)

Localize:

Found 9 expressions of interest:

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

Results

70.0ms

256×

valid

Compiler

Compiled 95 to 16 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 14.0ms (46.9% of total)

...c/correct-round.rkt:119:19: 12.0ms (40.2% of total)

ival-sub: 2.0ms (6.7% of total)

ival-add: 1.0ms (3.3% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

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

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

Calls

30 calls:

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

rewrite274.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	84	60
2	680	56
0	8206	56

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 287

Calls

Call 1

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

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

simplify179.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	753
1	162	604
2	476	604
3	1243	600
4	2914	598
5	7726	598
0	8073	598

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

eval53.0ms (0.4%)

Compiler: Compiled 15017 to 1063 computations (92.9% saved)

prune33.0ms (0.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	422	3	425
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	422	6	428

Accuracy

100.0%

Counts

428 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
▶	99.4%	(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 #s(literal 1/3 binary64) x))
▶	99.6%	(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
✓	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)))))))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	98.7%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 76 to 52 computations (31.6% saved)

simplify39.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

524×	`-lowering-.f32`
524×	`-lowering-.f64`
232×	`fma-define`
230×	`associate-r`
214×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	125
1	55	106
2	109	106
3	215	106
4	388	106
5	444	106
6	485	106
7	492	106
8	602	106
9	679	106
10	694	106
11	696	106
12	696	106
0	696	106

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (+ 1/9 (* (* x (* x (* x x))) -1/2025)) (/ x (+ 1/3 (* (* x x) -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 x)
-1/2025
(/ x (+ 1/3 (* (* x x) -1/45)))
(+ 1/3 (* (* x x) -1/45))
1/3
(* (* x x) -1/45)
-1/45
(+ (* x (* (* x x) 1/45)) (* 1/3 x))
(* x (* (* x x) 1/45))
x
(* (* x x) 1/45)
(* x x)
1/45
(* 1/3 x)
1/3
(/ x (/ 1 (+ 1/3 (* (* x x) 1/45))))
x
(/ 1 (+ 1/3 (* (* x x) 1/45)))
1
(+ 1/3 (* (* x x) 1/45))
1/3
(* (* x x) 1/45)
(* x x)
1/45

Outputs
(* (+ 1/9 (* (* x (* x (* x x))) -1/2025)) (/ x (+ 1/3 (* (* x x) -1/45))))
(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(+ 1/9 (* (* x (* x (* x x))) -1/2025))
(+.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)
(* (* x (* x (* x x))) -1/2025)
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))
(* x (* x (* x x)))
(.f64 x (.f64 x (*.f64 x x)))
x
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
-1/2025
#s(literal -1/2025 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)))
-1/45
#s(literal -1/45 binary64)
(+ (* x (* (* x x) 1/45)) (* 1/3 x))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(* x (* (* x x) 1/45))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64))
x
(* (* 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)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
1/3
#s(literal 1/3 binary64)
(/ x (/ 1 (+ 1/3 (* (* x x) 1/45))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
x
(/ 1 (+ 1/3 (* (* x x) 1/45)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))))
1
#s(literal 1 binary64)
(+ 1/3 (* (* x x) 1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))
1/3
#s(literal 1/3 binary64)
(* (* x x) 1/45)
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* x x)
(*.f64 x x)
1/45
#s(literal 1/45 binary64)

localize307.0ms (2.4%)

Localize:

Found 12 expressions of interest:

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

Results

95.0ms	38×	3	valid
68.0ms	181×	0	valid
20.0ms	17×	2	valid
16.0ms	20×	1	valid

Compiler

Compiled 155 to 24 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

...c/correct-round.rkt:119:19: 27.0ms (33.4% of total)

ival-mult: 27.0ms (33.4% of total)

backward-pass: 10.0ms (12.4% of total)

ival-div: 9.0ms (11.1% of total)

ival-add: 8.0ms (9.9% of total)

const: 0.0ms (0% of total)

series8.0ms (0.1%)

Counts

15 → 180

Calls

Call 1

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

Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt 1/9>
#<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 (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)>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 3))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (* 1/45 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))>
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
#<alt 1/3>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 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 (* -1/45 (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 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 (* 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)>

Calls

45 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* (+ 1/9 (* (* x (* x (* x x))) -1/2025)) (/ x (+ 1/3 (* (* x x) -1/45))))
1.0ms	x	@	0	(* (+ 1/9 (* (* x (* x (* x x))) -1/2025)) (/ x (+ 1/3 (* (* x x) -1/45))))
0.0ms	x	@	inf	(+ (* x (* (* x x) 1/45)) (* 1/3 x))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	inf	(* (* x (* x (* x x))) -1/2025)

rewrite499.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3742×	`-lowering-.f32`
3742×	`-lowering-.f64`
3496×	`/-lowering-/.f32`
3496×	`/-lowering-/.f64`
1682×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	99
1	127	81
2	1058	81
0	8363	81

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 700

Calls

Call 1

Inputs
(* (+ 1/9 (* (* x (* x (* x x))) -1/2025)) (/ x (+ 1/3 (* (* x x) -1/45))))
(+ 1/9 (* (* x (* x (* x x))) -1/2025))
(* (* x (* x (* x x))) -1/2025)
(* x (* x (* x x)))
(+ (* x (* (* x x) 1/45)) (* 1/3 x))
(* x (* (* x x) 1/45))
(* (* x x) 1/45)
(* x x)
(/ x (/ 1 (+ 1/3 (* (* x x) 1/45))))
(/ 1 (+ 1/3 (* (* x x) 1/45)))
(+ 1/3 (* (* x x) 1/45))
(/ x (+ 1/3 (* (* x x) -1/45)))
(* (* x x) -1/45)
(* x (* x x))
(* 1/3 x)

Outputs
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) #s(literal 1/9 binary64)) (.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64)))))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64)))) (.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) #s(literal 1/9 binary64)))
(+.f64 (/.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x)) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x)))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x)) (/.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x)))
(-.f64 (/.f64 (/.f64 #s(literal 1/81 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x)) (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64)) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x)))
(fma.f64 #s(literal 1/9 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x)))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (/.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x)))
(fma.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) #s(literal 1/9 binary64) (.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -1/2025 binary64)))))
(fma.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))) #s(literal 1/9 binary64)))
(/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))))) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(/.f64 x (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -1/2025 binary64)))))))
(/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64)))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x))
(/.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -1/2025 binary64)))))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))) x)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -1/2025 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -1/2025 binary64)))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) #s(literal -1/9 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1/8303765625 binary64)))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) #s(literal -1/9 binary64)))) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1/8303765625 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) #s(literal -1/9 binary64)))) (-.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1/8303765625 binary64)))) (-.f64 #s(literal 0 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))) (-.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64))) (-.f64 #s(literal 0 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) #s(literal -1/9 binary64))))) (.f64 x (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1/8303765625 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x 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 x (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) #s(literal -1/9 binary64))))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8303765625 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/2025 binary64))) #s(literal -1/9 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1/8303765625 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal -1/3 binary64) (.f64 (.f64 x 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 #s(literal 0 binary64) x) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -1/2025 binary64)))) (-.f64 #s(literal 0 binary64) x))))
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(/.f64 (.f64 x (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64))))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)))) (+.f64 #s(literal 1/81 binary64) (-.f64 (.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) (.f64 #s(literal 1/9 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64))))))))
(/.f64 (.f64 x (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64))))))
(pow.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x) #s(literal -1 binary64))
(.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal -1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))) x))))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))) x)
(.f64 (/.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))))
(.f64 (/.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))))))
(.f64 (/.f64 x (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(/.f64 (*.f64 x #s(literal -1/45 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(.f64 #s(literal -1/45 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/45 binary64)) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 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 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)

simplify230.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

2318×	`fma-lowering-fma.f32`
2318×	`fma-lowering-fma.f64`
1976×	`fma-define`
1852×	`-lowering-.f32`
1852×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	1114
1	308	942
2	867	936
3	2330	935
4	5522	935
0	8360	935

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
1/9
(+ 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))
(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)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 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))
(* -1/45 (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 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)
(* 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)

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
1/9
#s(literal 1/9 binary64)
(+ 1/9 (* -1/2025 (pow x 4)))
(+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+ 1/9 (* -1/2025 (pow x 4)))
(+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+ 1/9 (* -1/2025 (pow x 4)))
(+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(* -1/2025 (pow x 4))
(.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.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 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 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 (.f64 x x) (+.f64 #s(literal 1/75 binary64) (.f64 (.f64 x 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 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -675 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.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 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -675 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.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
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* x (+ 3 (* 1/5 (pow x 2))))
(.f64 x (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64))))
(* x (+ 3 (* (pow x 2) (+ 1/5 (* 1/75 (pow x 2))))))
(.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 (.f64 (*.f64 x x) #s(literal 1/75 binary64)) #s(literal 1/5 binary64))))))
(* x (+ 3 (* (pow x 2) (+ 1/5 (* (pow x 2) (+ 1/75 (* 1/1125 (pow x 2))))))))
(.f64 x (+.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 (*.f64 x x) #s(literal 1/1125 binary64)))))))))
(/ -45 x)
(/.f64 #s(literal -45 binary64) x)
(* -1 (/ (+ 45 (* 675 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 675 (* 10125 (/ 1 (pow x 2)))) (pow x 2))) 45) x)
(/.f64 (+.f64 #s(literal -45 binary64) (/.f64 (+.f64 #s(literal -675 binary64) (/.f64 #s(literal -10125 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (* -1 (/ (+ 10125 (* 151875 (/ 1 (pow x 2)))) (pow x 4))) (+ 45 (* 675 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 (/.f64 (-.f64 #s(literal -10125 binary64) (/.f64 #s(literal 151875 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x)))) x)
(/ -45 x)
(/.f64 #s(literal -45 binary64) x)
(* -1 (/ (+ 45 (* 675 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) x)
(* -1 (/ (+ 45 (+ (* 675 (/ 1 (pow x 2))) (/ 10125 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal -45 binary64) (+.f64 (/.f64 #s(literal -675 binary64) (.f64 x x)) (/.f64 #s(literal -10125 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
(* -1 (/ (+ 45 (+ (* 675 (/ 1 (pow x 2))) (+ (* 151875 (/ 1 (pow x 6))) (/ 10125 (pow x 4))))) x))
(/.f64 (+.f64 (+.f64 #s(literal -45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal -151875 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -10125 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* 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)

eval151.0ms (1.2%)

Compiler: Compiled 29650 to 2045 computations (93.1% saved)

prune97.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	978	3	981
Fresh	0	0	0
Picked	3	0	3
Done	1	2	3
Total	982	5	987

Accuracy

100.0%

Counts

987 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
▶	99.2%	(/.f64 x #s(literal 3 binary64))
✓	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)))))))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
▶	99.6%	(.f64 #s(literal 1/9 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))

Compiler

Compiled 52 to 37 computations (28.8% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x #s(literal -1/5 binary64))
✓	cost-diff	(.f64 x (.f64 x #s(literal -1/5 binary64)))
✓	cost-diff	(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
✓	cost-diff	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
✓	cost-diff	(/.f64 x #s(literal 3 binary64))
✓	cost-diff	(.f64 (.f64 x x) #s(literal -1/45 binary64))
✓	cost-diff	(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
✓	cost-diff	(/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))
✓	cost-diff	(.f64 #s(literal 1/9 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))

Rules

38×	`-lowering-.f32`
38×	`-lowering-.f64`
16×	`*-commutative`
16×	`fma-lowering-fma.f32`
16×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	63
1	28	58
2	40	58
3	44	58
4	45	58
0	45	58

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* 1/9 (/ x (+ 1/3 (* (* x x) -1/45))))
1/9
(/ 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 3)
x
3
(/ x (+ 3 (* x (* x -1/5))))
x
(+ 3 (* x (* x -1/5)))
3
(* x (* x -1/5))
(* x -1/5)
-1/5

Outputs
(* 1/9 (/ x (+ 1/3 (* (* x x) -1/45))))
(/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
1/9
#s(literal 1/9 binary64)
(/ x (+ 1/3 (* (* x x) -1/45)))
(/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))
x
(+ 1/3 (* (* x x) -1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
1/3
#s(literal 1/3 binary64)
(* (* x x) -1/45)
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* x x)
(*.f64 x x)
-1/45
#s(literal -1/45 binary64)
(/ x 3)
(/.f64 x #s(literal 3 binary64))
x
3
#s(literal 3 binary64)
(/ x (+ 3 (* x (* x -1/5))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
x
(+ 3 (* x (* x -1/5)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
3
#s(literal 3 binary64)
(* x (* x -1/5))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* x -1/5)
(*.f64 x #s(literal -1/5 binary64))
-1/5
#s(literal -1/5 binary64)

localize219.0ms (1.7%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
✓	accuracy	100.0%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -1/5 binary64)))
✓	accuracy	99.4%	(*.f64 x #s(literal -1/5 binary64))
✓	accuracy	100.0%	(/.f64 x #s(literal 3 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal -1/45 binary64))
✓	accuracy	99.7%	(/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))
✓	accuracy	99.6%	(.f64 #s(literal 1/9 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))

Results

94.0ms	181×	0	valid
56.0ms	38×	3	valid
34.0ms	20×	1	valid
12.0ms	17×	2	valid

Compiler

Compiled 73 to 17 computations (76.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

...c/correct-round.rkt:119:19: 22.0ms (40.6% of total)

ival-mult: 14.0ms (25.8% of total)

ival-div: 8.0ms (14.7% of total)

backward-pass: 6.0ms (11.1% of total)

ival-add: 4.0ms (7.4% of total)

const: 0.0ms (0% of total)

series6.0ms (0%)

Counts

9 → 108

Calls

Call 1

Inputs
#<alt (* 1/9 (/ x (+ 1/3 (* (* x x) -1/45))))>
#<alt (/ x (+ 1/3 (* (* x x) -1/45)))>
#<alt (+ 1/3 (* (* x x) -1/45))>
#<alt (* (* x x) -1/45)>
#<alt (/ x 3)>
#<alt (/ x (+ 3 (* x (* x -1/5))))>
#<alt (+ 3 (* x (* x -1/5)))>
#<alt (* x (* x -1/5))>
#<alt (* x -1/5)>

Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 1/675 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)>
#<alt (/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))>
#<alt (* 3 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 (* 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 (* 1/675 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)>
#<alt (/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))>
#<alt 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (* -1/5 (pow x 2))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* -1/5 (pow x 2))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(* x (* x -1/5))
0.0ms	x	@	-inf	(* x -1/5)
0.0ms	x	@	inf	(/ x (+ 3 (* x (* x -1/5))))
0.0ms	x	@	-inf	(* 1/9 (/ x (+ 1/3 (* (* x x) -1/45))))
0.0ms	x	@	inf	(* 1/9 (/ x (+ 1/3 (* (* x x) -1/45))))

rewrite293.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3306×	`-lowering-.f32`
3306×	`-lowering-.f64`
2024×	`/-lowering-/.f32`
2024×	`/-lowering-/.f64`
1936×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	78	47
2	535	47
3	5082	47
0	8487	47

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 365

Calls

Call 1

Inputs
(* 1/9 (/ 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 3)
(/ x (+ 3 (* x (* x -1/5))))
(+ 3 (* x (* x -1/5)))
(* x (* x -1/5))
(* x -1/5)

Outputs
(+.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) #s(literal 1/9 binary64)) (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))
(+.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))) (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) #s(literal 1/9 binary64)))
(+.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) #s(literal 1/3 binary64)) (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (.f64 (.f64 x x) #s(literal 1/45 binary64))))
(+.f64 (.f64 #s(literal 1/9 binary64) (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64)))))) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64)))))))
(+.f64 (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64)))))) (.f64 #s(literal 1/9 binary64) (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64)))))))
(+.f64 (.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))))) (.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))))))
(neg.f64 (.f64 (/.f64 x (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) #s(literal 1/9 binary64)))
(neg.f64 (.f64 #s(literal 1/9 binary64) (/.f64 x (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))))
(neg.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(neg.f64 (/.f64 (.f64 x #s(literal -1/9 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(/.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (*.f64 #s(literal 1/9 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (*.f64 #s(literal 1/9 binary64) x)) #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (*.f64 #s(literal 1/9 binary64) x))))
(/.f64 (.f64 x #s(literal -1/9 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
(/.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(/.f64 (/.f64 (.f64 #s(literal 1/9 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 (*.f64 x x) #s(literal 1/45 binary64)))))
(/.f64 #s(literal -1/9 binary64) (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)) x))
(/.f64 (.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64)))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) #s(literal 1/9 binary64))))))
(/.f64 (.f64 (.f64 #s(literal 1/9 binary64) x) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(/.f64 (.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(/.f64 (.f64 (.f64 #s(literal 1/9 binary64) x) (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(/.f64 (neg.f64 (.f64 x #s(literal -1/9 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (.f64 #s(literal 1/9 binary64) x) #s(literal 1 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))
(/.f64 (.f64 (.f64 #s(literal 1/9 binary64) x) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
(/.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) #s(literal 1/9 binary64)))))
(/.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))
(/.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))
(/.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))
(/.f64 (.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64)))))
(/.f64 (.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x 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 x #s(literal -1/9 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(pow.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (*.f64 #s(literal 1/9 binary64) x)) #s(literal -1 binary64))
(.f64 #s(literal 1/9 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(.f64 x (/.f64 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))) #s(literal 1/9 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) #s(literal 1/9 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))) (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/9 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))) (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))))
(.f64 (.f64 #s(literal 1/9 binary64) x) (/.f64 #s(literal 1 binary64) (+.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 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 #s(literal 1/9 binary64) x))
(.f64 (/.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (/.f64 #s(literal 1/9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))))
(.f64 (/.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))) #s(literal 1/9 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 1/9 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x 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 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))) #s(literal 1/9 binary64)))
(.f64 (/.f64 (.f64 #s(literal 1/9 binary64) x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))
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(/.f64 (.f64 (+.f64 #s(literal 19683 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/15625 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64)))))) (+.f64 #s(literal 729 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))) #s(literal 27 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 729 binary64) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/15625 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64)))))) (-.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 729 binary64) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/15625 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal 1/5 binary64)))))) (+.f64 #s(literal 81 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/25 binary64)) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/25 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 81 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/625 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal 1/5 binary64)))))) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/25 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 3 binary64) (.f64 x (*.f64 x #s(literal -1/5 binary64)))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64))))))
(.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64))))) #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (*.f64 x #s(literal -1/5 binary64)))))
(.f64 (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (*.f64 x #s(literal 1/5 binary64))))))
(.f64 (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (*.f64 x #s(literal 1/5 binary64))))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (+.f64 #s(literal -3 binary64) (.f64 x (*.f64 x #s(literal 1/5 binary64)))))
(.f64 (+.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)))) #s(literal -27 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64)))) #s(literal -9 binary64))))
(.f64 (+.f64 #s(literal -9 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (*.f64 x #s(literal 1/5 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64))))) (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal 1/5 binary64))))) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/25 binary64))))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/25 binary64)) #s(literal -9 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64))) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) (+.f64 #s(literal 3 binary64) (.f64 x (*.f64 x #s(literal -1/5 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)))) (+.f64 #s(literal 729 binary64) (.f64 (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/25 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64))))))) (+.f64 #s(literal 81 binary64) (.f64 (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64))) #s(literal 9 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)))) (-.f64 #s(literal 81 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/25 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64)))))) (-.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) #s(literal -3 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64))) (-.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/5 binary64))) (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(.f64 #s(literal -1/5 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/5 binary64)) x)
(*.f64 x #s(literal -1/5 binary64))
(*.f64 #s(literal -1/5 binary64) x)

simplify221.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

2096×	`sum3-define`
1972×	`-lowering-.f32`
1972×	`-lowering-.f64`
1762×	`+-lowering-+.f64`
1762×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	790
1	372	657
2	1089	639
3	2929	636
4	5316	636
0	8046	636

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 1/675 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
(* 3 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)
(* 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 (* 1/675 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 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 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 1/675 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 1/675 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/675 binary64) (.f64 (*.f64 x x) #s(literal 1/10125 binary64))))))))
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 (-.f64 #s(literal -75 binary64) (/.f64 #s(literal 1125 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 #s(literal -5 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1125 binary64) (/.f64 #s(literal -16875 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -75 binary64) (*.f64 x x)))) x)
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 (-.f64 #s(literal -75 binary64) (/.f64 #s(literal 1125 binary64) (.f64 x x))) (.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
(/.f64 (+.f64 (/.f64 (-.f64 #s(literal -75 binary64) (/.f64 #s(literal 1125 binary64) (.f64 x x))) (.f64 x x)) (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -16875 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))))) x)
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* x (+ 3 (* 1/5 (pow x 2))))
(.f64 x (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64))))
(* x (+ 3 (* (pow x 2) (+ 1/5 (* 1/75 (pow x 2))))))
(.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/5 binary64) (.f64 (*.f64 x x) #s(literal 1/75 binary64))))))
(* x (+ 3 (* (pow x 2) (+ 1/5 (* (pow x 2) (+ 1/75 (* 1/1125 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/5 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/75 binary64) (.f64 (*.f64 x x) #s(literal 1/1125 binary64))))))))
(/ -45 x)
(/.f64 #s(literal -45 binary64) x)
(* -1 (/ (+ 45 (* 675 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 675 (* 10125 (/ 1 (pow x 2)))) (pow x 2))) 45) x)
(/.f64 (+.f64 #s(literal -45 binary64) (/.f64 (+.f64 #s(literal -675 binary64) (/.f64 #s(literal -10125 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (* -1 (/ (+ 10125 (* 151875 (/ 1 (pow x 2)))) (pow x 4))) (+ 45 (* 675 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 (/.f64 (-.f64 #s(literal -10125 binary64) (/.f64 #s(literal 151875 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x)))) x)
(/ -45 x)
(/.f64 #s(literal -45 binary64) x)
(* -1 (/ (+ 45 (* 675 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -45 binary64) (/.f64 #s(literal -675 binary64) (*.f64 x x))) x)
(* -1 (/ (+ 45 (+ (* 675 (/ 1 (pow x 2))) (/ 10125 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal -45 binary64) (/.f64 (+.f64 #s(literal -675 binary64) (/.f64 #s(literal -10125 binary64) (.f64 x x))) (.f64 x x))) x)
(* -1 (/ (+ 45 (+ (* 675 (/ 1 (pow x 2))) (+ (* 151875 (/ 1 (pow x 6))) (/ 10125 (pow x 4))))) x))
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal -675 binary64) (/.f64 #s(literal -10125 binary64) (.f64 x x))) (.f64 x x)) (+.f64 #s(literal 45 binary64) (/.f64 #s(literal 151875 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))))) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* -1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(+ 1/3 (* -1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(+ 1/3 (* -1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* -1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 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 (* (pow x 2) (+ 1/45 (* 1/675 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 1/675 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/675 binary64) (.f64 (*.f64 x x) #s(literal 1/10125 binary64))))))))
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 (-.f64 #s(literal -75 binary64) (/.f64 #s(literal 1125 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 #s(literal -5 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1125 binary64) (/.f64 #s(literal -16875 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -75 binary64) (*.f64 x x)))) x)
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 (-.f64 #s(literal -75 binary64) (/.f64 #s(literal 1125 binary64) (.f64 x x))) (.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
(/.f64 (+.f64 (/.f64 (-.f64 #s(literal -75 binary64) (/.f64 #s(literal 1125 binary64) (.f64 x x))) (.f64 x x)) (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -16875 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))))) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))

eval62.0ms (0.5%)

Compiler: Compiled 11486 to 1180 computations (89.7% saved)

prune62.0ms (0.5%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	471	2	473
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	471	7	478

Accuracy

100.0%

Counts

478 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
✓	99.2%	(/.f64 x #s(literal 3 binary64))
	98.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
✓	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)))))))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	99.6%	(.f64 #s(literal 1/9 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
	98.9%	(*.f64 #s(literal 1/9 binary64) (/.f64 x #s(literal 1/3 binary64)))

Compiler

Compiled 176 to 95 computations (46% saved)

regimes7.0ms (0.1%)

Counts

12 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 x #s(literal 3 binary64))
(*.f64 #s(literal 1/9 binary64) (/.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
(.f64 #s(literal 1/9 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 #s(literal 1/3 binary64) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes2.0ms (0%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	26	24
2	41	24
3	49	24
4	55	24
5	57	24

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness886.0ms (7%)

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	84	60
2	680	56
0	8206	56
0	109	1114
1	308	942
2	867	936
3	2330	935
4	5522	935
0	8360	935
0	67	302
1	189	269
2	564	266
3	1805	266
4	2707	266
5	4420	266
6	6039	266
7	6587	266
0	8075	266

Stop Event

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

Compiler

Compiled 97 to 67 computations (30.9% saved)

preprocess55.0ms (0.4%)

Remove: (negabs x)
Compiler: Compiled 158 to 104 computations (34.2% saved)

Iter	Nodes	Cost
0	12	17
1	37	16
2	72	15
3	156	15
4	311	15
5	480	15
6	523	15
7	531	15
0	6	5
1	16	5
2	24	5
3	36	5
4	50	5
5	87	5
6	158	5
7	255	5
8	356	5
9	499	5
10	621	5
11	653	5
0	653	5

Iter	Nodes	Cost
0	6	13
1	16	13
2	24	13
3	36	13
4	50	13
5	87	13
6	158	13
7	255	13
8	356	13
9	499	13
10	621	13
11	653	13
0	653	13

Iter	Nodes	Cost
0	23	125
1	55	106
2	109	106
3	215	106
4	388	106
5	444	106
6	485	106
7	492	106
8	602	106
9	679	106
10	694	106
11	696	106
12	696	106
0	696	106

Iter	Nodes	Cost
0	12	17
1	37	16
2	72	15
3	156	15
4	311	15
5	480	15
6	523	15
7	531	15
0	6	5
1	16	5
2	24	5
3	36	5
4	50	5
5	87	5
6	158	5
7	255	5
8	356	5
9	499	5
10	621	5
11	653	5
0	653	5

Iter	Nodes	Cost
0	6	13
1	16	13
2	24	13
3	36	13
4	50	13
5	87	13
6	158	13
7	255	13
8	356	13
9	499	13
10	621	13
11	653	13
0	653	13

Iter	Nodes	Cost
0	23	125
1	55	106
2	109	106
3	215	106
4	388	106
5	444	106
6	485	106
7	492	106
8	602	106
9	679	106
10	694	106
11	696	106
12	696	106
0	696	106

analyze8.0ms (0.1%)

sample7.3s (57.8%)

preprocess67.0ms (0.5%)

explain660.0ms (5.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify21.0ms (0.2%)

localize201.0ms (1.6%)

series4.0ms (0%)

rewrite208.0ms (1.6%)

simplify196.0ms (1.5%)

eval35.0ms (0.3%)

prune28.0ms (0.2%)

simplify117.0ms (0.9%)

localize91.0ms (0.7%)

series8.0ms (0.1%)

rewrite274.0ms (2.2%)

simplify179.0ms (1.4%)

eval53.0ms (0.4%)

prune33.0ms (0.3%)

simplify39.0ms (0.3%)

localize307.0ms (2.4%)

series8.0ms (0.1%)

rewrite499.0ms (3.9%)

simplify230.0ms (1.8%)

eval151.0ms (1.2%)

prune97.0ms (0.8%)

simplify7.0ms (0.1%)

localize219.0ms (1.7%)

series6.0ms (0%)

rewrite293.0ms (2.3%)

simplify221.0ms (1.7%)

eval62.0ms (0.5%)

prune62.0ms (0.5%)

regimes7.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify8.0ms (0.1%)

soundness886.0ms (7%)

preprocess55.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	17
1	37	16
2	72	15
3	156	15
4	311	15
5	480	15
6	523	15
7	531	15
0	6	5
1	16	5
2	24	5
3	36	5
4	50	5
5	87	5
6	158	5
7	255	5
8	356	5
9	499	5
10	621	5
11	653	5
0	653	5

Iter	Nodes	Cost
0	6	13
1	16	13
2	24	13
3	36	13
4	50	13
5	87	13
6	158	13
7	255	13
8	356	13
9	499	13
10	621	13
11	653	13
0	653	13

Iter	Nodes	Cost
0	23	125
1	55	106
2	109	106
3	215	106
4	388	106
5	444	106
6	485	106
7	492	106
8	602	106
9	679	106
10	694	106
11	696	106
12	696	106
0	696	106